OPTIMAL INVESTMENT DECISIONS OF
COFFEE FARMERS IN VIETNAM
Tran Cong Thang
A thesis submitted for the degree of
Doctor of Philosophy at
THE UNIVERSITY OF WESTERN AUSTRALIA
(School of Agricultural and Resource Economics)
October 2011
Acknowledgements
Acknowledgements
I would like to give special thanks to my principal supervisors Prof. Michael Burton and
Dr. Donna Brennan for their role in supervising my work on this thesis. They are
generous with their wisdom and encouragement. They are not only my supervisors but
also my very good friends in Australia. Sincere thanks are due to my supervisor Prof.
Ben White, for his helpful comments and suggestions.
The supportive co-operation of staff and colleagues from the School of Agricultural and
Resource Economics and AusAID officers at the University of Western Australia
gratefully acknowledged - particularly Jan Taylor, Deborah Swindells, Theresa Goh,
Sally Marsh, Vilaphonh, Sharon Harvey, Rhonda Haskell, Cathy Tang, Christine Kerin,
Deborah Pyatt and Alicia Zabah.
My sincere thanks go to Dr. Dang Kim Son for his approval and encouragement.
Sincere thanks are due to my colleagues in the Center for Agricultural Policy for their
useful support: Nguyen Ngoc Que, Nguyen Do Anh Tuan, Tran Thi Quynh Chi,
Nguyen Le Hoa, Truong Thi Thu Trang, Pham Huong Giang, Nguyen Nghia Lan and
Phan Van Dan.
Support from my friends in Perth during my program is gratefully acknowledged;
particularly from Ngoc Linh, Bich Ngoc, Lan Huong, Trung Khanh, Manh Hieu, Thanh
Nhan, Tu-Huong, Ha-Trong, Lam-Huong, Van Liem and Doc Lap.
The generous financial support from the Australian Centre for International Agricultural
Research (ACIAR) I gratefully acknowledge.
Finally, I owe thanks to my parents and my wife for their great support, encouragement
and love.
Perth, August 2010
i
Abstract
Abstract
For perennial crops like coffee, identifying the prices at which farmers should cut or
replant is a key investment decision. Optimal cutting and replanting can help farmers
use their resource to maximise income. The response of individual households may also
significantly affect the supply response at the aggregate level. In addition, knowledge of
how supply responds to different variables can help planners forecast supply.
While coffee is a major crop in Vietnam, the number of studies on the aggregate supply
response, or on optimal production decisions at farm level, is limited. In this study, two
types of models are developed to analyze the supply response of coffee in Vietnam and
identify optimal investment and production decisions of coffee farmers. The first model
uses the fixed form optimization method to solve a stochastic optimal control model of
the household’s cutting and replanting problem. The model identifies optimal ‘trigger’
coffee prices for cutting and replanting. The second predictive model estimates an
aggregate coffee supply function. This model gives the determinants of coffee area
variation in Vietnam.
The results from the stochastic optimal control model explore the optimal trigger prices
in different scenarios. The first result shows that coffee farmers can have a low ‘trigger’
price for cutting and a high trigger price for replanting. Between these two values is a
range of price values for which there is a ‘hysteresis effect’ where neither cutting
standing trees nor replanting occurs. Second, if this model extends to allow age
dependent trigger prices, as opposed to fixed trigger prices, the income is significantly
increased. These results reckon that farmers should not cut the trees before the 11th year
of planting
A third set of simulations analyse the importance of credit on the availability of working
capital. Poor or cash constrained households are more likely to remove coffee trees
compared to the unconstrained households. Thus, the cutting frequency of the poor
households is higher than that of the non-poor for all ages of coffee trees. The cash
constraint leads to a higher cutting percentage of coffee trees for poor households,
especially young trees. Furthermore, the poor farmers wait for significantly higher
trigger prices before replanting. Due to their cash constraint, farmers cannot follow the
ii
Abstract
same decisions as their richer neighbors, and this reduces their average income. The
credit available to poor household has a significant impact on the poor farmer’s income
and behavior. However, the importance of credit depends on the age of coffee trees: it is
more important for farmers with young trees that have not started to produce as harvest.
Fourth, if the model is generalised to allow for the short-run application of inputs such
as fertilizer, this has a significant impact on income. Furthermore, farmers are much less
likely to cut if they can adjust input use efficiently in response to coffee price changes.
Fifth, the cutting/replanting decision of farmers is influenced by the profit of alternative
crops. If the profit of the alternative crop falls, farmers are less likely to cut and more
likely to replant.
Previous studies of the coffee supply response for Vietnam assumed that the supply
function of coffee was symmetric with respect to changes in prices. The possibility of
an irreversible response was neglected. The results of this study show that the response
of coffee supply in Vietnam to price is asymmetric: it reacts more to a price increase
than to a price decrease. The asymmetric response of coffee area at the aggregate level
to price changes is consistent with the optimal decisions of farmers because they
optimize their decision by different ‘trigger’ prices for cutting and replanting. The area
response is similar across regions.
Studies of the response of coffee at both aggregate and farm level are useful for
households and planners. Despite some limitations, the modeling approaches used in
this thesis can be applied to supply response and farmers’ decision for other perennial
crops.
iii
Table of Contents
Table of Contents
Acknowledgements ............................................................................................................ i
Abstract ............................................................................................................................. ii
Table of Contents ............................................................................................................. iv
List of Tables..................................................................................................................viii
List of Figures ................................................................................................................... x
Table of Abbreviations ...................................................................................................xiii
CHAPTER 1. INTRODUCTION ..................................................................................... 1
1.1. Rationale of Study .................................................................................................. 1
1.2. Objectives ............................................................................................................... 3
1.3. Methodology .......................................................................................................... 4
1.4. Data ........................................................................................................................ 6
1.5. Thesis Structure...................................................................................................... 7
CHAPTER 2. THE COFFEE SECTOR IN VIETNAM ................................................... 9
2.1. Introduction ............................................................................................................ 9
2.2. Agricultural Sector in Vietnam .............................................................................. 9
2.3. Coffee Production ................................................................................................ 13
2.4. Coffee Export ....................................................................................................... 18
2.5. Coffee Households ............................................................................................... 23
2.5.1. Farm Size and Distribution ........................................................................... 23
2.5.2. Starting Year of Coffee Production............................................................... 25
2.5.3. Income Sources ............................................................................................. 27
2.5.4. Profitability of Coffee Production ................................................................. 28
2.5.5. Source of Water............................................................................................. 30
2.6. Conclusion ........................................................................................................... 32
CHAPTER 3. STOCHASTIC OPTIMAL INVESTMENT DECISION FOR
PERENNIAL CROPS: A LITERATURE REVIEW ...................................................... 34
3.1. Introduction .......................................................................................................... 34
3.2. Theoretical Models for Optimal Investment Decision ......................................... 35
3.3. Faustmann Model with Risk ................................................................................ 40
3.4. Stochastic Optimal Control Methods ................................................................... 41
iv
Table of Contents
3.4.1. Dynamic Programming (DP) ........................................................................ 41
3.4.2. Real Option Approach .................................................................................. 45
3.4.3. Other Techniques of Solving the Complex Dynamic Stochastic Models ..... 53
3.5. Conclusion ........................................................................................................... 55
CHAPTER 4. OPTIMAL REPLANTING AND CUTTING RULES FOR COFFEE
FARMERS IN VIETNAM: FIXED YIELD MODEL ................................................... 57
4.1. Introduction .......................................................................................................... 57
4.2. Coffee Farm System in Dak Lak .......................................................................... 58
4.3. Model Structure.................................................................................................... 61
4.3.1. Objective Function ........................................................................................ 61
4.3.2. Profit Function .............................................................................................. 63
4.3.3. Decision Rule ................................................................................................ 63
4.3.4. Yield Function ............................................................................................... 67
4.3.5. Production Cost ............................................................................................. 68
4.3.6. Price Simulation ............................................................................................ 69
4.3.6.1. Lagged Price Model ..................................................................................... 70
4.3.6.2. Price Cycle Model ........................................................................................ 72
4.3.7. Procedure for Estimation .............................................................................. 75
4.4. Results of the FY Model ...................................................................................... 78
4.4.1. Optimal Rule with Lagged Price Model ...................................................... 78
4.4.2. Impact of Substitute Crop on Coffee Farmer’s Decision .............................. 84
4.4.3. Optimal Rules with Price Cycle Simulation Model ...................................... 85
4.5. Conclusion ........................................................................................................... 89
CHAPTER 5. OPTIMAL COFFEE PLANTING DECISIONS UNDER A CASH
CONSTRAINT ............................................................................................................... 91
5.1. Introduction .......................................................................................................... 91
5.2. Impact of Cash Constraints on Farmer’s Decision .............................................. 91
5.3. Poverty Trends in Vietnam .................................................................................. 93
5.3.1. Saving and Income Level in Vietnam ........................................................... 98
5.3.2. Relationship between Income and Expenditure of Poor Farmers ............... 102
5.4. Structure of the FY-CC Model........................................................................... 105
5.4.1. Objective Function ...................................................................................... 107
5.4.2. Profit, Yield and Production Cost Function ................................................ 108
5.4.3. Expenditure, Saving and Loan .................................................................... 108
5.4.4. Decision Rule .............................................................................................. 110
v
Table of Contents
5.5. Results of the FY-CC Model ............................................................................. 111
5.5.1. Impact of Cash Constraints on Income ....................................................... 112
5.5.2. Effect of Loans and Savings ....................................................................... 113
5.5.3. Optimal Rule for Poor Coffee Farmers ....................................................... 117
5.6. Conclusion ......................................................................................................... 122
CHAPTER 6. SHORT-RUN RESPONSE AND OPTIMAL RULES FOR COFFEE
FARMERS IN VIETNAM ........................................................................................... 124
6.1. Introduction ........................................................................................................ 124
6.2. Review of Literature on Yield Response Functions .......................................... 124
6.3. Coffee Yield Function in Vietnam ..................................................................... 127
6.3.1. Yield Coffee Function Estimation .............................................................. 127
6.3.2. Optimal Cost Specification by Output Price ............................................... 130
6.3.3. Supply Price Elasticity ................................................................................ 131
6.4. Variable Yield Model (VY model) .................................................................... 132
6.4.1. Model Structure........................................................................................... 132
6.4.2. Adjustment of Yield function...................................................................... 133
6.4.3. Optimal Rule of the VY model ................................................................... 136
6.5. The Variable Yield – Cash Constraint Model (VY-CC model) ......................... 140
6.5.1. Model Structure........................................................................................... 140
6.5.2. Optimal Rule of the VY-CC model ............................................................ 141
6.6. Conclusion ......................................................................................................... 145
CHAPTER 7. SUMMARY OF THE OPTIMAL MODELS ........................................ 147
7.1. Introduction ........................................................................................................ 147
7.2. Model Development ........................................................................................... 147
7.2.1. Objectives of Models .................................................................................. 147
7.2.2. Rules and Constraints.................................................................................. 148
7.3. Changes in Coffee Farmer’s Decision ............................................................... 150
7.4. Conclusion ......................................................................................................... 154
CHAPTER 8. COFFEE SUPPLY RESPONSE IN VIETNAM ................................... 155
8.1. Introduction ........................................................................................................ 155
8.2. Literature Review on Supply Response Analysis using the Econometric
Approach ................................................................................................................... 156
8.2.1. Nerlovian Approach .................................................................................... 157
8.2.2. Extended Nerlovian Approach .................................................................... 160
8.2.3. Wicken - Greenfield Approach ................................................................... 161
vi
Table of Contents
8.2.4. Price Asymmetric Response ....................................................................... 163
8.2.5. Previous Studies on Supply Response of Coffee in Vietnam ..................... 167
8.3. Empirical Model of Coffee Supply Response in Vietnam ................................. 169
8.3.1. Data ............................................................................................................. 169
8.3.2. Model Results ............................................................................................. 169
8.4. Conclusion ......................................................................................................... 177
CHAPTER 9. CONCLUSIONS ................................................................................... 178
9.1. Background ........................................................................................................ 178
9.2. Key results .......................................................................................................... 181
9.2.1. Response at the Farm Level ........................................................................ 181
9.2.1.1. Cutting and Replanting Decision ............................................................... 181
9.2.1.2. Impact of Cash Constraints on Farmer’s Behaviors .................................. 182
9.2.1.3. Change of Farmer’s Decision with Short-run Response ............................ 183
9.2.1.4. Impact of the Profitability of the Substitute Crop ...................................... 184
9.2.2. Coffee Supply Response at Aggregate Level ............................................. 184
9.3. Policy implications ............................................................................................. 185
9.4. Limitations ......................................................................................................... 186
9.5. Further Studies ................................................................................................... 188
References ..................................................................................................................... 190
Appendix A ................................................................................................................... 199
Appendix B ................................................................................................................... 206
Appendix C ................................................................................................................... 210
Appendix D ................................................................................................................... 211
vii
List of Tables
List of Tables
Table 1.1: Sample of Coffee Farm Survey 2007 in Dak Lak............................................ 6
Table 2.1: Key Economic Indicators of Vietnam............................................................ 10
Table 2.2: GDP in agriculture, forestry and fisheries 2005-2008 (current price, %) ..... 10
Table 2.3: Area and output of crops in Vietnam, 1990-2008.......................................... 11
Table 2.4: Agricultural commodity exports in Vietnam, 2007-2008 (mill. $)................ 12
Table 2.5: Value and share in import-export of agricultural commodity ....................... 12
Table 2.6: Changes in coffee production in different periods (%) ................................. 14
Table 2.7: Coffee production by region in Vietnam, 2008 ............................................. 17
Table 2.8: Main markets for Vietnamese coffee in 2005 and 2008 ................................ 20
Table 2.9: SWOT analysis of coffee ............................................................................... 22
Table 2.10: Number of perennial crop households and size in Vietnam ........................ 23
Table 2.11: Distribution of coffee household by groups................................................. 26
Table 2.12: Average crop area of coffee households by district (m2) ............................ 27
Table 2.13: Earning sources of coffee households in 2006 ($) ....................................... 28
Table 2.14: Coffee farm performance in Daklak province, Vietnam 2006 ($/ha) ........ 29
Table 2.15: Main source of water (%) ............................................................................ 30
Table 2.16: Is yield limited by water (%) ....................................................................... 31
Table 4.1: Percentage of household with other activities excluding cropping (%) ........ 60
Table 4.2: Percentage of households reducing coffee area ............................................ 60
Table 4.3: Percentage of farmer switched to other crops ................................................ 60
Table 4.4: Coffee production cost by age of tree (US$/ha) ............................................ 69
Table 4.5: Distributions of actual international price and price data set simulated from
two models ...................................................................................................................... 74
Table 4.6: Summarized results of different cutting rules of FY model .......................... 83
Table 5.1: Perceived causes of poverty in Dak Lak Province ........................................ 95
Table 5.2: Coffee farming in Central Highlands ............................................................. 96
Table 5.3: Poverty incidence of coffee farmers in Central Highlands, Vietnam ............ 97
Table 5.4: Household income and expenditure in rural area in 2006 ($/year) ................ 99
Table 5.5: Household income and saving in rural by region in 2006($)....................... 100
Table 5.6: The saving flows of household by types ...................................................... 101
viii
List of Tables
Table 5.7: Number of poor households by region in VHLSS2006 ............................... 103
Table 5.8: Regression between per capita income and expenditure of poor HHs ........ 104
Table 5.9: General data of poor coffee household ........................................................ 105
Table 5.10: Loan amount and duration ......................................................................... 109
Table 5.11: Main loan purpose (% respondent) ............................................................ 110
Table 5.12: Percentage of loan by different sources by districts .................................. 110
Table 6.1: Sample distribution of coffee households in Agrocensus_2006 .................. 127
Table 6.2: Regression Results of Coffee Yield Function .............................................. 128
Table 6.3: Comparison of optimal rule between FY and VY model ............................ 137
Table 6.4: Average cost and yield from the VY model and the FY model................... 139
Table 6.5: The results of FY model with average cost and yield from VY model ...... 139
Table 7.1: Main objective of models ............................................................................ 148
Table 7.2: Decision rules and constraints ..................................................................... 149
Table 7.3: Main results of simulation models ............................................................... 150
Table 8.1: Data series and source .................................................................................. 169
Table 8.2: Estimated results from different models ...................................................... 172
Table 8.3: Results for testing the difference of coefficients among provinces, Modified
Wolfram model with window=6 ................................................................................... 174
Table 8.4: Elasticities of coffee acreage to price .......................................................... 175
ix
List of Figures
List of Figures
Figure 2.1: Migration to Dak Lak province, 1976 to 2000 ............................................. 15
Figure 2.2: Coffee area development in Vietnam, 1975-2008 ........................................ 16
Figure 2.3: Coffee area structure by age group in Vietnam, 2007 .................................. 18
Figure 2.4: Quantity and value of coffee export in Vietnam, 1991-2008 ....................... 19
Figure 2.5: Vietnam coffee price export, 1988-2008 (FOB-$ per tonne) ....................... 19
Figure 2.6: Coffee export value of Vietnam by destination (%) ..................................... 20
Figure 2.7: Exporting cost for coffee in some countries (cent/lb) .................................. 21
Figure 2.8: DRC of coffee and other export commodities in Vietnam ........................... 22
Figure 2.9: Coffee Household Structure by farm-size (%) ............................................. 24
Figure 2.10: Distribution of coffee households across Vietnam ..................................... 24
Figure 2.11: Coffee household structure by number of plots (%)................................... 25
Figure 2.12: Percentage of new coffee farmers and farm-gate price .............................. 26
Figure 2.13: Distribution of coffee production cost, 2006 ($ per ha) ............................. 30
Figure 3.1: The determination of PH and PL .................................................................. 51
Figure 4.1: Development of coffee area in Dak Lak, 1986-2008 ................................... 59
Figure 4.2. Example of optimal cutting and replanting rule ........................................... 67
Figure 4.3: Coffee yield by age of tree ........................................................................... 68
Figure 4.4: Fitted and actual value of logarithm of price ($/kg) ..................................... 71
Figure 4.5: Examples of price trajectories predicted from Lagged price model ............. 72
Figure 4.6: Price cycle of coffee in the world market (UScent/lb) ................................. 72
Figure 4.7: Example of price trajectories predicted from Price Cycle model ................. 74
Figure 4.8: Model Structure Map ................................................................................... 77
Figure 4.9: Optimal cutting and replanting rule from the FY model .............................. 79
Figure 4.10: Proportion of actual cut in FY model with Lagged price simulation ......... 80
Figure 4.11: Comparison of optimal RP of FY model and farmer’s estimates .............. 81
Figure 4.12: Optimal quadratic CP and best constant CP from the FY model .............. 82
Figure 4.13: The maximum ENPV per ha among different CP rules ............................. 82
Figure 4.14: ENPV with different starting ages for quadratic CP and no cutting rule ... 83
Figure 4.15: Changes in optimal rule when maize profit varies ..................................... 84
Figure 4.16: Changes in the maximum ENPV when maize profit varies ....................... 85
x
List of Figures
Figure 4.17: Optimal rule of the FY model with Price cycle model ............................... 86
Figure 4.18: Optimal rules of Price cycle and Lagged price simulations ....................... 86
Figure 4.19: Distribution of farm-gate price data set simulated from two models ......... 87
Figure 4.20: Simulated percentage cut at each age of trees from two data sets .............. 88
Figure 4.21: Different optimal rules of FY model with Price cycle simulation ............. 89
Figure 4.22: Actual cut of the FY with Price cycle model and different CP forms........ 89
Figure 5.1: Poverty trend in Vietnam 1993-2006 ........................................................... 94
Figure 5.2: Poverty trend in Vietnam by regions 1993-2004.......................................... 95
Figure 5.3: Coffee area of poor farmers in Central Highlands by provinces ................. 97
Figure 5.4: Structure of family size of poor and non-poor coffee household ................. 98
Figure 5.5: Per capita income and expenditure by area in 2006 ($/year) ..................... 100
Figure 5.6: Per capita income and expenditure of the poor in rural areas by regions,
2006 ($) ......................................................................................................................... 101
Figure 5.7: Fitted per capita income and expenditure by family size ........................... 104
Figure 5.8: Plot of per capita income and expenditure of the poor ............................... 105
Figure 5.9: ENPV from FY-CC if imposing optimal rule of FY and optimal ENPV from
FY ($/poor farm) ........................................................................................................... 112
Figure 5.10: ENPV from FY-CC at different initial savings at annual loan of 625$ .. 113
Figure 5.11: ENPV of farm income at different annual loans and savings................... 114
Figure 5.12: ENPV of FY-CC with different starting age of trees and loans ............... 116
Figure 5.13: Optimal Rules of the FY-CC model ......................................................... 118
Figure 5.14: Optimal rule of FY model and FY-CC model .......................................... 118
Figure 5.15: Actual cutting percentages by age of trees ............................................... 119
Figure 5.16: Impact of cutting decision by CP rule and by cash constraint in the FY-CC
model ............................................................................................................................. 120
Figure 5.17: Optimal rule of the FY-CC model with different initial savings .............. 121
Figure 5.18: Optimal rules of FY model and FY-CC with initial saving of $1500 ...... 121
Figure 6.1: Coffee yield – age relationship at average cost .......................................... 129
Figure 6.2: Cost –yield relation for 11 year old coffee trees ........................................ 130
Figure 6.3: Simulation of cost and yield relationship (age of tree =11 year old, medium
yield level district)......................................................................................................... 131
Figure 6.4: Simulation of price and coffee yield........................................................... 132
Figure 6.5: Coffee yield by age of tree in FY model .................................................... 133
Figure 6.6: Yield in the FY model and Adjusted Yield in the VY model at cost of
$930/ha .......................................................................................................................... 135
xi
List of Figures
Figure 6.7: Yield variation at different production costs .............................................. 135
Figure 6.8: Optimal cutting and replanting rules in the VY model .............................. 136
Figure 6.9: Optimal rules for FY model and VY model ............................................... 137
Figure 6.10: Percentage of cases in which farmers cut coffee at optimal rule.............. 138
Figure 6.11: Optimal rule of the VY-CC model ........................................................... 142
Figure 6.12: A comparison of optimal rule between FY-CC and VY-CC model......... 142
Figure 6.13: Percentage of cases in which farmers cut coffee at optimal rules ............ 143
Figure 6.14: Percentage of actual cut of the VY-CC model by cutting rule and by cash
constraint ....................................................................................................................... 143
Figure 6.15: Comparison of ENPV from different models at poor farm-size ............. 144
Figure 7.1: Maximum ENPV achieved from models ................................................... 151
Figure 7.2: Optimal cutting and replanting rules in different models ........................... 152
Figure 7.3: Actual cutting percentage at optimal rules in FY and FY-CC model ........ 152
Figure 7.4: Cutting percentage at optimal rule in FY and VY model ........................... 153
Figure 7.5: Optimal replanting prices for different models .......................................... 154
Figure 8.1: Hypothetical response overtime of Wolffram model and Modified Wolffram
model ............................................................................................................................. 165
Figure 8.2: Fitted and actual area from Modified Wolffram model (ha) ...................... 176
xii
Table of Abbreviations
Table of Abbreviations
ACIAR
Australian Centre for International Agricultural Research
ADB
Asian Development Bank
Agrocensus
Agricultural Census Survey
Agroinfo
Information Center for Agriculture and Rural Development
CAP
Centre for Agricultural Policy
CH
Central Highlands
CPI
Consumer Price Index
CP
Cutting Price
DARDD
Department of Agriculture and Rural Development of Dak Lak
DP
Dynamic Programming
DRC
Domestic Resource Cost index
EMA
Equivalent Mature Area
ENPV
Expected Net Present Value
FY
Fixed Yield Optimal
FY-CC
Fixed Yield-Cash Constraint Optimal
GDP
Gross Domestic Product
GSO
General Statistical Office of Vietnam
ICARD
Information Center for Agriculture and Rural Development
ICO
International Coffee Organization
IPSARD
Institute of Policy and Strategy for Agriculture and Rural
Development
LP
Linear Programming
MARD
Ministry of Agriculture and Rural Development
Mill.
million
MOLISA
Ministry of Labour and Invalid Social Affair
MRD
Mekong River Delta
NCC
North Central Coast
NES
Northern East South
NPV
Net Present Value
xiii
Table of Abbreviations
RP
Replanting Price
RRD
Red river delta
SCC
South Central Coast
VHLSS
Vietnam Household Living Standard Survey
VND
Vietnam Dong
VY
Variable Yield Optimal Model
VY-CC
Variable Yield – Cash Constraint Optimal
YMA
Yield of Mature Area
$, USD
United State Dollar
xiv
Chapter 1. Introduction
CHAPTER 1. INTRODUCTION
1.1. Rationale of Study
Vietnam has an agriculture-based economy in which the sector accounts for about 22
percent (in 2008) of Gross Domestic Product (GDP). The coffee crop, with its rapid
expansion in the 1990s, became the second largest export agricultural commodity after
rice. In 2007, the total coffee exports of Vietnam were over one million tonnes, with a
value of $1.8 billion. At present Vietnam is the second largest coffee exporter in the
world. In addition, the coffee sector plays an important role in labour absorption in rural
areas. In the peak harvest season, the coffee sector employs about 800,000 workers (The
World Bank, 2002).
Since the early 1990s, the coffee area in Vietnam has increased rapidly, from only
100,000 ha in 1990 to about 600,000 ha in 2000 (GSO, 2001)1. Coffee trees are planted
in 30 provinces in Vietnam, of which Dac Lak, Dak Nong, Gia Lai, Kon Tum and Lam
Dong in the Central Highlands are the main producing areas with 90 percent of national
output.
Natural conditions in the Central Highlands of Vietnam are favorable for coffee
cultivation. In addition, labour in rural areas in Vietnam is abundant and relatively
cheap. Thus, the production costs for coffee in Vietnam are normally lower than that in
other countries such as Brazil, Colombia and Indonesia (PI-IPSARD, 2007). Other
studies by Oxfam (2002) and CAP (2006)2 also show that Vietnam has a comparative
advantage in coffee production.
Coffee production in Vietnam is dominated by small farm households. The average
coffee area of coffee farms in Vietnam is only 8799 m2 and in total 477,000 coffee
farms, over 60 percent had less than one ha of land (GSO, 2007).
1
2
GSO denotes General Statistical Office of Vietnam
CAP signifies Centre for Agricultural Policy, Hanoi.
1
Chapter 1. Introduction
Many coffee farmers are relatively poor and are from ethnic minorities. Over 30 percent
of coffee farmers in the Central Highlands belong to minority ethnic groups3 and about
25 percent of coffee households are poor people4. Thus, coffee farm households are
typically economically vulnerable, and so the coffee sector contributes significantly to
development and household income in the rural economy.
As a major coffee exporter, the coffee price for Vietnamese producers is determined on
the world market. This means that Vietnamese producers are vulnerable to price
variability. This clearly shows by the low prices in the early 2000s. The farm gate
coffee price in Central Highlands reduced from $2 per kg in 1995 to less than $0.25 in
2001 (Thang, 2008). According to the Financial Times, coffee farmers in Vietnam's
Central Highlands lost $172 million from their 2000/01 coffee crop because of low
world prices5. In Dak Lak province, where household incomes had grown by 9 per cent
annually from 1996 to 1999, this growth rate fell by reductions of around 10 per cent
when the price of coffee fell. By 2002, about 45 per cent of coffee growing households
lacked adequate food, 66 per cent had bank debts and nearly 45 per cent had members
of the family who had turned to off-farm wage labour to earn money (Oxfam 2002).
When the price of coffee dropped, many smallholders fell into debt, they could not
afford to pay the loans and input costs. Due to losses, some coffee farmers cut down
trees and switched to other crops. In Dak Lak province alone, during 2002 and 2003
over 25,000 ha of coffee trees were cut down and replaced with other crops6. The rapid
decline in price reduced the coffee area in Vietnam from 600,000 ha in 2001 to about
491,000 ha in 2005. The cutting decision raises several issues.
First, replacing coffee by other crops is a complex and difficult decision for farmers. If
they switch too early, and the coffee price increases sharply then they bear the cost of
re-establishing trees. High replanting costs and other switching costs are a significant
proportion of costs for coffee households, especially poor households.
Second, it is likely that the cutting decision will depend heavily on the age of the coffee
trees. It may be appropriate to cut older trees first as the coffee price reduces. Thus, the
3
Vietnam has 54 people’s groups in which Kinh is major group with occupation of 87% total population.
Others are ethnic people. This number is calculated by author based on Agricultural Census in Vietnam in
2006.
4
According to the definition of the Ministry of Labour and War Invalid and Social Affairs: The people
are defined as poor are ones whose per capita income of less than $12.5 per month for rural areas and
$16.25 per month for urban areas. The poverty issues will be mentioned more detail in Chapter 5.
5
Available at http://www.allbusiness.com, accessed on 14/09/2009
6
DARDD: Department of Agriculture and Rural Development of Dak Lak.
2
Chapter 1. Introduction
relationship between the age of coffee trees and optimal cutting prices are an important
parameters.
Third, the identification of price at which farmers should replant coffee is also important
because it can help farmers (or their advisors) optimize their decision and significantly
increase their income. Farmers may consistently replant before or after the optimal
replanting price.
Fourth, it is possible that many poor coffee households cut earlier to meet cash
requirements for household expenditure, and inputs for subsistence crops. The
replacement of coffee by annual crops such as maize, and rice may help them meet their
cash requirements in the short-term. However, this decision may be more costly in the
long-term than keeping coffee and waiting for a price increase. The availability and cost
of credit is critical to this decision. If credit is cheaply available then farmers could
delay the cutting decision by borrowing to cover living expenditure and input costs.
Fifth, understanding the response of input application to coffee price may help farmers
to reduce short-run production costs to improve their income. The relationship between
the short-run response of inputs and the cutting decision for those under cash constraints
is important to understand.
Finally, coffee farmers may optimize their decision by different ‘trigger’ prices for
cutting and replanting. This asymmetric response of coffee households could reflect in
an asymmetric response of the aggregate coffee area to price changes. Thus, analyzing
the pattern of coffee supply in Vietnam may show an asymmetric response to price.
An understanding of the coffee supply response in Vietnam provides useful insights for
participants in the coffee sector and policymakers. Identification of optimal cutting and
replanting rules will be beneficial to coffee producers.
1.2. Objectives
Although agriculture and rural development in Vietnam has received great attention
from researchers from both Vietnamese institutions and international organizations,
there have been limited attempts to study coffee supply response in Vietnam either in
aggregate or at farm level. The only published research on Vietnamese coffee farmer
cutting and replanting decisions is by Luong and Loren (2006). There have been two
3
Chapter 1. Introduction
studies that present estimates of the coffee supply function (Tien, 2006, EDE-IPSARD,
2007). Both considered a symmetric price response of coffee area in Vietnam and
estimated the supply function based on aggregate time series data. The lack of empirical
research on coffee in general and on farmer’s decisions in particular is a principal
motivation for this study.
The detailed objectives of the study are:
1. Determine the optimal cutting and replanting rule for coffee farmers in Vietnam, in
particular:
identify the price at which farmers should cut and replant coffee to maximise their
income;
investigate how the cutting rule changes with age of the coffee trees;
examine how optimal rules change if profit from a substitute crop varies
2. Assess the loss of farm income due to cash constraints, in particular:
examine the relationship between expenditure and saving of poor farmers;
investigate how saving and loan availability affects the income and optimal rules of
farmers
3. Analyze how much farmers can improve their income if they can adjust crop input
levels:
first, examine the relationship between the yield of coffee and variable costs using
cross-sectional data
second, investigate changes of farmers’ planting/cutting behaviors and income if they
have an optimal short run response
4. Estimate the supply response function for coffee in Vietnam based on time series
data.
1.3. Methodology
4
Chapter 1. Introduction
Determining the optimal replanting and cutting rules for coffee farmers is a stochastic
control problem. In this study, the Dynamic Model with Fixed Form Optimization is
used to solve this problem. The Dynamic Model with Fixed Form Optimization is
structured as a system of equations (such as revenue, cost and profit) and decision rules
for cutting and replanting. The core objective of the models is to find the optimal cutting
rules and replanting price to maximise income per unit of land under price uncertainty7.
A number of optimal models are developed:
The Fixed Yield Optimal Model (FY model) investigates the optimal cutting and
replanting price for coffee farmers. The FY model maximises the net present value from
a unit of land (here one ha). In this model, the coffee yield function only depends on the
age of trees. In addition, representative farmers in the FY model are not restricted by
cash constraints when making replanting decisions.
Fixed Yield-Cash Constraint Optimal Model (FY-CC model) expands the FY model by
adding cash constraints into the FY model. In the FY-CC model, representative farmers
take cutting/replanting decisions in a household context, in which expenditure, other
income and loan factors constrain choices. Farmers spend their income on living
expenses and inputs including hired labour. Thus, the decision rules for the FY-CC
model are more complicated than in the FY model. Farmers cannot continue producing
coffee if their total budget (income and loans) cannot cover household expenditure and
production costs. Similarly, they cannot resume coffee production if their budget is less
than the replanting cost.
Further development of the FY model and the FY-CC model that captures the short-run
response of farmers is presented through Variable Yield Optimal Model (VY model) and
Variable Yield – Cash Constraint Optimal Model (VY-CC). In these models, coffee
yield varies according to the use of variable inputs, and the level of variable inputs is
determined by the price of output. The VY model and VY-CC model answer the main
question of how much farmers can improve their income if they can follow an optimal
adjustment of input application in the short-run.
The “Positive” approach estimates the aggregate coffee supply function using historical
time series data. The data used includes coffee area, output, world price, export price,
7
In the model, it is assumed that in cases where farmers cut their coffee trees they will switch to maize.
Thus, the income from farm land is the sum of coffee and maize income.
5
Chapter 1. Introduction
domestic price, consumer price index (CPI). The data covers a period from 1986 to
2007.
1.4. Data
The data used in this study stems from three main sources. The most important source is
the Coffee Farm Survey in early 2007 in Dak Lak province by the author. The total
sample of the Coffee Farm Survey is 150 households in three districts of Dak Lak: Cu
Mgar, Krong Pak and Eakar. All farmers in the Coffee Farm Survey are private
smallholders.
Table 1.1: Sample of Coffee Farm Survey 2007 in Dak Lak
Districts
Cu Mgar
Krong Pak
Eakar
Surveyed
Communes
Number of interviewed
households
Cuor dang
Cu se
Hoa Tien
Ea Kuang
Cu ri
Ea pal
25
25
25
25
25
25
150
Total
Source: Thang (2008)
The survey collected general information about the households (farm size, land area,
education, sources of income), coffee production (coffee area, yield, output, number of
plots, sale price, input use, input price, irrigation), credit issues and response of coffee
farmers to price uncertainty. The full questionnaire is presented in Appendix C.
The Agricultural Census Survey in 2006 (Agrocensus_2006) from General Statistical
Office consists of several secondary surveys of which Coffee Efficiency Survey and
General Household Survey are used to estimate yield coffee function and analyze coffee
household characteristics of Vietnam.
Vietnam Household Living Standard Surveys (VHLSS) is the source of additional data..
The General Statistic Office (GSO) implemented the first VHLSS in 1992. From 1992
to 2002, the VHLSS was done every 5 years. After 2002, the VHLSS has been
implemented every 2 years. VHLSS covers many aspects of household income and
expenditure. In this study, the VHLSS are used to investigate saving and expenditure of
poor coffee households and to investigate the relationship between income and
expenditure.
6
Chapter 1. Introduction
1.5. Thesis Structure
Following this introductory chapter, Chapter 2 reviews the recent development of the
coffee sector in Vietnam. The main coffee household characteristics discussed in the
chapter are from the Coffee Farm Survey of 2007. An analysis from Chapter 2 provides
a review of existing issues of the coffee sector in Vietnam.
Chapter 3 reviews the literature on optimal planting and clearing decisions. This chapter
discusses different methods of solving the stochastic optimization problems, such as
dynamic programming, real option theory, and approximate dynamic programming.
Chapters 4, 5 and 6 report the alternative models of optimal cutting/replacement rules.
Chapter 4 develops the Fixed Yield Optimal Model (FY model) to determine the cutting
and replanting price to maximise the expected NPV per hectare given uncertain coffee
prices. Chapter 4 also investigates changes in farmer’s decision when the income of the
substitute changes.
In Chapter 5, the Fixed Yield-Cash Constraint Optimal Model (FY-CC model)
investigates modifications to the optimal rules to account for a situation where coffee
farmers are poor and they do not have enough money to cover annual costs or invest in
new trees. A brief analysis of poor coffee farmers’ income- expenditure relationship is
included in this chapter.
Chapter 6 explores the optimal cutting and replanting decisions of coffee farmers with a
variable coffee yield function. An estimated yield function identifies the relationship
between yield, production cost and age of trees. Thus, optimal yield becomes a function
of the coffee price. By including the coffee yield function into the FY model and FYCC model two new models are obtained - the Variable Yield Optimal model (VY
model) and the Variable Yield – Cash Constraint Optimal Model (VY-CC model). This
chapter contains a discussion of the income and the farmer’s decision, including the
short-run response.
Chapter 7 presents a synthesis of results from Chapters 4, 5 and 6.
Chapter 8 estimates the supply response function of coffee in Vietnam based on
aggregate series data from 1985 to 2007. This chapter reports both symmetric and
7
Chapter 1. Introduction
asymmetric response functions, with the latter providing an improved explanation of
coffee areas in Vietnam.
Chapter 9 concludes the thesis and summarizes the main results – discussing the
limitations of the study and suggesting ideas for further studies on these issues.
8
Chapter 2 The coffee Sector in Vietnam
CHAPTER 2. THE COFFEE SECTOR IN VIETNAM
2.1. Introduction
This chapter provides an overview of the agricultural sector in Vietnam. It also reviews
recent developments in the coffee sector and highlights the importance of coffee in the
rural economy. In addition, this chapter describes the characteristics of farm households
producing coffee in Vietnam. The chapter is organised as follows. Section 2.2 presents a
brief overview on the agricultural sector in Vietnam. Section 2.3 and Section 2.4 discuss
coffee production and export trends, and Section 2.5 provides an analysis of the main
characteristics of coffee households. Some conclusions are presented in Section 2.6
2.2. Agricultural Sector in Vietnam
Vietnam is a developing country with average GDP in 2008 of $1020 per capita per
annum. The total population of Vietnam in 2008 was 86.2 million people of which
nearly three-fourths live in rural areas. Agriculture plays a central role in Vietnam’s
economy. The GDP from agriculture, forestry and fisheries accounted for 22 percent of
the national economy in 2008 (GSO, 2009). Vietnam has achieved strong growth in
agricultural production and trade over the past twenty years. This is commonly
attributed to infrastructure investment in irrigation and perennial crops before the 1988
“Doi Moi”(Innovation) policy changes that encouraged: market-oriented production and
input use; the allocation of individual land use rights; sound macroeconomic policies;
and improved credit access for farmers. The annual growth rate of the agricultural sector
has been maintained at a record high level of 3.7 per cent per annum for the five years
from 2003 to 2008 (MARD, 2008).
The rapid growth of the economy after “Doi Moi” policy has benefited most of the
Vietnamese population. However, the country remains one of the worlds’ poorest and a
relatively high 16 per cent of the population was below the poverty line in 20068.
8
The poverty incidence in Vietnam will be presented in more detail in Chapter 5.
9
Chapter 2 The coffee Sector in Vietnam
Agriculture contributes about 22 percent of GDP but employs about 70 percent of the
workforce. This reflects the low labour productivity in the agricultural sector compared
to the rest of the Vietnamese economy.
Table 2.1: Key Economic Indicators of Vietnam
Indicators
Vietnam
Population in 2008 (000 persons)
Rural population, 2008 (%)
GDP per capita (US$)
Agricultural GDP per capita, 2008 (US$)
Share of extended-agriculture in GDP, 2008 (%)
Share of extended-agriculture in labour force, 2008 (%)
Annual agricultural GDP growth, 2004-2008 (%)
Annual nonagricultural GDP growth, 2004-2008 (%)
Poverty rate in 2006* (%)
Share of rural poor in total poor in 2006* (%)
Source: GSO, 2008
86210
73
1020
304
22
70
3.7
8.7
16
90
*GSO, 2007
Note: Extended agriculture consists of agriculture, forestry and fisheries
Agriculture is the engine of rural development, accounting for 77 percent of GDP for
the extended agricultural sector (agriculture, forestry and fisheries). In recent years,
fisheries have become more important and accounted for nearly 20 percent of GDP in
agriculture, forestry and fisheries (see Table 2.2).
Table 2.2: GDP in agriculture, forestry and fisheries 2005-2008 (current price, %)
2005
2006
2007
2008
75.6
75.3
75.0
77.2
Forestry
5.7
5.4
5.2
4.9
Fisheries
18.7
19.3
19.8
17.9
Total
100
100
100
100
Agriculture
Source: GSO per com.
Growth in production has been across most food and industrial crops, with only jute and
cotton showing a reduction in output. Since the early 1990s, perennial crops have shown
the highest growth rates. In 2008, the total area of tea was 129,000 ha, more than double
the tea area in 1990. Over the 1990 to 2008 period, the coffee area increased 4.4 times
to over 500,000 ha in 2008. Pepper and cashew also increased significantly. In the same
period, the area of pepper rose 5.43 times, from 9200 ha in 1990 to 104,000 ha in 2008.
