ARTICLE # 13884-RJBS
Stochastic Frontier Model for Climatic Determinants on Rice Productive Efficiency
Ismail Hossain1 Md. Azizul Baten1,2
1
Department of Statistics, School of Physical Sciences, Shahjalal University of Science and Technology Sylhet-3114,
Bangladesh. Email: ismail_stat_sust@yahoo.com. Phone Number: +8801613938989, +8801713938989
2
Department of Decision Science, School of Quantitative Sciences, Universiti Utara Malaysia, 01610 UUM Sintok,
Kedah, Malaysia.Email, baten _math@yahoo.com. Phone Number: +6049286886
Abstract
Identifying climatic determinants of efficiency is a major task in efficiency analysis. An attempt has
been made to investigate the climatic effects on efficiency levels of rice production in Bangladesh.
Three types of rice crops (Boro, Aus and Aman) in Bangladesh are considered and the model
proposed by Battese and Coelli (1995) are revisited in this study to see the effects on rice productive
efficiency in Bangladesh. We used the collected data from agricultural sector consisting three main
rice crops in Bangladesh for the period of 1980 to 2008. The results showed that temperature has a
significant effect on rice production. The negative coefficients of rainfall, fertilizer are indicated that
the technical efficiency level tended to decrease by 37 and 16 percent respectively over the time
period. It was observed that humidity and wage rate of labor were found decreasing the level of
inefficiency. The coefficient of wage rate of labor was found negative but significant which indicated
that the labors involved in rice production are not skilled enough. The most efficient rice production
system in Bangladesh is Boro with the technical efficiency (0.86) than other two crops.
Key Words: Stochastic frontier model, Climatic change, Technical inefficiency; Bangladesh rice
production; Panel data.
Corresponding author name:
Visiting Associate Professor Dr. Md. Azizul Baten,
Department of Decision Science, School of Quantitative Sciences, Universiti Utara Malaysia, 01610
UUM, Sintok, Kedah, Malaysia
Email: baten_math@yahoo.com
1 Introduction
Climate is one of the major controlling factors for well-being of the residents of the world. But Climate
variability and change, its impacts and vulnerabilities are growing concern worldwide. Climate change and
agriculture are interrelated processes, both of which take place on a global scale (Fraser 2008). The climate of
Bangladesh is changing and it is becoming more unpredictable every year. Global warming induced changes in
temperature and rainfall are already evident in many parts of the world, as well as in Bangladesh (Ahmed and
M.Alam, 1999). The overall effect of changing climatic condition on agriculture will depend on the balance of
these effects. Assessment of the effects of global climate condition change on agriculture might help to
properly anticipate and adapt farming to maximize agricultural production. Rice is one of the most important
foods in the world, being the staple food of over 50% of the world population, particularly in India, China, and
a number of other countries in Africa and Asia (Olorunfemi and Victor 2006). Rice is a major source of
livelihood of rural population in most Asian countries as like as in Bangladesh. There are about 4 billion
people who consume over 90 percent of the world’s rice production. Rice was selected in this study because of
its prominent position in the national economy of Bangladesh. The share of agriculture to GDP in Bangladesh
is about 18.64 percent (BER, 2008-09). Agriculture accounts for 21% of the gross domestic product
(GDP) (different information about GDP) and 50% of overall employment (Bangladesh Agricultural
Census, 2008). Therefore we have to be given the importance of changing climatic conditions on rice
production because of adaptation problem of producing rice. It is observed that there have been a few studies
on the efficiency of rice production measurement on the basis of climatic condition in Bangladesh. Have
farmers grown their product efficiently with the available technologies? How have the policies undertaken to
be aware of farmers regarding the effect of climatic condition on rice production in Bangladesh. These are
some of the questions the study partly sought to answer.
Efficiency measures are important because of its vital role on productivity growth. The efficiency of rice
production has been of longstanding interest to the economists and policymakers in Asia because of the strong
relationship between rice production and food security in the region (Richard et al. 2007). A number of studies
examined productivity efficiency of crops in Asia and other country (Kalirajan 1981; Erwidodo 1990;
Kalirajan and Shand 1989; Ekanayake, S.A.B. (1987); Hanley, N. and Spash, C. L. 1993 ; Mythili and
Shanmugan 2000; ‘Shanmugam 2000; Squires and Tabor 1991; Ahad, Rafiq and Ali 1999; Ajibefun, Battese
and Daramola 2002; Ali and Flinn 1989; Battese 1992; Battese and Coelli 1992; Battese and Coelli 1995;
Travers and Ma 1994; Fan et al. 1994; Wang et al. 1996a, 1996b; Xu and Jeffrey 1998; Fan 1999; and Tian
and Wan 2000; Wadud and White 2000). The impacts of using advanced techniques on the rice production
efficiency in developing countries have been conducted by Bordey 2004; Chengappa et al. 2003; and Khuda
2005. In this context, Stochastic Frontier Approach has found wide acceptance within the agricultural
economics (Battese and Coelli 1992; Coelli and Battese 1995). There exist few literatures in estimating
stochastic frontier production and consequently dealing with technical inefficiency in rice production of
Bangladesh (Rahman et al. 1999; Deb and Hossain 1995; Banik 1994; Rahman 2002). Khan et al. (2010)
examined the influenced of farmers’ age, education and experience on technical efficiency of boro
and aman
production using Cobb-Douglas production function
and found that education was
positively related to technical efficiency. However, none of these studies focused on the potential
influence of climatic conditions to enhancing technical efficiency of rice production. Given this back
drop, the present study assesses the effects of climatic conditions (Rainfall, Humidity and
Temperature) to Rice production in Bangladesh on technical efficiency by applying stochastic
frontier model (Battese and Coelli 1995). This study also attempts to investigate the effect of other
agricultural inputs such as area, seed and variety of fertilizer in rice production in Bangladesh. An
improved understanding of these relationships can help the farmers to allocate scarce resources more
efficiently and may assist policy makers to design and formulate agricultural policy to increase
agricultural production in Bangladesh.
2 Materials and Methods
2.1Data Sources and Variables Construction
2.1.1Data Set
The data on rice production in Bangladesh is obtained from