10
Chapter 2 The coffee Sector in Vietnam
Prior to 1990, cashews were a minor crop, however, from 1992 rapid growth has led to
over 300,000 ha in 2008 (Table 2.3).
Rice is the mainstay of smallholders in the agricultural sector and is important for
ensuring food security. Between 1990 and 2008, rice area and production grew 1.22
times and 2.01 times, respectively. The rapid development of rice changed Vietnam
from a rice importer to an exporter; in 1999 Vietnam ranked third in rice exports behind
Thailand and the United States.
Some annual industrial crops such as sugar, cassava and soybean also increased
markedly. The area under some minor commodities (jute, cotton and tobacco) have
tended decline in the 1990-2008 period (see Table 2.3).
Table 2.3: Area and output of crops in Vietnam, 1990-2008
1990
Crop
Paddy
Cassava
Cotton
Jute
Rush
Sugarcane
Peanut
Soybean
Tobacco
Tea
Coffee
Rubber
Pepper
Cashew
Agricultural land
2008
Area
Output
(000 ha) (000 tonnes)
6042.8
256.8
19.2
11.6
11
146.4
217.4
97.3
31.4
59.9
119.3
221.7
9.2
79*
19225.1
2275.8
3.1
23.8
63.6
5405.5
213.2
86.6
21.8
145.1
92.0
57.9
8.6
23.7*
6693
Area
(000 ha)
7400.2
543.8
5.8
3.3
11.7
270.7
255.3
192.1
16.6
129.6
525.1
618.6
50
404.9
9436
Output
(000
tonnes)
38729
9090.3
8
7.8
84.8
16145
530.3
267.6
28.8
706.8
996.3
662.9
104.5
313.4
Change in area
2008/1990
(times)
1.22
2.12
0.30
0.28
1.06
1.85
1.17
1.97
0.53
2.16
4.40
2.79
5.43
5.13
1.4
Source: GSO per com.
Note: * data for cashew area and output are for 1992
Vietnam has become a major world exporter of several agricultural products. Vietnam is
the largest exporter of Robusta coffee and pepper and the second largest exporter of rice
and cashew. Rice is the largest export commodity in terms of value from Vietnam. In
2008, the export value of rice was over $2.7 billion. Coffee is the second largest export
commodity in agriculture, with an export value of $2.1 billion in 2008. Alongside
11
Chapter 2 The coffee Sector in Vietnam
agricultural commodities, aquaculture and forestry contribute markedly to earnings from
international trade. In 2008, export value of aquaculture and forestry was about $7.4
billion (see Table 2.4).
Table 2.4: Agricultural commodity exports in Vietnam, 2007-2008 (mill. $)
2007
2008
% change 2008/2007
Agriculture
Coffee
6153
1881
8572
2116
+ 39.3
Rubber
1296
1675
+ 29.2
Rice
1472
2758
+ 87.4
Tea
128
147
+ 15.2
Cashew nut
642
914
+ 42.4
Groundnut
30
14
- 45.8
Pepper
267
310
+ 16.1
Fruit/vegetable
303
394
+ 30.0
5
9
+ 60.7
Milk, Milk products
Oils
35
47
76
101
+ 117.1
+114.9
Meat, meat products
46
57
+ 25.7
Aquaculture
3752
4436
+ 18.2
Forestry
Wood, wood products
2564
2330
3004
2764
+ 17.2
218
223
+ 2.3
16
17
+ 6.3
12469
16012
Sugar
Bamboo, Jute
Cinnamon
Total
Source: AGROINFO per com9
+ 12.5
+ 18.6
In 2008, the value of agriculture, forestry and fishery export accounted for over 25
percent of total export of Vietnam (Table 2.5)
Table 2.5: Value and share in import-export of agricultural commodity
Year
2007
2008
Export
Value (bil. $)
(%)
Value (bil. $)
(%)
Total
48.56
100
62.68
100
Extended agriculture
12.47
25.68
7.02
11.20
Others
36.09
74.32
55.66
88.80
Total
62.90
100
80.40
100
Extended agriculture
16.01
25.45
10.14
12.61
46.89
74.55
70.26
87.39
Others
Source: GSO (2007) and GSO (2009)
9
Import
Agroinfo denotes Information Center for Agriculture and Rural Development.
12
Chapter 2 The coffee Sector in Vietnam
The development of the agricultural sector has contributed greatly to improving
livelihoods of people in rural areas as well as the positioning of Vietnam in international
markets. However, despite the success of “Doi Moi”(“Innovation”), the agricultural
sector in Vietnam still has a number of economic problems, such as high labour surplus
in rural areas, limited land endowment, high poverty incidence, low labour productivity
and environmental degradation (Son, 2008).
2.3. Coffee Production
Coffee is an important part of Vietnam’s economy – even though the price collapsed in
early 2000s it is still the second largest export agricultural commodity after rice, and
employs over 600,000 workers, rising to nearly 800,000 workers at the peak of the
season or 2.93 percent of the agricultural labour force (The World Bank, 2002).
French missionaries introduced coffee to Vietnam in 1857. However, coffee production
developed after the unification of Vietnam in 1975. Following reunification and as a
result of resettlement programs to move people from densely populated provinces
towards sparsely populated provinces in the Central Highlands, the coffee area more
than doubled to reach nearly 45,000 ha in 1985 (GSO, 2000). Although ethnic
minorities predominated in the region, almost all of the immigrants and most of the new
coffee farmers were Kinh people. However, the growth rate of coffee area in 1975-1980
was not high, only 3.56 percent annum on average (see Table 2.6).
Coffee production has expanded rapidly since 1980, especially after the “Doi Moi”
(Innovation) policy in 1986 that transformed Vietnam from a centrally planned to
market-oriented economy. From 1980-1990 the rapid development of coffee was
fostered by a policy of land use reforms and relaxed government control. Before 1981,
farmers belonged to a cooperative and land belonged to the government. The production
contract (“Contract 100”) policy introduced in 1981 radically changed the role of
households. Contract 100, reallocated land to individual households, meaning they were
still members of cooperatives but it gave farmers more rights in the management of their
land. They were required to produce a predetermined quota by cooperatives but they
could sell output above the quota. However, maximum forestry land allocated to
farmers was only three ha. In addition, all input purchases were through the cooperative
(fertilizer, seed, pesticide and irrigation water).
13
Chapter 2 The coffee Sector in Vietnam
In 1988, the Contract 10 policy introduced rights for households which had not been
covered by the Contract 100 policy. According to Contract 10, farmers had control over
the entire management of their land including the purchase and utilization of inputs. The
land, assigned for a maximum of 15 years gave households a strong incentive to invest
in their farms.
The land reforms (Contract 100 and Contract 10) and mass migration to the Central
Highlands are the main drivers of the rapid development of the coffee sector from 1980
to 1990. During that period, the coffee area in Vietnam grew on average by 23.2 percent
per annum. With considerable improvement in yield, the coffee output in that period
had a very high annual growth rate of over 40 percent (Table 2.6).
Table 2.6: Changes in coffee production in different periods (%)
Period
1975-1980
1981-1990
1991-1999
2000-2008
Area
Output
Yield
3.56
9.51
6.38
23.29
41.58
13.06
17.27
22.73
5.72
-1.71
7.95
9.81
Source: GSO per com.
In the following five-year period, coffee production continued expanding rapidly. The
area of coffee increased from around 100,000 ha in early 1990s to nearly 600,000 ha in
1999. A trade liberalization policy within Vietnam and relatively high coffee prices
since early 1990 drove the development of coffee during this period. The export price of
coffee in Vietnam increased from about $700 per ton in 1990 to over $2000 in the
middle of the 1990s (GSO, 2008). Furthermore, land reform continued improving
through the Land Law in 1993, strengthening the rights of households. According to the
Law, households can use, exchange, transfer, lease, inherit, and mortgage their land.
Furthermore, land allocates to households for long-term use (20 years for annual crops
and aquaculture, 50 years for perennial crops). In addition, the maximum arable area for
perennials was not limited. By removing restrictions to expansion, the Land Law in
1993 facilitated the development of the coffee sector. During the period from 1991 to
1999, the coffee area kept increasing, on average, 17.2 percent per year. The second half
of 1990s was a boom period for coffee in Vietnam. The coffee area rose from nearly
160,000 ha in 1993 to 600,000 ha in 1999 (see Figure 2.2).
Together with land policy reform, the re-settlement policy generated mass migration to
the Central Highlands and contributed significantly to the expansion of the coffee area
14
Chapter 2 The coffee Sector in Vietnam
(D’Haeze et al., 2005). Besides large planned migration flows, spontaneous migration
was also significant. Attracted by high economic returns for Robusta coffee,
spontaneous migration increased rapidly between 1991 and 1995. According to the
Settlement Committee of Dak Lak province, about 100,000 people moved to this
province in 1991-1995 (see Figure 2.1). Immigrants to the Central Highlands exploited
uncultivated land to grow crops (mainly coffee) but the expansion of agricultural land in
Central Highland resulted primarily from the conversion of forestland. For example,
between 1976 and 2001 forest cover in Dak Lak province decreased by approximately
235,000 hectares to approximately 1 million hectares, approximately the increase in
coffee area (D’Haeze et al., 2005).
200000
Official migration
Number of people
160000
Spontaneous migration
120000
80000
40000
0
1976-80
1981-1985
1986-90
1991-95
1995-99
2000
Figure 2.1: Migration to Dak Lak province, 1976 to 2000
Source: Settlement Committee of Dak Lak per com
The coffee price collapse in the early 2000s had a detrimental effect on coffee
producers, processors, traders and exporters. In response to the price fall, many coffee
farmers cut their trees and switched to other crops. At that time, the coffee area in
Vietnam reduced, from 600,000 ha in 2001 to about 491,000 ha in 2005. The
government response to the crisis was to reduce the coffee area. In 2001/2002, the
Vietnam government suggested a reduction of about 150,000 ha of coffee. Furthermore,
provincial authorities in the main coffee areas such as Dak Lak, Lam Dong proposed to
keep the existing area of coffee but not allow any expansion (The World Bank, 2004).
More recently, however, in response to an increase in the coffee price, many producers
have replanted coffee trees as the price has been gradually increasing (see Figure 2.2).
15
Chapter 2 The coffee Sector in Vietnam
Alongside the rapid expansion of area, coffee yield has been increasing, especially in
the past 10 years. During 1998-2006, coffee yield had an average annual growth rate of
9.8 percent. In general, however, the coffee sector in Vietnam has been developed
extensively via area expansion, although
yield improvements have contributed to
output increase.
700000
2500
Area (ha)
yield(kg/ha)
600000
2000
Yield (kg/ha)
Area (ha)
500000
1500
400000
300000
1000
200000
500
100000
0
1975
1978
1981
1984
1987
1990
1993
1996
1999
2002
2005
0
2008
Figure 2.2: Coffee area development in Vietnam, 1975-2008
Source: GSO per com.
There are two coffee varieties in Vietnam– Robusta and Arabica, of which Robusta is
the major one, accounting for more than 95 percent of the total coffee cultivation area.
Coffee has been planted mainly in the North West of Vietnam, Central Highlands (see
Table 2.7)10. The Central Highlands region (including Dak Lak, Dak Nong, Gia Lai,
Kon Tum, Lam Dong province) is the main coffee production area, producing over 90
percent of the national coffee output. Dak Lak is the largest coffee province with total
area of about 180,000 ha (approximately 35 percent of national area).
10
The regions of Vietnam are mapped in Figure A1 in Appendix A. The coffee area and output maps in
Vietnam are presented in Figure A3 and Figure A4 in Appendix A.
16
Chapter 2 The coffee Sector in Vietnam
Table 2.7: Coffee production by region in Vietnam, 2008
North West
Area
New plant
(ha)
(ha)
Harvested
Yield
Output
area
(ha)
(quital/ha) (tonnes)
4478
707
2 931
12.46
3651
Dien Bien
1029
575
374
16.63
622
Son La
3449
132
2 557
11.85
3029
6621
472
5 491
14.75
8097
82
15.61
128
North Central Coast
Thanh Hoa
102
Nghe An
1269
49
1 077
14.08
1516
Quang Tri
4335
209
3 681
16.65
6128
915
214
651
4.99
325
1729
79
1 650
13.15
2170
278
7.01
195
Hue
South Central Coast
Binh Dinh
Phu Yen
278
1174
70
1 104
14.00
1546
277
9
268
16.01
429
480774
10023
456862
21.69
990924
Kon Tum
10360
476
9626
22.61
21764
Gia Lai
76368
337
75788
17.76
134595
Dak Lak
182434
2946
173233
23.98
415494
Dak Nong
75470
2898
70341
19.40
136484
Lam Dong
136142
3366
127874
22.10
282587
37 306
3 011
33 246
15.32
50931
Binh Phuoc
11 130
556
10 215
12.92
13198
Dong Nai
17 729
2 189
15 516
16.30
25294
Binh Thuan
1 381
92
994
13.55
1347
Ba Ria-Vung Tau
Source: ICARD per com.11.
7 066
174
6 521
17.01
11092
Khanh Hoa
Central Highlands
North East South
Despite its position as a major exporter, the quality of Vietnamese coffee is still
relatively low due to inferior harvest and post-harvest technologies. For instance, about
65 percent of Vietnam’s coffee is graded second class due to high proportions of black
and broken beans and high humidity. This affects the price of Vietnam’s coffee in the
world market (Chi et al., 2009).
11
ICARD denotes Information Center for Agriculture and Rural Development, Ministry of Agriculture
and Rural Development, Vietnam.
17
Chapter 2 The coffee Sector in Vietnam
The normal production cycle of coffee trees is from 20 to 25 years, of which the first
two to three years is the gestation period. Normally, the coffee tree starts to produce
‘‘berries’ from the third year. From the eighth to sixteenth year, the tree reaches its
highest yield. The age distribution of coffee trees in 2007 is represented in Figure 2.3.
15-20
years
24%
>20
years
9%
0-4 years
5%
5-9
years
22%
10-15
years
40%
Figure 2.3: Coffee area structure by age group in Vietnam, 2007
Source: MARD, 2008
With a relatively large share of aging trees, there is a prospect that the quality and yield
of coffee in Vietnam will decline in coming years. Thus, policies for encouraging
farmers to replace old trees are a big concern of the Vietnam governments.
2.4. Coffee Export
More than 90 percent of coffee in Vietnam is exported. The export quantity has
increased rapidly since the early 1990s from less than 100 thousand tonnes in 1991 to
over 1 million tonnes in 2007. Similarly, export value rose to over $2 billion in 2008.
During the period 1991-2008, export quantity grew on average by 17 percent per year,
while value increased on average at 30 percent annum (see Figure 2.4 ).
18
Chapter 2 The coffee Sector in Vietnam
1400
2500
Quantity (000 tons)
1200
Value (Mil.USD)
2000
1500
800
mil.$
000 tons
1000
600
1000
400
500
200
0
0
Figure 2.4: Quantity and value of coffee export in Vietnam, 1991-2008
Source: MARD per com
Vietnam is currently the second largest coffee exporter after Brazil. In 2008, Vietnam
contributed over 40 percent of Robusta coffee and 13 percent of overall coffee trade in
the world market. During the 1995 to 2002 period, the export value of coffee has
stagnated due to the falling real price. The export price reduced from over $2000 per ton
to less then $500 per tonne in 2001. Since 2002, the coffee price has recovered
gradually, resulting in an increase in export value and quantity12.
3000
2500
$/tonne
2000
1500
1000
500
20
08
20
06
20
04
20
02
20
00
19
98
19
96
19
94
19
92
19
90
19
88
0
Figure 2.5: Vietnam coffee price export, 1988-2008 (FOB-$ per tonne)
Source: MARD per com.
12
The time series data of coffee exports from Vietnam is presented in Table B3 in Appendix B.
19
Chapter 2 The coffee Sector in Vietnam
The number of countries to which Vietnam exports is increasing over time. In 2000,
Vietnam exported coffee to only about 50 countries. In 2005, the number rose to 80
countries and in 2008, Vietnamese coffee has been exported to about 100 countries
throughout the world. The main export markets are the EU (Germany, Switzerland,
England, Netherlands, Spain, Italy …), USA and Asia (Japan, Singapore, China,
Philippine, Malaysia and Indonesia); those markets accounts for 58 percent, 15 percent
and 21 percent of total export coffee value of Vietnam in 2008, respectively (see Figure
2.6).
Ocean
Cont.
2%
Other
5%
Ocean
Cont.
1%
Asia
12%
Africa
7%
Asia
21%
Latin
America
18%
West
European
59%
East
European
4%
West
European
51%
Latin
America
13%
East
European
7%
In 2005
In 2008
Figure 2.6: Coffee export value of Vietnam by destination (%)
Source: General Custom Office of Vietnam per com.
Table 2.8 gives the main destinations of Vietnamese coffee in 2005 and 2008. The
United States and Germany, Italy, Japan, Spain are the main export markets.
Table 2.8: Main markets for Vietnamese coffee in 2005 and 2008
In 2005
In 2008
Quantity
Value Destination
Quantity
(000 tonnes)
(mil. $)
(000 tonnes)
United States
117.7
97.5 Germany
138.5
Germany
92.1
76.1 United States
131.5
Italia
62.6
54.2 Italy
86.4
Spain
63.9
53.8 Belgium
88.5
United Kingdom
46.4
36.7 Spain
78.5
Japan
29.4
25.9 Japan
59.2
France
27.5
22.7 Korea
42.1
Switzerland
27.1
19.5 United Kingdom
35.2
Belgium
23.4
19.3 Switzerland
29.4
South Korea
23.0
18.2 Algeria
22.4
Total Export
892
735 Total Export
1000
Source: General Custom Office of Vietnam per com
Destination
Value
(mil. $)
274.1
211.4
171.1
168.1
148.5
127.5
82.8
69.3
54.4
47.7
2115
20
Chapter 2 The coffee Sector in Vietnam
Vietnam has important advantages in coffee exports. The natural conditions in the
Central Highlands of Vietnam are suitable for growing Robusta coffee (D’Haeze, 2004).
The production cost of coffee in Vietnam is relatively low. According to Chi et al
(2009), the cost for exported coffee (which includes both production cost and ex-farm
gate cost, defined as the cost from farm gate to port) in Vietnam is only 25 cent/lb,
while exporting costs for India and Indonesia where Robusta coffee is the important
crop are 34 cent/lb and 37 cent/lb, respectively.
60
50
Extra cost
Production cost
cent/lb
40
30
20
10
0
Vietnam
India
Indonesia
Brazil
Figure 2.7: Exporting cost for coffee in some countries (cent/lb)
Source: PI-IPSARD (2008) quoted in Chi et al (2009)
The advantage of coffee production in Vietnam reflects the Domestic Resource Cost
index (DRC)13. Generally, DRC ranges from 0 to 1, with a smaller value implying a
competitive advantage because it means Vietnam utilizes less domestic resource to
produce one unit of coffee for export. A study by the CAP (2006) on Competition under
AFTA shows that the DRC of coffee in 2006 is only 0.37, smaller than rice (0.59) and
much lower than rubber (0.7) or tea (0.79). This suggests Vietnam has a comparative
advantage in coffee production (see Figure 2.8).
n
aij p*j
13
j k 1
k
Formally, the DRC is defined as
p
b
i
, where j=1…k are traded inputs, j=k+1…n are
aij p
b
j
j 1
domestic resources and/or non-traded inputs, p* is the shadow price of domestic resources and non-traded
inputs, pib is the border price of traded output calculated at the shadow exchange rate and p jb is the border
price of the traded input at the shadow exchange rate (Sadoulet and deJanvry 1995)
21
Chapter 2 The coffee Sector in Vietnam
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Rice
Coffee
Rubber
Tea
Figure 2.8: DRC of coffee and other export commodities in Vietnam
Source: CAP (2006)
Son et al. (2005) summarizes strengths, weakness, opportunities and threats (SWOT) in
the context of export assessment of coffee. The core strengths of coffee in Vietnam are
high yield and low production costs. However, low/inconsistent quality, undeveloped
post harvest process technology and the shortage of storage capacity are the main
problems (see Table 2.9).
Table 2.9: SWOT analysis of coffee
Strengths
Weaknesses
Opportunities
Suitable natural conditions for coffee
Low production cost
High yield
Good experience in coffee cultivation
Having concentration area
Large export market share , specially Robusta
Development of private export
Dominated by small households
Low/inconsistent quality
no brand name/mostly export coffee bean
over expansion of coffee area
Lack of storage facilities, marketing services
Export through intermediaries
Underdevelopment of future market, transaction floors
Vietnam standards are inconsistent with international standards.
Overuse of fertilizer and pesticides
Mainly dry process application
Lack of risk management measurements
Export market diversification
Recovery of export market
Development of wet processing technique
22
Chapter 2 The coffee Sector in Vietnam
Government supports to develop brand name , trade promotion
Competition from other crops
Competition from other exporters
Unstable price
Over expansion of Robusta
Inefficient plan for Arabica development
Drought
Water resource limitation
Source: Son D.K. et al (2005)
Threats
2.5. Coffee Households
2.5.1. Farm Size and Distribution
Coffee is the most important perennial crop in Vietnam with over 477 thousand
households producing in Vietnam, accounting for 3.29 percent of the total number of
farm households in Vietnam. The share of coffee households in Vietnam is much higher
than rubber households (0.73 percent) and pepper households (1.24 percent) and slightly
larger than cashew household’s (3.14 percent). The average of coffee area is 8799 m 2,
much higher than average farm-size of tea households and pepper households, but
smaller than rubber and cashew (see Table 2.10).
Table 2.10: Number of perennial crop households and size in Vietnam
Tea
Coffee
Rubber
Cashew
Pepper
380751
477235
106139
456141
179478
% farm household
2.62
3.29
0.73
3.14
1.24
Average area (m2/household)
Source: GSO (2007)
2414
8799
16906
10274
2470
Number of household
The coffee sector in Vietnam is dominated by small households. According to GSO
(2007), over 60 percent of coffee households have less than 1 ha of coffee land and 10
percent of households have more than 2 ha of coffee land (see Figure 2.9). Small size
and land fragmentation are problems for the coffee sector in Vietnam. Small farms are
unable to invest in improved harvest and post-harvest technology and this has led to
variable coffee quality.
23
Chapter 2 The coffee Sector in Vietnam
35
30
25
20
15
10
5
0
under 0.5 ha
0.5-1 ha
1-2 ha
2-3 ha
3-4 ha
over 5 ha
Figure 2.9: Coffee Household Structure by farm-size (%)
Source: GSO (2007)
Most coffee households are concentrated in the Central Highlands. According to
Agrocensus_2006, nearly 90 percent of coffee households are located in the five
provinces in Central Highlands (Gia Lai, Dak Lak, Dak Nong, Kon Tum and Lam
Dong), of which nearly 40 percent of total households are located in Dak Lak province;
24 percent in Lam Dong and 7.5 percent in North East South. Recently, Vietnam has
tried to expand coffee in some provinces in the North Mountains of Vietnam. However,
programs for developing Arabica in the North Mountains could not achieve successful
results. Thus, coffee area in the region is still very limited14.
427,316
450000
400000
350000
300000
250000
200000
150000
100000
50000
36,054
10,463
3,364
North Central Coast
South Central Coast
0
Central Highlands
North East South
Figure 2.10: Distribution of coffee households across Vietnam
Source: GSO (2007)
14
The structure of coffee households in Vietnam by farm size in all provinces in Vietnam is presented in
Table B6 (Appendix B).
24
Chapter 2 The coffee Sector in Vietnam
Figure 2.11 gives the distribution of coffee households by number of plots farmed.
Nearly 70 percent of household own one plot of coffee land. Small size and land
fragmentation are general characteristics of agricultural production in Vietnam. In 2008,
the average agricultural land per person in Vietnam was approximately 0.11 ha (GSO,
2008). Due to the high population growth, this number is projected to be only 0.08 ha
by the year 2020 (D’Haeze, 2004). However, land for coffee as well as other perennial
crops is spatially concentrated compared to that for annual crops such as rice.
3 plots
11%
4 plots
3%
2 plots
17%
1 plot
69%
Figure 2.11: Coffee household structure by number of plots (%)
Source: Thang (2008)
2.5.2. Starting Year of Coffee Production
Coffee became a major crop in Vietnam in the 1980s following its introduction during
the French colonization period. As mentioned in Section 2.3, this expansion of the
coffee area was due to stimulation by policy reform, migration into the Central
Highlands and the development of a coffee market. The most rapid growth of coffee
area occurred in the mid 1990s when coffee prices were high. According to the Coffee
Farm Survey 2007, about 30 percent of coffee households in Dak Lak province started
producing in 1994-1995.
25
Chapter 2 The coffee Sector in Vietnam
20.0
proportion of new coffee growers (%)
4.00
18.0
farm-gate price (USD/kg)
3.50
16.0
3.00
12.0
10.0
8.0
2.50
2.00
price
% of new grower
14.0
1.50
6.0
1.00
4.0
2.0
0.0
0.50
0.00
Figure 2.12: Percentage of new coffee farmers and farm-gate price
Source: Thang (2008) and GSO (2009)
The expansion of coffee area in Central Highlands goes hand in hand with migration
into that region. Thus, many coffee households are migrants from other regions. They
came to the Central Highlands and exploited bare land or forest for coffee cultivation or
bought coffee land from ethnic people. The migration to the Central Highlands has
changed the ethnic distribution of the population. Indigenous minorities such as the EDe and the H’Mong, who had made up 48 percent of Dak Lak’s population in 1975,
now only account for 20 percent of the population (D’Haeze et al., 2005). According to
Agrocensus_2006, in the Central Highlands about 70 percent of coffee households were
Kinh people who are not originally local people (see Table 2.11). The rest are local
people such as E-De (9.8%), Gia-Rai (5.1%), Co Ho (4.9%). The involvement of a large
percentage of ethnic households in coffee production shows the importance of this
sector in rural development and social stability. Because a disproportionally large
number of ethnic minority people are in low-income groups, they are vulnerable to
coffee price shocks.
Table 2.11: Distribution of coffee household by groups
26
Chapter 2 The coffee Sector in Vietnam
Groups
Number of households
Percent
Kinh people
Minor ethnic people
In which:
E de
Gia-Rai
Co Ho
Nung
Ba Na
Tay
Ma
Other
263292
110491
70.44
29.56
36570
19052
18250
7451
6365
6196
3475
139349
9.78
5.1
4.88
1.99
1.7
1.66
0.93
3.52
Total surveyed households
373783
100
Source: Author’s calculation based on Agrocensus_2006
2.5.3. Income Sources
Besides coffee, farmers in Central Highlands also cultivate other annual crops such as
rice, maize, cassava and sugarcane. Some people also grow other perennial crops such
as rubber, pepper, cashew and durian. However, the area of those crops is very limited.
Table 2.12: Average crop area of coffee households by district (m2)
Rice
Maize
Cassava
Sugarcane
Coffee
Rubber
Pepper
Cashew
Durian
Cu Mgar
Krong Pak
Eakar
104
60
0
0
19376
200
101
0
0
2529.0
279.6
20.4
0
9038.8
0
0
0
20.4
2118
0
20
1600
7354
0
234
3270
0
Souce: Thang (2008)
Beside crop production, coffee households also participate in other economic activities
with livestock production and waged labour as the other main sources. The income and
production diversification are important to ensure food security. According to the
Coffee Farm Survey 2007, the average revenues of coffee households from livestock in
Krong Pak and Cu Mgar were nearly $300 (8.1%) and $200 (3%), respectively. Waged
labour is also a good source of income and it is stable across surveyed districts.
However, analysis of income sources shows coffee is the most important source of
27
Chapter 2 The coffee Sector in Vietnam
income and coffee households have limited opportunities to diversify their income. This
makes coffee households vulnerable when the price of coffee goes down.
Ability to diversify income of coffee farmers depends on different factors. Agergaard et
al (2009) indentified four factors which influence the possibility for livelihood
diversification of coffee farmers in Daklak province such as (i) the ethnic background of
the inhabitants. (ii) the specific period in which settlements become coupled to the
dynamics of the global value chain. This relates to the timing of when smallholders
started to benefit from their investments in coffee (iii) organisation of coffee marketing
activities, (iv) constraints of remote and undeveloped areas.
Table 2.13: Earning sources of coffee households in 2006 ($)
Source of revenue
1.Crop
from coffee
2.Livestock
3. Aquaculture
4. Wage/salary
5. Pension
6.Other income
Total
Cu Mgar
Krong Pak
Eakar
5643
5565
204.7
0
295.7
2.1
37.5
6182.9
3042
2906
299.9
5.1
144.2
39.8
169.2
3700.4
2680
1918
29.9
303.8
263.2
0
37.5
3314.8
Source: Thang (2008)
Note: earning sources from activities are measured by sale revenue.
2.5.4. Profitability of Coffee Production
The production cost of coffee varies across districts. This depends on favorable natural
conditions for coffee such as soil, water, slope and the weather. According to a Coffee
Farm Survey in 2007, the average annual cost of coffee production in Cu Mgar district
and Krong Pak district was about $980 per ha. This cost was lower at $920 per ha in the
Eakar district (Table 2.14).
Fertilizer is the largest cost component with about 45-50 percent of total cost. Next is
labour, with about 35-40 percent. Expenditure for electricity and fuels are also
important, accounting for 15-20 percent of total annual production cost.
Yield varied across districts. This affects revenue and profit for coffee farmers. On
average, profit per ha achieved by coffee farmers in Cu Mgar was $1775, Krong Pak
($1638) and Eakar ($1395). These profits reflect the relatively high price of coffee in
28
Chapter 2 The coffee Sector in Vietnam
that year. A simple simulation of coffee revenue earned by coffee household at the 2002
price with an assumption of the same cost in 2006 are presented in Table 2.14. This
assumption may not hold because farmers respond by reducing input use during periods
of low prices.
Table 2.14: Coffee farm performance in Daklak province, Vietnam 2006 ($/ha)
Annual cost ($/ha)
Fertilizer
Manure
Micro fertilizer
Labour
Electricity/fuel
Irrigation fee
Others
Yield (kg of coffee
bean/ha)
Price ($/kg coffee bean)
Revenue ($/ha)
Profit ($/ha)
Price in 2002 ($/ha)
Revenue 2002 ($/ha)
Simulated profit in 2002
($/ha)
Source: Thang (2008)
Cu Mgar district
Value ($)
%
978.1
100
290.9
29.7
67.0
6.9
26.0
2.7
363.7
37.2
199.5
20.4
0
0
30.9
3.2
2165
1.3
2753.3
1775.2
0.31
671.1
-307
Krong Pak district
Value ($)
%
977.5
100
475.7
48.7
38.6
4.0
5.7
0.6
345.7
35.4
111.8
11.4
0
0
33.3
3.4
2037
1.3
2615.6
1638.1
0.31
631.4
346.1
Eakar district
Value ($)
%
920.5
100
367.6
39.9
0.5
0.1
60.6
6.6
368.8
40.1
153.5
16.7
2.6
0.3
24.7
2.7
1867
1.2
2316.3
1395.7
0.31
578.7
341.8
Production cost varies among regions and households but most values are between $900
and $1200 per ha. Figure 2.13 shows the distribution of coffee production cost during
2006.
29
Chapter 2 The coffee Sector in Vietnam
0.0015
Density
0.001
0.0005
0
0
500
700
900 1100 1300 1500 1700 1900 2100 2300 2500 2700 2900
Cost per ha (USD)
Figure 2.13: Distribution of coffee production cost, 2006 ($ per ha)
Source: Thang (2008)
2.5.5. Source of Water
The coffee households use different water sources for coffee, namely surface water
resources (reservoirs and irrigation perimeters) and groundwater sources (i.e. from,
hand-dug and drilled wells). According to the Coffee Farm Survey, over 60 percent of
farmers used water from wells as their main source, and in Cu Mgar this proportion
reached 96 percent. About 30 percent of the households principally used water from a
nearby reservoir and lakes (see Table 2.15). This result is quite similar to a study by
D’haeze (2004) in which he estimated that 21 percent of irrigation water in Dak Lak
was extracted from surface water stored in artificial ponds and water reservoirs, 29
percent comes from natural rivers, streams and lakes and 57 percent is extracted from
ground resources.
Table 2.15: Main source of water (%)
District
Cu Mgar
Krong Pak
Eakar
Total
Source: Thang (2008)
Wells
96
51.02
34
60.4
Lake, dam
0
28.57
66
31.54
Streams
4
20.41
0
8.05
Total
100
100
100
100
30
Chapter 2 The coffee Sector in Vietnam
According to Chi and D’haeze (2005), coffee producers in Dak Lak mainly use two
irrigation methods: basin and overhead sprinkler irrigations. Sprinkler irrigation is the
most widespread method in coffee growing countries because this irrigation system can
operate efficiently even in mountainous areas with uneven topography. Sprinkler
irrigation can also apply a uniform amount of water over the tree canopy. Nevertheless,
this method requires expensive irrigation facilities, high risk of water losses especially
in windy conditions, and high-energy consumption because of high pumping pressure
required for sprinklers. Coffee producers also use a basin irrigation method. This
method has several advantages such as low initial investment cost, inconsiderable water
losses, lower energy costs and low evaporative losses. However, basin irrigation method
is labor intensive (operation costs and basin maintenance). Chi and D’haeze (2005)
found that 85 % of their households in surveyed sites used the basin irrigation method,
while only 15% used sprinklers. All the interviewed households of ethnic minority
origin used basin irrigation, while sprinkler systems were only observed in Kinh
households.
Water supply is an important factor affecting the yield and quality of coffee cherries.
According to farmers’ assessment, only 72 percent of households reported that they had
enough water for coffee. Those farmers estimated that if there was a sufficient supply of
water for coffee the yield could increase by about 20 percent compared to the current
level.
Table 2.16: Is yield limited by water (%)
District
Cu Mgar
Krong Pak
Eakar
Total
Source: Thang (2008)
Enough
Not enough
64
89.8
48
72.97
36
10.2
52
27.03
% increase with
enough water
30
9.64
20.85
21.06
However, coffee production in the Central Highlands is facing water scarcity. There was
a reduction of water flows in all rivers in the Central Highlands in 2003 – down by 20
and 50 percent on 2002 levels. The drought conditions resulted in a water supply
shortage for 100,000 households in the Central Highlands (The World Bank, 2004).
Similarly, in 2004 approximately 70,000 hectares of coffee was damaged or lost due to
the water shortage. However, previous studies (D’Haeze et al., 2003, D’Haeze, 2004)
pointed out that the amount of water presently used by coffee farmers exceeds the crop
31
Chapter 2 The coffee Sector in Vietnam
water requirement and therefore endangers water resources in the region. To develop
sustainable coffee production, apart from an irrigation program for constructing water
reservoirs, training for farmers is also necessary.
2.6. Conclusion
Coffee is an important crop in Vietnam’s agricultural sector. It is the second largest
export agricultural commodity in Vietnam after rice. The coffee sector accounts for
about 3.29 percent of total households in Vietnam. Most coffee households are located
in provinces in the Central Highlands of Vietnam such as Dak Lak, Dak Nong, Gia Lai,
Kon Tum, Lam Dong. The coffee production in Central Highlands accounts for over 90
percent of national output.
The first planting of coffee in Vietnam occurred in 1857 but only became a
commercially significant crop after the “Doi Moi” policy of Vietnam in 1986. The area
of coffee increased exponentially, from 50,000 ha in 1986 to a peak level of about
600,000 ha in 2000. Policy reform (Contract 100, Contract 10, Land Law in 1993, resettlement policy, trade liberalization policy) and the development of a high price in the
international market was a major contributing factor in the development of the coffee
sector in Vietnam.
The rapid expansion of the coffee area has made Vietnam an important coffee exporting
country. At present, Vietnam contributes over 40 percent of Robusta and about 13
percent of the total world coffee market. In general, Vietnam has a comparative
advantage in coffee production with high yields and low cost.
With more than 90 percent of coffee output in Vietnam exported, the coffee price in
Vietnam depends heavily on the international price. Low prices in 2002 led many
farmers to cut coffee and switch to other crops. During three seasons (2001/2002 to
2004/2005), the coffee area in Vietnam reduced over 100,000 ha.
In addition, despite achieving this rapid expansion, the coffee sector in Vietnam faces
significant economic challenges. First, small farm sizes dominate the coffee sector.
Second, a high percentage of coffee households are minority ethnic people with low
levels of education. Third, a high proportion of coffee households are poor and have
limited opportunities to diversify their income.
32
Chapter 2 The coffee Sector in Vietnam
With such characteristics, coffee farmers are vulnerable to price fluctuations. In the
following chapters, several models analyze the supply response of coffee and identify
the optimal rules for coffee farmers in Vietnam. Chapters 4, 5, 6 apply the Fixed Form
Optimization approach to analyze coffee farmer’s decision at individual or household
level. Chapter 8 uses a “positive” approach to analyze the coffee supply response at an
aggregate level.
33
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
CHAPTER 3. STOCHASTIC OPTIMAL INVESTMENT
DECISION FOR PERENNIAL CROPS: A LITERATURE
REVIEW
3.1. Introduction
As established in Chapter 2, coffee is vitally important to Vietnam’s economy. The
increased supply of coffee since the early 1990s led to the price reduction in the early
2000s that significantly reduced producers’ incomes. Due to the price collapse, a large
number of households cut down coffee trees and switched to other crops. Many farmers
lost money on their investments in coffee gardens.
The expansion of the coffee area by farmers in Vietnam occurred rapidly without the
intervention of the Government. Managing a farm is complex and the choice of farm
strategy may be influenced by the farmer's knowledge of crop husbandry, machinery
availability, economic/commercial factors, political events, legal constraints, historical
trends, climate/weather, environmental issues, personal circumstances and any number
of practical considerations (Pannell, 1996). In addition, coffee is a perennial crop, thus
deciding when to plant or when to clear coffee trees is much more complicated than for
annual crops. The investment decisions of farmers (including the planting, replanting,
and cutting decision) are determined by factors such as: (i) resource availability, land,
capital and labour; (ii) the age of orchards; (iii) profit expectations; (iv) relative
profitability of substitute crops, such as rice and (v) risk aversion (Ruf and Burger,
2001).
The main objective of this study is to solve the stochastic optimal control problem of
coffee farmers by identifying the optimal removal and replanting price for coffee
farmers to maximise the expected income from land use. Thus, the problem for the
representative coffee producer considered in this study is one of achieving an optimal
harvest, including planting and removing trees, under stochastic conditions.
This chapter reviews the literature on optimal planting and clearing decisions. Prior to
detailing stochastic optimal control methods, the next section begins with some basic
theoretical models for optimal harvest of perennial crops.
34
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
3.2. Theoretical Models for Optimal Investment Decision
The fundamental questions for perennial crop and forestry economics are: when should
farmers harvest or clear fell and when should they replant? This issue was first
considered by forestry economists when they tred to determine the optimal harvesting
rotation. Faustmann (1849) presents the first robust solution to the optimal rotation
problem (Faustmann, 1995, Samuelson, 1976, Brazee, 2007). In this model, all
parameters including stumpage price, replanting cost, the discount rate and timber
volume function are deterministic and constant over time. The forest owners maximise
the net present value (NPV) of their land. These assumptions imply that the optimal
harvesting age is the same in every rotation. The basic Faustmann optimal NPV is given
as (Samuelson, 1976, Faustmann, 1995, Buongiono, 2001, Brazee, 2007):
Maximise
V (T ) e iT G (T ) C e
iT
(e iT G (T ) C ) e
(e iT G (T ) C )(1 e
iT
e
2 iT
2iT
(e iT G (T ) C ) ...
(3.1)
...)
iT
e G (T ) C
1 e iT
where C is replanting cost, i is discount rate, T is harvest age and G(T ) is the value of
stumpage harvested at age T.
In the basic Faustmann model, the opportunity cost of land is the present value of future
rotations. The opportunity cost may be the income from non-forestry crops. Let S be
the maximum NPV of land from either non-forestry uses ( W ) or land expectation value
(site value). Thus, the objective function (3.1) becomes:
Maximize V (T )
e iT G (T ) C e
iT
S
(3.2)
To find the optimal harvest time, (3.2) is differentiated with respect to T and the
derivative is set equal to zero
e
iT
dG(T )
iG (T )
iS
dT
(3.3)
0
or
dG(T )
dT
(3.4)
iG(T ) iS
35
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
After the first rotation, if non-forestry crops are more profitable than forestry uses, S is
replaced by W in (3.4). Otherwise, income from forestry uses is higher, then (3.4) is
rearranged as
e it G(T ) C
iG(T ) i
1 e iT
dG(T )
dT
i(G(T ) C )
1 e iT
(3.5)
The results in (3.3) to (3.5) are the “Faustmann rule”.
The assumptions of the Faustmann model characterize its weaknesses. The assumptions
of the basic Faustmann model omits many important factors that affect the optimal
rotation age and decision of farmers. Providing a more complete analysis for optimal
decision of forestry growers, many economists extend the Faustmann model in various
ways: by adding tax on forest value (Klemperer, 1976, Chang, 1982), including
silvicultural efforts of the forest (Samuelson, 1976) and subtracting harvest cost, road
building and maintenance costs at the time of harvest from the revenue (Heaps and
Neher, 1979).
The Faustmann rule has been applied not only in defining the optimal harvest age for a
forest, where the yield is determined at the end of the economic life of the tree, but also
in investigating the investment decision of agricultural crops (perennial crops) where
there are continuous flows of benefits. Jayasuriya et al (1981) used a dynamic profit
maximization model for analyzing the long-term investment decision of Sri Lankan
rubber smallholders. The rubber farmers face the decision problem of when to replant
existing trees. The study presents an analysis of planting decision and investigates the
relevance of conventional investment decision criteria for rubber smallholders. The
analysis starts from the formulation of NPV of the crop sequence:
(3.6)
T
iT
NPV
R(t )e dt S (T )e
iT
0
where R(t ) is net revenue in the year when the age of trees is t year; S (T ) is a salvage
value at the end of its life in year T ; i is the discount rate
36
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
The optimal condition for maximizing NPV of the earning stream is:
i
R(T ) S '(T )
1 e
(3.7)
T
iT
R(t )e dt S (T )
iT
o
When data is available in discrete form, this equation can be expressed as
R(T )
S (T )
1 (1 i)
(3.8)
S
i
t
(1 i) R(t ) S (T )
T
where i is the interest rate,
t 1
S is change in salvage value in year T
The optimal replacement age occurs when the marginal revenue from these trees (i.e
income in current period plus the increase in salvage value as a result of keeping it for
another period) falls below the highest perpetual annuity from the replacement crop.
Farmers select the crop with highest NPV to replace the standing rubber tree and they
replace the current trees when marginal revenue from these trees fall below the level of
highest perpetual annuity from the replacement crop. By analyzing two groups: rubber
replanters and non-rubber replanters (people who do not replant rubber), the study
identifies the main reasons to explain why they continue tapping the existing trees
(mainly due to low current income from current trees), why they decide on replacement
(the common reason is old trees). However, this study does not investigate the
relationship between cutting decision and age of rubber trees. Furthermore, the study
does not investigate the price levels at which rubber smallholders should cut or replant.
Applying the Faustmann formula, Kearnev (1994) used a dynamic LP approach to
analyze the planting and replacement decision of farmers for pip fruit in New Zealand.
The objective of the model is to explore the optimal variety mix for an individual apple
orchard. The choice of variety mix within the orchard is an important strategic decision
because the trees take 10 years to reach the maturity and consumer’s preferences change
over time. The decision variables are NP1tj (where NP1tj is area of new planting of
variety j at the beginning of year t in age class 1) and Aijt (where Aijt is area of age group
i of variety j at the end of year t after removals have been deducted)
The objective function is given by:
37
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
T
Rt
Maximise Z = t
in which
Rt
1
1
(1 i )t
Akjt GM kjt
FC t
where R t is net return from Akjt and Akjt is area planted for each age group k and variety
j, GM ijt is gross margin for age class k for variety j in year t, FC t is fixed costs in year t,
i is the discount rate.
The constraints of the model include land limitation, a cash constraint and harvest
capacity constraint. The apple prices in the model were the average national price in the
first year. The prices, assumed to reduce over the following 10 years at different rates
for each variety and become stable for the remaining 10 years. The results from the
model show the maximised profit, the removal of each variety and area change from
1991 to 2000. However, the model is deterministic with the impact of age on the cutting
rule and possible input response of farmer in the short-run when ignoring price changes.
The determination of the optimal harvest age for a growing forest has received a great
deal of attention by economists. However, in the Faustmann model, the only economic
value of a forest is through its wood production. However, other values of the standing
trees ignore issues such as flood control, recreation, and other services. To incorporate
those benefits into the basic Faustmann model, Hartman (1976) develops a model to
analyse the optimal harvesting time when a standing forests has a additional non-timber
values (denoted by F (t ) ). The additional non-timber values are assumed to increase
with the age of trees.
Let G(t ) be still the stumpage value at age t. In the simple model of one cutting forest,
the objective is to maxinise the sum of the integral of discounted benefits F (t ) plus the
discounted value of timber at harvest time. Mathematically, the problem is to find t to
maximise (Hartman, 1976):
(3.9)
t
it
V (t )
it
e F (t )dt e G (t )
0
where i is the discount rate and t is the harvest age.
38
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
To find the optimal age T , one needs to solve the first order condition for a maximum
V ' (t ) e
it
F (t ) G ' (t ) iG (t )
(3.10)
0
F (t ) G ' (t ) iG (t )
G ' (t ) G (t ) i F (t ) G (t )
and the second order condition is
V '' (t )
ie
it
F (t ) G ' (t ) iG(t )
e
it
F ' (t ) G '' (t ) iG ' (t )
0
(3.11)
After replacing (3.10) into (3.11), the second order condition simplifies to:
(3.12)
F ' (t ) G '' (t ) iG ' (t )
The first order condition for optimality shows that the marginal loss by delaying cutting
the trees one period is equal to the gain from postponing the harvest (it is the summation
of recreational value and timber value over one period). In the absence of recreational
value ( ( F (t ) 0) , the landowner should harvest the forest if its growth is equal to the
discount rate. With recreational values, the landowner should harvest at a later age,
when the growth rate is less than the discount rate.
The conditions in (3.10)-(3.12), as mentioned earlier, are applied for the first harvest.
For indefinite sequence of harvests, the objective now is to maximise
(3.13)
T
it
V (t ) G (t ) e
e
2 it
e
3it
it
...
e F (t )dt 1 e
it
e
2 it
...
0
T
G (t )e
it
e ix F (t )dt
0
1 e
it
The first order condition for maximizing V (t ) is
V ' (t )
ie it G (t ) e it G ' (t ) e it F (t ) (1 e it )
(3.14)
T
G (t )e
it
e ix F (t )dt ie
it
(1 e it ) 2
0
39
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
(3.15)
T
e F (t )dt
ix
G ' (t )
G (t )
1
i
1 e
0
it
it
G (t )(1 e )
F (t )
G (t )
T
The difference between (3.15) and (3.10) is the term in the brace. Because
e ix F (t )dt
0
T
and
are positive, thus
G(t )
1
1 e
e ix F (t )dt
0
it
G (t )(1 e it )
is greater than 1, so
T
1
i
1 e
e ix F (t )dt
0
it
G (t )(1 e it )
(which is referred to as the effective discount rate) is greater
than the normal discount rate i. This change makes the optimal harvest age of the
infinite time horizon harvest decision different from the one harvest horizon.
3.3. Faustmann Model with Risk
In the optimal Faustmann model, a standing tree will grow until it reaches maturity
unless cut down by the landowners. However, it is assumed that this is known with
certainty - ignoring risk factors that affect optimal harvesting. Reed (1984) investigates
risk of fire on the optimal rotation of a forest. Based on the basic Faustmann formula,
Reed investigated the optimal harvest age for maximizing the expected return of a forest
under the risk of fire.
According to Reed’s model, the optimal cutting age to maximise the long-run expected
yield is 15
'
V (T )
(3.16)
(V (T ) C )
1 e T
where C is replanting cost and
is the probability of fire occurrence per unit of time
in a Poisson process. V (t ) is the stumpage value of a stand of trees at age t. This is the
15
To see how to get the optimal rules with risk of fire in detail, see Reed (1984)
40
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
same as Faustmann formula in (3.5) with the discount rate i replaced by the probability
of fire occurrence
.
The optimal cutting age to maximise the expected discounted yield is
'
V (T )
(
i)(V (T ) C )
1 e ( i )T
(3.17)
This is also as the same as Faustmann formula in (3.5) but the discount rate i is
replaced by (
i) . Thus, the effect on optimal rotation of fire risk is the same as that of
an increase in discount rate by an amount of average rate at which fire occurs. This
shortens the rotation length.
In general, theoretical models for optimal harvest decision by Faustmann (1995),
Hartman (1976) and Reed (1984) are useful to identify the optimal age for cutting the
standing trees. However, they do not address the price uncertainty problem. In this case,
there is no fixed output price as in the Faustmann model, and it varies stochastically. In
addition, those models have not developed the detailed analytical framework to analyse
the optimal cutting and replanting decision. When adding such factors into a problem of
the optimal cutting decision, the problem becomes much more complicated. However,
different mathematical methods may solve these problems. The next section will review
different methods for solving the stochastic optimal control problem.
3.4. Stochastic Optimal Control Methods
This section provides a literature review of different methods to solve the problem of
stochastic optimal control. The discussion summarizes different methods including
Dynamic programming, Real option approach, and other techniques for solving the
complex dynamic problem.
3.4.1. Dynamic Programming (DP)
Dynamic programming (DP) is a numerical and analytical method to solve dynamic
optimization problems. It is based upon the principle of optimality which states that an
optimal policy has the property that whatever the initial state and initial decision are, the
remaining decisions must constitute an optimal policy with regard to the state resulting
41
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
from the first decision (Bellman, 1957). This principle gives the recurrence relation
function or Bellman equation as (Dixit and Pyndyck, 1994, Kennedy, 1986):
Ft ( xt )
Maxut
t
(3.18)
1
( xt , ut )
1 i
t
Ft 1 ( xt 1 )
where Ft ( xt ) is the outcome - the expected net present value, ut is a control variable,
xt is a state variable,
t
( xt , ut ) is intermediate profit flow, (1 1 i) is the discount
factor and i is the discount rate. The aim is to choose the sequence of controls ut
over time to maximise the expected net present value.
DP is a technique ideally suited for use in finding the optimal sequencing problems of
inputs and harvesting outputs in many types of agricultural products. Those problems
entail decisions which are sequential, risky and irreversible (Kennedy, 1986).
Furthermore, Kennedy (1986) also points out that DP is a technique particularly suited
for obtaining numerical solutions to problems that involve functions which are nonlinear, stochastic or models in which state and decision variables are constrained to a
finite range of values.
Dynamic programming has found wide use in pest management, water resources,
fisheries, and in the management of animal populations. However, DP can analyze crop
rotations, and find the optimal cutting time for forest trees.
Burt and Allison (1963) applied stochastic dynamic programming to analyze the
decision to leave land fallow or plant wheat with soil moisture as the state variable. The
model answered the question “when should the farmers fallow land?” The study
indicates that an optimal policy based on soil moisture at wheat planting time will give
an expected return per year of about 13 percent higher than a policy of continuous
wheat and 30 percent than the fallow and wheat.
Dynamic Programming applies in farm forestry analysis to identify the optimal cutting
time. As noted previously, the question of optimally deciding when to cut down a tree is
a major concern for forestry economics. Matheson (2007) applied DP for finding
optimal harvest length when replanting is addressed. This is different from the previous
standard model without replanting decision. Without replanting, farmers simply cut the
timber if the growth rate is equal to the discount rate. However, with the presence of
replanting and cutting costs, the tree-cutter has three options in each period: (i) leaving
42
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
the trees for later harvest (ii) cutting the trees and replant; (iii) cutting the trees and
leaving land idle.
The decision is based on the objective of present value maximization. The functional
equation is given by:
v(k )
max
(3.19)
v h(k ) , k v(0) RC , k
In this equation, v k
decision options.
is the maximum value of the tree given the three alternative
is the discount factor {
1/ (1 i) }; h is the growth function of
the tree and represented by a third-degree polynomial form of time; k is the size of tree
and kt
1
h( kt ) . RC is the replanting cost and is assumed constant overtime. Price of
timber is exogenous and assumed to be 1.
This equation is not solved analytically. The author uses a numerical method to find the
optimal time for cutting. In this study, the author also simulated to find the optimal time
when the discount rate was changed.
Different factors determine the forestry yield such as variety, resource management and
more importantly climate. To analyze the decision of the forester with weather
uncertainty, Jia (2006) applied DP to find out the optimal forest rotation decision for
loblolly pine in North Carolina (USA) under climate fluctuations. Two factors
determine the growth of trees: genetics and climate in which the genetic effect is
deterministic, and climate fluctuation is stochastic. A quadratic function of tree age
expresses the growth of timber.
The climate effect is introduced by using a multiplicative factor L, and in the paper, Jia
investigated the optimal rotation in two possible cases: (i) L is assumed to follow a firstorder autoregressive process and (ii) L is a random walk model.
The growth function with both effects would be:
Y R (nt 1 ) Y R (nt ) L(nt ) Y (nt )
(3.20)
R
R
n
where Y (nt 1 ) is realized yield in year t 1 , Y (nt ) is realized yield in the previous
year nt, L(nt ) Y (nt ) is the realized new growth in year nt , which is the product of
43
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
natural growth and the climatic fluctuation effect.
The revenue function from timber is:
R Y (nt , Lt )
PY ( Lt , nt ) K
(3.21)
where Y ( Lt , nt ) is saw timber yield (mbf/ac) obtained from a t year-old forest-stand, K
is the given value of bare-land.
The Bellman’s equation for a planning horizon of T years is:
Vt (Yt , Lt , nt , X t ) max R(Yt , Lt ), ERt 1 (Yt 1 , Lt 1 )
where
(3.22)
is the discount factor, V is a reward function, and E is the expected value of
timber.
With the decision of cutting or keeping to maximise present value of forest over a
certain time horizon, the author used DP to solve the problem of finding the optimal
rotation age. The results of the study could identify the relationship between the climatic
effect and age of tree and the expected rotation ages in both climate simulations.
However, the model assumed a constant price so it did not identify at what price farmers
should cut and replant.
With biological features of forestry crops, DP has been applied to analyze tree
production cycle/cutting time under the different impacts and conditions such as timber
stock and resource management (Dixon and Howitt, 1980), stochastic price (Penttinen,
2006, Chladná, 2007), change in environment (Chladná, 2007), and interest rate
variability (Alvarez and Koskela, 2004).
The application of DP is very popular to solve optimization problems for farmers’
planning horizon in number of years. However, the increase in number of state and
decision variables brings a computation burden when solving the DP problem. This
issue has been termed “the curse of dimensionality” (Bellman and Dreyfus, 1962),
often causing it to be dismissed. With the support of modern computation techniques,
the capacity of current computers limits the maximum number of state variables to
three. However, in many cases it is possible to use other approaches to solve
approximately a DP problem with many state variables (Kennedy, 1981). One of the
important approaches refers to Reinforcement Learning (RL) or Neuro- Dynamic
44
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
Programming (NDP) or Approximate Dynamic Programming (ADP). In this approach,
they use basis functions or neural networks to retain an estimate of the value function at
each iteration within a dynamic programming algorithm. ADP primarily solves “the
curse of dimensionality”. ADP avoids the exponential increase of computations by
using parametric approximate representations of the cost-to-go function. Compared to
traditional DP, which performs exhaustive sampling of the entire state space in solving
the stage-wise optimization, these approaches sample only a small, crucial fraction of
state space and thus require less computation. The detailed descriptions of RL, NDP or
ADP is presented in Bertsekas and Tsitsiklis (1996), Sutton and Barto (1998), and
Powell (2007).
3.4.2. Real Option Approach
The conventional approach in selecting investment projects where there is uncertainty
about future market conditions is based on the comparison of expected net present
value. However, this basic principle is often erroneous because the expected net present
value is built on faulty assumptions. Either the investment is reversible (it can somehow
be undone and the expenditure recovered should market conditions turn out to be worse
than anticipated), or if the investment is irreversible, it is a now or never proposition: if
the firm does not make the investment now, it will not be available in the future (Dixit
and Pyndyck, 1994).
In most cases, one can delay investment. Thus to analyze the investment decision one
needs to develop a better framework to address the issues of irreversibility, uncertainty
and time. A firm that has an opportunity to invest is holding something like a financial
option. The development of the option approach brings a richer framework for
investment analysis. There are a number of detailed introductions to the options
approach to investment (Dixit and Pindyck, 1994, Smith, 2004, Gilbert, 2004). An
option exists when a decision maker has the right, but not the obligation, to perform an
act. For example, financial options, the mostly common option in economics, give the
owners the right, but not an obligation, to buy or sell financial assets at a predetermined
price before a particular event. According to Gilbert (2004) and Mauboussin (1999), the
real-options approach applies financial options theory to real investments, such as
manufacturing plants, product line extensions, and research and development.
Analogously, companies that make strategic investments have the right, but not the
obligation, to exploit these opportunities in the future.
45
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
Real options refer to the fact that firms have similar rights with regard to real (nonfinancial) assets. Options add value as they provide opportunities to take advantage of
an uncertain situation as the uncertainty resolves itself over time. The combination of
two things need to be in place for a real option to exist: there must be uncertainty in
terms of future project cash flows and management must have the flexibility to respond
to this uncertainty as it evolves.
Two well-known approaches for valuing an investment using real options theory are
dynamic programming (DP) and contingent claims (CC). DP, presented in the previous
section, is an older approach developed by Bellman and others in the 1950s and used
extensively in management science. The Contingent Claims approach assumes the
existence of a sufficiently rich set of markets in risky assets so that the stochastic
component of the risky project under consideration can be exactly replicated (Insley and
Wirjanto, 2010).
Both CC and DP get a mention in the natural resources literature, especially in forestry
economic modeling to determine the optimal harvesting decision. In the forestry
economics literature, however, the DP approach has generally dominated (Insley and
Wirjanto, 2010). There are numerous studies on forestry investment analysis by
applying the real option approach and using DP. Most recent studies have focused on
the optimal harvesting time of standing trees under price uncertainty. Thomson (1992)
compares the optimal rotation ages of the Faustmann model with fixed timber prices
with a binomial option-pricing model when prices follow a diffusion process. The study
shows that the stand NPV from diffusion model is generally higher than Faustmann
NPV and the rotation lengths are longer except at high prices where they are the same as
the Faustmann rotation. Most studies of forestry investment analysis using option
models have tried to expand the conventional approach by looking at more complicated
variation process of timber price. Gjolberg and Guttormsen (2002) also investigate the
impact of price variability on cutting decisions of forestry owners by looking at real
option valuation of forest when prices are mean reverting. They indicate that the mean
reverting price may significantly increase the option value in the forest investment as
compared to the Faustmann rules. Insley (2002) applies DP and the real option approach
to determine the value of the option to harvest standing trees in Canada and the optimal
cutting time when lumber price is assumed to follow a known stochastic process (mean
reversion and geometric Brownian motion). This study found that the mean reverting
process had a significant impact on the optimal cutting decision and on the value of the
46
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
forestry investment rather than geometric Brownian motion process. In addition, for
prices below the mean, a process of mean reversion has an option value higher than that
of geometric Brownian motion.
Kaakyire and Nanang (2004) also compare the forestry investment using the static
Faustmann model and the real options approach but they use the binomial optionpricing model, where timber values are assumed to follow a multiplicative binomial
process. By looking at four different management options (reforestation delay,
expansion of the wood processing plant, abandon of the processing plant because of low
timber prices and multiple options),
the model results show that option analysis
supported the reforestation investment although the Faustmann model rejected it. All
options show that the reforestation investment was highly valuable for the owner. Insley
and Rollins (2005) extend the model of Insley (2002) to a multi-rotational framework
using a linear complementary formulation to estimate the value of a representative stand
in Ontario’s boreal forest (Canada)16. The multi-rotation model can represent the “pathdependent option”. For the multi-rotational optimal harvest problem, the value of a
stand today depends on the quantity of lumber, and thus depends on when harvesting of
the stand took place. The important improvement of the linear complementary
formulation is that it can assure that the solution will converge to a correct answer and
the accuracy can be checked easily.
Most recent studies using a real options approach and DP technique just focus on
identifying the optimal harvesting decision for the stand of trees under different random
price processes. They are rarely concerned about the price level at which cutting and
replanting should occur. Furthermore, in many projects, the investment sequence covers
many stages and control variables. Sometimes a firm in a sequential investment using
DP cannot compute the identification of entry and exit points because of “the curse of
dimensionality”. As mentioned earlier, however, in many cases, researcher can use
Approximate Dynamic Programming approach for solving the problem of the curse of
dimensionality (Powell, 2007).
Although application of real options theory to study “entry and exit” decision of farmers
is limited, it is more popular in financial and other sectors (Dixit and Pindyck, 1994).
The expected output of entry and exit model using option theory is very similar to the
coffee model in this study when identifying the optimal cutting (actually it is the exit
16
linear complementary formulation is described detail in Insley and Rollins (2005)
47
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
point) and replanting (entry point) prices. In the entry and exist model, the solution is a
pair of trigger prices for entry and exits. Mathematically, the model can be described as
follows (Dixit, 1989, Dixit and Pindyck, 1994):
Let P be market price, determined exogenously. P follows the geometric Brownian
motion as:
dP
P
(3.23)
dt
dz or dP
Pdt
dt
Where dz is the increment of a standard Wiener process, uncorrelated across time and
E (dz )
0, E (dz 2 )
dt .
is trend growth rate of market price P and
is the firm’s discount rate.
where
is a random number.
Let V0 ( P ) be the expected net present value of an idle investment. Similarly V1 ( P)
is the variable cost of a unit; k is the cost of investment
defines for the active state;
per unit of output; l is the cost of investment suspension per unit of output; PH is the
market price level at which investment occurs and P L is the market price level at which
abandonment occurs.
The value of investment is V ( P, t ) . By a second order Taylor series, dV can be
approximated as
dV
V
dP
P
V
dt
t
1 2V
(dP)2
2
2 P
2
V
dPdt
P t
In the limit, dP, dt go to zero but (dP ) 2
V
dP
P
V
dt
t
Replacing dP
Pdt
dV
dV
V
P
P
V
t
1 2V
2 P2
2
1 2V
(dt )2
2
2 t
(3.24)
P 2 dt . So (3.24) becomes
(3.25)
2
2
P dt
dt , it yields:
1 2V
2 P2
2
P
2
dt
V
P
P
(3.26)
dt
Since this is an infinite horizon problem, the derivative
V
can be deleted.
t
48
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
1 ''
V ( P) P
V ( P)
2
'
dV
(3.27)
2
P
2
'
dt V ( P) P
dt
Taking the expected value of both sides, because E (
1 ''
V ( P) P
V ( P)
2
'
E (dV )
dt )
0 , so we have
(3.28)
2
P
2
dt
In asset equilibrium conditions, the expected capital gain of an idle project ( dV0 ( P ) ) is
equal to normal return ( V0 ( P )dt ), so
(3.29)
1 ''
V0 ( P) P
V0 ( P)
2
'
2
P
2
dt
V0 ( P)dt
(3.30)
1 ''
V0 ( P) P
V0 ( P)
2
'
2
P
2
V0 ( P) 0
Similarly, one can calculate the return on assets of an active project. The only difference
is that there is dividend added to the expected capital gain.
(3.31)
1 ''
V ( P) P
V1 ( P)
2
'
1
2
P
2
V1 ( P) P
0
The general solutions for (3.30) and (3.31) are easy to obtain. The solution (3.30) can
write as:
V0 ( P)
A0 P
(3.32)
B0 P
and for (3.31) as
V1 ( P)
A1P
B1P
(
P
(3.33)
)
where A0 , B0 , A1 , B1 are constants to be determined and
2
2
((
2
2
2 )2 8
2
2
)
1
,
is formulated as:
(3.34)
2
0
and
49
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
2
2
((
2
2 )2 8
2
2
)
1
2
(3.35)
2
1
For the idle project, the value of an investment should go to zero as price P goes zero.
Because
if A0
V0 ( P)
1 so V0 ( P)
0,
A0 P
B0 P goes to zero when P goes to infinity only
0 , so the function form value of the idle project now become:
(3.36)
BP
Similarly, as price goes to infinity, option value of abandonment goes to zero. Because
1 so V1 ( P) goes to zero when P goes to infinity only if B 0 . Thus,
0,
V1 ( P)
A1P
(
(3.37)
PL
)
Because PH is the price that triggers entry. The firm has to pay K to get V1 ( P) . Thus,
PH must satisfy the value matching condition and the higher contact or smooth pasting
condition:
(3.38)
V0 ( PH ) V1 ( PH ) k
(3.39)
V0' ( PH ) V1' ( PH )
Similarly, PL must satisfy:
(3.40)
V0 ( PL ) V1 ( PL ) l
(3.41)
V0' ( PL ) V1' ( PL )
Replacing V0 and V1 in (3.36) - (3.37) into (3.38)-(3.41), we get the system of 4
equations:
APL
APH
PL
PH
(3.42)
BPL
l
(3.43)
BPH
k
50
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
APL
A PH
(3.44)
1
1
1
B PL
(3.45)
1
The parameters
1
BPH
, ,
2
1
are estimated from empirical data. Then,
,
can be easily
calculated from (3.34) - (3.35). Finally, A, B, PH , PL can be obtained numerically. The
determination of PH , PL is illustrated in Figure 3.1.
Figure 3.1: The determination of PH and PL
Note: G ( P ) V1 ( P ) V0 ( P )
So far, applying real option theory using entry and exit decision model for analyzing the
cutting and replanting decision of perennial crops is very limited. To our knowledge,
only one study implemented by Luong and Loren (2006) analyses the optimal decision
for coffee farmers. The objective of this study is similar to one of objectives in the
present thesis. In the study, Luong and Loren used a real option model to examine
Vietnamese coffee farmers’ investment decisions. Starting with the role of fixed assets
in agricultural production, the authors point out that the coffee production investment
and disinvestment decision depends on the difference between the acquisitions and
salvage price. This approach permits the authors to build a model of investment under
uncertainty and captures the response in investment decision. Luong and Loren (2006)
applied the same entry-exit model as described above to identify the entry/exit points
for different groups of coffee farmers in Vietnam. There are three steps in their model:
51
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
Step 1: Determine the value of an idle project. At this stage, the value of the investment
is equal to the value of the option to invest.
Step 2: Specify the value of an active project, the value of the investment now
comprises both the present value of the net revenue generated by the project and the
value of the option to abandon the project.
Step 3: Determine the entry and exit points. At the investment entry/exit points, the
investor must be indifferent between being “idle” or “active”. This may result in two
equilibrium conditions: (i) the value of an idle project is equal to the value of an active
project, and (ii) the rate of change of an idle project’s value is equal to the rate of
change of an active project’s value. So, equating the values of the idle and active project
as well as their derivatives produces a system of four equations ((3.42)- (3.45)).
By solving the system of equations simultaneously, the model finds the entry and exit
points. The entry-exit model found that a small farmer would enter coffee production
when the farm-gate price was above 47.2 cents/lb and exit the business if price dropped
below 14.2 cents/lb. When price fluctuates between 14.2 and 47.2 cents/lb, no entry or
exit would occur. The exit and entry points were calculated for three groups of farmers
by production cost. The low cost/more efficient producers will decide to plant/or cut
coffee at lower prices, while the less productive producers have to wait for better prices.
The efficient farmers (with average yield of 3 tonnes per hectare) enter coffee
production at price level of 38.8 cents/lb and exit at a price of 10.2 cents/lb. Meanwhile
the entry and exit prices for average cost farmers (average yield of 2.08 tonnes per
hectare) are 47.2cents/lb and 14.2 cents/lb, respectively. The low advantage producers
who achieved only 70 percent of the average yield of 2.08 tonnes per decide price levels
for entry and exit at 58.4 cents/lb and 20 cents/lb.
The real option model by Luong and Loren (2006) identifies the optimal entry and exit
points for coffee farmers. However, coffee is a multi-year crop in which yield and
production cost vary by age of the trees. Thus, the age of the trees may influence the
cutting decision. Other factors such as a cash constraint might influence coffee owners’
cutting and planting decisions. In addition, real options models assume that price
follows a continuous time stochastic process while in many cases the problem is a
discrete time process.
52
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
3.4.3. Other Techniques of Solving the Complex Dynamic Stochastic Models
These include a range of techniques developed to solve complex dynamic stochastic
optimization models not solved by standard DP because of “the curse of
dimensionality”. Two primary techniques popularly used for solving the problem of
“the curse of dimensionality” are: Neurodynamic Programming
–NDP (or
Reinforcement Learning -RL or Approximate Dynamic Programming-ADP (Bertsekas
and Tsitsiklis, 1996, Sutton and Barto, 1998, Powell, 2007)) and Simulation-based
optimization (Carson, 1997, Azadivar, 1999, Ólafsson and Kim, 2002).
As mentioned earlier, NDP/RL/ADP is primarily viewed as a way to solve optimal
problems using the traditional DP because of “the curse of dimensionality”. In the
NDP/RL/ADP they use basis functions or neural networks to retain an estimate of the
value function at each iteration within a dynamic programming algorithm. The potential
benefit of NDP/RL/ADP
can be summarized as follows (Powell, 2007). First, in
general they do not require an explicit model of the system that is to be controlled. The
controller can learn to control ‘on the fly’. Second, they may avoid the ‘curse of
dimensionality’ by providing approximate solutions. Third, they may not require an
explicitly defined system performance measure, which is usually a function of the
system states and the control actions in the classical optimal control theory. Some
examples of NDP/RL/ADP are Bertsekas and Tsitsiklis (1996) Roy et al. (1997),
Schutze and Schmitz (2007), Castelletti (2007), Powell (2007).
Simulation optimization provides a structured approach to determine optimal input
parameter values, where optimal is measured by a function of output variables (steady
state or transient) associated with a simulation model (Swisher and Hyden, 1998).
Simulation optimization can be seen as a process of finding the best values of some
decision variables for a system where the performance is evaluated based on the output
of a simulation model of this system (Ólafsson and Kim, 2002). Thus, the techniques of
simulation optimization vary greatly depending on the exact problem setting. A survey
of techniques for simulation optimization are described in Andradottir (1998), Swisher
and Hyden (1998) Azadivar (1999) and Ólafsson and Kim (2002). Some recent
examples of application of simulation optimization are L'Ecuyer et al (1994), Marbach
and Tsitsiklis (2001), Konda and Tsitsiklis (2003) and Barton (2009).
53
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
Fixed form or policy space optimization is a special case of these techniques that
obtains near-optimal feedback policies for complex ecosystem problems. It is a
multidimensional extension of control-space optimization. In control-space evaluation,
the analyst is largely limited to two control dimensions due to the curse of
dimensionality17. However, when a objective function is defined with many control
variables, it is still possible to find the optimization by adding additional parameters
which make this function more flexible and general (Walters and Hilborn, 1978).
According to Walters and Hilborn (1978), there are two basic steps in the development
of fixed form optimization. The first is to find the algebraic form of the control function.
Commonly, one can intuitively guess the form, and in systems with a few state variables
and controls, one can simply make the control a polynomial function of the state
variables.
The second step in fixed-form optimization is to find the optimal values of the control
parameters (Walters and Hilborn, 1978). There are two alternative approaches to this
problem. The most elaborate is to use one of the many general gradient search
algorithms developed for nonlinear optimization. However, each evaluation of a set of
parameters involves a large number of numerical simulations. A second approach is
much simpler: by testing a large set of randomly chosen values for the control
parameters. Such random searching methods can work as well as gradient search
methods for problems that involve discontinuous response surfaces, or ones with several
peaks. In this thesis, to find the parameters of the optimal rule for cutting and replanting
of coffee trees in Vietnam, the GRID method is used. The GRID method is presented in
Section 4.3.7.
Peterman (1977) applied the fixed form method for hazard index function (H) of
budworm. He determined the optimal threshold value of H at which spraying should
happen. Generally, spraying and tree harvesting are the two primary management
options present for the budworm-forest system in eastern Canada. The paper
investigated the "rules" for these options: the age above which trees were harvested and
the ‘threat state’ above which insecticide should be applied. ‘Threat state’ measured by
the hazard index was dependent upon egg density and amount of defoliation of both old
and new foliage. A simple fixed-form optimization for spraying was defined as follows
(see more in Peterman 1977; Walters and Hilborn 1978):
17
See more about control space optimization in Walters and Hilborn (1978)
54
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
H
1
(defoliation)
2
(eggs)
Spray if H>1
Then, by seeking the values for
1
and
2
, the model can maximise the objective
function. This form can extend by including the product of defoliation and eggs to
account for potential interaction between these variables.
When searching for the algebraic form of the control function, in a system with few
state variables, authors can make the control a polynomial function of state variables.
Walters (1975) explored the optimal harvest strategies for salmon in relation to
environmental variability and uncertainty about production parameters. To meet the
objective, Walters applied the fixed-form for exploitation rate as a function of total
population (N) as follows:
Exploitation rate
1
2
N
3
N2
4
N3
(3.46)
After the different steps, Walter found the αi to give the best overall return and the
relationship between harvest rate and population is the optimal control law.
In a further study of budworm management, Sonntag and Hilborn (1978)18 used fixed
form optimization for spruce budworm to decide whether farmers should spray or cut
the trees. The fixed form is given by:
Using this form of control law, they applied a random searching algorithm to optimize
the objective function. The process used by Walters (1975) and Sonntag and Hilborn
(1978) could more accurately be described as solving DP by approximation. They used
“approximate” fixed forms to identifying the relations between variables in their
models, from which they can simply solve the problem.
3.5. Conclusion
In conclusion, there have been many studies that analyse the stochastic optimal control
problems faced by farmers using three main methods: Dynamic Programming, Real
18
Quoted in Walters, J.C. and Hilborn, R. (1978)
55
Chapter 3.Stochastic Optimal Investment Decision for Perennial Crops: A Literature Review
Options Approach and other techniques for solving the complex DP (including the
Fixed form optimization). The model in this study aims to identify the optimal cutting
and replanting rules for coffee farmers. The problem for optimal cutting and replanting
decision of coffee in Vietnam is a stochastic dynamic problem. Coffee is a perennial
crop, thus the decision made in any period will affect the state of following periods and
in turn influence the total income from land. The model includes only two state
variables (age of coffee tree and price) but a number of different control variables.
There are five control variables in the coffee model reflecting the decision of farmers at
each stage. They are: (i) keep coffee if land is occupied by coffee, (ii) cutting standing
trees for other crop (maize) if land is occupied by coffee, (iii) cutting standing trees and
replanting new trees, (iv) keeping other crop (maize) if land is not occupied by coffee,
and (v) going back to coffee if land is occupied by maize. In addition, the model is
stochastic dynamic because the price of coffee is uncertain.
With such characteristics, it is not possible to apply the standard DP for solving the
coffee model because of the problem of the “Curse of dimensionality”.To solve the
coffee optimal rule problem, the study applies the fixed form approach. By assuming
the fixed functional forms for cutting price and replanting price, the model can be
solved with DP by approximation. The next chapter will describe the model structure,
content and its results in detail.
56
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
CHAPTER 4. OPTIMAL REPLANTING AND CUTTING
RULES FOR COFFEE FARMERS IN VIETNAM: FIXED
YIELD MODEL
4.1. Introduction
The main objective of the study is to solve the stochastic decision problem for coffee
farmers in Vietnam. More specifically, the study builds a main model (and some
extended models) to identify the optimal cutting and replanting prices for coffee farmers
to achieve the maximum net present value that farmers can earn from their land. Given
that coffee is a multi-year crop, the application of DP seems an appropriate method to
solve the dynamic optimization problem of coffee farmers. However, this study is not
using stochastic DP because of "the curse of dimensionality”. The models in this study
use a horizon of 50 years for farmers and they have four decision options in each period:
(i) keep growing coffee, (ii) cut and grow maize, (iii) cut and replant coffee; and (iv)
switch to coffee if they are growing maize. In addition, models in this study also cover
different groups of farmers categorized by the age of their coffee trees. Moreover, the
coffee price in the model fluctuates stochastically. Thus, the number of decision and
state variables becomes very large so one cannot use DP to solve them. In addition, the
objective of the models in this study is a little different from traditional DP. The
objective of the present model is to find the maximum net present value for coffee
farmers earned from their land by identifying the optimal rules of cutting and replanting.
There are only two previous studies that have examined the optimal ‘trigger’ prices at
which farmers should change their coffee plantings in Vietnam (Luong and Loren,
2006; Oxfam, 2002). These studies are limited to presenting single period cost-benefit
analysis and do not investigate the relationship between tree age and farmer’s decisions.
To identify the optimal cutting and replanting price for coffee farmers in Vietnam under
price uncertainty, this study applies the fixed-form optimization approach (Walters and
Hilborn, 1978). The fixed form approach is applied to a specific functional form of the
cutting and replanting price. Farmers will cut coffee trees to switch to other crops if
output price is very low. However, the coffee yield and production cost of coffee
normally varies by the age of coffee trees. Thus, replanting and cutting prices are related
57
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
(via an appropriate polynomial functional form) to tree age. With the assumption of
fixed forms for cutting and replanting price, identifying the solutions for the optimal
rules is much simpler as compared to conventional DP.
This chapter starts with the Fixed Yield Optimal Model (FY model). The core objective
of the FY model is to identify the optimal cutting and replanting rules for coffee farmers
with the assumption of a fixed coffee yield function. In the FY model, yield of coffee
varies via the age of the coffee tree but otherwise cannot be altered through
management. The model is extended in the following chapters by adding a cash
constraint and the possibility of a short-run yield response.
Before moving to the detailed FY model, it is useful to understand the coffee farmers
and their production system in Vietnam. The coffee farm system in Vietnam will be
described in Section 4.2. The FY model structure is described in Section 4.3. Section
4.4 presents the results of the model. Section 4.5 gives some conclusions.
4.2. Coffee Farm System in Dak Lak
Prior to discussing the practical optimization model, this section describes the farm
system of coffee households based on a Coffee Farm Survey in Dak Lak province in
2007. Dak Lak is located in the Central Highlands of Vietnam. With favorable climate
and land, Dak Lak (including Dak Nong19) is the principal coffee producing area in
Vietnam, accounting for about 50 percent of national output. In the 1990s, the area for
coffee in the province increased rapidly with an annual area growth rate of 14.1 percent.
In 2000, the coffee area in Dak Lak reached the peak level of 260,000 ha, accounting
for approximately 60 percent of cultivated land and 86 percent of the area of multi-year
industrial crops in the province.
19
Dak Lak province was divided into two provinces in 2003: Dak Lak and Dak Nong. The map of Dak
Lak location is presented in Appendix A.
58
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
300000
250000
ha
200000
150000
100000
50000
0
1986
1989
1992
1995
1998
2001
2004
2007
Figure 4.1: Development of coffee area in Dak Lak, 1986-2008
Source: MARD per com.
After 2000, due to the price reduction, the coffee area in Dak Lak fell sharply. Since
2004, when prices started to increase, most cutters replanted again. According to a
report of Department of Agriculture and Rural Development of Dak Lak province, to
the end of 2007 most of the farmers who had cut coffee grew coffee again (DARDD,
2008).
As presented in Chapter 2, coffee households in Dak Lak are highly specialized, with
the major land use being for coffee cultivation. Beside coffee, households utilize flat
land to grow annual crops such as rice for both home consumption and cash. Maize,
rubber, cashew and sugarcane are also the main alternative crops cultivated by coffee
farms (see Table 2.12).
The farm size varies highly among households and districts. In three surveyed districts
in Coffee Farm Survey, coffee households in Cu Mgar have the largest land area with an
average of over 1.9 ha while farmers in Krong Pak and Eakar have a smaller scale with
the average of 0.9 ha and 0.73 ha, respectively.
59
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
Table 4.1: Percentage of household with other activities excluding cropping (%)
District
Chicken
Pig
Cattle/buffalo
Other animal
Aquaculture
Wage
Other activities
Cu Mgar
Krong Pak
Eakar
20
20
14
0
0
10
2
8.2
49.0
16.3
2.0
4.1
26.5
30.6
8
4
0
0
58
50
4
Source: Thang (2008).
When the price of coffee is depressed, most farmers had to reduce their inputs and
labour cost to save money. Some farmers had to cut coffee and change to other crops,
with maize as the main substitute crops for farmers in Dak Lak. According to the Coffee
Farm Survey 2007, over 6 percent of coffee farmers in Dak Lak had to cut trees early
because of the price fall (see Table 4.2). The majority of cut trees were in low yield
areas and where farmers were relatively poor. These farmers replanted coffee land to
other crops. The largest proportion cut coffee to grow maize (29.2 percent) and paddy
(25 percent) (see Table 4.3).
Table 4.2: Percentage of households reducing coffee area
District
Yes
No
Cu Mgar
Krong Pak
Eakar
Total
0
4.0
14
6.0
100
95.9
86
93.9
Source: Thang (2008).
Table 4.3: Percentage of farmer switched to other crops
Paddy
Maize
Durian
Sugarcane
Cassava
Pepper
Bean
Cashew
Percent
Cumulative
25.0
29.2
2.1
6.3
2.1
14.6
2.1
18.8
25
54.2
56.3
62.5
64.6
79.2
81.3
100.0
Source: Thang (2008).
A large proportion of farmers (29.2%) switched to maize due to the price fall. Hence, to
simplify the model it is assumed that coffee is always replaced by maize.
.
60
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
4.3. Model Structure
This section describes the structure of the Fixed Yield model (FY model) and introduces
the procedure to get the solution. The FY model includes a profit function, a coffee
yield function, a production cost function and a revenue function. The objective of the
model is to identify the optimal cutting price and replanting price for coffee farmers to
maximise expected net present value (ENPV).
The model is similar to the option model by Luong and Loren (2006) because both aim
to identify the cutting and replanting prices. However, their model does not cover the
impact of tree age on the cutting decision of the farmers. Nor does it capture the
presence of a competitive crop, while the FY model investigates the farmer’s decision
when the profit of the replacement crop (maize) changes.
4.3.1. Objective Function
The FY model aims at identifying the optimal cutting and replanting decisions that
maximise the ENPV from “land use choice” per one unit of land (1 hectare) over the
entire planning horizon. The representative farmer can either produce coffee on the land
or switch the entire area to maize.
The ENPV depends on the current tree age, coffee price and production costs. Thus, the
ENPV of a block of land with coffee trees aged a at year 1, evaluated over a 50 years
planning horizon given N possible random price sequences is given by:
ENPVa
1
N
N
T
e
t
t ,r ,a
V (T )
(4.1)
T
r 1 t 1
where ENPVa is expected NPV given coffee trees at starting age a , for the next 50
years given N possible random price sequences;
trajectory r and starting age a ; and
e
t , r. a
is profit per ha in year t for price
is the discount factor. V T denotes the terminal
value of the coffee garden. However, given the model is defined over a long period of
50 years, at the end of the period the terminal value { V T
T
} will be insignificant and
hence is set to zero in the model; and r identifies the replicate number for one age
group. In this model, one hundred replicates are employed for each starting age group.
61
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
For each replicate, a separate random price trajectory is simulated. The method used to
generate price simulations over 50 years are presented in Section 4.3.6
In the FY model, it is assumed that the farmer controls one hectare of land and the
planning decision applies to the whole area i.e. they cannot make decisions on a fraction
of the land area. This means farmers can produce either coffee or maize in a given year
but not both. The model focuses on finding the price at which farmers switch to grow
maize and investigating the age dependent cutting price. It does not allow for the case
where farmers cut the coffee down and leave the land bare, even though this is a
technically feasible option for farmers.
Equation (4.1) assumes a particular age of the coffee tree at the start of the simulation.
Although it would be possible to solve for the optimal cutting and planting assuming an
arbitrary initial age (i.e. 1 year old), the impact of discounting would mean that the rule
developed for trees at the end of the cycle would be relatively imprecise, as changes in
the rule would have relatively little impact on ENPV. Therefore, it is important to solve
for the optimal rule using a simulation that has all ages of trees represented in the initial
period. Thus, it is necessary to develop a model that covers all different starting ages,
such that the optimal cutting/replanting rule is the one that maximises the average
expected NPV across all starting ages. Thus, the functional form and parameters of the
optimal rule will be independent of any assumption about the starting age of tree used in
the solution algorithm. In all optimal models in this study, the life cycle of coffee trees
is assumed to be 22 years. Hence, the final objective function of the FY model and
following optimal models is defined as the ENPV, averaged across all 22 initial ages:
ENPV
1 22
ENPVa
22 a 1
(4.2)
Thus, the ENPV in the FY model is average ENPV of all ENPV attained from 2200
random price trajectories (100 replications for each of 22 initial aged groups), over 50
years for each trajectory. This is used as the criterion for assessing the optimum when
evaluating parameters in the decision rule function described in Section 4.3.3. From
now when the maximum or optimal ENPV is mentioned in optimal models, it means the
ENPV as given in (4.2)
62
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
4.3.2. Profit Function
To develop the profit function from land use choice, whether coffee trees exist on the
land or not is denoted by a binary variable. According to the model’s assumption if
coffee is not on the land, maize is grown. Thus, profit at time t is as follows:
e
t , r .a
( Pt cYt c vtc ) St
( Pt mYt m vtm )(1 St )
(4.3)
where St denotes the existence of coffee and equals 1 if coffee is growing and 0
otherwise; Pt c is the price of coffee in year t; Yt c is the coffee yield in year t; Pt m is price
of maize in year t and vtc , vtm are annual costs of coffee and maize, respectively.
In the model, the profit of maize is assumed constant and estimated from the Coffee
Farm Survey 2007 (Thang, 2008). The annual profit of maize is fixed at $440 per ha.
However, a sensitivity analysis is undertaken to investigate the impact of efficiency of
maize on the farmer’s decision by changing maize profit to see how the optimal cutting
and replanting rules respond.
The decision of the farmer on whether to cut/plant coffee depends on the interaction
between the price of coffee and the rule for keeping or cutting the existing trees. The
farmer’s decision will be described in the following section.
4.3.3. Decision Rule
The planting and replanting of coffee trees represent long-term investment problems for
farmers, with a number of control variables. The first decision is the (re)planting
decision; should the farmer (re)invest in coffee production, given current land area is
not in coffee. Their second decision is when, within the tree’s life cycle, should they
cut or replace coffee or leave the land idle. The cutting or replanting decision of farmers
are based on future or expected prices, which are unknown.
Yield of coffee trees relates closely to the age of the tree. Generally, after reaching the
peak level, yield will start decreasing gradually. With coffee, yield usually attains the
maximum level after the 7th year and the mature period generally lasts about 8-9 years.
After that, the coffee yield declines. Thus, the cutting decision not only depends on the
expected price of coffee but also depends on the current age of the tree. Within the
63
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
model, it is assumed that the maximal age of a tree is 22 years, at which point yield falls
to zero.
Conceptually, the farmers may cut existing coffee trees before they reach the maximum
age for two main reasons. Firstly, the output price is relatively low so they may incur
losses from coffee production and they will switch to other crops (as maize in FY
model). The price at which farmers cut down the trees and switch to maize because it is
too low is denoted as CP. In this study, whenever we refer to cutting price or replanting
price, it means the prices at farm-gate and not the international or other prices.
Secondly, however, one hypothesis also considered by the model is that if output price
is very high and existing coffee trees are quite old, farmers may cut coffee trees earlier
and replant new trees. The expected net benefit from bringing the future profit stream
forward exceeds the loss associated with cutting trees before the net annual profit falls
to zero. The price at which farmers cut coffee earlier and replant new trees are denoted
as CP .
In other cases, farmers have to cut trees because of cash flow concerns i.e. expected
profit over the remaining lifetime of the tree is positive, but transitory losses mean that
the tree has to be removed early. However, this issue is not analysed in the FY model.
The cash constraint is analyzed later in the Fixed Yield – Cash Constraint model (FYCC model) in Chapter 5.
When the coffee price is less than the CP, farmers cut trees down and switch to maize.
However, they will grow coffee again if the price increases to the replanting price (RP).
If the price is higher than CP , farmers with old trees may cut down the existing trees
and replant new trees. Both CP and CP are expected to be age dependent.
The identification of the optimal cutting (CP, CP ) and replanting rule (RP) based on
the age of coffee trees with random prices are the outcomes of the FY model. The
model covers both the stochastic and dynamic aspect of the problem. To deal with those
problems, a sensitive fixed-form optimization technique is used for describing the
decision of farmers. This approach is similar to the method applied by Sonntag and
Hilborn (1978).
To describe the decision rules of farmers, whether coffee trees exist on the land or not is
denoted by a (0, 1) variable (St). The choice of the farmers is as follows:
64
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
St = 1 if St-1=1 and Pt > min (CP, RP)

keep growing coffee
St = 0 if St-1=1 and Pt ≤ min (CP, RP)

cut coffee and switch to maize
St = 1 if St-1=1 and Pt ≥ CP

cut coffee and replant new trees
St=1 if St-1=0 and Pt>=RP

switch back from maize
Because the life cycle of coffee is 22 years, all trees are cut down during their 22nd year
regardless of the price level. In the above decision, farmers will cut coffee if P t is
greater than the minimum value of CP and RP. This condition means farmers never cut
down the trees and switch to maize if price is above RP.
In its simplest formulation, the model will identify at what prevailing price should
coffee producers cut and when they should replant. The main fixed-forms for CP in the
FY model are defined as follows:
The quadratic form CP:
CP
o
age
1
2
(4.4)
age2
The quadratic form of CP with price change effect:
CPt
o
age
1
2
age2
( Pt
Pt 1 )
(4.5)
In the “quadratic form”, CP is a quadratic function of the age of coffee trees (“age”).
Hence, CP of trees at different age may not be similar. It is anticipated that younger
trees that have a longer remaining productive life will be retained at lower prices than
those closer to their maximum age.
In the “quadratic form CP with price change effect”, the critical value for the current
coffee price at year t depends not only on the age of trees but also on the change in
coffee price between year t and t 1 . The price change effect allows for information
on the direction of change in prices to influence decisions. Thus, if there is structure in
the price series, one might expect that the cutting decision will be different - for the
same current price level - if the change in price implies future increases, as compared to
future falls.
The fixed form of CP in FY model is defined as:
65
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
CPage
(4.6)
age
As mentioned earlier, the appearance of CP in the model is to test whether farmers
will cut and immediately replant with new trees, before the maximal age. The model
does not identify the CP for all ages of coffee, it only identifies the CP for coffee
trees over 18 years old, the ages at which yield tends to go down. Hence, age+ takes the
values 18, 19, 20, 21.
According to the decision rules, farmers will cut coffee to grow maize if the coffee price
at time t is lower than age dependent CP. Hence, they cut to replant new trees if price at
time t is greater than age independent CP .
The replanting decision does not depend on the age of trees so RP function can be
defined more simply as follows:
RP
(4.7)
3
If the land is planted to maize (or left bare) or the coffee tree are in the last year of the
cycle (age of tree =22 year old), the farmer will replant if the price of coffee is greater
than
3
A search procedure is implemented to estimate the values of
i
,
i
and
which
maximise the ENPV. All steps of the estimation procedure are described in Section
4.3.7.
The profitability of substitute or competitive crops may change the decision of farmers.
The CP or RP functions in the FY model do not include any measure of profit of the
substitute crop. However, as mentioned earlier, a sensitivity analysis is conducted to see
how the profit of maize influences the farmer’s decision.
A hypothetical example of the optimal cutting and replanting rule is illustrated in Figure
4.2. As seen in the figure, farmers will cut coffee to grow maize if the coffee price is
under the CP curve. If the coffee price is greater than RP, farmers will grow coffee
again if they have maize or bare land. In another case, if the price is above the CP
curve, farmers will cut older stands and replant new trees.
66
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
There is a hysteresis effect in farmer’s decision in Figure 4.2. If price drops below the
RP but it does not go below the CP, farmer will continue to maintain existing trees.
CP+
3
CP
coffee price ($/kg)
2.5
RP
cut and
replant
CP+
keep
coffee
2
1.5
1
CP
keep coffee
0.5
0
1
3
5
7
9
11
13
15
17
19
21
age of trees
Figure 4.2. Example of optimal cutting and replanting rule
4.3.4. Yield Function
The yield of a crop depends on various factors such as natural conditions (land quality,
weather, and water supply), variety, level of intensive farming, farmer characteristics
(such as experience, farm size, education) and so on. With perennial crops such as
coffee, rubber, cashew or forestry, tree age strongly affects the yield.
In the current model, yield is assumed fixed for any given age of coffee tree but variable
with age (Figure 4.3). The first two years of the tree’s cycle are unproductive. Farmers
can start to harvest coffee in the 3rd year, although the yield is still very low (only about
500 kg of coffee bean per hectare). After that, the coffee yield increases as the age of
the tree increases and it gets to the peak level at age 8. Once hitting the mature yield,
generally coffee yield becomes stable until it starts falling at around age 15-16. During
the mature period, an average farmer can attain approximately 2500 kg per ha. The
productivity of coffee starts declining when the trees are in its 16th year. In general, the
coffee cycle is about 20 to 25 years. In the model, the coffee life cycle is 22. After that,
farmers will cut down their trees and if price is profitable, they will replant new coffee
trees.
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Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
3000
yield (kg coffee bean/ha)
2500
2000
1500
1000
500
0
1
4
7
10
13
16
19
22
age of trees
Figure 4.3: Coffee yield by age of tree
Source: Thang (2008).
The yield cycle by age in Figure 4.3 is based on the Coffee Farm Survey 2007 and
experience of coffee experts. In practice, however, yield of coffee is affected
considerably by input use, with some who farm intensively reporting yields of 2200 kg
per ha for trees more than 17 year old, according to the Coffee Farm Survey 2007. This
is the motivation for the study to develop the Variable Yield Optimal Model (VY
model) in Chapter 6.
4.3.5. Production Cost
Production costs by age group were estimated from the Coffee Farm Survey 2007.
Production costs by age of tree are summarized in Table 4.4. The initial investment for
(one-year old) coffee trees (replanting cost) is very high ($1440) because of expenditure
on new trees, fixtures and land preparation and planting. In the model, it is assumed that
the annual production cost in the 5-20 year age range are the same, about $930 per ha.
In the last two years of the coffee cycle, the cost reduces to just over $600 per ha
because of the reduction in labour cost for harvesting, and lower level of input
application.
68
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
Table 4.4: Coffee production cost by age of tree (US$/ha)
Items
Seedlings
Labour cost
Chemical fertilizer
Manure/organic
Pesticide
Lime
Fixed asset
Fuel/electricity
Others
Total cost
Year 1
179.7
517.5
106.9
312.5
2.5
34.4
156.3
114.3
16.3
1440.2
Year 2
18.8
480.1
118.4
0.0
6.5
0.0
0.0
149.3
21.2
794.3
Year 3
9.4
420.0
134.7
312.5
7.5
0.0
0.0
114.3
16.3
1014.6
Year 4 Year 5-20 Year 21-22
0.0
0.0
0.0
515.0
602.5
301.3
168.8
181.3
90.6
0.0
0.0
0.0
10.0
15.0
7.5
0.0
0.0
0.0
0.0
0.0
0.0
114.3
114.3
114.3
16.3
16.3
16.3
824.3
929.3
613.0
Source: Thang (2008).
Based on the yield function and production cost data, we use a simple model to identify
the rotation length. The results of the model determine that the optimal time for cutting
and replanting is around 21 to 23 years depending on price levels. This strongly
supports the assumption of a 22-year cycle for coffee trees used in the optimal models.
4.3.6. Price Simulation
As mentioned earlier, the model operates over a period of 50 years. In order to get
revenue and profit of coffee production, series of coffee prices for 50 years are
simulated. This is an important step in the development of the optimal models in this as
well as subsequent chapters.
To attain the required age-structure, the model is based on 2200 price trajectories over
50 years, 100 series for each starting-age group. The simulation of these price
trajectories was based on the historical price data and a price simulation model. The
functional form of the statistical price model will generate different price structures that
may change the optimal cutting and replanting rules. Two price models are estimated
using the annual international Robusta price series from 1964 to 2006. These prices are
taken from International Coffee Organization and measured in USD per kg20. The first
model estimates the current price as a function of lagged prices, which is called the
Lagged price model. Alternatively, the second model, Cycled price model, is based on a
9-year price cycle, and a trend. These estimated price functions for each model are
used, in conjunction with a stochastic error term to produce the required coffee price
trajectories. These price trajectories are used as exogenous variables in the model.
20
www.ico.org
69
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
It should be noted that in this study we are not trying to find the best price forecast
model based on historical price series. We are just generating the price simulations from
estimated models. These price simulations are expected to be consistent with the real
price in history in terms of mean, variation or time series property.
The following part of this step will provide the functional forms and results of two price
models.
4.3.6.1. Lagged Price Model
The dependent variable in this model is current price and the explanatory variables are
prices in previous years. By testing various functional forms with different numbers of
lag, a parsimonious model is identified in which the logarithm of price lagged one and
two years. The regression equation is specified as:
lnPt
=
0.093
p- value
(0.08)
se
(0.05)
R2
= 0.78%
Prob. of Portmanteau =0.80
+ 1.15lnPt-1
(0.000)
(0.15)
–
0.334lnPt-2
(4.8)
(0.000)
(0.15)
The model results show a good fit with high R2 (0.78), and all coefficients are
statistically significant. In this model, current price increases when the previous price
goes up, but with some reversal from the second lag. The model also tests the
autocorrelation property using the Portmanteau test or Q test (Ljung and Box, 1978,
Pena and Rodriguez, 2002). The Portmanteau probability value is 0.80, meaning that the
null hypothesis of no autocorrelation is accepted. The fitted logarithm of price and
observed logarithm of price since 1964 are shown in Figure 4.4
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Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
2
log of price
fitted values
1.5
1
0.5
0
1965
1970
1975
1980
1985
1990
1995
2000
2005
-0.5
-1
Figure 4.4: Fitted and actual value of logarithm of price ($/kg)
When conducting simulations, the price in year t is specified as:
Pt e0.093
1.15lnPt 1 – 0.334lnPt
2
t
(4.9)
In (4.9), μt is a random variable. μt follows a normal distribution with a mean of zero
and a variance equal to that of the regression error from (4.8).
To get price trajectories over 50 years, it is necessary to have initial prices. The initial
price is drawn from a random distribution with a mean and standard deviation of
historical coffee price from 1964 to 2006.
Figure 4.5 provides some examples of international price simulation from the lagged
model. These simulated international prices are converted to a farm gate price in the
model, represented as a proportion of the international price. This proportion estimated
from simple regression between farm-gate prices and international price is equal to
0.52521.
21
The farm gate coffee price in Vietnam is not sufficiently available in all provinces; the series is quite
short which is not representative thus the author has to use the international prices for estimating price
function. An attempt is made to estimate the relation between farm-gate price and international price.
71
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
12
10
USD/kg
8
6
4
2
0
1
5
9
13
17
21
25
29
33
37
41
45
49
time period (years)
Figure 4.5: Examples of price trajectories predicted from Lagged price model
Source: Simulated from Lagged Price model
4.3.6.2. Price Cycle Model
The Price Cycle model was motivated from observing the historical trend of coffee
prices. By analyzing coffee price over the last 30 years, results show the coffee price
seemingly follows a 9-year cycle. Although the Lagged price model does show some
degree of lagged structure, it will not generate cycles within the simulated series.
350
Robustas Group (Dry and wet processed)
Composite Indicator Price
300
250
200
150
100
2004
1995
1986
0
1977
50
Figure 4.6: Price cycle of coffee in the world market (UScent/lb)
Source: ICO per com.
Thus, an alternative model that simulates a 9-year price cycle is estimated as follows:
72
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
Pt
a0
a1 sin(2 year / 9) a2 cos(2 year / 9) a3 year error _ term
where
(4.10)
is the ratio of the circumference to the diameter of a circle; approximately
equal to 3.14, year is a trend variable.
Equation (4.10) imposes a nine-year cycle, but the amptitude of the cycles and the trend
effect is estimated. Using price series from 1964 to 2006 and applying a regression
method, the estimated price cycle model is:
Pt
175.5
p-val (0.00)
se
(21.7)
0.43sin(2 year / 9)
(0.02)
(0.13)
0.33cos(2 year / 9)
(0.00)
(0.14)
0.085 year
(4.11)
(0.00)
(0.01)
Prob > F
= 0.0000
R-squared = 0.74
Prob. of Portmanteau = 0.83
The results give a strong goodness of fit and the coefficients are statistically significant.
The negative coefficient on the year variable captures the general downward trend in the
price series. The Portmanteau probability value of 0.83 means that it accepts the null
hypothesis of no autocorrelation in this model (Pena and Rodriguez, 2002, Ljung and
Box, 1978). Based on (4.11), alternative series of price data for the model are generated.
Similar to the Lagged price model, it is necessary to identify the starting price.
However, rather than select an initial price at random, here the model selects an initial
point in the cycle at random (each simulation employs a time trend yeart where the
value of year0 is selected with uniform probability from 1-9)
Pt 175.5 0.43sin(2 year / 9) 0.33cos(2 year / 9) 0.085* 2000
t
(4.12)
where μt is a random variable. Values of μt distribute normally with a mean of zero and
a variance equal to that of the regression error from (4.11). The trend is held at 2000
because the coffee price in 2000 is closest to the mean of coffee price series from 1964
to 2006.
Figure 4.7 gives an example of the international price trajectories predicted from the
price cycle model.
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Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
1
6
11
16
21
26
31
36
41
46
51
Figure 4.7: Example of price trajectories predicted from Price Cycle model
Source: Simulated from the Price Cycle Model
Table 4.5 compares the distribution of historical international price series from 1964 to
2006 and simulated price data sets from the Lagged model and the Price Cycle model.
The mean of price distribution generated from the two models is very close but variation
of price distribution from the Lagged model is much larger. The distribution of price
data set from the Lagged model gives a better fit to the historical data.
Table 4.5: Distributions of actual international price and price data set simulated
from two models
Actual
pricesa
Lagged
modelb
Price Cycle
Modelb
53
1.76
1.02
0.92
110,000
1.91
1.14
1.0
110,000
1.98
0.66
1.04
International price
Number of observations
Mean
Standard deviation
Farm-gate average pricec
Note: a data price series from 1964 to 2006; b 2200 simulated price trajectories for 50 years
c
farm-gate price is derived from international price
In the FY model, the identification of the optimal cutting and replanting price for coffee
farmers is implemented using the price data set simulated from both price models
(Lagged price model and Price cycle model). The price data set simulated from each
model has its own characteristics. The price data in the Lagged model are quite quick to
reverse to the mean but in the Cycled price model, price trajectories have a strong
74
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
structure with a 9-year cycle. The difference of price data simulations may affect the
optimal rules as well as farmers’ income.
4.3.7. Procedure for Estimation
To identify the optimal CP (and CP ) and RP that maximises the expected net profit,
the model applies a search procedure for retrieving αi, γ and
age
in (4.4), (4.5), (4.6)
and (4.7). The procedure for estimation includes the steps as follows:
Step 1: Preparing Input-Output data
In this step, data on coffee production cost, yield for 22 groups of coffee by tree ages,
maize profit were calculated from survey data and other sources.
Step 2: Price simulation
This step generates the price simulations as presented in Section 4.3.6 and puts them
into the model. In total, 2200 price trajectories for 50 years are generated by two
models- Lagged price model and Price Cycle model.
Step 3: Setting decision rule
Select the fixed-form for the cutting rule and replanting decision of coffee farmers as
presented in “decision rule” section of the model.
Step 4: Search for the best parameters in CP (and CP ) and RP
This step uses the searching method to find the cutting price rule (CP and CP ) and
replanting price (RP) to get the maximum ENPV. As described above, the CP was
expressed as a fixed form of coffee age, and change in price. Thus, the final objective of
searching is to find the αi and γ to get optimal CP, CP and later RP to achieve the
maximization of ENPV.
To get optimal value for CP, CP and RP, the model applies the one-at-a time method.
This is one of the simplest optimum seeking technique which may be applied to a
function of any number of decision variables (Taylor et al., 1973). To apply the one-at-a
time method, RP is first fixed by assigning an initial value and then finding the optimal
75
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
CP and CP . When having optimal CP and CP in Step 1, the cutting rule is now fixed
and RP is searched over until its optimal value is determined. The entire procedure is
repeated until CP, CP and RP converge, and the ENPV gets the maximum value.
The strategy used is to start with a relatively coarse grid of g values, giving a total
search space of gn (where n is the number of parameters) and then progressively refine
the search with a smaller grid size around the maximal values.
Excel software is used for running the model. The structure map of the spreadsheet
model in Excel is presented in Figure 4.8. The model consists of different sheets: coffee
price, decision sheet, coffee yield, production cost, revenue and profit. When the cutting
and replanting rule changes, the farmer’s decision will change which in turn brings
about the new cost, yield, profit and finally ENPV.
76
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
Figure 4.8: Model Structure Map
Coffee Price sheet:
2200 price series in 50 years for 22 age group of coffee trees
Decision sheet:
This sheet expresses the decision of farmers: cutting for maize or keeping;
replanting through the age of coffee tree. This sheet covers 22 starting age
groups of coffee x 100 replications for one group (total of age replication is
2200, equivalent to 2200 price series in Sheet “Coffee price”. Changes in
decision rule will vary age of tree, thus change cost, yield and profit
Decision sheet
Year 3
………….. ………….. ………….. Year 49
2
3
2
3
Year 50
……
Age-Year 1 Year 2
1
1
100 replicants
0
3
3
2
3
0
……
……
1
2
2
1
0
……
22
22
22
0
Coffee cost:
The production cost is derived from the age of coffee trees in Decision sheet.
Yield
The yield of coffee is also derived from the age of coffee trees in Decision
sheet.
Revenue
The revenue of coffee is calculated by multiplying Yield and Coffee Price
Coffee Profit
The revenue of coffee was calculated by taking the difference between coffee
cost and revenue
Farm profit = coffee profit +maize profit
To get the ENPV of farm profit for 2200 replications in 50 years, first we
calculate the NPVa of farm profit for each starting age a for 50 years, and take
the average of 2200 NPV. Changes in decision rule (
i
, ) will produce
a
particular NNPV
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Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
4.4. Results of the FY Model
This section presents results of the FY model. As mentioned above, the optimal rule
may depend on the way in which the price of coffee is simulated. Thus, the presentation
of results of the FY model is split into two parts. Section 4.4.1 discusses the results
based on price simulations generated from the Lagged price model. The results based on
price simulations from the Price Cycle model will be presented in Section 4.4.3.
4.4.1. Optimal Rule with Lagged Price Model
With price trajectories simulated from the lagged price model and application of the
searching procedure, the FY model finds the optimal quadratic CP and replanting rule
for coffee as follows:
CP = 0.402 - 0.0509age + 0.00367age2
(4.13)
RP =0.74 ($/kg of coffee bean)
Optimal ENPV = 9226 ($)
The FY model finds that the ENPV achieves a maximum when CP for the 18-21 age
group is infinitive (very high price). This means that it is never optimal within the model
to cut trees early and immediately replant, in an effort to bring the future benefit stream
from subsequent trees forward. However, in other cases if the replacement cost was
relatively low and discount rates close to zero, CP would be finite.
Because CP does not influence farmer’s decision, thus from now the FY model and
other optimal models in following chapters eliminates the hypothesis which states that
farmers cut very old trees and replace by new plantings if the coffee price is very high.
Hence, only cutting rules of CP in which farmers cut coffee trees and switch to maize if
price is low are considered hereafter by the FY model and other optimal models.
Figure 4.9 depicts the optimal rule with quadratic CP for all age groups of coffee. The
results shows that the optimal CP for one year old coffee is 0.34 $/kg. In initial years of
the life cycle, the CP decreases slightly when tree age increases and CP is smallest for
7-year old trees, at only $0.23 per kg.
78
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
The replanting price of $0.74 per kg indicates that if farmers have bare land or land is
occupied by maize production, they should switch back to coffee if the coffee price is
equal to or greater than $0.74 per kg.
1
Optimal CP
farm-gate price ($/kg)
0.9
keep coffee
Optimal RP
0.8
RP=0.74
0.7
0.6
0.5
keep coffee
0.4
0.3
0.2
cut and switch to maize
0.1
0
1
3
5
7
9
11
13
15
17
19
21
age of tree
Figure 4.9: Optimal cutting and replanting rule from the FY model
This optimal replanting price ($0.74 per kg) is significantly smaller than the optimal
replanting price ($0.91 per kg) when the model is solved assuming constant
deterministic price (i.e the price at which the NPV of coffee production is equal to NPV
from maize only). This is because the average of simulated farm-gate prices is equal to
$1 per kg of coffee bean and hence it is optimal to replant at lower price given that one
expects the price to rise on average over the life of the tree.
The model was also solved with a cubic form CP ( CP
o
age
1
2
age2
3
age3 ).
However, the results are almost the same in terms of the cutting rule per age of tree, and
ENPV generated, but the cubic model takes longer to determine the optimal rule
because of the additional parameter (
3
). Thus, to save searching time with different
scenarios, the model uses the quadratic function as the optimal form of CP.
The optimal rule of the FY model is presented in Figure 4.9. However, the optimal rules
do not show the frequency cutting decision. Thus, it is useful to see how many times the
cutting rule is invoked at each age or the percentage of cases in which farmers actually
cut their coffee at optimal rules. Perhaps the cutting rule is not invoked for some ages of
trees due to the range of prices, and hence little reliance can be placed on the precise
79
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
value given for the cutting rule. Figure 4.10 presents the proportion of times a tree of a
specific age is cut due to the optimal cutting rule being invoked. As shown in this
figure, with price trajectories generated by the lagged model, farmers rarely cut if the
age of the coffee tree is less than 11 year old. The cutting frequency is increasing
continuously for trees of ages from 11 to 20. The implication is that, for the simulated
price series used, which is based on historical data, it is seldom optimal to cut in this
early period. This result may not hold in alternative circumstance i.e. where the price
actual cut (%)
series follow different distributions.
20
18
16
14
12
10
8
6
4
2
0
1
3
5
7
9
11
13
15
17
19
21
age of trees
Figure 4.10: Proportion of actual cut in FY model with Lagged price simulation
The optimal RP is quite consistent with stated replanting prices from the Coffee Farm
Survey 2007. The optimal RP from the FY model ($0.74 per kg) is very close to the
replanting price reported by farmers in Krong Pak district (Dak Lak province, Central
Highlands of Vietnam). Krong Pak has a medium comparative advantage in coffee
production. Coffee yield in 2006 in Krong Pak district was about 1920 kg coffee bean
per ha (Thang 2008). The replanting price reported by farmers in the more productive
area, Cu Mgar district with average coffee yield of 2100 kg per ha, is lower, only $0.706
per kg. By contrast, the replanting price of farmers in Eakar district was reported at
$0.809 per kg. This means farmers in lower yield areas are less likely to replant coffee,
for any given price.
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Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
0.820
0.809
0.800
0.780
$/kg
0.760
0.740
0.720
Optimal RP =0.74
0.743
0.706
0.700
0.680
0.660
0.640
Cu Mgar
Krong Pak
Eakar
district
Figure 4.11: Comparison of optimal RP of FY model and farmer’s estimates
The decision to cut early is implicitly dependent on the prices that are expected to hold
over the remaining lifetime of the trees. According to the cutting rule, the current price
of coffee summarizes all possible information about that future trajectory. However, it
is possible that this is not the case, and that additional information may be of value in
making the optimal decision. The FY model also specifies the fixed-form cutting rule
as a quadratic function of age with an additional price change effect. The hypothesis is
that information on the most recent change in price may moderate the cutting decision
(i.e. if the previous price change was positive, one may be less willing to cut than if it
were negative, for any given price level). The results from this FY model show that the
difference in price does not seem to influence the cutting rule (i.e =0.002). Similarly,
the optimal ENPV and RP are almost unchanged.
CPt = 0.40 - 0.050age + 0.0036age2 + 0.002 (Pt –Pt-1)
(4.14)
RP=0.74 ($/kg)
Optimal ENPV =9228 ($/ha)
The FY model was also solved with the constant CP form (i.e. CP=
0
). This means CP
does not depend on the age of trees. With such constant form of CP, the results show
that the coffee farmer will get the maximum income if they cut trees at a price of $0.36
per kg. The optimal RP when there is a constant CP was found to be the same as RP
when CP is a function of age (see Figure 4.12).
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Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
1
0.9
Optimal CP
Best contant CP
0.8
RP
RP=0.74
price ($/kg)
0.7
0.6
0.5
0.4
CP =0.36
0.3
0.2
0.1
0
1
6
11
16
21
age of tree
Figure 4.12: Optimal quadratic CP and best constant CP from the FY model
Figure 4.13 presents the optimal income per ha attained by applying the three cutting
rules: (i) the constant CP, (ii) the quadratic CP and (iii) no cutting rule (CP=0). The
results show that ENPV per ha gained from the optimal quadratic CP rule is about 3
percent higher than income with a constant CP (the best constant CP =0.36), and nearly
5 percent higher than income if farmers never cut early.
9300
100%
9200
NPV ($)
9100
9000
97%
8900
95%
8800
8700
8600
NPV with constant CP
Optimal NPV
NPV with no cutting rule
Figure 4.13: The maximum ENPV per ha among different CP rules
The results of different cutting rules are summarized in Table 4.6
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Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
Table 4.6: Summarized results of different cutting rules of FY model
Cutting rule (CP)
Optimal cutting price
Optimal
RP
ENPV
($/ha)
Quadratic form
CP = 0.402 -0.0509age + 0.00367age2
0.74
9226
Quadratic with
price change effect
CPt = 0.4 -0.05age + 0.0036age2 + 0.002(Pt –Pt-1)
0.74
9228
0.36
0.74
8950
n.a
0.74
8760
Constant
never cut early
Source: optimal model results
To explore the benefit from the application of the optimal quadratic CP against “no
cutting” rules, the FY model is used to identify the ENPV for different starting age of
trees in two cases. Figure 4.14 shows the results of ENPV (per ha) for “never cut early”
and quadratic CP by the starting ages (the age of the tree at first year of period in the
model). With the younger trees, ENPV does not show a big change but the difference
gets larger with the increasing starting age. This is consistent with the evidence
presented earlier that the optimal cutting rule was seldom invoked for young tree ages.
As a result, for blocks with initial trees of young ages, divergences in behavior will only
occur after a significant number of years have lapsed, and the impacts of these will be
discounted. On the other hand, blocks with trees that are of older age will see
divergences in behavior more quickly in the time sequence.
13000
12000
11000
no-cut
NPV ($)
10000
Optimal rule
9000
8000
7000
6000
5000
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22
initial age of tree
Figure 4.14: ENPV with different starting ages for quadratic CP and no cutting
rule
83
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
4.4.2. Impact of Substitute Crop on Coffee Farmer’s Decision
In the FY model, maize is assumed to be the sole replacement for coffee. If the coffee
price is too low, farmers will cut coffee and switch to maize until the price comes back
to the replanting price. In addition, maize profit is also assumed fixed. However, the
change in profit for the substitute crop may affect the cutting and replanting decision of
coffee farmers. To examine how the profit of the substitute crop affects the farmer’s
decision, the FY model has been resolved for a number of alternative values for the
maize profit. The model is only solved with the quadratic form of CP (
CP
age
o
1
2
age2 ).
First, maize profit is assumed to increase by 20 percent. With young coffee groves, the
CP is seemingly unchanged when maize profit rises by 20 percent. However, farmers
are more likely to cut older trees. With 20 percent increase in maize profit, total income
per ha is $9405, approximately 2 percent higher than the previous ENPV.
With a reduction in maize profit, coffee farmers are less likely to cut and the ENPV is
also lower (see Figure 4.15 and Figure 4.16). This happens because with lower income
from replacing crop, farmers will not cut earlier and they should continue to grow
coffee trees if the expected profit from coffee production is still greater than that from
maize.
1.2
1.5
Optimal CP
20% reduction in maize prof it CP
Optimal CP
20% increase in maize profit CP
Optimal RP
20% increase in maize profit RP
1.3
1
Optimal RP
20% reduction in maize prof it RP
1.1
price ($/kg)
price ($/kg)
0.8
0.6
0.4
0.9
0.7
0.5
0.3
0.2
0.1
0
1
3
5
7
9
11
13
age of coffee trees
15
17
19
21
-0.1 1
3
5
7
9
11
13
15
17
19
21
age of coffee trees
Figure 4.15: Changes in optimal rule when maize profit varies
84
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
9500
9405
9400
($/ha)
9300
9226
9200
9080
9100
9000
8900
Optimal
20% reduction in maize profit
20% increase in maize prof it
Figure 4.16: Changes in the maximum ENPV when maize profit varies
Another simulation in which maize profit is increased to $1500 per year has been
solved. The results shows that in this case all coffee farmers will cut their coffee trees
and switch to maize. They will never grow coffee trees except under the circumstances
that the farm-gate price of coffee bean exceeds $7.6 per kg.
4.4.3. Optimal Rules with Price Cycle Simulation Model
In the previous section, the FY model identifies the optimal rule for coffee farmers
based on price series simulated by using an autoregressive model. The estimated
equation implies some structure in the price series, but no structural cycles. If a coffee
cycle exists, then it may make prices more predictable. In this case, the decision to cut
and replant trees may depend on not only the level of the price, but also where price is
in the cycle. However, the lack of significance of the change in prices term in the fixed
form rule may be accounted for by the relatively weak structure within the price
simulation (i.e. it closely approximates a random walk). This may not be the case if
there are clearly predictable cycles in prices. This section reports the results from
solving the FY model with the same procedures but with price data generated from the
Cycle model.
With the Price Cycle model, the optimal quadratic CP and RP are identified as follows:
CP = -0.07 - 0.087age + 0.0065age2
(4.15)
RP = 0.61 ($/kg)
ENPV= 9659 ($/ha)
85
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
The rules are depicted in Figure 4.17 below. The results show that if price follows the
cycles with the same distribution as occurred in the past, farmers should never cut
coffee if trees are younger than 14 years. If land is either bare or grows maize, they
replant earlier, and the optimal RP is only $0.61 per kg of coffee bean. The optimal
ENPV with the Price cycle model is similar to the maximum ENPV from the Lagged
price model simulation.
1.4
Optimal CP
1.2
optimal RP
price ($/kg)
1
keep coffee
0.8
0.6
0.4
cut and
switch to
maize
keep coffee
0.2
0
-0.2
1
3
5
7
9
11
13
15
17
19
21
-0.4
age of trees
Figure 4.17: Optimal rule of the FY model with Price cycle model
1.4
CP-Price cycle simulation
RP-Price cycle simulation
CP-Lagged price simulation
RP-Lagged price simulation
1.2
1
price ($/kg)
0.8
0.6
0.4
0.2
0
1
3
5
7
9
11
13
15
17
19
21
-0.2
-0.4
age of trees
Figure 4.18: Optimal rules of Price cycle and Lagged price simulations
86
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
The difference between the optimal rules in the two price simulations is in part due to
the distribution of price trajectories predicted from the two models. Figure 4.19 graphs
the distribution of farm-gate price data sets simulated from the Lagged price model and
the Price cycle model. The mean of the two data sets is similar but the distribution is
quite different. Price data generated from the Lagged price model is skewed to the left
with a long tail to the right and a higher standard deviation (0.6) whereas the Price cycle
.5
Density
.6
.4
0
.2
0
Density
.8
1
1
data is symmetric with similar mean (1.04) and smaller standard deviation (0.34).
0
1
2
Lagged price model
3
4
0
.5
1
1.5
Cycle price model
2
Figure 4.19: Distribution of farm-gate price data set simulated from two models
From the optimal rule, the model identifies the actual percentage of trees at each age
that is cut in this case. Figure 4.20 compares the percentage of times trees are cut at
each age under the two alternative models. As shown in the histogram, with the Lagged
price model simulation farmers are more likely to cut earlier. With the Price Cycle
model, the cutting percentages of trees increase rapidly in the 17 to 19 age group.
Although the two rules look visually quite different, in terms of economic implications,
both predict very low levels of cutting up to age 10.
87
2.5
% actutal cut
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
20
18
16
14
12
10
8
6
4
2
0
Lagged price model
Price Cycle model
1
3
5
7
9
11
13
15
17
19
21
age of coffee
Figure 4.20: Simulated percentage cut at each age of trees from two data sets
As was undertaken with the Lagged price model, the Price cycle model was simulated
allowing for a price change effect in CP. In this case, the form of CP can be repeated as
follows:
CPt
o
age
1
2
age2
( Pt
Pt 1 )
With the above cutting function, the model was solved again and the new optimal rule is
identified as follows:
CPt = -0.16 - 0.083age +0.0063age2 -0.24(Pt-Pt-1)
(4.16)
RP = 0.61 ($/kg)
NPV = 9660 ($)
The negative sign of price difference coefficient (-0.24) in (4.16) is expected and it
shows that if the current price follows a downward trend, farmers should cut earlier and
vice versa. The coefficient (-0.24) also shows the more significant impact of price
differences in the Price Cycle model simulation compared to the Lagged Price model.
However, the new results from (4.16) give an almost unchanged optimal ENPV and the
same RP when compared with those from (4.15), suggesting that allowing for this
additional information does little to improve the economic performance of the farmer.
Figure 4.21 presents the optimal rules for the quadratic model with price change effect
CP assuming that the price difference is equal to zero. Similarly, the actual cutting
percentages at different age of coffee trees are illustrated in Figure 4.22. According to
88
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
the results, with the CP form of quadratic and price change effect, farmers are less
likely to cut. The cutting percentage in this case is a little bit lower than in the Price
cycle model and quadratic form of CP.
1.3
Quadratic CP
1.1
RP
Quadratic with price change effect CP (assume price change =0)
price ($/kg)
0.9
0.7
0.5
0.3
0.1
-0.1
1
3
5
7
9
11
13
15
17
19
21
-0.3
-0.5
age of trees
Figure 4.21: Different optimal rules of FY model with Price cycle simulation
12
With cycled price model, quadratic CP
% actual cut
10
With Price cycle model, quadratic with price
change effect CP
8
6
4
2
0
1
3
5
7
9
11
13
15
17
19
21
age of trees
Figure 4.22: Actual cut of the FY with Price cycle model and different CP forms
4.5. Conclusion
There are many approaches to analyze farmer’s decisions and identify the optimal
cutting and replanting rules. By using fixed form optimization, this chapter develops the
89
Chapter 4.Optimal Replanting and Cutting Rules for Coffee Farmers in Vietnam: Fixed Yield Model
FY model to identify the optimal cutting rule and replanting rule for coffee farmers in
Vietnam.
Results from the FY model found the optimal CP is dependent on the age of coffee
trees. In addition, the FY model found that the optimal RP is $0.74 per kg of coffee
bean. The maximum ENPV earned from one hectare of land is $9226.
With optimal rules, farmers rarely cut if the age of coffee trees is less than 11 year old.
The cutting frequency increases continuously for the coffee trees from the 12th year.
The FY model was also solved with other fixed forms of CP (i.e. age dependent cubic
CP, and quadratic CP with price change effect). However, the results are very similar.
Solving the FY model with constant form CP, the results shows that the maximum
ENPV from optimal quadratic CP is higher than the ENPV from the optimal constant
CP (CP is not a function of age) by 5 percent.
The coffee farmer’s decision changes when the profit of maize (substitute crop) varies.
The results from the FY model indicate that if the profit of maize increases, coffee
farmers are more likely to cut, and then only replant coffee at a higher price. By
contrast, coffee farmers are less likely to cut with a lower profit of maize and they will
plant coffee again at lower prices.
In general, the FY model identified the optimal CP and RP for achieving the maximum
ENPV for coffee farmers. Furthermore, the model can investigate the change of coffee
grower’s decision when the price of the substitute crop changes. However, farmers in
the FY model are assumed to have no cash constraint i.e. they can take on high levels of
debt in initial years in anticipation of profit streams in the future. In practice, coffee
farmers, especially poor farmers may not be able to follow this optimal decision. Based
on the FY model, the following chapter will develop the Fixed Yield- Cash Constraint
model (FY-CC model) to investigate changes of the coffee farmer’s decision if they
face cash constraint, and the impact on their income.
90
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
CHAPTER 5. OPTIMAL COFFEE PLANTING DECISIONS
UNDER A CASH CONSTRAINT
5.1. Introduction
In the previous chapter, the Fixed Yield (FY) model was developed to determine the
optimal cutting and replanting price for coffee farmers in Vietnam to get the maximum
ENPV per ha of land. In the FY model, it was assumed that the farmer’s decision only
depends on the price of coffee and returns to maize. However, if farmers do not have
enough working capital from either retained profits or credit to pay for new coffee
gardens they may be unable to replant optimally. In addition, they have to wait several
years to get income from coffee. During those years, they need money to cover their
living expenditure and pay for inputs. This chapter will look at the coffee farm as a
household and analyze the impact of cash constraints on the farmer’s decision. With that
goal, this chapter focuses on relatively poor coffee farmers, who are presumed to have a
shortage of cash for farm investment and living expenses.
This chapter aims to identify to what extent the expected profit from coffee/maize is
reduced under a cash constraint and examine the impact of credit policy on the income
and planting decisions of poor coffee farmers;
To achieve the above objectives, this chapter develops the Fixed Yield- Cash Constraint
model (FY-CC). This differs from the FY model in Chapter 4, as the model includes
other aspects of the household such as expenditure, savings, loans and household size.
However, yield and production costs remain fixed in the same manner as in the FY
model.
The remainder of the Chapter is organized as follows. Section 5.2 briefly reviews the
theoretical literature on the impact of cash constraints on farmer decisions. Section 5.3
describes the main characteristics of poor coffee households in Vietnam including
income, expenditure and savings. Section 5.4 describes the FY-CC model and its
decision rules. The final section presents results from the FY-CC model.
5.2. Impact of Cash Constraints on Farmer’s Decision
91
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
Rural households in developing countries like Vietnam are characterised by low and
variable incomes. These households suffer from income variability due to fluctuations
in weather and output prices. Farmers are also vulnerable to other risks associated with
small businesses. During periods of low income, farm households have to use their
savings and borrow money to continue farming and cover living expenses. Agricultural
investments tend to be funded by credit from banks and other organizations. Thus the
development of financial markets has become more important for households as well as
the agricultural sector, especially for poor households (Gutierrez, 2002). A shortage of
cash results in many problems for households. According to Mendola (2007), having
poor initial asset endowments means that poor households may not be able to use their
existing resources as efficiently as better-off households. In other words, poverty
contributes to deviations in the behavior of farm households from full efficiency.
Similarly, Winter-Nelson and Temu (2005) indicate that small farmers in developing
countries are trapped in poverty for lack of cash needed to make profitable investments.
Thus, increased access to credit could generate economic growth amongst poor
households.
There have been many studies to evaluate the role of credit and the impact of cash
constraints on household’s behaviors and income. It is widely believed that farm
households in developing countries are credit constrained and the provision of credit
would lead to an increase in production and income (Simtowe et al., 2006, Freeman et
al., 1998).
Credit access may affect the household production and income in various ways.
Through access to credit markets, households can move away from risk reducing but
low return diversification strategies and concentrate on risky investment that gives
higher returns (Simtowe et al., 2006). Similarly, by using a dynamic inter-temporal
model for the analysis of the rate of investment in the agricultural sector in Italy,
Gutierrez (2002) pointed out the importance of financial constraints in capital markets
in determining the rate of investment. He showed that when credit constraints hold, the
expected marginal profit per unit of capital is reduced. In a similar vein, through looking
at the role of a credit constraint on dairy households, Rosenzweig and Wolpin (1993)
found that low incomes combined with borrowing constraints are the primary reasons
for underinvestment in bullocks in India, with improvements in earnings increasing
agricultural profitability by permitting farmers to accumulate larger capital stocks. With
better access to credit, farm productivity increases. By comparing the impact of credit
92
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
programs on capital constrained and non-constrained dairy small holders in Ethiopia
and Kenya, Freeman and Ehui (1998) showed the significant impact of loans on farm
productivity. According to the study, the marginal contribution of credit to milk
productivity is relatively high on liquidity-constrained farms compared to liquidity nonconstrained farms: one percent increase in credit used to purchase crossbred dairy cows
leads to 0.6 percent increase in milk productivity on credit-constrained farms and 0.4
percent increase on non-credit constrained farms in Ethiopia. In Kenya one percent
increase in credit for investment in crossbred dairy cows leads to 1.6 percent increase in
milk productivity on credit constrained farms and 0.9 percent increase on non-credit
constrained farms.
Issues related to poor households and poverty in Vietnam have been extensively
studied. However, most of them focused on the causes of the poor and suggesting
solutions for attacking the household poverty (SRV, 2002, MOLISA, 2003, Svendsen,
2003, The World Bank, 1999, The World Bank, 2003, The World Bank, 2005, The
World Bank, 2007, Inter-Ministerial Poverty Mapping Task Force, 2003 , Shenggan et
al., 2003). Very few studies were concerned about the poor coffee households, and
mostly focused on the Central Highlands region, especially the Dak Lak province. For
example, ICARD and Oxfam (2002) implemented a study to evaluate the impact of the
collapse in the global coffee trade on Dak Lak province. This study described some
problems of coffee farmers and poor households under the price crisis in early 2000.
Similarly, ADB and ActionAid Vietnam (2003) investigated determinants of poverty in
Dak Lak and analyzed solutions that can support poor households. Those studies on the
poor coffee farmers did not investigate the optimal cutting and replanting decision of
the poor coffee farmers as well as the impact of credit policy on their income. These
issues will be analysed in the FY-CC model. Before moving to the model section to
estimate the impact of cash constraints and identify behaviors of coffee household under
a cash shortage for investment, the next section will review the poverty trend in
Vietnam and investigate some characteristics of poor coffee households in Vietnam,
especially in the Central Highlands where most of coffee producers are located.
5.3. Poverty Trends in Vietnam
Economic growth over the 1990s generated significant improvements in living
standards in Vietnam. The national trend shows strong poverty reduction in the past 15
93
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
years throughout Vietnam. Poverty incidence22 was reduced from nearly 60 percent in
1993 to only 16 percent in 2006. The rate of decline in poverty was faster in urban
areas, but rural populations also saw improvements in well-being.
70
60
66
Vietnam
58.1
poverty incidience (%)
Urban
50
40
30
Rural
46
37.4
36
28.9
25
25
20
19.5
20
16
9
10
7
4
4
2004
2006
0
1993
1998
2002
Figure 5.1: Poverty trend in Vietnam 1993-2006
Source: GSO per com
The declining trend in poverty is evident in all regions. Poverty rates and the speed of
poverty reduction vary from region to region. The North West is the poorest region in
the country, followed by the Central Highlands and the North Central Coast. Poverty
rates are also relatively high in the two deltas, and in the South Central Coast, but are
much lower than in the Central Highland. The poverty map and poverty depth map by
provinces in Vietnam are presented in Figure A5 and Figure A6 in Appendix A.
Figure 5.2 shows the poverty trend in all regions in Vietnam since 1993. It is noted that
in the period 1998-2002, the fraction of the population deemed poor was declining in all
regions, excepting the Central Highlands. There was no reduction in poverty in the
Central Highlands from 1998 to 2002. Coffee is the main crop in the Central Highlands
and the slow rate of poverty reduction in this period could be explained by the sharp fall
in the coffee price during the same period. The nominal farm gate price in 2002 was one
fourth of that in 199823. Consequently, the percentage of coffee producers with incomes
below the poverty line in Vietnam remained at around 35 percent in 1998-2002.
22
This is based on the poverty line of per capita income of less than $12.5 a month in rural areas and
$16.25 a month in urban areas
23
Calculation based on VHLSS1998 and VHLSS2002
94
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
100
90
80
1993
1998
2002
2004
70
60
50
40
30
20
10
0
Vietnam
North
East
North
West
RRD
NCC
SCC
CH
NES
MRD
Figure 5.2: Poverty trend in Vietnam by regions 1993-2004
Note: RRD: Red river delta; NCC: North Central Coast; SCC: South Central Coast, CH: Central
Highlands, NES: Northern East South; Mekong River Delta
The decline in the coffee price in the early 2000s forced many farmers to reduce their
coffee area, as revenue did not cover variable costs. Many producers, mainly poor
farmers, could not cover their expenditures (living costs and input investment) so they
had to shift to other crops such as rice or maize for food security. Poor farmers are
especially vulnerable and influenced strongly by external shocks such as price
reductions and natural disasters. The causes of poverty are diverse. Table 5.1 presents
the main causes of poverty from the perception of poor people and local authorities in
Dak Lak province (the largest coffee production province in Vietnam) with lack of
capital, shortage of land, uncertainty of market, and poor infrastructure are the main
reasons.
Table 5.1: Perceived causes of poverty in Dak Lak Province
Perceptions of Poor People
Poor infrastructure: irrigation systems,
roads
Poorly developed markets
Ineffectiveness
of
Government
policies and programs at grass-root
level
Lack of transparency, accountability,
resulting in corruption; lack of
Perceptions of Local Authorities
Lack of capital
Shortage of land
Many dependents to support/subsidy
Lack of experience, and inability and
incapability to apply new farming
techniques
Investment failure, risks in agriculture
(coffee price dropped)
95
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
people’s participation in decision
making
Inability and weakness of grass-roots
authorities and cadres
Villagers’ inability to apply new
farming techniques and low level of
education
Shortage of land
Lack of capital
Free in-migration
Poor health and lack of labour
Harsh climatic conditions: drought
Poor health, disability, getting old
Lack of labour
Committed to social diseases (drug
addicted), and laziness
Harsh climatic conditions: drought,
flood
Source: ActionAid Vietnam & Asian Development Bank (2003)
Of the eight ecological regions in Vietnam, the Central Highlands is the major coffee
area with nearly 90 percent of coffee output produced in this region24. Farmers in the
Central Highlands invested heavily in coffee over the mid to late 1990s and the
subsequent fall in coffee prices left many of them with low incomes. About 40 percent
of households in the Central Highlands produce coffee. This proportion does not vary
across the population, except for the richest fifth who were much less involved in coffee
growing. According to ActionAid Vietnam & Asian Development Bank (2003), the
number of trees planted, on the other hand, varies substantially. Coffee farmers in the
poorest population quintile have, on average, 6500 trees. Those in the second-richest
quintile have nearly doubled this number (see Table 5.2).
Table 5.2: Coffee farming in Central Highlands
Expenditure quintile
I-lowest
Households growing
coffee (% of total
household)
Average area (m2)
38
6539
II
43
9499
III
40
9184
IV
44
12820
Vhighest
Central
Highlands
24
11487
39
8881
Source: ActionAid Vietnam & Asian Development Bank (2003)
Generally, the coffee farm size in Vietnam is quite small with less than 1 ha per
household. The result provided by ActionAid Vietnam & Asian Development Bank
24
GSO (2006)
96
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
(2003) is consistent with data from Agrocensus_2006. According to Agrocensus_2006,
the farm size of poor coffee farmers is much less than higher income households, only
5287 m2. Even poor farmers in Kon Tum province have nearly 3500 m2 land of coffee
(see Figure 5.3). The expansion of coffee area in Central Highlands has been limited by
land availability. The development of the coffee area in Central Highlands and in
Vietnam has moving together with migration and forest exploitation. The Central
Highlands region has become an important destination for migrants since 1980, with the
population of Dak Lak increasing from 35,000 people to more than 2 million in 2003.
According to provincial statistical authorities, sixty percent of current population is
migrants (ActionAid Vietnam & Asian Development Bank, 2003). The Statistical
Office of Dak Lak indicates that one million hectares of forestry land has been
converted to other uses (especially coffee) since 1975.
10000
Overall
Poor household
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
Kon Tum
Gia Lai
Dak Lak
Lam Dong
Average
Figure 5.3: Coffee area of poor farmers in Central Highlands by provinces
Source: Calculation based on Agrocensus_2006
Within coffee farmers in the Central Highlands, there are approximately 25 percent of
households living under the poverty line. In four provinces in Central Highlands, Kon
Tum province has the largest proportion of poor coffee farmers with over 39 percent;
followed by Gia Lai (24.4 percent)25.
Table 5.3: Poverty incidence of coffee farmers in Central Highlands, Vietnam
Province
Poor
Non-poor
Total
Kon Tum
Gia Lai
39.9
24.4
60.0
75.5
100
100
25
Calculation based on Agrocensus_2006.
97
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
Dak Lak
Lam Dong
24.0
20.4
75.9
79.5
100
100
Overall
24.58
75.4
100
Source: Calculation based on Agrocensus_2006
There is not much difference in family size between poor and non-poor farmers. Most
households have four or five people. On average, there are 5.23 people in poor
household while this number in non-poor household is 4.11 persons. Only 15 percent of
coffee household have more than six people
30
Poor
Non-poor
percentage
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
people per household
Figure 5.4: Structure of family size of poor and non-poor coffee household
Source: Calculation based on Agrocensus_2006
In general, poverty in Vietnam is still relatively high, especially in rural areas and
amongst coffee households. The next section will look at the relationships between
income, expenditure and savings, as savings are the principle way in which households
overcome variability in income.
5.3.1. Saving and Income Level in Vietnam
The analysis of income and savings is important for modeling the decisions of poor
coffee households in the FY-CC model because savings determines the investment
capability of households. The cutting and replanting decision of farmers depends on
various factors, but mainly based on (i) coffee and replaced crop price levels and (ii)
cash available to the household. Farmers cannot replant coffee if they do not have
enough money for new investment and for household expenditure especially while
coffee trees are unproductive. In addition, analysing the relationship between household
98
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
expenditure and income of household helps us understand how much farmers spend on
living costs and other expenditure, and how much they save for production investment.
Unfortunately, data on expenditure and income for poor coffee farmers is not available.
Hence, in this study, the relationship between savings and income of poor household is
investigated using the VHLSS2006 data26. One important issue should be noted that the
poverty line is usually based on household expenditure rather than income. Poverty is
measured using expenditure because income data is less reliable than expenditure data
in the VHLSS. In this section, per capita expenditure is the criteria for distinguishing
between poor and non-poor households and applying the poverty line set by the General
Statistical Office of Vietnam and Ministry of Labour and Invalid Social Affair
(MOLISA). According to this line, households in rural area are poor if their per capita
expenditure is less than US$12.5 a month. This number increases to US$16.25 a month
for households in urban areas.
According to the VHLSS2006, the average total income of non-poor households in rural
areas was $2420 per year while poor household earnt $1168 per year. Non-poor
households expenditure was on average about $1300 per year while for poor households
it was $628 per year (see Table 5.4). On average, poor farmers in rural areas could save
$540 per year.
Table 5.4: Household income and expenditure in rural area in 2006 ($/year)
Total household income
Total household
expenditure
Household
savings
Non-poor
2422
1310
1111
Poor
1168
628
540
Type of household
Source: calculation from VHLSS2006
There is a big gap in household income between urban and rural areas. According to
VHLSS2006, per capita income of households in urban areas in 2006 was
approximately $900 whereas in rural area it was only $550. However, the expenditure
of households in urban area is much higher than those in rural area. The average per
capita expenditure in urban areas was over $600, doubled that of rural areas (see Figure
5.5)
26
Actually, data on poor coffee farmers can be extracted from VHLSS2006 but the sample is very small
which cannot represent poor coffee household’s behaviours.
99
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
1000
Urban area
900
Rural area
800
700
600
500
400
300
200
100
0
per capita income
per capita expenditure
Figure 5.5: Per capita income and expenditure by area in 2006 ($/year)
Source: calculation from VHLSS2006
Rural household income and savings vary slightly among regions. Surprisingly, even
being one of poorest region in Vietnam, rural households in Central Highlands (CH) has
the highest average income as well as saving. The average household’s income and
saving in Central Highlands in 2006 were $1450 and $790, respectively. The higher
saving of household in Central Highlands in 2006 was mainly due to relatively high
profit from coffee in that year. The farm gate price of coffee in 2006 was over $1 per
kg, triple the price level of 200127
Table 5.5: Household income and saving in rural by region in 2006($)28
Region
Red River Delta
North East
North West
North Central Coast
South Central Coast
Central Highlands
North East South
Mekong River Delta
Poor household
Household
Household
income
saving
1066
530
1170
509
1162
473
1051
487
929
360
1452
790
1329
674
1234
617
Non-poor household
Household
income
Household saving
2053
868
2176
1008
1886
738
1880
800
2005
759
3343
1905
3261
1368
2878
1474
Source: calculation based on VHLSS2006
27
Coffee Farm Survey 2007
Vietnam is currently divided into 8 regions: Red river delta (RRD), North East (NE), North West
(NW), North Central Coast (NCC), South Central Coast (SCC), Central Highlands (CH), Northern East
South (NES) and Mekong River Delta (MRD). The regional map of Vietnam is presented in Figure A1 in
the Appendix A.
28
100
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
Although having the highest household income and savings, due to the large household
size, the average per capita income of poor households in the rural area of Central
Highlands (CH) was only $ 230. This level is similar to per capita income in Northern
East South (NES) and slightly lower than per capita income of poor households in rural
areas of the two deltas (Red River delta and Mekong River delta).
300
per capita expenditure
per capita income
250
USD
200
150
100
50
0
RRD
NE
NW
NCC
SCC
CH
NES
MRD
Figure 5.6: Per capita income and expenditure of the poor in rural areas by
regions, 2006 ($)
Source: calculation based on VHLSS2006
Households usually keep their savings in several different forms. A study by CAP
(2008)29 shows that the main types of total savings are cash (accounting for nearly 40
percent of total saving) and gold, silver (23%). The study also pointed out that
agricultural households generally have the lowest saving level ($526), much smaller
than that of households in the service sector ($927).
Table 5.6: The saving flows of household by types
29
CAP: Center for Agricultural Policy
101
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
% by type of saving
Total
saving
($)
Assets
Deposit
Cash
Gold,
silvers…
Holdings,
Others
602
551
14.5
7.3
10.3
18.8
38.4
37.5
22.6
23.9
14.2
12.4
100
100
Household
head’s gender
Male
Female
Household
types
Total
Agriculture
Industry
Service
Gov. officer
Others
Income group
Poorest
2
3
4
Richest
526
588
927
787
696
18.4
7.7
5.4
9.9
7.1
10.3
5.1
4.6
8.8
31.0
35.2
51.8
42.5
35.9
33.6
22.0
21.8
23.0
29.1
23.6
14.1
13.7
24.5
16.2
4.6
100
100
100
100
100
143
263
483
648
1344
38.7
21.4
19.9
14.1
6.9
0.0
15.7
6.3
9.3
14.9
36.7
37.9
32.8
36.0
41.3
14.7
20.3
20.2
22.5
24.9
10.0
4.7
20.7
18.0
12.0
100
100
100
100
100
Average
594.3
13.4
11.7
38.2
22.8
13.9
100
Source: CAP (2008)
5.3.2. Relationship between Income and Expenditure of Poor Farmers
Because of the dynamic nature of the household model used, one needs a model of how
savings are accumulated over time. This requires an understanding of the relationship
between income, expenditure and savings.
The relationship between income and expenditure is estimated using the econometric
method. These estimates are important for the FY-CC model when identifying the
saving level of household, a key factor determines the coffee farmer decision to cut,
keep or replant coffee. As mentioned earlier, data on expenditure and income for poor
coffee farmers are not available. Thus, data on the poor households in VHLSS2006 is
used as a basis for this analysis.
The total number of poor households in VHLSS2006 is 1038 of which 912 households
are located in rural area. Table 5.7 presents the number of poor households extracted
from VHLSS2006 by regions to estimate the relationship between income and
expenditure.
102
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
Table 5.7: Number of poor households by region in VHLSS2006
Region
Red River Delta
North East
North West
North Central Coast
South Central Coast
Central Highlands
North East South
Mekong River Delta
Total
Frequency
92
209
191
175
60
119
58
134
1,038
Percent
8.86
20.13
18.40
16.86
5.78
11.46
5.59
12.91
100
Source: Summarised from VHLSS2006
There is expected to be a non-linear relationship between expenditure and income. By
testing different functional forms it was found that a simple linear spline function
provided the best fit, with two sections and a ‘knot’ at $180 per capita (Table 5.8). The
dependent variable is per capita income while household size, income group 1 (less than
$180 per person per year), income group 2 (greater than $180 per person per year) are
explanatory variables. The negative coefficient of family size (-3.53) means per capita
expenditure decreases as the number of people in the household increases, possibly
reflecting economies of size in consumption or a reflection of poverty in particular. The
positive coefficients of both income groups indicate the per capita expenditure will
increase with higher income. However, the much higher coefficient of income group 1
(0.42) compared to group 2 (only 0.02) means that with lower per capita income,
farmers tend to spend a larger share of income. As income increases farmers tend to
save more for other activities. This pattern can be seen more clearly in Figure 5.7 with
the variation of fitted expenditure per person versus per capita income for different
family sizes and Figure 5.8 with observed values.
103
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
Table 5.8: Regression between per capita income and expenditure of poor HHs
Type of
variables
Dependent
Variable
name
Pcexpend
Description
Per capita expenditure
Independent
Hhsize
Family size
variables
Pcincome1
Income per capita if income
Coefficient
Standard
Errors
P>t
variable
< $180, 180 otherwise
Pcincome2
-3.53
0.34
0
0.42
0.03
0
0.02
0.01
0.01
73.53
4.49
0
(Income per capita -180$)
if income > $180, 0
otherwise
_cons
Constant term
160
Source: Estimated from VHLSS2006
140
household size =6
household size=4
80
100
120
household size=2
100
200
300
per capita income ($/year)
400
500
Figure 5.7: Fitted per capita income and expenditure by family size
104
50
100
150
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
0
100
200
300
per capita income ($/year)
400
500
Figure 5.8: Plot of per capita income and expenditure of the poor
Source: based on VHLSS2006
Next section will describe the structure of the Fixed Yield–Cash Constraint Model (FYCC model) with its objectives, functions and decision rules.
5.4. Structure of the FY-CC Model
The FY-CC model is a representative cash-constrained farm based on the characteristics
of the household set out in Table 5.9. The average land holding of poor coffee farmers is
5287 m2. The annual average loan and saving of poor households are $625 and $567,
respectively. These values of loan and saving are used as base loan and base saving.
Table 5.9: General data of poor coffee household
Indicators
Value
Sources
Farm size (m )
Non-coffee maize income ($)
% family labour
Family size (persons)
Average loan (base loan) ($/year)
Average saving (base saving) ($ per year)
5287
200
30
4.7
625
567
Agrocensus_2006
Thang (2008)
Thang (2008)
Agrocensus_2006
Thang (2008)
VHLSS2006
Replanting cost ($/ha)
1440
Thang (2008)
2
Note: Non-coffee maize income or other income from other activities of households
105
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
Before moving to look at the detailed functions and decision rule of the FY-CC model,
it is important to note the main differences between the FY model and the FY-CC
model. The differences include:
First, the FY model identified the optimal rule to maximise the ENPV per hectare of
land. The FY model did not consider other issues such as farm size, expenditure, saving,
credit, other income, and family labour return. The FY-CC model tries to integrate all
the above issues to investigate the optimal rules of resource poor coffee households, so
the FY-CC is a resource poor coffee household model. In the FY-CC model, the
objective function is not the ENPV per one hectare, it is replaced by the ENPV per
resource poor farm (only 5287 m2).
Second, farmers in the FY model are assumed unconstrained by liquidity issues. Thus,
the household’s budget does not restrict decisions to keep or replant the coffee trees.
However, in the FY-CC model, resource poor coffee households may operate under a
cash constraint and this may affect their decision. Thus, decision rules of the FY-CC
model are different from the FY model.
Third, the FY model considered several fixed form equations of age dependent CP
(quadratic, cubic and quadratic with price change effect) solved to find the
corresponding optimal rules and ENPV. However, the results of different age dependent
CP were quite similar. Thus, the FY-CC model assumes a quadratic form of CP (
CP
o
age
1
2
age2 ). The CP is found infinite in the FY model thus it is ignored
in the FY-CC model
Fourth, the FY model in the previous chapter identified the optimal cutting and
replanting rules for coffee farmers with two price simulation models (Lagged price
model and Price Cycle model). However, the price data simulations generated by the
Lagged price model are more realistic in terms of the underlying stochastic process.
Besides that, the estimated price function using Lagged prices had a more suitable
match with higher R2 and F-value. Thus, this chapter only considers the case where
prices are generated using the Lagged price structure.
The following sections will describe the main functions in the FY-CC model such as the
objective function, profit function, yield and production cost function, expenditure and
106
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
saving, decision rules. The general structure of the model is similar to the FY model, but
there are significant differences.
5.4.1. Objective Function
The FY-CC model aims to identify the optimal rules to maximise the ENPV for a
resource poor farm. Thus, the objective function of the FY-CC model is the same as the
objective function of the FY model in (4.1) and (4.2).
The ENPV function is given by:
ENPV
(5.1)
1 22
ENPVa
22 a 1
in which
ENPVa
1
N
N
(5.2)
T
e
t
t ,r ,a
V (T )
T
r 1 t 1
where ENPVa is expected NPV given coffee trees at starting age a , for the next 50
years given N possible random price sequences;
trajectory r and starting age a ; and
e
t , r. a
is profit per ha in year t for price
is the discount factor. V T
denotes the
terminal value of the coffee garden and it is set to zero in the model; and r identifies
the replication number for one age group. As same as in the FY model, one hundred
replications are employed for each starting age group. For each replication, a separate
random price trajectory from the Lagged Price model is simulated.
The only difference in the objective function between the FY model and the FY-CC
model is the size of land area managed by farmers. In the FY model, it is assumed that
the farmer controls one hectare of land and the planning decision applies to one hectare.
However, the poor coffee farmers in the FY-CC only control 5287 m2 (the average
coffee area of poor coffee farmers). Thus, the ENPV in the FY-CC model is achieved
for that farm size.
107
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
5.4.2. Profit, Yield and Production Cost Function
The yield and production cost function in the FY-CC model are the same as those used
in the FY model. The coffee yield and production cost are fixed for any given age of
coffee tree but variable with age. In reality, resource poor coffee farmers usually own
the less productive coffee land so the yield of poor households is generally lower than
that of non-poor households. However, the FY-CC model assumes no yield difference
between poor and non-poor households. With this assumption, it makes the comparison
of results between the FY model and FY-CC model possible.
The profit function in the FY-CC model here has a very small change with the inclusion
of the “other income” component.
The profit of coffee poor household at time t is as follows:
e
t ,r ,a
[( Pt c .Yt c vtc ).St
( Pt m .Yt m vtm ).(1 St )] I o
(5.3)
where St denotes for the existence of coffee. St is equal to1 if coffee is growing and 0
otherwise; Pt c is price of coffee at year t; Yt c is coffee yield at year t; Pt m is price of
maize at year t; Yt m is coffee yield at year t; I o is the other household income that is
besides profit from coffee and maize.
In common with the FY model, in the FY-CC model the profit of maize and other
income are assumed constant. The profit of maize is fixed at $440 per hectare or $232
per poor farm. The other income of poor coffee households is estimated by Thang
(2008) and is fixed at $200 per year.
5.4.3. Expenditure, Saving and Loan
The household expenditure (HE) is estimated from income based on the regression
result in Table 5.8. HE is given by:
HE = hhsize (73.53 -3.53hhsize +0.42pcincome) if per capita income
(5.4)
of household is less than $180 per year
HE = hhsize (73.53 -3.53hhsize +0.42*180 +0.02(pcincome-180) if
(5.5)
per capita income of household is greater than $180 per year
108
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
where hhsize is number of persons in household; pcincome is per capita income of poor
household.
The annual saving of the household is measured as the difference between household
income and expenditure. Thus, aggregate savings available in year t will be given by:
Savingt
Savingt
ă
t
(5.6)
HEt
Farmers cannot invest in a new coffee garden if they do not have enough money, even if
the expected profit from the investment is positive. In general, farmers can mobilize
capital from two sources: household saving and loans. Thus, the capital function in the
model is given by:
(5.7)
Capitalt = Savingt + Loant
According to Coffee Farm Survey 2007 in Dak Lak province, the average loan of coffee
farmer was $837. This level is slightly larger than the base loan borrowed by poor
coffee household in the FY-CC model ($625 per year). Farmers in Cu Mgar district
borrowed larger amounts because they have a larger farm size and more productive
land. Most loans have a term of one or two years (see Table 5.10).
Table 5.10: Loan amount and duration
District
Cu Mgar
Krong Pak
Eakar
Overall
Average Loan ($)
Duration (months)
921.5
848.5
741.1
837.0
18.3
16.2
13.1
15.9
Source: Coffee Farm Survey 2007
The main proportion of loans is used for buying inputs and hiring labour (over 70%). In
Cu Mgar district, farmers spend 90 percent of loan value for input purchases and labour
payment. Only 2 percent of loans borrowed by farmers in Eakar are used for hiring
labour. This can be explained because farmers in Eakar are quite poor so they employ
mainly family labour. About 17 percent of loans are spent for other economic activities
of households (see Table 5.11).
109
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
Table 5.11: Main loan purpose (% respondent)
Loan purpose
Cu Mgar
Buy inputs
Hire labour
Other economic activities
Other
Total
Krong Pak
82.0
7.6
10.2
0
100
57.5
6.0
27.2
9.1
100
Eakar
Total
66.6
2
14.2
17.0
100
69.8
6.3
16.2
7.5
100
Source: Coffee Farm Survey 2007
The main sources of loans for farmers are banks. According to the Coffee Farm Survey
2007, over 70 percent of loan value was borrowed from banks. In Krong pak, this
number reached nearly 85 percent. Private lenders are also important credit providers. In
Eakar, over 50 percent of loans came from private lenders.
Table 5.12: Percentage of loan by different sources by districts
Sources of loan
Banks
Private lenders
Relatives
Women's association
Commune Committee
Other support
programs
Total
Cu Mgar
Krong Pak
Eakar
Total
76.9
2.5
10.2
0
0
84.8
0
0
3.0
9.0
42.8
52.3
4.7
0
0
72.0
12.9
5.3
1.0
3.2
10.2
100
3.0
100
0
100
5.3
100
Source: Thang (2008)
5.4.4. Decision Rule
The decision rule for deciding when to replant/cut coffee in the FY-CC model is slightly
different from the FY model. To describe the decision rule, St is denoted for the coffee
area at year t. Whether coffee trees exist on the land or not is denoted by a (0, 1)
variable. Thus, St is equal to 1 if coffee is planting, otherwise it takes 0. The decision of
poor coffee household in the FY-CC model is as follows:
(i)
St = 1 if St-1=1 and Pt > min [(CP, RP) and (Capitalt + Io>= Costt+1 + Minexpend)]
where Io is other income of household, Minexpendt is the minimum expenditure for
household in year t and it is about $270. The minimum expenditure is estimated from
regression results of income and expenditure in Table 5.8; Pt is the price of coffee,
Costt+1 is production cost in year t+1, Capitalt is capital of household in year t
(Capitalt= savingt + loant)
110
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
This condition means that if farmers are growing coffee, they will keep coffee if price is
greater than the minimum level of CP and RP and the household’s budget can at least
cover the minimum household expenditure and the production cost in the coming year.
(ii)
[St = 0 if St-1=1 and Pt ≤ min (CP, RP)] or
St = 0 if St-1=1 and [Pt > min (CP, RP) but (Capitalt + Io< Costt+1 + Minexpend)]
This constraint indicates that farmers will cut coffee and switch to maize if (i) price is
below the minimum level of CP and RP or (ii) despite price being higher than the
minimum level of CP and RP if the household’s budget cannot cover the minimum
household’s expenditure and production cost in next year.
(iii)
St=1 if St-1=0 and Pt>=RP and (Capitalt + Io< replanting cost + Minexpend)
This relationship gives the condition for replanting coffee if farmers are growing maize.
The farmers grow coffee again if price is above the RP and the household budget can at
least cover the minimum expenditure and replanting cost.
As mentioned earlier, the FY-CC model is limited to only the quadratic CP. Thus, the
fixed-form law for cutting price in the model will be defined as follows:
CP
age
o
1
2
age2
(5.8)
The replanting price is again specified as:
RP =
(5.9)
3
To find the optimal CP and RP, it is necessary to solve the FY-CC identifying
o
,
1
,
2
,
3
for the maximum ENPV.
5.5. Results of the FY-CC Model
111
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
5.5.1. Impact of Cash Constraints on Income
Before re-solving for the optimal cutting/replanting rules under cash constraints, it is
informative to identify the extent to which the poor farmers lose income because of cash
constraints if they still apply the optimal rules of the FY model as in the previous
chapter. Recall, the optimal rules in the FY model are identified as follows:
CP = 0.402 - 0.0509age + 0.00367age2
(5.10)
RP =0.74 ($/kg of coffee bean)
(5.11)
With optimal rules, the maximum ENPV per hectare from FY model is $9226. This
number falls to $4878 if farm size is reduced from one hectare to the average farm size
of poor coffee households (5287 m2).
Now, this rule applies to household in the FY-CC model in conjunction with
characteristics of poor coffee households presented in Table 5.9. The result shows that
the maximum ENPV of farm income is about $4300 per poor farm size, about 15
percent lower than the ENPV achieved by the FY model for the same coffee area (see
Figure 5.9). The income reduction is due to cash shortages that prevent farmers
replanting coffee even if the current coffee price is greater than the RP ($0.74 per kg).
Furthermore, income is also reduced because in some simulations farmers may not have
enough money to sustain both their production and living costs so they have to cut and
switch to maize.
5000
4900
Expected NPV($)
4800
4700
4600
4500
4400
4300
4200
4100
4000
ENPV from FY-CC if imposing optimal rule of
FY model
Optimal ENPV from FY at poor farmsize
Figure 5.9: ENPV from FY-CC if imposing optimal rule of FY and optimal ENPV
from FY ($/poor farm)
112
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
5.5.2. Effect of Loans and Savings
The income loss when applying the optimal rule of the FY model into the FY-CC model
shows the important role of saving and credit to support farmers. To investigate the
importance of saving and loan on income, the FY-CC model can be solved by changing
the saving and loan levels while still keeping the optimal rules of the FY. Figure 5.10
presents the results for different levels of initial savings, holding all other factors
constant. As expected, with high initial savings levels, the maximum ENPV from the
FY-CC model is close to the ENPV from the FY model. However, as initial savings fall,
so does ENPV. The results of the FY-CC model give an interesting point with respect to
the contribution of initial savings in the range of $500-$1100. It would appear that in
this range, changes in initial savings have little impact on ENPV, suggesting threshold
effects within the model. The saving range of $500-$1100 cannot cover the production
cost of coffee in non-productive period and other living expenditure of household. Thus,
it may not help the poor people optimize their investment decision, so the ENPV
remains unchanged.
4900
4800
loan =$625
ENPV($)
4700
4600
4500
4400
4300
4200
0
500
1000
1500
2000
2500
initial saving ($)
Figure 5.10: ENPV from FY-CC at different initial savings at annual loan of 625$
Similarly, to investigate the impact of limits on credit on income, the FY-CC model is
solved with a fixed initial saving value and exploring the impact of changes in the
maximum level of annual loan. The results are depicted in Figure 5.11. As shown in
Figure 5.11, the increase in annual loan strongly improves ENPV if farmers do not have
any savings. The ENPV increases from $3300 (with loan = 0) to about $4400 (with
113
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
annual loan of $1100). The growth of ENPV is much lower once the loan is over $1200
and mostly unchanged with loans over $2500.
4800
4600
Average NPV($)
4400
4200
NPV with initial saving = 567$
4000
NPV with initial saving =0
3800
3600
3400
3200
3000
0
500
1000
1500
2000
2500
3000
3500
annual loan ($)
Figure 5.11: ENPV of farm income at different annual loans and savings
With initial savings of $ 567 (base saving), the increase in loan has much less impact on
farm income. The ENPVs with two different initial saving levels converge when the
available loan is over $2500. This means the initial savings does not affect ENPV once
the annual loan exceeds $2500 and if farmers can get enough credit they will achieve
the optimal decision regardless of the initial saving.
The small increase in ENPV with base saving ($567) explains the way in which ENPV
is calculated. The ENPV here is the mean of ENPV from 22 starting age groups.
However, it is anticipated that the importance of savings will vary according to age of
coffee trees. Figure 5.12 reports the results for ENPV over a 50-year horizon time for
farmers with different initial ages of coffee trees. As shown in Figure 5.12a, the ENPV
with different annual loans varies significantly by the starting ages of coffee trees. For
farmers who have just replanted coffee trees, loans under $500 do not help them change
their income. More interestingly, even with a loan from $500 to $1100, the average
income of farmers tends to be low. This can be explained by the fact that with this level
of loan, farmers can only afford to replant coffee but they do not have enough money
for keeping coffee in the following years. The amount of loan is effective for farmers
who want to replant coffee when it is over $1100. With over $1100, household’s farm
income increases steadily and nears the maximum level at a loan of about $2000.
114
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
With the starting age of 2-year old coffee trees, the variation of ENPV by loans is less
complicated. After reducing slightly with loan under $400, average ENPV increases
quickly with loan amounts and get close to the maximum at loan of $1500. The results
in Figure 5.12a also indicate that the ENPV of farm income with starting age of coffee
from 3 to 5 year old are getting higher with bigger loans. However, the amount of loans
that helps income to reach maximum level at different starting ages is not similar. For
the farmers with trees of an initial age of 5, the amount of loan does not significantly
affect the ENPV. This suggests that once trees are established the income stream from
coffee is sufficient for even poor farmers to follow the optimal decision rules.
The variations of ENPV for starting age of trees in the mature period (from 6 to 15) are
quite similar and increase slightly with higher loans. However, the higher amount of
loan does not produce a large impact on farm income for those groups. This happens
because with mature coffee garden, farmers may have a good income that helps them
save enough for keeping coffee or replanting new trees (see Figure 5.12b).
However, when trees are in the last years of the life cycle with downward yield, the size
of loan becomes more important and has significant effects on farm income. Figure
5.12c presents the change in ENPV by loan for different starting ages from 17 year old
to 22 year old. With trees from 20 to 22 year old, the impact of loan is quite similar to
young trees in gestation period. The ENPV rises with greater credit and the role of loans
are much more significant when trees are getting older. This is because, at this stage in
the cycle, landholders are approaching the point at which they will replace trees, and if
they have not built sufficient savings over the productive portion of the trees lifecycle,
they will find it difficult to re-establish the coffee trees, if the replanting rule suggests
that that is appropriate.
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Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
7000
starting age of trees =5 years old
6000
average NPV ($)
starting age =4
5000
4000
3000 starting age =3
starting age =2
2000
starting age =1
1000
10
00
12
00
14
00
16
00
18
00
20
00
22
00
24
00
26
00
28
00
30
00
80
0
60
0
40
0
20
0
0
0
annual loan ($)
(a) with starting age from 1 to 5 year old
starting age of tree =8
Average NPV ($)
6400
6200
starting age =9
6000
starting age =10
5800
starting age =11
5600
starting age =12
5400
5200
5000
0
200
400
600
800
1000 1200 1400 1600 1800 2000
annual loan ($)
(b) with starting age from 8 to 12 year old
4000
starting age of trees =17 years old
3800
3600
starting age =18
Average NPV ($)
3400
starting age =19
3200
3000
starting age =20
2800
starting age =21
2600
starting age =22
2400
2200
2000
0
200
400
600
800
1000 1200 1400 1600 1800 2000 2200 2400 2600
Annual loan ($)
(c) with starting age from 17 to 22 year old
Figure 5.12: ENPV of FY-CC with different starting age of trees and loans
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Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
5.5.3. Optimal Rule for Poor Coffee Farmers
The previous analysis has taken the estimated optimal decision rules, estimated without
liquidity constraints, and simulating behavior in the presence of such constraints.
However, it is also of interest to see if the behavioral rules themselves would change if
the fixed form optimization process were repeated, with explicit consideration given to
the presence of liquidity constraints.
To find the optimal rules for poor coffee households, the FY-CC model repeats the
searching procedures for the FY model.
As mentioned earlier, The FY-CC model only investigates the optimal rule for poor
coffee households with the Lagged price simulation model and quadratic form of CP.
With application of the grid searching procedure, the FY-CC identifies the optimal rules
for poor coffee households as follows:
CP =0.458 -0.46age +0.00325age2
(5.12)
RP=1.4 ($/kg)
(5.13)
ENPV =4375 ($)
(5.14)
The optimal rules of the FY-CC model are illustrated in Figure 5.13. The optimal CP
for one year old trees is about 0.4($/kg). The CP reduces slightly when the age of trees
is getting close to their mature period. After that, the CP increases gradually with older
ages.
The comparison of optimal rules between the FY model and the FY-CC model is
presented in Figure 5.14. As shown in the Figure 5.14, the CP of poor coffee growers is
generally higher than CP in the FY model. This means that poor households in the FYCC model are more likely to cut compared to farmers without a cash constraint in the
FY model. This may happens because of cash shortage for buying inputs and for
household consumption. That is why the poor farmers have to cut earlier and switch to
maize.
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Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
1.6
replanting
1.4
1.2
price ($/kg)
CP of FY-CC model
1
keep coffee
RP of FY-CC model
0.8
0.6
0.4
0.2
cut and switch to maize
0
1
3
5
7
9
11
13
15
17
19
21
age of trees
Figure 5.13: Optimal Rules of the FY-CC model
1.6
price ($/kg)
1.4
1.2
CP of FY model
CP of FY-CC model
1
RP of FY model
RP of FY-CC model
0.8
0.6
0.4
0.2
0
0
3
6
9
12
15
18
21
age of trees
Figure 5.14: Optimal rule of FY model and FY-CC model
The optimal RP in the FY-CC model ($1.4 per kg of coffee bean) is much higher than in
the FY model ($0.74 per kg of coffee bean). This suggests a much more cautious
approach to replanting which is logical: because of the period when trees are
unproductive, it is highly disadvantageous to plant trees and then remove them within a
couple of years because of cash flow shortages. Thus, the poor farmers usually wait for
significantly higher prices before making replanting decisions.
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Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
Due to the cash constraint, poor farmers in the FY-CC model cannot make the optimal
decision as in the FY model. Thus, the optimal ENPV of the FY-CC model is only
$4370 per poor coffee household size (5287m2). This value is still much lower than
optimal ENPV of the FY model ($4878) at same area of coffee.
With optimal rules, the actual cutting percentage of coffee farmers in the FY-CC model
is quite different from the FY model. In general, poor farmers in the FY-CC model are
more likely to cut than coffee farmers in the FY model, especially when the trees are
still young (less than 4 year old) and very old (over 20 year old). The cutting frequency
is not much different when trees are 6-19 year old (see Figure 5.15).
30
FY model
% actual cut
25
FY-CC model
20
15
10
5
0
1
3
5
7
9
11
13
15
17
19
21
age of coffee trees
Figure 5.15: Actual cutting percentages by age of trees
The higher cutting frequency of poor coffee farmers can be derived from the optimal
cutting rule and cash constraint. Hence, it is much better to split the impact of those two
factors on cutting decision of poor coffee farmers. Figure 5.16 below presents the
separated cutting percentage by age of coffee trees under the impact of CP rule and cash
constraint. When trees are young (less than 4 year old), cash constraint influences
significantly on cutting decision of poor farmers. However, when trees are older, the
cutting decision is mostly not affected by cash constraint.
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Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
30
by CP rules
actual cutting (%)
25
by cash constraint
20
15
10
5
0
1
3
5
7
9
11
13
15
17
19
21
age of coffee trees
Figure 5.16: Impact of cutting decision by CP rule and by cash constraint in the
FY-CC model
To investigate the change in the optimal rules of the FY-CC when initial savings varies,
a simulation in which $1500 replaces the base initial saving ($567) is solved. The model
output shows that with higher initial saving, poor coffee farmers are less like to cut and
more likely to replant than with the base initial saving. Furthermore, the new maximum
ENPV increases to $4712. This level is higher than the maximum ENPV from the FYCC model with base saving and near to optimal ENPV of the FY model with poor
farms. In addition, the optimal CP in the FY-CC model with initial saving of $1500 is
very close to the optimal CP in the FY model. However, the optimal RP in the FY-CC
model ($1.07 per kg of coffee) with initial savings of $1500 is still relatively high
compared to the FY model (RP=$ 0.74) (see Figure 5.18).
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Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
1.8
CP with initial base saving
CP with initial saving of $ 1500
RP with initial saving of $ 1500
RP with initial base saving
1.6
coffee price ($/kg)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
3
6
9
12
15
18
21
age of coffee trees
Figure 5.17: Optimal rule of the FY-CC model with different initial savings
1.6
1.4
price ($/kg)
1.2
CP of FY-CC, initial saving=$1500
RP of FY-CC, initial saving=$1500
CP of FY model
RP of FY model
RP =1.07
1
RP = 0.74
0.8
0.6
0.4
0.2
0
0
3
6
9
12
15
18
21
age of coffee trees
Figure 5.18: Optimal rules of FY model and FY-CC with initial saving of $1500
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Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
5.6. Conclusion
Rural households in general and coffee farmers in Vietnam have volatile and low
incomes. Many coffee farmers are poor and they often have cash constraints on
investment. Due to the cash shortage, poor farmers may not be able to use their own
assets as efficiently as the non-poor’. They are disadvantaged when trying to optimize
their decisions. This is a common finding in other developing countries where
agricultural investments tend to rely heavily on credit from banks and other
organizations.
The FY-CC model in this chapter investigates the changes of coffee farmer’s decision
when they face a cash shortage. The model found that the poor coffee farmers could not
be optimal compared to whose without a cash constraints. Compared to the FY model,
due to cash constraint, poor coffee households in the FY-CC model have to cut coffee
earlier and switch to maize. Furthermore, they replant coffee at a higher price as
compared to the FY model.
Savings and loans play an important role in helping farmers allocating their resource
optimally. In general, poor coffee households can get higher income with access to
larger loans. However, the importance of loans and saving varies according to the initial
age of coffee trees. The amount of loan plays a more important role in improving
household’s income when trees are younger. For farmers who have just replanted coffee
trees, loans under $1000 do not help them change their income but the ENPV increase
considerably with loans above that. The amount of annual loan is also important for
starting age of trees under 4 years old. With the initial age of trees in mature period, the
increase in loans does not have a substantial impact on household income.
The result of the analysis of actual cutting decisions when optimal rules are invoked
show that poor farmers in the FY-CC model are more likely to cut than the coffee
farmers in the FY model, especially when the trees are less than 4 year old and over 20
year old. The cutting frequency is not much different when trees are in the 6-19 year old
group. The model result also indicates that the liquidity constraint affects considerably
on the cutting decision for young trees in the gestation period.
The FY-CC model identifies the change in the decision rules needed when considering
poor coffee household with the cash constraint. The impacts of savings and loans on
122
Chapter 5. Optimal Coffee Planting Decisions under a Cash Constraint
different coffee groups are also investigated using the FY-CC model. However, in both
the FY model and the FY-CC model, the cost and yield of coffee are fixed according to
the age of trees. In practice, coffee yield is influenced by input use (including labour). In
addition, farmers often change their input application in response to the output price.
The response of production cost to output price and the yield response to input use are
the possible short-run responses of farmers. The presence of short-run responses reflects
closely to coffee farmer’s behavior in practice. The decision of farmers and the ENPV
may change considerably with the appearance of short-run responses. In the next
chapter, the yield function of coffee will be estimated based on the age of coffee trees
and the production cost. After that, the estimated yield function will be integrated into
the FY and the FY-CC model to see how farmers’ decisions change with the possibility
of the short-run response.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
CHAPTER 6. SHORT-RUN RESPONSE AND OPTIMAL
RULES FOR COFFEE FARMERS IN VIETNAM
6.1. Introduction
This chapter investigates the farmer’s decision when it is possible to make short-run
‘tactical’ changes to coffee yields by adjusting input levels. In the previous models FY
and FY-CC, the farmer’s decision merely determines the coffee area. In this chapter,
the farmer adjusts variable inputs within the production season. However, the response
to yield, cost and price in the short-run, can also influence the optimal decision of
farmers in terms of cutting and replacement rules. Thus, input use is included as a
decision variable in the simulation model. The model is then re-solved to identify
optimal rules and farmer’s choices under an extended choice set. To this end, this
chapter develops two extended models: Variable Yield Optimal Model (VY model) and
Variable Yield- Cash Constrained Model (VY-CC model)
This chapter consists of five sections. Section 6.2 will review previous studies on yield
response functions. Section 6.3 will estimate the relationship between coffee yield and
variable inputs in Vietnam. An analysis of the supply elasticity with respect to price
based on the estimated yield function is reported in Section 6.4. The optimal rule and
income of coffee farmers under these conditions will be analyzed in Section 6.5 and
Section 6.6.
6.2. Review of Literature on Yield Response Functions
There have been numerous studies on crop yield response functions. Much of the work
has been focused on the best functional form to identify crop yield response to fertilizer
as well as using these models to identify the optimal level of fertilizer (Reeder and
McGinnies, 1989, Wight and Godfrey, 1985, Ackello-Ogutu et al., 1985, Taylor and
Swanson, 1973, Mendelssohn, 1979, Rajsic et al., 2009).
The majority of studies have applied polynomial functions (quadratic or square root) to
represent the relationship between fertilizer and yield (Mendelssohn 1979; Reeder and
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
McGinnies 1989; Rajsic et al. 2009). However, other researchers have pointed out the
inappropriateness of polynomial crop response functions because they allow
substitution between nutrients and tend to overestimate the maximum yield and optimal
fertilizer application (Anderson and Nelson, 1975). Thus, some have applied different
forms when estimating the response of the crop yield. For instance, Anderson and
Nelson (1975) used linear-plateau models to estimate a Tennesse corn yield function in
North Carolina. Similarly, Tembo et al (2008) developed a method of estimating a
response function with a stochastic plateau that can capture random effects and
determine economically optimal levels of nitrogen fertilizer for wheat in the Southern
Great Plains of the United States. Ackello-Ogutu et al. (1985) used the von Liebig
response function instead of a polynomial function to analyze fertilizer and yield
response for corn, soybean, wheat and hay rice using data from a thirty year experiment
conducted on the agronomy farm at Purdue University (USA).
Water and fertilizer management are crucial to high yields. Irrigation water is becoming
an increasingly limited resource in many areas in different countries, and as a result, an
appropriate choice of irrigation is needed. Furthermore, optimal combinations of
fertilizer and water can increase crop yield and reduce groundwater pollution. Thus,
previous papers have tried to estimate the relationship between yield and fertilizer
levels, in combination with irrigation (Di Paolo and Rinaldi, 2008, Reid et al., 2002,
Pandey et al., 2000, Lovelli et al., 2007) or evaluate the impact of water deficit as well
as irrigation method on crop yield (Dagdelen et al., 2006, Oktem, 2008, Karama et al.,
2003, Pandey et al., 2000, Panda et al., 2004, Topcu et al., 2007, Melgar et al., 2008,
Jalota et al., 2009, Karam et al., 2009, Kunzová and Hejcman, 2009, Li et al., 2009).
Literature on measurement and effects of fertilizer-water use efficiency are reported in
Zwart and Bastiaanssen (2004) and Oktem (2008).
In agricultural production, the effects of input use can carry over from season to season.
Input carryover effects have been included in a number of studies. Akbar (2003) used
field studies to estimate residuals of input (N, NPK) from cereal and legume cultivation.
Segarra (1989) applied a dynamic optimization model in which an intertemporal nitratenitrogen residual function was used to derive and evaluate nitrogen fertilizer optimal
decision rules for irrigated cotton production in the Southern High Plains of Texas
(United States). Ackello-Ogutu (1985) estimated an econometric model for phosphorus
carryover in United States based on the geometric distributed lag form, prices and yields
of hay, wheat and corn.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
Studies on yield response have been extended to include the impact of weather and price
risks. Rötter and Van Keulen (1997) analysed risks and opportunities of small farmers
in Kenya when they assessed the variation in yield response to fertilizer application for
maize. The risk assessment approach in this paper is based on crop growth modeling in
which risk is assessed based on yield probability distributions, product prices, costs of
inputs and the level of the most important economic and environmental risks.
Stochastic weather and soil conditions explain why farmers tend to apply more than the
recommended levels of nitrogen. Rajsic et al (2009) examined the effect of temporal
uncertainty on the optimal level of nitrogen application for both risk-neutral and riskaverse corn producers in Haldimand-Norfolk County, United States. The authors found
that uncertainty plays a role in the application decision of farmers but not in the manner
typically assumed. While uncertainty can justify farmers applying more than the
recommended inputs for risk neutral farmers, it does not for risk-averse farmers.
Most studies on yield response to inputs have focused on annual crops. The number of
papers looking at the response of perennial crop is limited. Salardini (1978) investigated
the response of tea to fertilizer in Iran. However, this study is only based on
experiments on different sites with a single treatment of fertilizer. Similarly, Cong
(2001) estimated the response of some crops (rice, coffee, cabbage, and rambutan) on
different types of land in the south of Vietnam. This study identified that the coffee
yield increases with nitrogen application as well as potassium. However, this study only
did an experiment with three levels of input application, and it did not estimate a
relationship between yield and fertilizer. Garcia and Sively (2001) used DEA method to
measure the technical efficiency of coffee producers in Daklak province, Vietnam. They
studied the effect of different inputs on technical efficiency and found that 30% of farms
are identified as efficient under an assumption of CRTS (Constant returns to scale) and
39% are identified as efficient under an assumption of VRTS (variable returns to scale).
The following section reports a yield response function of coffee based on Vietnamese
Agrocensus_2006 data. After estimation, the yield function is incorporated into the FY
model and the FY-CC model to investigate whether the possibility of a short-run
response changes the optimal cutting/replanting decisions, and incomes. In previous
models (FY, FY-CC), yield of coffee trees is assumed to be constant for a given age.
However, in this model (VY, VY-CC), the yield of coffee trees will be determined as a
function of production cost.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
6.3. Coffee Yield Function in Vietnam
6.3.1. Yield Coffee Function Estimation
This section estimates a coffee yield function based on two explanatory variables:
annual production cost and age of trees. Unlike the yield response functions for inputs
(such as fertilizer inputs or water) reviewed in Section 6.2, this study does not use yield
response as a function of physical inputs (nitrogen, potassium or phosphate, and labour
or water), but instead uses variable input costs as an index of aggregate inputs. To
investigate the impact of short-run response on coffee farmer’s behaviors and ENPV,
the assumption is that coffee farmers will optimize input use to maximise profit, and the
relationship between inputs and yield will be incorporated into the FY model and the
FY-CC model to develop the VY model and the VY-CC model, respectively.
The data used for estimating the coffee yield function are based on a sub-set of the
coffee production efficiency survey reported in Agrocensus_2006. In the data set, 500
coffee farmers in four provinces in the Central Highlands were interviewed. The sample
of this survey is presented in Table 6.1. Variables in the data set relate to coffee area,
age of coffee, production cost, selling price and quantity sold.
Table 6.1: Sample distribution of coffee households in Agrocensus_2006
Number of surveyed
coffee households*
Province
Dak Lak
Kon Tum
Gia Lai
Lam Dong
Average coffee
Average age
area/household (m2)
of trees
200
100
100
100
Average
sale price
($/kg)
9471
12894
12080
7.6
9.7
10.2
1.0
1.1
1.0
7541
8.5
1.1
Source: calculated from Agrocensus_2006
A number of potential functional forms could be used for the relationship. One
restriction is that the functional form has to be amenable to the solution for the optimal
input use, and to be easily implemental within the optimization model. The quadratic
form has a satisfactory fit (high R2, F_value and the significant level of estimates) while
allowing a simple expression for the optimal input use, conditional upon coffee price.
The estimated equation takes the form of:
q
0
C
1
2
C2
3
A
4
A2
i
Di
(6.1)
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
where q is the yield of coffee (kg per ha), C is production cost of coffee per ha ($), A
denotes the age of coffee trees and Di is dummy variable for district i30.
The regression results are presented in Table 6.2. As shown in the table, R2 value is
quite high, 75 percent. The negative sign of cost per ha squared and age squared give a
concave function. Coefficient values of the region dummy variables are highly
statistically significant. This means that coffee yield varies among selected districts.
Table 6.2: Regression Results of Coffee Yield Function
Number of obs :
F( 16, 477):
Prob > F :
Adj R-squared :
Variable
Dependent variable
yield kg/ha
Independent variables
District Dummies
Kon Tum, Dak To
Kon Tum
Kon Tum, Dak Ha
Gia Lai, Ia Grai
Gia Lai, Chu Se
Dak Lak, C M'gar
Dak Lak, Krong Buk
Dak Lak, Krong A Na
Lam Dong, Da Lat city
Lam Dong, Lam Ha
Lam Dong, Di Linh
Lam Dong, Bao Lam
C
C2
A
A2
_Cons
494
91.81
0.0000
0.75
Coefficient
T-value
-462.79
-121.71
-13.74
-303.81
-543.16
-403.14
367.58
-408.33
-213.71
12.41
-126.23
-13.07
2.55
-0.00043
62.05
-2.60
-665.72
-4.88
-1.35
-0.14
-3.04
-4.99
-4.41
4.35
-4.21
-2.03
0.13
-1.04
-0.11
12.17
-5.84
2.41
-2.18
-3.63
Source: Estimated from Agrocensus_2006 data
Note: C is annual cost per hectare of coffee ($), C2 is square of cost per hectare, A is age of
coffee trees and A2 is square of age of coffee trees.
30
The extension of (6.1) by adding the interaction term between age of tree and
production cost (CA) was also tested but was not statistically significant.
128
Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
To see the impact of age of trees on coffee yield, the cost is fixed at the average cost
from Agrocensus_2006 ($1230 per ha). The relation between coffee ages and yield is
presented in Figure 6.1. In the early years, after the gestation period, coffee yield
increases as trees get older. The coffee trees reach a maximum yield at 11 year and then
reduce gradually. However, the variation in the coffee yield by age is not large
(although statistically significant). The difference of yield by age in the estimated yield
function is much smaller than that in the yield function used in the FY model in Chapter
4 and the FY-CC model in Chapter 5, which was based on judgments from a coffee
expert focus group and Coffee Farm Survey 2007. A change in yield by coffee age is
small, possibly because the age of trees in the sample are mainly mature, with only a
few households with young and very old trees.
2600
2550
yield (kg/ha)
2500
2450
2400
2350
2300
2250
2200
2150
2100
0
5
10
15
20
25
age of coffee
Figure 6.1: Coffee yield – age relationship at average cost
Figure 6.2 illustrates the cost-yield relation for 11-year old trees. According to the
estimated results, the yield of coffee increases as variable inputs increase and reaches a
maximum yield of 3600 kg per ha when the production cost is approximately $3000 per
ha. After reaching the maximum level, coffee yield tends to reduce. However, the
maximum cost in the sample is $2880 per hectare, implying that, within the data range,
there is a positive relationship between yield and inputs.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
4500
range of surveyed cost
4000
3500
yield (kg/ha)
3000
2500
2000
1500
1000
500
2883
0
0 339
1000
2000
3000
4000
5000
cost (USD/ha)
Figure 6.2: Cost –yield relation for 11 year old coffee trees
The result of the estimated yield function will be used (with some modification) in the
farm model to investigate changes in coffee farmer’s behavior and income if they have
optimal responsiveness to price. The next section will identify the optimal variable cost.
6.3.2. Optimal Cost Specification by Output Price
This section estimates the optimal cost as a function of price based on the yield function
estimated in the previous section.
Starting from the yield equation based on cost per hectare of coffee land and age
q
0
C
1
2
C2
3
A
4
A2
i
Di
The profit of coffee per ha is the difference between revenue and production cost
pq C
Profit reaches a maximum level when its first derivative equates to zero, and so
Coptimal
1 p 1
2p 2
In the estimated coffee yield model,
(6.2)
1
=2.55 and
2
=0.00043. Figure 6.3 graphs the
cost and yield relationship base on the estimated function for Ia Grai district (Gia Lai
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
province) and the price of coffee in 2006 for 11-year old trees. As shown in the figure,
farmers can get the maximum yield of 3600 kg per ha when they invest a cost of about
$2800.
4500
Maximum yield
4000
Optimal yield
Yield (kg per ha)
3500
3000
2500
2000
Surveyed yield
1500
1000
500
0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Cost per ha (USD)
Figure 6.3: Simulation of cost and yield relationship (age of tree =11 year old,
medium yield level district)
6.3.3. Supply Price Elasticity
To get the supply price elasticity, optimal cost in (6.2) is substituted into the estimated
yield function:
q
q
q
q(' P )
p
q
0
C
1
2
0
1 p 1
1
2p 2
0
3A
1
2 2 p3
p
q(' P )
q 2
C2
2
4A
3
2
A
4
2
1 p 1
2p 2
1
4 p2
(6.3)
A2
3
A
4
A2
2
1
2
4
2
(6.4)
1
2
2p q
(6.5)
With the average sale price and average yield from data set of $1.05 per kg and 1932.8
kg per ha respectively, the supply price elasticity is 0.54. This means that if price
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
increases by 1 percent, yield of coffee increases by 0.54 percent. The relationship
between price and yield of coffee is given in Figure 6.4. As p increases, the price
elasticity is getting smaller. This happens due to a declining marginal yield.
price
Yield
Ymax
Figure 6.4: Simulation of price and coffee yield
6.4. Variable Yield Model (VY model)
6.4.1. Model Structure
The model structure of the VY model is the same as the FY model presented in Chapter
4. The objective function, profit function and decision rule are unchanged. The VY
model as well as the VY-CC model in this chapter only investigate the optimal rules
with lagged price simulation and the quadratic CP ( CP
o
age
1
2
age2 ).
The only difference between the FY model and the VY model is the definition of the
yield and cost function. As presented in the FY model, yield and cost depends only on
the age of coffee trees and these functions derive from the Coffee Farm Survey data and
estimation of coffee experts. Figure 6.5 repeats the yield-age function used in the FY
model. However, in the VY model, the yield of coffee is a function of optimal
production cost and age of trees in which optimal cost is a function of coffee price as
shown in (6.2).
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
3000
yield (kg bean/ha)
2500
2000
1500
1000
500
0
0
5
10
15
20
25
-500
age of tree
Figure 6.5: Coffee yield by age of tree in FY model
However, there is a difference between the estimated yield function in Table 6.2 and
yield in Figure 6.5. Thus, to compare farmer’s behavior for optimizing profit in both
cases with and without short-run response, it is necessary to adjust the estimated yield
function to make it consistent with yield function in the FY model. The next section will
present the adjustment of the yield function used in the VY model. In addition, the
optimal cost in the VY model is a function of price.
6.4.2. Adjustment of Yield function
The estimated yield function from Agrocensus_2006 is different from the yield function
used for the FY model in Chapter 4. To compare farmer’s optimal decisions in the FY
model (where yield is only a function of age), and in the VY model (where yield is a
function of age and production cost), it is necessary to adjust the yield function so as to
give the same yield at mean level of input, while at the same time reflecting the shortrun response to prices. This means when the average production cost of coffee used in
the FY model is used in the yield function and for the VY model, yields should be
similar.
The adjustment changes the intercept term in the estimated yield function in Table 6.2
and fixing yield for trees of age 7 to 17 years at a constant level. The adjusted yield
function for coffee in the mature period is:
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
Ym
89
2.55*cos tpha 0.00043cos tpha2 62agemax
2
2.6agemax
(6.6)
where Ym denotes for yield at mature period; agemax is age at which coffee attains the
maximum yield and costpha stands for cost of production per hectare ($/ha). This
function describes yield of trees in the mature period only.
The yield of coffee in non-mature years is rescaled by yield in the mature period to
make yields in both cases (yield is constant at each age of coffee trees and yield is
function of production cost and age of coffee trees) consistent, and shows as follows:
If age of coffee trees is smaller than 3 years (age <3), yield of coffee trees is equal to
zero
If age coffee trees is greater than 2 and smaller than 7 (2<age<7),
Yield
Ym
age 2
5
If age of coffee trees is greater than 16 year old,
Yield
Ym
27 age
11
The yield function used in the FY model and the adjusted yield function in the VY
model are presented in Figure 6.6, for the case where the average production cost is
$930 per ha. They are very close to each other at all ages. In summary, the adjusted
yield function replicates the age-dependent yields based on expert judgment, while at
the same time incorporating the estimated impact of variable inputs.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
3000
2500
kg per ha
2000
1500
yield in optimal model
1000
Adjusted yield function
500
0
1
3
5
7
9
11
13
15
17
19
21
age of tree
Figure 6.6: Yield in the FY model and Adjusted Yield in the VY model at cost of
$930/ha
The adjusted yield function moves up and down based on production cost as shown in
Figure 6.7.
3500
3000
kg per ha
2500
2000
1500
Adjusted yield (Cost =930USD)
1000
Adjusted yield (Cost =600USD)
500
Adjusted yield (Cost =1200USD)
0
1
3
5
7
9
11
13
15
17
19
21
age of coffee tree
Figure 6.7: Yield variation at different production costs
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
6.4.3. Optimal Rule of the VY model
The optimal cutting and replanting rules are re-solved in the VY the model, given the
new opportunity for short run yield response. The optimal rule for the VY model is as
follows:
CP
= 0.14 - 0.029age+0.0034age2
(6.7)
RP
= 0.51 ($/kg)
(6.8)
(6.9)
Maximum ENPV = 14369 ($)
The optimal rule for the VY model, sketched in Figure 6.8
1.2
CP of VY Model
RP of VY Model
1
price ($/kg)
0.8
keep coffee
keep coffee
Replanting price
0.6
0.4
keep coffee
Cut and grow
maize
0.2
0
0
3
6
9
12
age of trees
15
18
21
Figure 6.8: Optimal cutting and replanting rules in the VY model
More importantly, the profit of farmers with a short-run response increases significantly
compared to the FY model. The maximum ENPV achieved by the VY model is
approximately $14380, an increase at over 50 percent compared to the maximum ENPV
in the FY model (see Table 6.3 and Figure 6.9).
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
Table 6.3: Comparison of optimal rule between FY and VY model
Models
Results
Unit
Cutting rule
CP =0.402 -0.05age +0.0036age2
$/kg
Replanting price
RP =0.74
$/kg
maximum ENPV
NPV =9226
$
VY model
Cutting rule
CP =0.14 - 0.029age+0.0034age2
$/kg
Replanting price
RP=0.51
$/kg
maximum ENPV
NPV=14369
$
FY model
1
CP of FY Model
CP of VY Model
RP of FY Model
RP of VY Model
coffee price ($/kg)
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
14
16
18
20
22
age of coffee trees
Figure 6.9: Optimal rules for FY model and VY model
As illustrated in Figure 6.9, the optimal replanting price in the VY model is only 0.51
($/kg), much smaller than that in the FY model (0.74 $/kg). In addition, the results from
the models show that in the FY model coffee farmers are more likely to cut than in the
VY model. However, the calculation of the percentage of farmers who really cut the
coffee when the optimal rule is invoked with our price simulation gives alternative
trends. The percentage of cutting cases in both models is not much different for trees
under 15 years old. However, with older trees, the percentage cutting coffee in the FY
model is much higher than in the VY model (see Figure 6.10). This implies the
difference in the cutting prices at low ages is not binding on behavior, but at higher ages
is.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
20
FY model
18
VY model
16
% cutting
14
12
10
8
6
4
2
0
0
2
4
6
8
10
12
14
16
18
20
22
age of coffee trees
Figure 6.10: Percentage of cases in which farmers cut coffee at optimal rule
The comparison between profit levels generated from the FY model and the VY model
may not be fully accurate, as the yield and cost in the FY model are not representative
for the average cost yield in the VY model. This is because the optimal variable input
costs, as solved within the VY model is much higher, and hence gives a higher yield,
than in the FY model (see Table 6.4). Thus, to see more clearly the change in benefit
gained by farmers with the short-run response, the FY model is re-solved for the
optimal rule, with the yield replaced by the higher average yield in the VY model. The
results of both models are presented in Table 6.5. Farmers in the FY model are still
more likely to cut than in the VY model. However, the replanting price is the same in
both. In addition, the maximum ENPV in the re-solved FY model is still much lower
than in the VY model. This shows that if farmers have the opportunity for a short-run
response of cost and yield to price, they can greatly improve their profit.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
Table 6.4: Average cost and yield from the VY model and the FY model
Age of
trees
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Average cost
from the VY
model
1440
800
296
592
877
1166
1466
1466
1474
1476
1471
1470
1465
1466
1469
1470
1344
1204
1074
940
808
672
Annual cost in
the FY model
1440
800
1015
824
929
929
929
929
929
929
929
929
929
929
929
929
929
929
929
929
613
613
Average yield
from the VY
model
0
0
987
1603
2102
2519
2870
2874
2886
2889
2882
2876
2867
2865
2871
2878
2743
2573
2403
2204
1989
1752
Yield in the
FY model
0
0
500
1200
1500
2000
2300
2500
2500
2500
2500
2500
2500
2500
2500
2300
2100
2000
1800
1600
1400
1200
Table 6.5: The results of FY model with average cost and yield from VY model
Models
Results
Unit
FY model with average cost and yield from VY model
Cutting rule
CP =0.3 -0.025age +0.0034age2
$/kg
Replanting price
RP =0.51
$/kg
maximum ENPV
NPV =10966
$
VY model
Cutting rule
CP =0.14 - 0.029age+0.0034age2
$/kg
Replanting price
RP=0.51
$/kg
maximum ENPV
NPV=14369
$
The next section will incorporate the short-run response in the FY-CC model which was
presented in Chapter 5 and investigate how the poor household’s decision changes.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
6.5. The Variable Yield – Cash Constraint Model (VY-CC model)
6.5.1. Model Structure
The structure of the VY-CC model is almost the same as the FY-CC model but the
coffee yield is replaced by the adjusted yield function as presented in Section 6.4.2 and
a small change in decision rules is introduced. The objective function is still the
maximum ENPV from land choice per poor farm size (5287 m2). The coffee yield
function in the VY-CC is the same as in the VY model. Similar to the VY model,
production cost of coffee in the VY-CC model is determined by the coffee price as
follows:
Coptimal
where
1
1 p
2p
(6.10)
1
2
=2.55 and
2
=0.00043
The yield is a function of production cost and age of coffee trees as presented in (6.6).
However, the production costs for the first two years of gestation period are not
dependent on price; they are estimated from Coffee Farm Survey 2007. This is the same
as the VY model.
There is a small change in decision rule in the VY-CC model compared to the FY-CC
model. With the FY-CC model, production cost is fixed for a given age so farmers keep
growing coffee if:
coffee price >min (CP,RP) and
Capitalt + Io>= Costt+1 + Minexpend
In the VY-CC model, only production costs for the first year coffee trees (replanting
price) and the second year are fixed. The production costs for older trees are a function
of output price. If prices are too low, farmers may not apply inputs for coffee
production. This means the variable cost for trees greater than 2 years can be zero.
However, this decision will affect the coffee output through the yield function. Thus, in
the VY-CC model when farmers are growing coffee, they will keep coffee if:
coffee price >min (CP,RP) and
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
Capitalt + Io>= Cost2 (if aget-1 =1) + Minexpend
where Io is other income of poor household, Cost2 is production cost of 2 year old
coffee trees, Minexpend is the minimum expenditure of household.
If farmers are growing maize or they want to replace old coffee trees (if coffee age is 22
year old), price and household budget must satisfy two conditions:
coffee price >= replanting price, and
Capitalt + Io>= replanting cost + Minexpend
The VY-CC only investigates the optimal rules using the lagged price simulation and
the quadratic fixed form of CP (i.e. CP
o
age
1
2
age2 )
6.5.2. Optimal Rule of the VY-CC model
Using the grid search method to solve the VY-CC model, the optimal rules are
identified as follows:
CP = 0.19 – 0.067age + 0.0044age2
(6.11)
RP = 0.59 ($/kg)
Optimal ENPV per poor farm size = 7086 ($)
The output from the VY-CC model shows significant changes compared to the FY-CC
model in Chapter 5. Model results indicate that poor coffee farmers with short-run
response in the VY-CC are much less likely to cut. Poor farmers with 4 year old to 11
year old coffee trees should not cut coffee even if price reduces to 0 ($/kg). A farmer
with trees over 12-year old is much more likely to cut. Model output also shows that
farmers should replant coffee when price reaches 0.59 ($/kg). The optimal cutting and
replanting rules for poor farmers with short-run response is illustrated in Figure 6.11. A
comparison of optimal rules between the FY-CC model and the VY-CC model is
presented in Figure 6.12. As shown in the figure, with the option of a short-run
response, poor coffee farmers replant much earlier and are much less likely to cut for
growing maize.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
1
0.9
CP of VY-CC Model
RP of VY-CC Model
0.8
keep growing coffee
price ($/kg)
0.7
replanting
price
0.6
0.5
0.4
keep growing coffee
0.3
0.2
cut and grow
maize
0.1
0
1
3
5
7
9
11
13
15
17
19
21
age of coffee trees
Figure 6.11: Optimal rule of the VY-CC model
1.6
price ($/kg)
1.4
1.2
CP of FY-CC model
RP of FY-CC Model
1
CP of VY-CC Model
RP of VY-CC Model
0.8
0.6
0.4
0.2
0
1
3
5
7
9
11
13
15
17
19
21
age of trees
Figure 6.12: A comparison of optimal rule between FY-CC and VY-CC model
The difference between the FY-CC model and the VY-CC model is shown clearly by
the percentage of cases in which farmers cut their coffee trees when optimal rules and
the cash constraint are invoked. As presented in Figure 6.13, the actual cutting
frequency in the FY-CC model is always higher than that in the VY-CC model,
especially for 2-year old trees. As shown in the FY-CC model, some farmers have to cut
their coffee trees because they cannot afford to keep coffee when the price goes down.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
According to the VY-CC model output, the percentage of farmers who cut their trees in
the first year remains high. The reason is the same as in the FY-CC model in which
farmers have to cut trees because of the cash constraint. This is shown clearly in Figure
6.14. Similar to the FY-CC model, the liquidity constraint is the main cause that force
farmers with young coffee trees to cut down. Meanwhile, farmers cut old trees when the
CP rule is invoked.
30
% cases optimal rule invoked
FY-CC model
25
VY-CC model
20
15
10
5
0
0
2
4
6
8
10
12
14
16
18
20
22
age of coffee tree
Figure 6.13: Percentage of cases in which farmers cut coffee at optimal rules
14
by CP
12
by cash constraint
% actual cut
10
8
6
4
2
0
1
3
5
7
9
11
13
15
17
19
21
age of coffee trees
Figure 6.14: Percentage of actual cut of the VY-CC model by cutting rule and by
cash constraint
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
Figure 6.15 compares maximum ENPV gained by farmers for different models with a
farm size of 5287m2. As is shown clearly in the figure, with the short-run response, poor
coffee farmers can get much higher income compared to the FY-CC model. The
maximum ENPV from the VY-CC model is 7086 ($/poor farm-size), much higher than
income from the FY-CC model in Chapter 5 (only $ 4375). However, due to the cash
constraint, poor farmers in the VY-CC model cannot optimize their decision, thus the
maximum ENPV in the VY-CC model is still lower than the ENPV in the VY model.
8000
7600
7086
ENPV-$/per poor farmsize
7000
6000
5000
4376
4000
3000
2000
1000
0
FY-CC model
VY-CC model
VY Model
Figure 6.15: Comparison of ENPV from different models at poor farm-size
The comparison between incomes from two models (FY-CC and VY-CC) is to some
extent incomplete because production cost and yield from the FY-CC model is not
compatible with those from the VY-CC model. Thus, to see the ENPV gained by poor
farmers from being able to utilize the short-run response, the FY-CC model is re-solved
and cost and yield are replaced by average cost and average yield from the VY-CC
model. The re-solved optimal rules of the FY-CC model with average cost and yield
from the VY-CC model are presented in (6.12). The model output shows the
improvement of maximum ENPV, but it is much lower than maximum ENPV from the
VY-CC model. Again, this result confirms the importance of short-run response and its
impact on coffee farmers’ decision.
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
CP = 0.38 - 0.026age + 0.0018age2
(6.12)
RP = 0.74 ($/kg)
Optimal ENPV at poor farm size=5323 ($)
6.6. Conclusion
This chapter investigates the coffee farmer’s decision when it is possible to change
yields in the short-run. By integrating the coffee yield function in the short-run into the
FY model and the FY-CC model, this chapter develops two corresponding models: the
VY model and the VY-CC model.
In general, in the presence of a short-run response, farmers in both the VY model and
the VY-CC model are much less like to cut as compared to the FY model and FY-CC
model. Farmers in the VY model seem never cut if the coffee trees are less than 11
years old.
With the short-run response, the actual cutting percentages in the VY-CC model at
optimal rules reduces significantly compared to the FY-CC model. The VY-CC model
shows that the poor farmers never cut when coffee trees are in 4-16 age groups. They
only cut in the early years of the cycle or when the trees are getting quite old. Similar to
the FY-CC model, farmers with young trees in the VY-CC model have to cut coffee
trees because of the liquidity constraint.
Furthermore, with the short-run response, farmers are more likely to replant coffee if
they are growing maize or having bare land. The VY model found that farmers should
replant when the price is $0.51 per kg. The optimal replanting price in the VY-CC
model is only $0.59 per kg of coffee, much lower than that in the FY-CC model ($1.4
per kg).
The short-run response of farmers improves the value of ENPV considerably. The
maximum ENPV from the VY model increases by over 50 percent compared to the
ENPV in the FY model. Similarly, the maximum ENPV of the VY-CC model is about
60 percent higher than that in the FY-CC model. The ENPV of the FY model and the
FY-CC model is changed when the yield and cost functions in these models are replaced
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Chapter 6. Short-run Response and Optimal Rules for Coffee Farmers in Vietnam
by the average cost and average yield from short-run response, however it does not
improve significantly.
In chapters 4, 5 and 6, different optimal models are developed to investigate the coffee
farmer’s decision in different scenarios. The following models are expanded from the
FY model. The objective and general structure of models are similar but the detail
functions and decision rules are quite different. Thus, it would give a much better
understanding when comparing and summarizing main ideas, structure and output of all
models. This will be done in next chapter.
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Chapter 7. Summary of the optimal models
CHAPTER 7. SUMMARY OF THE OPTIMAL MODELS
7.1. Introduction
In the three previous chapters (4, 5 and 6), four version of a simulation model were
developed to identify the optimal cutting and replanting rules for coffee farmers in
Vietnam. The four model version are:
Fixed yield optimal model (FY model)
Fixed yield optimal model with cash constraint (FY-CC model)
Variable yield optimal model (VY model), and
Variable yield optimal model with cash constraint (VY-CC model)
Latter models have a similar structure and specification to the FY model but with
additional constraints added to explore different aspects of the economic behavior of
coffee farmers. This chapter is a synthesis of the previous optimal model discussion to
compare results across the models.
The purpose of this chapter is to provide a synthesis of the results from these models,
and provide some interpretation as to their implications. Following the introductory
part, Section 7.2 will summarize the differences of objective, structure and particular
constraints among models. The change in farmer’s decision will be presented in Section
7.3.
7.2. Model Development
7.2.1. Objectives of Models
In general, all models aim to identify the cutting price (CP) and replanting price (RP)
for maximizing the expected net present value from “land use choice” (ENPV).
However, each model investigates the optimal rules in different contexts. The FY and
VY model identify the optimal rules to maximise ENPV per ha of farm land. The land
can be used to grow coffee or maize (as a substitute crop).
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Chapter 7. Summary of the optimal models
Similarly, the main objective of the FY-CC and the VY-CC model is to investigate the
change in the poor coffee farmer’s decision, when they face a cash constraint. These
latter models concern a household as a whole, and cover other aspects of a household
such as living expenditure, other income, loans and family labour. In addition, the farm
size in those models is fixed at an appropriate size (5287 m2). The aims and objective
function of the models are summarized in Table 7.1
Table 7.1: Main objective of models
Models
Core objective
FY model
Identifying the optimal CP and RP to maximise the ENPV for
1 ha of land
Objective function: maximum ENPV per ha
FY-CC model
Investigating the optimal CP and RP to maximise the ENPV
for poor coffee farmers in the presence of a cash constraint
Objective function: maximum ENPV per poor coffee farm (size
5287 m2)
VY model
Finding CP and RP to get the maximum ENPV with the
incorporation of short-run response in which coffee yield is a
function of production cost and tree age
Objective function: maximum ENPV per ha
VY-CC Model
Specifying the optimal cutting and replanting rule to maximise
ENPV for poor coffee farmers in the presence of a cash
constraint and short-run response
Objective function: maximum ENPV per poor coffee farm (size
5287 m2)
7.2.2. Rules and Constraints
The models apply the fixed form optimization approach to specify the cutting and
replanting prices for obtaining the maximum ENPV. The fixed form used for CP and
RP is as follows:
CP
o
RP
3
age
1
2
age2
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Chapter 7. Summary of the optimal models
To find CP and RP, models finally need to identify
o
,
1
,
2
and
3
.
Each model contains particular rules and constraints. In the FY and the FY-CC model,
coffee yield and production cost vary by age of tree, but cannot be altered by the
farmers. In FY model, coffee farmers are assumed to not have a cash constraint. Thus,
the cutting and replanting decision are only dependent on the price of coffee at which
farmers will cut coffee and switch to maize (as a substitute crop) if coffee price falls
below CP. They will decide to grow coffee again if price increase to RP (see Table 7.2).
The cutting and planting decision rules of the VY model are the same as the FY model.
The structure of the FC-CC and the VY-CC model are different from that of the FY and
the VY model. The FC-CC and the VY-CC model concern the farm as a household and
focus on the decision of the poor coffee household. Some additional equations are added
into these models such as living expenditure, family labour return, saving and credit.
However, coffee yield in the FY-CC model is the same as in the FY model: yield is
fixed at a given age of coffee trees. The decision of poor coffee households in the FYCC model and the VY-CC model depends on both the price and the cash availability of
the household. Decision rules can be presented as follows:
Keep growing coffee if (i) the price is greater than the CP and (ii) the household budget
(savings + borrowings + other income) can at least cover the minimum household
expenditure and production cost in the following year. Otherwise, they will switch to
maize.
Replant coffee if the price is greater than or equal to the RP and the budget of
households is greater than the sum of replanting cost and minimum household
expenditure.
Table 7.2 summarizes the decision rules and constraints in the four optimal models.
Table 7.2: Decision rules and constraints
Models
FY model
VY model
Relaxed constraints
o
o
o
o
Yield is fixed by age of coffee trees
yield =f(age);cost =f(age)
no cash constraint
decision rule: cut and replace with maize if price <CP otherwise
keep growing; and replant if price >=RP
o Yield is now a function of age and production cost
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Chapter 7. Summary of the optimal models
FY-CC model
VY-CC Model
o yield =f(age, production cost); cost =f(coffee price)
o no cash constraint
o decision rule: cut and replace with maize if price <CP otherwise
keep growing; and replanting if price >=RP
o include expenditure function, saving, other income, loan
o yield =f(age); cost =f(age) (as for FY model)
o New rule:
 keep coffee if price > CP and household’s budget >=
minimum household expenditure+ production cost in next
year. Otherwise, cut for maize.
 Replant coffee if (price >=RP) and (household’s budget>
replanting cost + minimum household expenditure)
o including expenditure function, saving, other income, loan
o yield =f(age, production cost);optimal cost =f(coffee price)
o rule:
 keep coffee if price > CP and household’s budget >=
minimum household expenditure+ production cost in next
year. Otherwise, cut for maize.
 replant coffee if (price >=RP) and (household’s budget>
replanting cost + minimum household expenditure
7.3. Changes in Coffee Farmer’s Decision
The main outputs of all models are summarized in Table 7.3. The maximum ENPV
from the VY model is highest with about $14370 per hectare (or equivalent to $7600
per poor farm size). This means that if coffee farmers are not restricted by a cash
constraint and input use is responsive to the output price, they can achieve the
maximum returns from investment in coffee and optimize their decision. The maximum
ENPV in the VY model is about 50 percent higher than in the FY model (see Figure
7.1). The difference reduces to 31 percent if the yield function in the FY model is
replaced by the average yield of the VY model.
Table 7.3: Main results of simulation models
Models
Main output
FY model
CP
= 0.402 - 0.0509age + 0.00367age2
RP
= 0.74 ($/kg of coffee bean)
ENPV = 9226 ($/ha) ~= 4878 ($/poor farm size)
VY model
CP
= 0.14 - 0.029age+0.0034age2
RP
= 0.51 ($/kg)
ENPV = 14369 ($/ha) ~=7600 ($/poor farm size)
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Chapter 7. Summary of the optimal models
FY-CC model
CP
= 0.458 -0.46age +0.00325age2
RP
= 1.4 ($/kg)
ENPV = 4375 ($/poor farm size)
CP = 0.19 – 0.067age + 0.0044age2
VY-CC Model
RP = 0.59 ($/kg)
ENPV = 7086 ($/poor farm size)
Note: poor farm size is 5287m2
100%
Expected NPV ($/poor farm size)
8000
92%
7000
6000
5000
64%
57%
4000
3000
2000
1000
0
FY model
FY-CC model
VY model
VY-CC model
Figure 7.1: Maximum ENPV achieved from models
The hypothesis behind the FY-CC and the VY-CC models is that in some cases farmer’s
efficiency may be altered by the cash constraint. They may have to cut earlier than the
original optimal point or they cannot replant because of the cash shortage. The results of
models are consistent with farmer’s expected behaviors. A comparison between the FY
and the FY-CC shows that farmers in the FY model are less likely to cut and they
replant earlier (see Figure 7.1 and Figure 7.2). Households represented by the FY-CC
model cannot achieve the oreginal optimal land use choice and earn less than those who
are represented by the FY model. The income of poor farmers reduces by 15 percent if
they follow the optimal decision of the non-poor farmers. However, despite the cash
constraint if coffee farmers adjust input use efficiently to coffee price, they can greatly
improve their income. This explains why the ENPV in the VY-CC is much higher than
in the FY-CC.
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Chapter 7. Summary of the optimal models
1.6
1.6
1.4
1.2
CP of FY model
CP of FY-CC model
1
RP of FY model
RP of FY-CC model
price ($/kg)
price ($/kg)
1.4
0.8
0.6
1.2
CP of FY-CC model
RP of FY-CC Model
1
CP of VY-CC Model
RP of VY-CC Model
0.8
0.6
0.4
0.4
0.2
0.2
0
0
1
0
5
10
15
3
5
7
9
11
13
15
17
19
21
20
age of trees
age of trees
Figure 7.2: Optimal cutting and replanting rules in different models
The effect of a cash constraint on farmer’s decision is expressed more clearly through
the actual cutting farmers in models when optimal rules are invoked. The cutting
frequency in the FY-CC is higher than that in the FY model, especially for young trees
and very old trees (see Figure 7.3). The cutting decision of poor coffee households is
influenced by both the optimal rules and cash constraint. This can also be seen in Figure
7.3 where the cutting percentage is affected by the combined impact of the CP rule and
the cash constraint. The result shows that cash problems have a significant effect on the
cutting decision of farmers with young trees.
30
30
by CP rules
FY model
25
FY-CC model
20
% actual cut
% actual cut
25
15
10
by cash constraint
20
FY-CC model
15
10
5
5
0
0
1
3
5
7
9
11
13
age of coffee trees
15
17
19
21
1
3
5
7
9
11
13
15
17
age of trees
Figure 7.3: Actual cutting percentage at optimal rules in FY and FY-CC model
The cutting percentage also changes if farmers have an efficient short-run response.
Figure 7.4 presents the cutting percentage at optimal rule in both the FY and the VY
models. There are two points to note in this figure. First, the optimal rule shows a
positive value of CP for all trees, but the real cutting percentage under the price
simulation in the FY and the VY models for young trees is very small. This means
152
19
21
Chapter 7. Summary of the optimal models
without cash problems, farmers mostly never cut if trees are less than 11 year old. In
addition, the actual cutting percentage under 15-year old trees is also quite small. This
pattern is almost the same for both the FY and the VY models. Secondly, the actual
cutting percentage in the VY model is generally smaller than in the FY model. The
actual cutting (%)
difference between models becomes significant for 17 year old and older trees.
20
18
16
14
12
10
8
6
4
2
0
FY model
VY model
0
2
4
6
8
10
12
14
16
18
20
22
age of trees
Figure 7.4: Cutting percentage at optimal rule in FY and VY model
The optimal replanting prices vary across different models. The replanting price reflects
the expected income earned by farmers from coffee production. According to model
output, farmers in the VY model decide to replant at a relatively low price of $0.51 per
kg. Due to the cash constraint, farmers in the VY-CC model wait for a higher price to
replant coffee trees and they grow coffee again at a price of $0.59 per kg (Figure 7.5).
The poor households in the FY-CC model optimize their decision to replant coffee at
$1.4 per kg. In this case, farmers do not have the response of input use to the output
price. In addition, their decision is constrained by a cash constraint so they wait until
there is a high price to reduce the chance of low future price occurring. This explains
why poor farmers without short-run response are much less likely to replant.
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Chapter 7. Summary of the optimal models
1.6
1.4
price ($/kg coffee bean)
1.4
1.2
1
0.8
0.74
0.59
0.6
0.51
0.4
0.2
0
The FY model
The FY-CC model
The VY model
The VY-CC model
Figure 7.5: Optimal replanting prices for different models
The optimal cutting and replanting prices for the fixed yield models in this study differ
from those of Luong and Loren (2006). Luong and Loren (2006) found that a farmer
would enter into coffee production when prices are above 1.04 $/kg and exit if the price
dropped below 0.32 $/kg. Hence, farmers without cash constraints in optimal models
replant earlier. An important improvement in decision analysis in this study compared
to the model by Luong and Loren (2006) is that, cutting prices in fixed form are a
function of the age of trees. It is not a fixed number for all coffee groups as presented in
Luong and Loren (2006).
7.4. Conclusion
The application of simulation models helps to understand the replanting and cutting
decisions of individual farmers. More clearly, the models identify at what price farmers
should cut their trees down and switch to other crops. In addition, the optimal models
point out when farmers should replant coffee if they currently have bare land or are
growing other crops.
One conclusion in all models is that coffee farmers optimized their decision at different
‘trigger’ prices for cutting and replanting. This asymmetric response of coffee
households may be reflected in an asymmetric response of coffee area at aggregate
levels to price changes. To test this hypothesis, the next chapter will analyze the supply
response of the aggregate coffee area.
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Chapter 8. Coffee Supply Response in Vietnam
CHAPTER 8. COFFEE SUPPLY RESPONSE IN VIETNAM
8.1. Introduction
The estimation of supply response functions could improve the understanding of the
price mechanism and the responsiveness of supply to price changes (Nerlove and
Bachman, 1960). Understanding supply responsiveness can assist policy makers in
achieving production targets in markets where price is considered as a policy tool. In
addition, estimated supply functions can be used for forecasting.
Estimating supply functions for perennial crops such as coffee is more complex than for
annual crops due to the time lags associated with the decision to increase production and
production capacity becoming available. Furthermore, supply decisions are a function
of expected cost and return over the whole life cycle of coffee trees. The input
requirements and yields of perennial crop vary as a function of tree age, implying that
annual production depends on the age composition of the tree stock. Furthermore, the
age composition of trees influences plantings and removals. The pioneering work of
Nerlove (1956) on supply response was concerned with annual crops (wheat, cotton and
corn). Nerlove’s model has been adopted by later authors to represent the supply
response of perennial crops.
From the output of the simulation models in previous chapters, it is optimal for different
farmers to cut and replant at different prices. The cutting/replanting gap may be
reflected in an asymmetric response of the coffee area at the aggregate level to price
changes.
This chapter investigates a supply function based on time series data to see if the
behaviour of farmers identified in previous chapters can be observed in the time series
data. The supply function is used to estimate short and long-run elasticities. The
function tests the hypothesis that the coffee supply in Vietnam shows an asymmetrical
price response, i.e. is relatively responsive to price rises but is unresponsive to price
falls.
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Chapter 8. Coffee Supply Response in Vietnam
Section 8.2 reviews previous methods and studies on supply response using time series
data. The application to coffee supply response in Vietnam is introduced in Section 8.3.
Some conclusions are highlighted in Section 8.4.
8.2. Literature Review on Supply Response Analysis using the
Econometric Approach
This section begins with standard models where supply response is symmetric or
reversible and then reviews studies of asymmetric supply responses.
The structural equation approach (Sadoulet and deJanvry, 1995) is based upon
production economics and the theory of the firm and includes primal approaches, based
around the production function and dual approaches using the profit function and the
cost function.
Alternatively, the reduced form supply function approach simply explains supply of a
commodity as a function of selected commodity prices, with relatively limited
constraints derived from theory. The Nerlovian model (Nerlove 1956b) is a reduced
form model and this approach will be applied here.
When looking at the crop supply response, researchers often study the area grown of a
crop, but not the output. For annual crops, the supply response model looks at the
change in area but for perennial crops such as coffee, the cutting and replanting area
should also be included. Thus, the area equation of perennial crops is identified as:
At
At
1
Nt
Rt
where At is crop area in year t, At
1
is the lagged area, N t is new planting area in year t
and Rt is the removal area in year t.
For perennial crops, the analysis of supply by decomposing the response into a response
for plantings and a response for removals would give understanding of the response to
price changes. However, time series data on new plantings or removals is often not
available, instead only an aggregate area is available.
.
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Chapter 8. Coffee Supply Response in Vietnam
8.2.1. Nerlovian Approach
Coffee is a perennial crop with a three to four year establishment period between initial
planting and the first harvest. Thus, when deciding to replant, coffee producers base
their decision on expected, not observed, prices. Because of the time lag in crop
production in general, modeling with expected prices has been an important
consideration in the analysis of crop supply response. The time lag in production means
that there is often a divergence between desired and actual output (Sadoulet and
deJanvry, 1995). To address these issues, a number of models have been developed in
the literature.
The Nerlovian model of crop supply response is formulated in terms of desired area,
yield and output. The generalized Nerlove’s model basically includes three equations
(Nerlove, 1956, Askari and Cummings, 1977, Sadoulet and deJanvry, 1995)
Atd
1
At
At
Pt e
Pt e1
Pt e
Pt
Pe
3
( Atd
At 1 ) vt ,......... 0
( Pt
Pt e1 ) wt
2 t
1
1
(1
1
Zt
(8.1)
ut
1
(8.2)
(8.3)
) Pt e1 wt
where At is the actual area under cultivation at time t , Atd is the area desired to be
under cultivation at the time t , Pt
is the actual price at time t , Pt e is the expected
prices at time t , Z t is the other exogenous factors affecting supply at the time t ,
and
γ are termed the expectation and adjustment coefficients, respectively, ut , vt and wt are
error terms.
In (8.1), desired area is a function of expected prices, own price and price of a
competing crop and other exogenous factors affecting supply (such as weather).
Equation (8.2) is a land adjustment equation. Full adjustment cannot be achieved in the
short run, thus the actual change between year t and t 1 is only a fraction ( ) of
desired adjustment. Equation (8.3) is an adaptive expectation price equation. Because
the expected price cannot be observed, the model expresses expected prices based on
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Chapter 8. Coffee Supply Response in Vietnam
actual/observed prices. This equation represents a price learning process where farmers
adjust their expectation as a fraction of the forecast error in the previous year.
Pt e and Atd are not observable, but by substituting Pt e and Atd from (8.2) and (8.3) into
(8.1), Pt e and Atd are eliminated and the reduced form of the area equation is:
At
1
2 t 1
P
3
) (1
)
)(1
)
At
1
4
At
2
5
Zt
6
Zt
1
et
(8.4)
where:
1
1
2
2
(1
3
4
(1
5
3
6
et
(1
3
vt
(1
)
)vt
ut
1
(1
1
There are six coefficients (
1
original equation system:
1
)ut
6
,
2
1
2
wt
) in the reduced form but only five parameters in the
,
3
, , . Hence, to get the unique solution for
parameters in original equation system, the following constraint has to be imposed on
the coefficients in the reduced form:
2
6
2
5
4
3
5
After estimating
0
6
1
6
from the reduced form, we can identify the parameters in the
original system.
2
(
3
1
4
2)
1
/(1
)
3
4
0
/
1
1
2
2
/
5
5
/
The general Nerlovian model described above has been applied in numerous crop
response studies (see Askari and Cumming (1977). Nerlove’s model has been modified
to represent livestock supply and perennial crops. Studies on the supply of perennial
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Chapter 8. Coffee Supply Response in Vietnam
crops are more common but are challenging due to the characteristics of perennial
crops, summarized by French and Matthews (1971) as follows:
(i) The long gestation period between initial input and first output or time of
establishment period
(ii) The extended period of output flowing from initial production or investment
(iii) The deterioration of plants over time
A supply response model for perennial crops has to explain not only the planting
process but also replanting and removal. Knapp (1987) also pointed out that perennial
crops pose additional challenges compared to annual crops because production extends
over several years. The planting decisions have to reflect expected costs and returns
over several years.
Despite the difficulties in studying supply response for perennial crops, a number of
researchers have used the Nerlovian model. One of the earlier applications of the
Nerlovian model to perennial crop supply response was Bateman (1965) who analyzed
the case of cocoa in Ghana. He assumed that the farmer’s objective was to maximise the
discounted value of the future stream of net returns from cocoa. The planting area of
cocoa was a function of its own expected real price and coffee price (as a substitute
crop) and the output was a function of yield. After taking the differences of output and
combining output and area equation, Bateman obtained the final reduced form function
in which output is a function of lagged prices of cocoa and coffee, rainfall, humidity and
lagged output. Similarly, Behrman (1968) applied a Nerlovian model to estimate the
supply function of cocoa for leading producing countries. In contrast to Bateman, he
started with an area function in which desired area is a function of expected cocoa price
and coffee price. After that, Behrman transformed this function to output function by
applying a yield factor. Similar to Bateman, by taking the first difference of output, the
change of cocoa output finally became a function of lagged cocoa price difference,
coffee price difference and the second and third difference of output.
Saylor (1974) applied Nerlovian equation systems to measure the supply elasticities of
coffee in Sao Paulo (Brazil). The data used in the model were coffee area in Sao Paulo
for the years 1947-1970 and farm-gate coffee price in the 1945-1969 period. In the
study, Saylor estimated several alternative models, with the main explanatory variables
being lagged price, lagged area, time trend and price index of 20 leading agricultural
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Chapter 8. Coffee Supply Response in Vietnam
31
commodities in Sao Paulo . Saylor pointed out that the Nerlove model could explain
most of the variation in coffee supply and found that the price elasticities are relatively
low for both short-run and long-run, with the long-run values (ranging from 0.5 to 0.73
depending on particular supply equations) much higher than the short-run (from 0.1 to
0.19).
8.2.2. Extended Nerlovian Approach
For perennial crops, removal and replanting are influenced by expected price and costs.
Replanting also allows new technology to be adopted. For these reasons, it is much
better for supply response analysis to explicitly represent planting and removal
decisions. Thus, to develop the Nerlovian model for analyzing total area response,
researchers have estimated new planting and removal equations. French and Bressler
(1962) used this approach to develop a supply model of lemons in California (USA) in
which they estimated new plantings and removals. Originating from the relationship in
which the acreage of new lemon trees depends on expected long run profitability, age
distribution and expected profitability of other activities, the authors tried to
approximate the relationship by a linear function of long-run profit expectation. The
profit expectation in this paper was calculated using five years of past net returns.
Similarly, tree removals were expressed as a function of expected current profit and
proportion of fruit bearing trees over 25 years. However, they found that the proportion
of fruit bearing trees over 25 years was insignificant due to its small variation during the
observed period, and expected profit did not give statistically significant results. Thus,
the estimate of the proportion of removals is simply the mean value of the ratio of
bearing acres divided by acres of trees removed.
To describe the characteristics of perennial asparagus crops, French and Matthews
(1971) provided a model of supply response with 5 major components: (1) functions
explaining quantity of production and crop bearing acreage desired by growers; (2) a
new plantings function, (3) removed acreage each year (4) relationships between
unobservable expectation variables and observable variables and (5) an equation
explaining variation in average yield. However, because of data constraints, they tried to
simplify their model by constructing an equation system to express those relationships
based on the expected profit function with explanatory variables such as price, a wage
index and a supply equation. The expected profit is:
31
This variable attempts to see whether the price of competing activities influence coffee area.
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Chapter 8. Coffee Supply Response in Vietnam
e
c0 c1 ( P / M )e u
e
where
denotes expected profit, P is grower price, W is wage rate. The e means an
expected value.
The supply function consists of change of acreage (At-At-1) and a number of independent
variables such as previous acreage and (P/M) ratio and dummy variables32. This
equation was estimated by the Ordinary Least of Square method (OLS). However, the
estimated coefficients could not be used to recover the structural parameters because the
model was under-identified. Thus, the effect of harvest and investment decisions could
not be measured separately.
8.2.3. Wicken - Greenfield Approach
Wicken and Greenfield (1973) criticized the Nerlovian model, because the model fails
to distinguish between the investment decision regarding the stock of trees and the
harvesting decision. Thus, they have attempted to develop a vintage production,
investment and supply response model for the coffee crop in Brazil. Their structural
equations are:
q
n
P
t
It
I ,
i t i
i 0
ao
a1I t-1
0
P
1qt
a 2 Pt
m
qt
P
qt
i 2 t i
1
i 0
where qtP is the potential output, qt is the actual output, I t denotes investment and Pt is
producer price.
Wicken and Greenfield obtained the reduced form of supply in which output is a
function of the distributed lag of price and area as follows:
m
qt
P
i t i
(
1
)qt
1
q
1 t 2
cons
(8.5)
i 0
Where:
32
See more detail in French and Matthews (1971).
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Chapter 8. Coffee Supply Response in Vietnam
i
2
i
i 2
2 1 0
i
a2
1 m 1
i
a2
1 i
cons
i=0
2 1 0
1 t 1
1 m 1
i = 1,…m
i = m+1
i=m+2,…..n.
is the constant term
The Wicken-Greenfield model has been applied to a number of crops. Dowling (1979)
used the Almon Lag model to analyze of the supply response of rubber in Thailand.
Hartley et al (1987) looked at a similar supply response of rubber in Sri Lanka. In their
models, new planting was a negligible component of total area so the researchers
focused on modeling the uprooting and replanting decision. Both authors conclude that
the relationship between production and the stock of trees was considerably more
complex than specified by the Wickens-Greenfield model. After estimating removal,
supply and new planting equations, they conclude that the Wicken-Greenfield model is
not appropriate for the rubber sector in Sri Lanka. Some coefficients in the estimated
equations had wrong signs: price was estimated to have a significant negative effect on
new planting, and the wage is significantly positive.
Akiyama and Trivedi (1987), provide an extended critique of the Wicken-Greenfield
approach. First, the model is over-identified. Second, it is difficult to add non-price
variables in the planting equation (because they appear as a distributed lag in the
reduced form). Akiyama and Trivedi (1987) developed a Vintage production model for
perennial crops and applied this to the tea sector in three countries (India, Sri Lanka and
Kenya). This model included new plantings, supply, replanting and uprooting based on
different explanatory variables such as moving average price, capacity for new
plantings, extension service (for India), expenditure per hectare for extension and
service, new plantings, real price (for Kenya), and tea production cost, tea price, new
plantings and uprootings, and a replanting subsidy (for Sri Lanka).
Akiyama and Trivedi’s vintage production model requires reliable time-series data for
production, area planted and credit availability. For many countries, these data are not
available. Furthermore, econometric models of commodity markets are valid only when
the relationships among variables are stable over time without any significant structural
changes. These are also problems raised by Nerlove (1979). According to Nerlove
(1979), there are four main problems when studying supply response for perennial crops
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Chapter 8. Coffee Supply Response in Vietnam
in developing countries using time series data. First, time series data needs to be
available, especially new planting data and current age structure data. Second,
government intervention is wide-spread and affects the supply response. Third, there is
frequently an imperfect relationship between output and stock of the perennial crop. The
depletion of stock varies not only because of cutting but also because of weather and
disease. Fourth, technical change (new varieties) produces an additional element of
uncertainty.
8.2.4. Price Asymmetric Response
When estimating the response of supply to price, the standard approach is to assume
that supply responds symmetrically to price increases and decreases. Based on Deaton
and Laroque (2003), Olsen (2005) built a model for world coffee supply response and
showed that the supply response is asymmetric. In particular, supply responds to price
increases but is unresponsive to price decreases. There is even some evidence of a
perverse supply response where decreasing prices may cause coffee farmers to increase
production. Olsen (2005) explains these findings by farmers being able to survive
through subsistence crops while they wait for the coffee price to increase; and a lack of
alternative income sources. Olsen (2005), proposes that the existence of a “fixed asset”
causes an asymmetric supply response. Low salvage values cause producers to continue
production even though prices are low because the acquisition costs are high.
A method for studying asymmetric supply response was introduced by Tweeten and
Quance (1969) when looking at crop and livestock supply in the United States. They
analyzed the supply response to price change by splitting the price variable into two
variables one each for price increases and price decreases, thus:
Qt
0
1
pt
t
pt
(8.6)
in which
p1
pt
p2
1, otherwise 0
p1
p
pt , if t 1, otherwise 0
pt 1
p1 , if
pt
pt , if pt
0 and
pt
0 , if pt
pt
However, according to Wolffram (1971), the price split by Tweeten and Quance causes
incorrect solutions for irreversible supply reaction and differentiation of partial
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Chapter 8. Coffee Supply Response in Vietnam
influence because the supply in Tweeten and Quance’s method cannot reflect by change
of price (decrease or reduce). Thus, Wolffram splits the price series by using price
differences. According to Wolffarm’s method the supply function can be estimated by:
Qt
0
WRt
1
(8.7)
WFt
2
Where WRt is the sum of all period to period increases in expected price from its initial
value up to period t and WFt is the sum of period to period decreases. Mathematically,
the split price series can be expressed as follows:
WR1
p1;
WRt
WRt
1
WF1
p1;
WFt
WFt
1
α =1 if p t -p t-1
( pt
(1
pt 1 )
)( pt
pt 1 )
0, else=0
Houck (1977) modified Wolffram’s approach by cumulating positive and negative first
differences, beginning with zero and not with the actual first observation. Furthermore,
to focus on the identification of starting points and measurement through levels, Houck
(1977) changed the dependent variable to Qt – Q0, where Q0 is quantity in the first
period. Traill et al (1978) criticized the Wolffram function because it implies that for
given starting and finishing prices, the greater are price changes in intermediate periods,
the larger is output at the end of the period. However, in practice highly variable prices
would lead to an output reduction due to risk concerns. Traill et al (1978) pointed out
that the response of supply to price will only become elastic once it has risen beyond the
previous maximum price. Thus, Traill et al (1978) modified Wolffram’s method so that
when the price increases but remains below the previous maximum level, price change
is added to the price fall series (modified Wolffram fall – MWF ) rather than to the price
rise series (modified Wolffram rise – MWR ). Following Wolffram’s model, the
modified Wolffram supply equation is
Qt
0
1
MWRt
2
MWFt
(8.8)
The responses of supply to price changes in both models Wolffram and Modified
Wolffram are presented in Figure 8.1. It should be noted that the coefficient of MWRt
no longer presents the response of output to every price rise, but the response to price
increase beyond the previous maximum.
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Chapter 8. Coffee Supply Response in Vietnam
Figure 8.1: Hypothetical response overtime of Wolffram model and Modified
Wolffram model
Source: Traill et al (1978)
Traill et al (1978) point out that using the maximum price in all previous periods to
specify rise and fall price series may cause the “eternal asset” problem. The method of
splitting the price data are only relevant in the short-run, as in the long-run depreciation
of crop specific assets will erode the asset fixity. However, when generating the
maximum price empirically, there is no historical limit because price has to rise above
its previous maximum before there is an elastic response. This implies that, once
bought, the asset exists eternally. This specification will cause estimation problems if
there is a high price early in the series that is not surpassed and the price rise effectively
becomes a constant. To overcome this difficulty, Burton (1988) suggested using the
“window” technique. This technique defines the previous maximum price as the
maximum level occurring in only n previous years, not all previous years and n is
determined empirically. This method ensures that at some point historically high levels
of investment cease to have an effect on current output decision. With the window
technique, the price difference can be expressed as:
pt
ptmax,n
n
ptmax,
1
if ptmax,n
max, n
t
pt
p
n
ptmax,
1
(8.9)
otherwise
And
pt
pt
ptmax,n
if ptmax,n
0
n
ptmax,
1
(8.10)
otherwise
Where
ptmax,n
max pt , pt 1 ,
, pt
n
In addition, Burton (1988) indicated that the introduction of a dynamic response makes
the price partitioning method used in the modified Wolffram technique invalid, as a
peak in the price series can only specify a maximum desired asset level, and not
necessarily the capital assets held on the farm. Thus, the modified Wolffram technique
should not be used in conjunction with a distributed lag on the price, as it produces
165
Chapter 8. Coffee Supply Response in Vietnam
incorrect signals of excess capacity. In addition, Burton suggested a new model based
on partial adjustment with a comparison between desired output and maximum level
output in previous periods. The model is:
St*
P
3
St
St
Stadj
(8.11)
4 t
1
2
Stmax
(Stadj
(1
St 1 )
1
(8.12)
D)(St* Stmax )
(8.13)
where St* is the desired output at time t, Pt is the price at time t, St is the output level at
time t, Stmax is the maximum level in n previous period. Stadj denotes adjusted desired
output, Dt is dummy variable taking a value of 1 if St* < Stmax and 0 otherwise.
By substituting (8.11) and (8.13) into (8.12), the supply response function is given as:
St
2
3
P (1
2
4 t
2
)St
1
2
1
Dt (Stmax
3
(8.14)
P)
4 t
Granger and Lee (1989) introduce an alternative approach using the error term. This
model is called the Error Correction Model (ECM) and instead of partitioning price, the
ECM splits the error correction term ut
1
into ut
max(ut 1 , 0) and ut
1
1
min(ut 1 ,0) .
The error correction term ( ut 1 ) is derived from the regression:
yt
ut
x
0
1
yt
1
(8.15)
ut
1 t
(8.16)
x
0
1 t 1
The reduced structure of an asymmetric error correction model is given by:
yt
0
1
xt
u
2 t 1
u
3 t 1
4
yt
1
5
xt
1
(8.17)
However, according to Wolffram (2005b), the asymmetric relations cannot be estimated
with positive and negative component of the split error correction term ( ut 1 ) from the
ECM proposed by Granger and Lee (1989). The reason is that the sign-separation of
ut 1 based on its sign does not correspond with asymmetry changes in yt 1 . Besides,
Wolffram (2005b) criticizes the symmetric as well as asymmetric ECM proposed as not
completely specified if the x-variable with level data and the time lag t-1, on which the
co-integrating regression is based, is not included in the function. Neglecting these
166
Chapter 8. Coffee Supply Response in Vietnam
variables causes the parameters to be biased. Alternatively, Wolffram (2005b) suggests
the calculation of error correction terms for yt 1 and yt
1
derived from yt 1 enabling the
quantification of asymmetric relations within ECM. The yt
1
and yt
1
variables are
given as
yt 1 = yt 1 if yt
1
yt
2
0
yt 1 = yt 1 if yt
1
yt
2
0
until
yt
1
yt
2
0
until
yt
1
yt
2
0
, otherwise 0
, otherwise 0
Thus,
yt
1
yt
yt
1
(8.18)
1
According to the calculation of error correction term ut 1 , the following co-integrating
relations are defined for the yt 1 and yt 1 as:
yt
1
a0
ut new
1
yt
a1 xt
1
1
a0
(8.19)
ut new
1
a1 xt
(8.20)
1
Similarly
yt
1
a0
ut new
1
yt
a1 xt
1
a0
1
Substitute yt
1
(8.21)
ut new
1
a1 xt
and yt
(8.22)
1
1
from (8.19) and (8.21) to (8.18), the transformed equation is
given as:
yt
1
a0
a1 xt
1
ut new
a0
1
a1 xt
1
ut new
1
(8.23)
This is similar to the Granger and Lee approach but with a different error correction
term. The difference between the two approaches is clarified by Wolffram (2005a)
when he applied different methods to analyze price transmission between a wholesale
price for pork in north-western Germany and the producer price.
8.2.5. Previous Studies on Supply Response of Coffee in Vietnam
167
Chapter 8. Coffee Supply Response in Vietnam
To date there have been only few econometric analyses of the supply response of coffee
in Vietnam. Ha and Shively (2008) used multinomial logistic regression model to
examine the responses to a drop in producer coffee prices of smallholder coffee farms in
the Central Highlands. They found that farmers responded to price drop by different
ways: no response, reductions in use of purchased inputs, changes in land use, and
responses aimed at enhancing liquidity through off-farm work or borrowing.
Tien (2006) analysed supply response in the Central Highland region and concluded that
the Nerlovian model was the best representation. The estimated supply equation for the
Central Highland region is:
ln At
1.3 0.28Pt
1
0.91At
1
where At is area of coffee in year t, and Pt the farm gate price in year t.
However, due to data limitations, Tien only used a time series data for one region in
Vietnam from 1990 to 2004, so the number of observation is very small.
The other study to estimate the supply function of coffee was prepared by EDEIPSARD (2007). This study estimates the coffee supply function to forecast supply. The
study used time series data for five main coffee producing provinces (Dak Lak, Kon
Tum, Gia Lai, Lam Dong and Dong Nai) and “all other” provinces in Vietnam over 20
years (1986-2005). The area model was given as:
ln( At At 1 )
2.12 0.69ET
0.17Pt 0.13Pt
where At is area of coffee in year t; At
1
2
is lagged area; Pt is the real FOB price of
coffee in year t; and E T is the exponential trend.
This model has a high level of fit and estimates are statistically significant. However,
the exponential trend term forces a trend on the data.
More importantly, both studies (Tien 2006; EDE-IPSARD 2007) assumed that supply
response of coffee area was symmetric. The following section provides an empirical
study on the supply response of coffee in Vietnam. Both reversible and irreversible
supply response of coffee will be analyzed.
168
Chapter 8. Coffee Supply Response in Vietnam
8.3. Empirical Model of Coffee Supply Response in Vietnam
8.3.1. Data
Table 8.1 gives the data used in this chapter. Coffee production data are collected by
General Statistical Office of Vietnam (GSO). Data on prices (coffee and fertilizer) are
from Ministry of Agriculture and Rural Development (MARD) and Institute of Policy
and Strategy for Agriculture and Rural Development (IPSARD).
Table 8.1: Data series and source
Data series
Time
Source
National coffee area & production
Coffee area & production in Dak Lak province
Coffee area & production in Gia Lai province
Coffee area & production in Lam Dong province
Coffee area & production in Kon Tum province
Coffee area & production in Dong Nai province
Coffee area & production in other provinces
FOB coffee price
Domestic urea price
National consumer price index
Agricultural land by provinces
US_CPI
1985 - 2006
1985 - 2006
1985 - 2006
1985 - 2006
1985 - 2006
1985 - 2006
1985 - 2006
1986 - 2006
1986 - 2006
1986 - 2006
1986 - 2006
1986 - 2006
GSO
GSO
GSO
GSO
GSO
GSO
GSO
MARD-IPSARD
MARD-IPSARD
GSO
GSO
World Bank
Source: Author’s summary
8.3.2. Model Results
The supply function for coffee in Vietnam is estimated in logarithmic form with the
logarithm of coffee area as the dependent variable. The use of the logarithmic form can
help to infer directly the impact of explanatory variables on coffee area as estimated
coefficients are elasticities. Several approaches reviewed in the previous section are
applied to investigate whether coffee supply response to price is symmetric (reversible
supply) or asymmetric (irreversible supply).
Because the replanting time series data in Vietnam is unavailable, application of models
with replanting area cannot be used. Instead, area is used. To analyze the coffee supply
response in Vietnam, a ‘mother’ model (or full model) which nests potential different
models, including Nerlovian, Burton and Modified Wolffram/or Wolffram models is
developed. This ‘mother’ model for coffee supply is:
169
Chapter 8. Coffee Supply Response in Vietnam
St
a3
a4 MWRt
a6 MWFt
a1 Dt ( S max t
a3
a5YMAt
a4 Pt
a2 St
1
a7 St
a5YMAt )
(8.24)
2
i
Di
where St denotes logarithm of coffee area in year t . MWRt and MWFt are log of price
rise and log of price fall in Modified Wolffram model. YMAt is the yield of mature
coffee area in year t . Stmax is maximum logarithm of coffee area in a window of length
n years. In the empirical model of supply response in Vietnam, the maximum coffee
area is defined as area in previous years. However, Stmax can be imposed by different
lengths n . Dt is a dummy variable and equal to 1 if S max t
a3 a4 Pt a5YMA and 0
otherwise. Dt shows the impact of the difference between the maximum area and the
desired area on variation of coffee area. Di is the provincial dummy variable. Note that,
this `mother’ model is not consistent with any individual model, but it provides a basis
for comparing alternative specifications, which can be identified by parameter
restrictions.
In this model, yield of mature area (YMA) is added into the area response model. The
YMA is a measure of yield per hectare corrected for the area of immature trees. It is
measured by the ratio of coffee output and equivalent mature area (EMA). The coffee
tree achieves mature yield (maximum yield) from 8th year to 16th year. Thus, the mature
area equivalent for other coffee groups out of 8-16 age groups is calculated as follows:
EMAa
Ya
Areaa
Ym
where Ya and Areaa are the yield and area of coffee at age a; Ym is yield at mature age.
This ‘mother’ model in (8.24) can be restricted down to the Nerlovian model, Burton
model, Modified Wolffram model. The ‘mother’ model becomes the Nerlovian model
by imposing a4
St
a3
a6 and a1 =0. In this case, model is given as:
a4 MWRt
a4 MWFt
The Burton model occurs if a4
a5YMAt
a2 St
1
a7 St
2
i
Di
(8.25)
a6 and a7 =0. The expression of the Burton model is
now:
170
Chapter 8. Coffee Supply Response in Vietnam
St
a3
a4 MWRt
a1 Dt ( S
max
a4 MWFt
a3
t
a4 Pt
a5YMAt
a2 St
a5YMAt )
(8.26)
1
i Di
The case of a1 =0, the full model becomes the Modified Wolffarm model. In this case,
the model is:
St
a3
a4 MWRt
a6 MWFt
a5YMAt
a2 St
1
a7 St
2
i
Di
(8.27)
The Wolffram model has the same form to the Modified Wolffram model, except that
the price rise and fall by Modified Wolffarm model presented in (8.8) are replaced by
price rise and price fall in (8.7)
The estimation of different models is tested by non-linear regression. The procedure for
estimating the full models includes several steps.
Step 1: Defining n. Defining the window length determines the relevant maximum area
in that period,
Step 2: Estimating the function St
value St*
a3 a4 Pt
a3 a4 Pt
a5YMAt
et and predicting the fitted
a5YMAt from the regression
Step 3: Generating dummy variable Dt . D takes 0 value if St* <St-1, otherwise D is
equal to 1
Step 4: Running the full model using non-linear regression method:
St
a3
a4 MWRt
a1 Dt ( S
a6 MWFt
max
t
a3
a5YMAt
a4 Pt
Step 5: Substituting the new value of
St
a3
a4 Pt
a5YMAt
a2 St
1
a5YMAt )
a7 St
i
2
Di
ut
a3 a4
a
,
and 5 from Step 4 into fitted equation
*
to get new value of St
a3 a4 Pt
a5YMAt
Step 6: Calculating Dt again and substituting it into the equation
St
a3
a4 MWRt
a1 Dt ( S
a6 MWFt
max
t
a3
a5YMAt
a4 Pt
a2 St
a5YMAt )
1
a7 St
i
Di
2
ut
171
Chapter 8. Coffee Supply Response in Vietnam
and run this regression again
Step 7: Iterating the steps above until
a3 a4 a5
, ,
and
i
converge
The procedure for estimating other models are the same as for the full model. However,
some parameters in the full model are restricted in particular models.
The estimated results of different models are presented in Table 8.2
Table 8.2: Estimated results from different models
Variable
names
‘Mother’
Nerlovian Burton
Wolffram
Parameters
model
model
Model
model
Constant
/a3
1.00*
-0.31
-0.18
0.97*
Price
rise
/a4
1.06*
0.23*
0.14**
0.35*
Price fall
/a6
0.17*
0.23*
0.14**
0.13*
Yield
/a5
0.20*
0.12*
0.05
0.23*
Lag(1)
/a2
0.73*
1.02*
1.04
0.87*
Asy. Adjb
/a1
0.03
---0.02
---Lag (2)
/a7
0.2
0.04
------/D2
Gia Lai
0.21
-0.04
-0.02
0.20*
/D3
Dak Lak
0.41
-0.15
-0.09
0.42*
/D4
Lam Dong
0.29
-0.09
-0.05
0.29*
/D5
Dong Nai
0.14
-0.13***
-0.08
0.17**
Other
/D6
0.18
-0.07
-0.04
0.19*
2
Adjusted R
0.99
0.98
0.98
0.98
P_value of autocorrelationc
0.013
0.01
0.01
0.01
2
Adjusted R
0.99
0.98
0.98
0.98
Note: *significant at 1%; ** significant at 5%; *** significant at 10%
a
Modified
Wolffram
modela
1.58*
0.87*
0.21*
0.12*
0.84*
------0.26*
0.45*
0.34*
0.12**
0.27*
0.99
0.06
0.99
with window length of 6 years; b asymmetric adjustment
c
: autocorrelation test for panel time series data using Wooldridge test. H0: no first order
autocorrelation
The ‘mother’ model results show that the estimate of a1 is not significant. This means
that the asymmetry variable can be dropped from the model. Similarly, the estimate of
a7 is not significant as well. This indicates the area lagged by two years does not affect
to the current coffee area in the full model.
The results of the Nerlovian model and the Burton model violate economic theory with
the estimates of a2 in both Nerlovian (1.02) and Burton models (1.04) being greater
than 1. This means that the current area of coffee will increase continuously holding
172
Chapter 8. Coffee Supply Response in Vietnam
other variables constant. In addition, the Burton model does not show the impact of area
adjustment to the previous maximum because the estimate of a1 is not significant.
The results of the Wolffram model and Modified Wolffram model (with window length
of six years33) indicates statistically significant estimates. According to the Wolffram
model, if price increases by one percent, the coffee area will increase correspondingly
by 0.35 percent. However, coffee area reduces only 0.13 percent in response to a one
percent reduction of output price. However, as mentioned earlier, the Wolffram model
is not consistent with economic theory. In addition, the regression results indicate the
autocorrelation problem.
The modified Wolffram model with window length of six years gives the best estimate.
The difference between price rise and fall coefficients in the Modified Wolffram model
is positive. The response to a price rise (with coefficient of 0.87) above the previous
maximum is about five times as large as the response to price fall (coefficient of 0.21
only). The Modified Wolffram model does not have autocorrelation problems.
The t-test proves that the difference between coffee acreage responses to a price rise
against a price fall is statistically significant34. All coefficients of the provincial dummy
variables are also different from zero and statistically significant with confidence level
of 10 percent. Given differences in size of the provinces, this is not surprising.
However, the response of coffee area to price rises and falls and to the lagged dependent
variables may or may not be the same. To test the hypothesis of the same response to
price as well as lagged dependent variables, we run unrestricted Modified-Wolffram
model in which provincial dummy variables are included in the Modified-Wolffram
equation with window length of 6 years for all independent variables. The results of this
model are presented in Table 8.3 and shows that coffee acreage responses to price rise
are not different among provinces while there is a significant difference of response to
price fall between Dak Lak and Lam Dong with Kon Tum.
33
Ihe study also estimated coefficients in the Modified Wolffram model with different window lengths.
The model with window length of six years gave the best estimates. The results of other Modified
Wolffram models are presented in Table C1 in the Appendix C.
34
To test the difference, author uses the “test” command in STATA after regression
test mwr =mwf
( 1) mwr- mwf = 0
F( 1, 115) = 36.05
Prob > F = 0.0000
With Prob>F =0.00, it strongly indicates the significant difference between the coefficients of price rise
and price fall.
173
Chapter 8. Coffee Supply Response in Vietnam
Table 8.3: Results for testing the difference of coefficients among provinces,
Modified Wolfram model with window=6
Independent variables
Coefficients
Constant
0.45
Constant dummy vars.
Gia Lai
2.54
Dak Lak
2.86
Lam Dong
3.73
Dong Nai
1.61
Other
1.03
Lnareat-1
0.99
Lnareat-1 dummy vars.
Gia Lai
-0.30
Dak Lak
-0.28
Lam Dong
-0.40
Dong Nai
-0.18
Other
-0.12
lnYMA
0.08
lnYMA dummy vars.
Gia Lai
0.03
Dak Lak
0.07
Lam Dong
-0.01
Dong Nai
0.05
Other
-0.02
MWR (n=6)
1.03
MWR dummy vars.
Gia Lai
0.60
Dak Lak
-0.22
Lam Dong
0.96
Dong Nai
-0.38
Other
-0.42
MWF (n=6)
0.37
MWF dummy vars.
Gia Lai
-0.26
Dak Lak
-0.32
Lam Dong
-0.30
Dong Nai
-0.17
Other
-0.21
R2
98.7
Prob > F
Note: In the regression, Kontum is the reference province
P-value
0.74
0.14
0.18
0.05
0.37
0.54
0.00
0.16
0.22
0.07
0.38
0.56
0.47
0.81
0.65
0.95
0.70
0.87
0.00
0.27
0.67
0.07
0.37
0.36
0.00
0.12
0.04
0.05
0.22
0.16
0.00
A general F-statistic is calculated to test the overall significance of this unrestricted
Modified-Wolffram model and the restricted Modified-Wolffram model (as its results
are presented in Table 8.2). The general F-statistic is given by
F
( SSER SSEU ) / J
SSEU / (T K )
174
Chapter 8. Coffee Supply Response in Vietnam
where J is the number of hypotheses, T
K is denominator degrees of freedom, SSER
is the restricted sum of squared errors, SSEU is the unrestricted sum of squared errors.
From regression results of both models, the F-test statistic value is only 1.07, smaller
than F critical value (F(20,84) ~=1.7). This concludes that the overall significance of
restricted Modified-Wolffram model is not statistically different from the unrestricted
one.
The elasticities of coffee area with respect to price fall and rise are summarized in Table
8.4 for three models. The estimates of short-run elasticities to a price fall produced by
the three models are not much different. In contrast, the estimates for short-run
elasticities with respect to price increases are quite different, increasing from the
Wolffram model (0.35) to the full model (1.06).
Table 8.4: Elasticities of coffee acreage to price
Model
‘mother’ model
Wolffram
Modified Wolffram (n=6)
Short-run price elasticities
Long-run price elasticities
Price fall
Price rise
Price fall
Price rise
0.17
0.13
0.21
1.06
0.35
0.87
3.9
2.7
5.4
3.9
2.7
5.4
Source: Summary from regression results
From previous discussion, it was concluded that the Modified Wolffram (n=6) is the
best choice of the three approaches for analyzing the asymmetric response of coffee
area in Vietnam in 1985-2006. The model is consistent with economic theory and
produces very high goodness of fit and statistically significant levels. Figure 8.2
presents the fitted and actual coffee area by provinces and it shows that the fitted value
and actual area are very similar in all provinces.
175
80000
15000
Chapter 8. Coffee Supply Response in Vietnam
Gia Lai province
0
0
20000
5000
40000
10000
60000
Kon Tum province
1985
1990
1995
year
2005
1985
1990
fitted value
1995
year
actual area
150000
300000
actual area
2000
2005
2000
2005
2000
2005
fitted value
Lam Dong province
0
0
100000
50000
200000
100000
Dak Lak province
2000
1985
1990
1995
year
2000
1985
2005
1990
1995
year
actual area
fitted value
fitted value
50000
80000
actual area
Dong Nai province
0
10000
20000
20000
30000
40000
40000
60000
other provinces
1985
1990
1995
year
2000
2005
1985
1990
1995
year
actual area
actual area
fitted value
fitted value
Figure 8.2: Fitted and actual area from Modified Wolffram model (ha)
176
Chapter 8. Coffee Supply Response in Vietnam
8.4. Conclusion
Studies of supply response play an important role for farmers and policy makers. They
can help farmers use their resource more efficiently. More importantly, the
understanding of supply response can support policy-makers to allocate production
resources and achieve targets. In addition, the supply response equation is useful in
forecasting future supply. However, studies on coffee supply response in Vietnam are
still limited and all of them have assumed a symmetric response when estimating the
coffee supply function.
This chapter uses the “positive approach” to estimate the supply response of coffee in
Vietnam. Both symmetric and asymmetric responses of coffee area in Vietnam are
estimated with different econometric models.
The Nerlovian model with reversible supply response was tested but it had the nonstationary problem. The estimates are not statistically significant. The symmetric model
cannot explain the variation of coffee area in Vietnam in the past.
Application of the Wolffram model and the Modified Wolffram model investigated
whether the coffee area in Vietnam has responded asymmetrically. The Modified
Wolffram model with window length of six years gave the best estimate. The output of
the model shows that if the price rises by one percent, the coffee area will increase by
0.87 percent, while if the price falls by one percent, the coffee area reduces by only 0.21
percent. However, the elasticity of price is much larger in the long-run (5.4). The
results of testing the overall significance of the model indicate that the response of
coffee area is not different among provinces. The estimated model of coffee predicts an
appropriate value for all provinces.
The optimal models in previous chapters provide insights into individual farmer’s
decisions, especially replanting and cutting decisions. The output of optimal models
showed that individual farmers decide to cut and replant at different “trigger” prices.
This cutting/replanting gap in farmer’s decision explains the asymmetry of coffee
supply response at the aggregate level.
177
Chapter 9.Conclusions
CHAPTER 9. CONCLUSIONS
This final chapter comprises four main sections. The first section provides a brief
summary of the background and objectives of the thesis. The second section presents
the main findings derived from the different models in the study. The third section
discusses some limitations of the study and other complexities not addressed in this
thesis. Finally, the opportunities for further work are mentioned.
9.1. Background
Coffee is an important crop in Vietnam’s agriculture sector. It is the second largest
export agro-commodity in Vietnam after rice. In addition, coffee plays an important role
in labour absorption in rural areas. In the peak season, the coffee sector employs about
800,000 workers (The World Bank, 2002).
Following the implementation of the “Innovation” policy in 1986, the coffee area in
Vietnam increased rapidly, from only 50,000 ha in 1986 to about 600,000 ha in 2000
(GSO, 2001). The rapid expansion of coffee area and production has made Vietnam
become a significant exporter: currently, Vietnam contributes over approximately 40
percent of Robusta and 13 percent of all coffee traded on the world market.
Despite its rapid expansion, the coffee sector in Vietnam faces a number of issues. First,
the coffee sector is dominated by small households with over 60 percent of households
having less than one ha of coffee land. Secondly, about one-fourth of coffee households
are poor and 30 percent of farmers are from one of Vietnam’s ethnic minorities. In
addition, coffee households are highly specialized and thus it is not easy for them to
diversify their income. Furthermore, the coffee price is highly volatile and depends
heavily on the international market. The price crisis in early 2000 adversely affected the
whole coffee sector in Vietnam, but especially coffee farmers. The coffee price received
at that time by coffee farmers did not cover the variable costs, thus many farmers had to
cut down coffee trees and switch to other crops such as maize. During three seasons
(from 2001/2002 to 2004/2005), over 100,000 ha of coffee trees in Vietnam were
uprooted.
178
Chapter 9.Conclusions
The reduction of coffee area in the early 2000s was in line with policies from both
Central and Local Government. At that time, the Government advised and supported
farmers with poor lands or households with old coffee gardens to clear trees and switch
to other crops. The Government partly subsidized uprooting costs and provided
substitute crops. Cutting coffee trees in response to price reductions is a complex
decision as establishment costs are high and a farmer may regret a decision to cut if a
price fall is temporary. To avoid the costly practice of cutting too early and to support
farmers in their decision-making process and planners in policy formulation, it is
necessary to have a thorough understanding of the optimal behavior for coffee
households with respect to price variation. To this end, this study examined two main
problems: (i) identifying the optimal price for cutting and replanting coffee trees so that
farmers can attain the maximum expected net present value (ENPV) when price varies
randomly and (ii) estimating the aggregate supply response function for coffee in
Vietnam.
Solving the first problem employed a number of models to:
(i) determine the optimal cutting and replanting rule for coffee farmers in Vietnam to
maximise their expected NPV from “land use choice”,
(ii) investigate to what extent poor farmers lose income from deviating from the optimal
rules because of cash constraints and
(iii) analyze how much farmers can improve their income if they follow an optimal
short-run yield response.
To identify the optimal cutting and replanting price of coffee farmers, the study
develops optimal models using the fixed form optimization approach. The fixed form
method specifies particular functional forms for cutting price and replanting price rules.
The purpose of the models is to identify the cutting and replanting price to maximise the
expected NPV from “land use choice” of coffee farmers. The term “land use choice”
refers to the planting decision of coffee farmers on their land: they can grow coffee or
switch to maize if the price of coffee is too low.
To solve this problem, the study develops four main optimal models. The first model is
the Fixed Yield model (FY model). This model identifies the optimal cutting and
replanting prices to achieve the maximum expected net present value (ENPV) while
179
Chapter 9.Conclusions
coffee yield is assumed to vary by age of trees but fixed at a given age. The second
model, Fixed Yield- Cash Constraint Model (FY-CC model), is an extension of the
Fixed Yield model. This model integrates the liquidity constraint of coffee households
when they make their decision. In the FY-CC model, the cutting/keeping or replanting
decision of coffee farmers does not only depend on price levels but is also based on the
availability of cash after living costs are subtracted. The third model, Variable Yield
Model (VY model), is based on the FY model but it goes a further step to investigate the
farmer’s decision when the yield in the short-run can change. The change in inputs
affects the yield of coffee as well as production cost and thus influences the optimal
decision of farmers in terms of the cutting and replacement rules. The fourth model is
the Variable Yield–Cash Constraint Model (VY-CC model). The structure of the VYCC model integrates the two previous variants: both cash constraints and variable yields
are included.
Coffee is a multi-year crop and the cutting/keeping or replanting decisions in the current
year affect the expected income of households in subsequent periods. In addition, the
objective function of the optimal models is to maximise the expected NPV under price
uncertainty. Thus, the conventional stochastic dynamic programming (DP) is seemingly
a useful technique to solve this problem. However, the application of DP for coffee
models in this study faces the problem of “the curse of dimensionality” because the
optimal models cover a period of 50 years. At a given stage, coffee farmers have to
choose different options: (i) keeping coffee, (ii) cutting standing trees and replace by a
substitute crop (maize), (iii) replanting coffee or keep growing maize if land is being
used for maize. In addition, the objective of the present modeling approach is more
complex because the aim is to also consider the effect of cash constraints and short-run
responses on optimal cutting and replanting rules. Thus, application of the fixed form
approach with a grid search method is a simpler way to solve the coffee models to find
out the optimal rules and the maximum expected NPV. Because of the impact of age of
the tree on current and expected future yield, we estimate optimal rules as a function of
the age of the tree.
The estimation of the coffee supply response function is based on historical data at
provincial levels of Vietnam from 1986 to 2006. Different symmetric and asymmetric
forms of supply function were estimated to find the best-fit function.
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Chapter 9.Conclusions
9.2. Key results
9.2.1. Response at the Farm Level
The analysis of response at the farm level explains the optimal decisions for an
individual farmer, especially the replanting and cutting decisions.
9.2.1.1. Cutting and Replanting Decision
Although details of the optimal rules vary among different models, the results of all
optimal models indicate that farmers have different trigger prices for cutting and
replanting. This asymmetric response of individual households leads to an asymmetric
supply response at the aggregate level. The cutting/replanting gap means farmers
usually switch out of coffee production more slowly than commencing and expanding
production. The asset fixity problem will lock them into the coffee sector and, should
prices go down, they may lose money. By contrast, farmers should not be in a hurry to
cut the coffee down and switch to other crops.
In addition, there is an obvious relationship between the cutting rules and age of coffee
trees. In general, optimal cutting price for trees which are at the age of starting to
produce cherries (5-6 year old) are lowest. However, results from the optimal models
indicate that farmers should not cut their trees down even if they are mature (up to 12
year old), even if the price is very low. Furthermore, farmers should never cut their
coffee earlier than its biological limit if the price of coffee at that time is very profitable.
That is because they would have to forgo yield for some years, and given the price
volatility of coffee it is better to get the benefit of existing yield at high prices, than to
wait for the new tree to mature because prices might not be as high then.
The optimal cutting price is significantly influenced by the age of the coffee tree. Thus,
the model with age-dependent optimal cutting price generates higher income as
compared to a constant cutting price. This finding lends support to the type of approach
used here, compared to a real options approach applied by Luong and Lorrent (2006)
which focuses on a fixed cutting and replanting price. However, the model results are
almost unchanged among different fixed forms of CP (cubic CP, quadratic CP and
quadratic with price change effect CP)
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Chapter 9.Conclusions
9.2.1.2. Impact of Cash Constraints on Farmer’s Behaviors
Farmers in developing countries like Vietnam have volatile and low incomes. They
often suffer from different risks caused by bad weather, agricultural price shocks,
business failure and illness. A shortage of cash for investment causes many problems
for rural households. About 25 percent of coffee households in Vietnam are poor and
they often need support from credit organizations. When farmers have cash problems
they cannot optimize their long-run income and they have to change cutting or
replanting decisions to satisfy their short-term cash needs. The FY-CC model results
indicated that when poor coffee farmers have a cash-constraint, they lose about 15
percent of their income if they follow the optimal rules of non-poor farmers. This is
because they do not have the cash to replant coffee when the price rises. If they use
rules derived explicitly for accounting for the constraint, there is a small change in CP
but a significant increase in RP. Generally, the poor households are more likely to cut as
compared to the non-poor. Furthermore, the poor farmers usually wait for significantly
higher prices before deciding to replant. In addition, under the new optimal rules to the
constraint, the income of poor farmers is about 11 percent lower than that of non-poor
farmers derived from the FY model.
From the optimal rule, optimal results indicate the frequency cutting decision or cutting
percentage of coffee farmers with respect to different age groups of trees. The cutting
percentage is the percentage of cases in which farmers actually cut their coffee trees
down at optimal rules. The cash constraint problem has a remarkable impact on the
cutting percentage of poor households, especially for those whose coffee trees are still
young (less than 4 year old). As indicated by the FY-CC model, the actual cutting
percentage of coffee trees under 4 year old due to the cash constraint is about 10
percent, and this number reduces to only 2 percent when trees become older. Due to the
cash constraint, farmers cannot optimize their decision so they earn less than they could.
This implies that credit supports are important for coffee farmers but the priorities
should go into new households or farmers with young trees.
The amount of loan available for the poor household has a significantly impact on the
farmer’s income and behavior. In general, poor farmers can get a higher income with
bigger loans. In many cases, it is inefficient to support poor households with a loan that
is too small, as it has little impact on incomes, as there appear to be threshold effects.
Moreover, the model output also shows that, if the annual loan increases to $1500, poor
182
Chapter 9.Conclusions
households can nearly optimize their investment, and their decision and expected
income is very close to the non-poor farmers.
The importance of loans varies depending on the age of coffee trees the farmer has at
the start of the period. The amount of annual loan is more important for farmers with the
young trees, especially for non-productive trees. With the mature trees, the impact of
loans becomes less important.
9.2.1.3. Change of Farmer’s Decision with Short-run Response
The liquidity constraint has a significant impact on the optimal decision of the coffee
farmers, especially for those whose trees are still young. Farmers cannot optimize their
long-run income if they are poor. The poor farmers often cut earlier and wait longer
before replanting.
The output of the optimal models shows that the optimal decisions of farmers
significantly change if they make efficient, short-run changes in input use in response to
output price changes. The change of input influences the yield of coffee trees. The
ability to respond in the short-run has a significant impact on the farmer’s planting and
cutting decision and on income. The income of coffee farmers increases significantly
when farmers can optimize their response of input use to output price. This is true
because they do not apply as much input in low-price years. With the short-run
response, coffee farmers can increase their expected income by over 30 percent of their
expected income when compared to the case without a short-run yield response at the
same average yield. In addition, with the presence of a short-run response, coffee
farmers are much less likely to cut and more likely to replant coffee. With short-run
response, the non-poor farmers optimize their decision to replant at a price of $0.51 per
kg. The poor farmers wait for a higher price and they decide to replant at a price of
$0.59 per kg of coffee. These replanting prices are much lower when compared to the
optimal RP of the poor and non-poor cases without the short-run response ($0.74 and
$1.4 per kg, respectively).
Significant improvements in profit that can be achieved as the result of being able to
change input use in the short-run implies that it would be valuable for farmers to be
educated about the benefit of short-run response.
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Chapter 9.Conclusions
9.2.1.4. Impact of the Profitability of the Substitute Crop
In the optimal models, maize is assumed to be the substitute crop when coffee trees are
cut down. The maize profit is constant in the optimal models. The sensitivity analysis
from the FY model in Chapter 4 concluded that if the replacement crop profit increases,
farmers are more likely to cut and less likely to replant and vice versa, as one would
expect. However, the model simulation shows that if the annual maize profit increases
by 20 percent, the ENPV will increase by only 2 percent.
The switching decision of coffee farmers to annual crops such as maize or rice is mainly
carried out to overcome a cash shortage, when there is insufficient cash for food. Thus,
this issue relates closely to credit and other subsidy policies. If the price is too low but
the household budget (including loans and household income) is sufficient for farmers
to cover living expenditure, they can continue producing coffee while waiting for higher
prices.
9.2.2. Coffee Supply Response at Aggregate Level
Empirical results in this study show that the supply response of the coffee area in
Vietnam is asymmetric. Farmers respond much more quickly to price rises than price
falls. The short-run elasticity of coffee area to output price rise (0.87) is much higher
than to the price fall (0.21). The irreversible supply response of coffee is consistent with
the asymmetry of individual farmer’s behavior in cutting/replanting found in the
individual-farmer decision models.
The asymmetric response of coffee in Vietnam is similar to the pattern of world coffee
supply found by Olsen (2005). According to Olsen, the supply response of world coffee
to price does not comply with standard economic theory, as it is asymmetric. The
reasons that coffee farmers in developing countries do not want to move away from the
coffee sector, even when prices are low are:
(i) possibility of subsistence farming in conjunction with coffee enables farmers to
survive, with an expectation to earn higher income from coffee,
(ii) lack of alternative income sources, and
(iii) low education
184
Chapter 9.Conclusions
Olsen (2005), also identified that the existence of a “fixed asset” is an important factor
which leads to the asymmetric supply response. Low salvage values motivate producers
to keep growing coffee even when output prices are low because of high acquisition
costs, which again is consistent with farm-level models developed in this thesis.
9.3. Policy implications
The analysis and results from the farm level and supply response models provides
insights into policy implications for Vietnam’s Government
Coffee farmers in Vietnam and other coffee producing countries clearly perceive that
the price of coffee is very volatile. Sometimes, the price of coffee drops below the
production cost. However, the government can provide the information about when its
optimal to switch out. At some times it is optimal but it might be difficult for farmers to
identify the optimal triggers. The intervention could either be information as to when it
should happen, or direct incentives such as grants for removal if that is seen as needed.
So assistance of Government to provide such information would be good for helping
farmers to optimize their decision.
In addition, the government could encourage coffee farmers with young trees under 10
years old to not cut coffee trees even if the price of coffee is very low. Historically,
coffee prices increase after several years of reduction thus if farmers cut down the
young coffee trees they will lose money from future coffee sales. In addition, the
models shows that farmers can make better decisions based on expected changes in
prices (i.e. they have better information about what is likely to happen) and if they do
not have that then presumably they will be in difficulties. Thus, Government could
provide information about price forecast for coffee growers so the growers can base
their investment decision on that information.
The aggregate supply model shows that response of coffee to coffee prices is
asymmetric, which is consistent with the farm level models. So the government should
advise farmers to not cut down their trees or hurriedly switch to other crops if coffee
price is declining, because the price of coffee will recover so farmers will lose their
income from coffee production.
Coffee farmers should perceive clearly that the yield of coffee trees do not always
increase accordingly to greater input use. Overuse of chemical fertilizer not only causes
185
Chapter 9.Conclusions
high expenditure but also lowers the yield of coffee trees. Furthermore, the model
shows that farmers can save their cost and increase their profit with better response in
input use to changes in output prices. So the diffusion of information by the
Government about the benefits of short run response in use of fertilizer is also needed.
The price of coffee is very volatile, and periods of low prices may induce farmers to cut
trees, especially if they have cash constraints. This suggests that policies to support
farmers via a stabilized market price would help make farmer’s income stable. A floor
price, or subsidized credit policy for coffee exporters can be good measures but it is
experienced in the past that farmers could not get much benefit from such policies. The
results from the optimal models with cash constraints show that credit policy for coffee
smallholders plays a very important role to help them overcome low price years and
optimise their investment decision. The provision of credit facilities would
assist
farmers in avoiding being forced to cut because of cash flow problems. However, it is
necessary to be concerned about the size of loans for farmers in a credit program.
Small/inefficient loans are not sufficient to allow them to improve their decision and
cannot improve their livelihood. The model shows that there is a need to make sure that
the loan for coffee farmers is provided at the efficient level. It means that there is no
point if it is too small because farmers cannot afford to invest, but also there comes a
point where larger loans provide little additional benefit.
9.4. Limitations
Despite numerous insights provided by this study, it has a number of limitations.
First, the optimal rules being identified in the optimization models are only valid for the
existing price simulation. This does not refer to the specific price series themselves, but
the assumptions about the mean and variance of the price distributions. If there was a
change in the behavior of these time series then it is likely that the rules would alter.
Second, all fixed forms for cutting prices and replanting price in optimal models (age
dependent quadratic CP, quadratic CP with price change effect, age dependent cubic
CP) are specific forms to present the relationship between age of coffee trees and CP.
However, those forms may not be the best/optimal form for CP in reflecting the cutting
decision and age of trees. There may exist some alternative specifications that could
improve expected returns for farmers. This is equivalent to the issue of identifying a
186
Chapter 9.Conclusions
local optimal in a conventional programming problem: although the search through the
existing set of functions suggests that the optimal has been identified, it cannot be
guaranteed.
Third, due to the unavailability of time series farm-gate price data by different
provinces, the study used FOB price as a proxy to estimate the supply function of coffee
at provincial level. In addition, FOB prices used in the study were average price at
national level. Thus, this may not reflect accurately the regional price received by
farmers.
Fourth, the optimal models assumed that all trees on a property are of a single age, so
when cutting coffee farmers switch all land to maize. The limitations of this assumption
will impinge on the results for the cash-constrained poor farmers, where their behaviour
may be different if they have the capacity to run mixed-age plantations, or remove only
part of their tree stock.
Fifth, the cutting and replanting decision of coffee farmers depends on the profit of
substitute crops. Thus, the replacement decision can be a function of certain maize
returns. In the optimal models, the sensitivity analyses were undertaken to see how the
optimal rule changed when maize profits varied. More realistically, the cutting price
might be influenced by the mean and variance of the maize price.
Sixth, the price of inputs may change the decision of farmers. In the optimal models,
prices of input (including fertilizer and labour) are assumed unchanged. In practice, the
price of inputs will vary over time, and again, have some degree of uncertainty
associated with them.
Seventh, the estimation of income and expenditure in this study for the poor coffee
households is based on data of all poor households from the VHLSS2006. The data for
income and expenditure for poor coffee households is not available. This result may
bring some bias when analyzing the structure of income distributed to investment and
household expenditure.
Eighth, the estimation of coffee yield neglected factors that significantly influence the
yield of coffee such as rainfall, type of land, education of households. Furthermore, the
same yield response function in this study is used for both poor and non-poor farmers.
187
Chapter 9.Conclusions
However, in reality, poor farmers usually have poorer land and their yield will respond
differently to the non-poor farmer.
9.5. Further Studies
There are some complexities which have not been addressed in this study. In the area of
optimal decision for coffee farmers, optimal models could be further improved in some
ways.
a. It would be useful to identify better empirical data on the productivity vs. age
relationship for the Robusta varieties in Vietnam. In this study, the author's assumption
of the production pattern over time is in line with suggestions in the literature. This
information is crucial to the models, since the question remains "should the government
stimulate replanting when plantations reach 22 years, or is production still economically
viable after 22 years and for how long" i.e is the assumption of a 22 year life span for
the trees appropriate.
b. In the optimal models, maize price was assumed to be unchanged. The sensitivity
analysis showed that farmer’s behavior would be changed when profit of maize varied.
An improvement to the model would be to see how maize price influences the cutting
and replanting decision by adding maize price into the function of CP and RP. This
would make the optimal models much larger and would take longer to solve.
c. The price simulations in the model were generated from a lagged price model using
the time series data. The distribution of such price simulation has an extended range.
The change of the distribution of price will change the farmer’s decision rules. It would
be useful to investigate the optimal rules with different limits of the price distribution.
d. The optimal models in this study identified the cutting and replanting price based on
the normative approach. However, it would be interesting to develop a model based on
actual data for individuals for cutting and replanting decisions, possibly derived from
farm surveys. This model would be based on the farmer’s reported data on the time
they cut down the trees, the price at which they cut, input price, other crop price and
other household’s characteristics. The output of this model could be compared with the
simulated behaviors of the normative models.
188
Chapter 9.Conclusions
e. When developing the yield response function to study the impact of short-run
response to farmer’s decision, this study did not address the dynamic effect of fertilizer
use. The application of inputs identifies only the yield of coffee in that year. In practice,
use of fertilizer has carry-over effects. Another improvement to the model would
include the carry-over effects in input use.
f. This study estimated econometrically the response of the coffee area. It would be
useful to estimate the yield response function at the aggregate level based on other
variables such as output price, input price, rainfall, humidity, price of competing crops.
The integration of area function and yield function would be useful to estimate and
forecast the output function. Ideally, such a model would be developed into a partial
equilibrium model for the coffee sector in Vietnam. The partial equilibrium model
would be helpful in evaluating the impact of government policies, price change and
other factors on farmers.
189
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198
Appendix A
Appendix A
Figure A1. Regions in Vietnam
Name of country
Surface area
Population
Population density
Percentage of urban population
GDP (nominal)
GNI per capita
Vietnam
329,241 km²
85.2 million(2007)
247/km²(2004)
26.4%(2005)
$ 71.6 billion(2007)
$ 656(2006)
199
Appendix A
Figure A2. Vietnam and Dak Lak province
200
Appendix A
Figure A3. Coffee Area Map in Vietnam
201
Appendix A
Figure A 4. Coffee Output Map in Vietnam
202
Appendix A
Figure A 5. Poverty map of Vietnam
203
Appendix A
Figure A 6. Depth of Poverty Map in Vietnam
204
Appendix B
205
Appendix B
Appendix B
Table B1. Vietnam GDP at current price in 2008 by sector
GDP at current price (bill. VND)
(%)
2007
2008
2007
2008
1144015
1478695
100
100
Agriculture, forestry and aquaculture
232188
325166
20.3
22.0
Construction and Industry
475681
590075
41.6
39.9
Services
436146
563454
38.1
38.1
Vietnam
Source: GSO per com
Table B2. Area and output of selected perennial crops in Vietnam, 2007-2008
2007
Fresh tea
Cultivated area (1000 ha)
Harvested area (1000 ha)
Yield (quita/ha)
Output (000 tonnes)
Coffee
Cultivated area (1000 ha)
Harvested area (1000 ha)
Yield (quita/ha)
Output (000 tonnes)
Rubber
Cultivated area (1000 ha)
Harvested area (1000 ha)
Yield (quita/ha)
Output (000 tonnes)
Pepper
Cultivated area (1000 ha)
Harvested area (1000 ha)
Yield (quita/ha)
Output (000 tonnes)
Cashew
Cultivated area (1000 ha)
Harvested area (1000 ha)
Yield (quita/ha)
Output (000 tonnes)
Source: GSO per com
2008
Change 2008/2007
Level
%
126.6
107.4
65.8
706.8
129.6
110.7
68.6
759.8
3.0
3.3
2.8
53.0
102.4
103.1
104.3
107.5
509.31
489.0
19.7
961.7
525.1
500.2
19.9
996.3
15.8
11.2
0.2
34.6
102.4
102.3
101.0
103.6
556.3
377.8
16.1
609.8
618.6
399
16.6
662.9
62.3
21.2
0.5
53.1
111.2
105.6
103.1
108.7
48.4
41.1
21.7
89.3
50
43
24.3
104.5
1.6
1.9
2.6
15.2
103.3
104.6
112.0
117.0
440.1
302.8
10.3
312.5
404.9
314.3
10
313.4
-35.2
11.5
-0.3
0.9
92.0
103.8
97.1
100.3
206
Appendix B
Table B 3. Vietnam coffee export, 1991-2008
Year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
Quantity (000 tonnes)
93.50
116.20
122.60
176.40
248.10
283.70
391.60
381.80
482.46
733.94
910.00
719.00
749.24
974.80
892.37
775.46
1200.00
1000.00
Value (Mil.$)
76.30
91.50
110.80
330.30
598.10
400.26
493.71
593.80
585.30
501.45
385.00
317.00
504.81
641.02
735.48
826.99
1800
2115.00
Source: MARD per com
Table B 4. A comparision of coffee export cost in some countries (cent/lb)
Countries
Production cost
extra cost
Vietnam
India
Indonesia
Brazil
20.5
30
29
55
4.5
4
8
0
Source: PI-IPSARD per com
Table B 5. DRC of main commodities of Vietnam
Commodity
DRC
Rice
0.59
Coffee
0.37
Rubber
0.7
Tea
0.79
Source: CAP (2006)
207
Appendix B
Table B 6. Number of coffee households by region and age structure in Vietnam
2006
Number of
coffee
Less than
households 0,5 ha
0.5-1 ha
Vietnam
+ Red River
Delta
By farm-size
1-2 ha
2-3 ha
3-5 ha
5-10 ha
Over 10
ha
128,491
32,093
11,638
2,113
192
18
1
477,235
156,611
146,097
7
5
2
7
5
2
+ North East
20
15
5
Ha Giang
8
6
2
Lao cai
12
9
3
+North West
11
9
2
Lai Chau
North CenTral
Coast
11
9
2
10,463
5,617
2,366
2,050
332
79
Thanh hoa
405
217
91
79
14
4
Nghe An
2,189
808
757
574
40
9
1
Ha Tinh
5
4
Quang Binh
245
184
59
2
Qung Tri
Thua Thien –
Hue
South Central
Coast
6,404
3,525
1,247
1,284
268
64
15
1,215
879
212
110
10
2
2
3,364
657
966
1,307
309
101
19
5
Binh Dinh
1,798
211
551
824
166
35
9
2
Phu Yen
1,035
168
280
400
119
55
10
3
Khánh Hoa
Central
Highlands
531
278
135
83
24
11
427,316
139,393
131,797
114,927
28,696
10,450
1,888
165
Kon Tum
9,877
4,327
2,138
2,385
689
276
49
13
Gia Lai
69,370
28,147
19,629
16,600
3,596
1,165
205
28
Dak Lak
180,434
62,224
60,770
44,195
9,650
3,054
507
34
Dak Nong
53,534
9,447
14,059
19,763
6,894
2,758
580
33
Lam Đong
North East
South
114,101
35,248
35,201
31,984
7,867
3,197
547
57
36,054
10,915
10,959
10,207
2,756
1,008
188
21
Ninh Thuan
7
3
2
2
Binh Thuan
1,144
186
328
418
140
63
9
Binh Phuoc
8,000
1,226
1,910
3,156
1,081
493
118
16
Binh Duong
221
84
39
47
21
17
11
2
Dang Nai
Ba Ria - Vung
Tau
18,352
5,638
6,074
5,068
1,197
336
37
2
8,330
3,778
2,608
1,516
315
99
13
1
Ha Tay
1
1
Source: GS0, 2007
208
Appendix B
Table B 7. Area of coffee in main provinces in Vietnam, 1986-2006 (ha)
Year
Kontum
Gia Lai
Dak Lak
Lam Dong
Dong Nai
Vietnam
1986
2536
5438
29949
10159
10890
65630
1987
3695
7926
39014
15854
17588
92300
1988
5152
11051
63265
23009
22270
135940
1989
5088
10911
61233
23909
26306
139568
1990
4660
9996
70242
24883
28326
153627
1991
4782
10381
69320
23120
29686
153060
1992
3006
8857
73546
23391
26553
153060
1993
3195
10548
82147
22031
21984
158729
1994
3046
11387
96768
25508
21358
176302
1995
4219
23999
112477
49561
23049
232424
1996
6479
29796
165694
67777
28823
323694
1997
7177
40274
216964
98435
31576
436504
1998
10667
58506
257504
119492
47089
549882
1999
14112
66005
267994
128734
49364
599768
2000
15492
87156
278596
122805
38516
604304
2001
15234
86898
277323
132922
35618
606571
2002
14110
85961
257558
129159
29305
566889
2003
12368
77571
232416
118229
25072
510200
2004
11513
76063
232961
116739
22471
496800
2005
10594
75854
241800
117428
20288
491400
2006
9844
75910
242250
118788
16857
497000
Note: the data for Dak Lak province includes Dak Nong
209
Appendix C
Appendix C
Table C 1. Estimated results from Modified Wolffram model with different
window length
Dependent variable: lnarea (logarithm of coffee area)
Independent
variables
Lnareat-1
lnYMA
MWR (n=3)
MWF (n=3)
MWR (n=4)
MWF (n=4)
MWR (n=5)
MWF (n=5)
MWR (n=6)
MWF (n=6)
Provincial dummy
variables
Gia Lai
Dak Lak
Lam Dong
Dong Nai
Other
constant
R2
F-value
MWM (window =3 years)
Coef.
t ratio
0.86
18.31
0.14
4.24
0.35
6.82
0.22
5.47
MWM
(n =4 years)
Coef.
t ratio
0.85
18.91
0.14
4.26
0.42
0.22
0.23
0.37
0.29
0.08
0.22
1.44
0.98
790
3.02
2.73
2.93
1.12
2.78
3.95
0.23
0.39
0.30
0.09
0.23
1.49
0.98
804
MWM
(n =5 years)
Coef. t ratio
0.85
18.95
0.14
4.27
6.31
5.62
3.22
2.97
3.16
1.28
2.97
4.22
0.45
0.22
6.19
5.62
0.24
0.40
0.31
0.10
0.24
1.53
0.98
912
3.34
3.11
3.29
1.39
3.07
4.36
210
Appendix D
Appendix D
COFFEE FARM SURVEY QUESTIONNAIRE
Name
Code
Province
District
Commune/town
Village
Interviewer
Respondent
Address of respondent
Phone
Date of interview
211
Appendix D
A. HOUSEHOLD CHARACTERISTICS
……………………………………………………………………………
1. Name of household head ?
2. Gender of household head ?
___________
3. Year of household head’s birth ?__________
1. Male
2. Female
……………………………………………………………………………
2. Other (specify) ………………………….
4. Ethnic origin ?____________
1. Kinh
5. Geographical origin ?_____________
1. Local resident
2. Migrant
6. [If migrant] When did you come here ? ………...(year)
7. [If migrant] Where do you come from ? province name__________
8. Total No. of HH members ?
provinve code________
……………………………………………………………………………
9. No of adults (>=15 year old and <= 65) ? ……………………………………………………………………………
No of children (< 15 year old) ?
…………………
10. How many people are usually working in agriculture? ____________
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Appendix D
B. LAND AND LANDUSE
rownum
1 Crop
name
2. Crop
code
3.Plant
area (m2)
4. Harvested
area (m2)
5. Harvested
output (kg)
6. sale
output (kg)
7. Sale price
(d/kg)
8. Sale value
(000 D)
Note: if forestry trees, “Harvested output” can be blank
213
Appendix D
C. OTHER SOURCES OF INCOME
Source of revenue
Revenue (000 D)
1.Livestock
from pig
from chicken
from cattle/buffalo
from other animal
2. Aquaculture
3. Wage/salary
4. Pension
5.Other income (specify____________________)
214
Appendix D
D.COFFEE PRODUCTION
1. When did you start growing coffee?____________(years)
2. Total area for coffee cultivation last years?
……………………… (m2). # of plots for coffee cultivation ?........
3. Coffee distribution per plot and land quality ?
#
Plot
1
Plot 1
2
Plot 2
3
4
Plot 3
Plot 4
Planting
year
Area
(m2)
% rented
Soil type code: 1. Ferralsol (đất đỏ)
5. % removal and replantings in each year
Age of tree (years)
% removed
0-3
3-8
8-15
15-20
20-25
>25
6. Yield of coffee by age (kg bean/ha) ?
Age
3
4
5
6
Yield
Registered with red
certificate
1. Yes
2. No
2. Arcrisol (đất xám)
% irrigated
Soil type (see Harveted
code)
ouput
(kg)
3. Luvisol (đất đen)
Yield
(kg/ha)
4. Other (specify)
% replantings
7
8-15
15-20
20-25
>25
215
Appendix D
E. THE LARGEST PLOT
How large the biggest plot is ________________(m2)….. Out put………..(kg) and how old is it?________________(years)
Could you please tell us the cost in last year for the biggest plot
#
A
1
2
3
4
B
5
6
7
8
9
10
11
13
C
14
15
16
17
18
19
20
D
21
22
Cost items
Preparation cost
seedlings (trees)
land rent
well
water system (pumb, tube…)
Fertlizer/pesticide
Ure (kg)
KCL(kg)
Nitro(kg)
DAP(kg)
SA(kg)
NPK
Manure
Pesticide
Labour
Hole, design
Growing
Weeding
Water
Prunning
Fertilize, pesticide
Harvest
Energy
Electricity, Petrol
irrigation
Quantity
Price(d/unit)
value (000VND)
216
Appendix D
F. GROW AND CUT DECISION
1. Have you ever reduced coffee area? __________1.yes
When was the most recent reduction?_______(year)
Why did you redude?_________1. fall in coffee price
If (1), At what price did you cut?_________(d/kg)
Maximum area did you cut? __________(m2)
2.no
2.Other ___________
3. When you decide grow coffee, what do you base on most?_________
1. Price of last year
2. Price of last several years
3. Advice of local authority
4. Price prediction
4. What was the received price in last year?___________(d/kg coffee bean)
5. At what minimum price/and how long it last do you intend to cut ?
Price level
(VND/kg)
8000
7000
6000
5000
4000
<4000
If price in one year
% reduction
If price in 3 years
% reduction
If price in 5 years
% reduction
6. After cut, do you intend to grow coffee again when price up?___________ 1. Yes
7. At what minimum price do you intend to grow coffee again ?_________(d/kg)
If price in 10 years
% reduction
2.No
217
Appendix D
G. FARMER’S RESPONSE TO COFFEE PRICE REDUCTION
When price reduced, did you reduce input application?
1. Have you ever switched to other crops due to price fall? __________1.YES 2.NO
If yes, please list two main crops which were replaced for coffee _________ __________
If not, why did not you change to other crops
#
1
2
3
4
5
Reasons
Keep coffee and expect higher price
Lack of capital to grow other crop
Do not know which crop should be
replace
Risk afraid
Other (specify)________________
1. True 2. False
2. In bad price years, could household income cover the household expenditure and annual cost? _______ 1.YES
2. NO
If not, what did you have to do for overcoming the problem?
#
1
2
3
4
5
6
Solutions
Using saving stock
Borrowing money
Reducing expense of household
Selling asset, animals
Finding other job
Selling coffee garden
1. True 2. False
218
Appendix D
H. CREDIT
1. When did you borrow last loans (year)?________
Amount of loan?___________(000 VND) interest rate ?_____(%/year)
loan duration_____(months)
4. Main purpose of loans?________
1. Buying input for coffee production 2. Paying for labour cost for coffee production
3. For other activities
4. Buy food
5. Other
5. If you want to get loan for coffee production, do you get sufficient loan ? _________1.YES 2.NO
If not, How many percent did loan account for total requirement ?_______(%)
6. Main source of loan?___________
1.Bank
2.Private lenders
3.Relatives
4.Women’s association
5.Commune Committee
6.Other credit
programs 7.Other
I. HIRING LABOUR
1. In last season (2005/2006), did you hire labour for coffee production? _____1.YES 2.NO
2. If yes, percentage of hired labour in total?________ (%)
3. Did you get any problems to hire labours?________1.YES 2.NO
If yes, which problems?_____________
K.WATER
1. What is main source of water for coffee plantation?__________1. Wells
2. Lake, reservoir
3. Streams
2. Are your coffee plantation provided enough water?_____1.YES 2.NO
3. According to your estimation, Is yield of your coffee plantation limited by water scarcity ?________1.YES 2.NO
4. If yes, how much can coffee yield increase with enough water ?_________(%)
4.Other
219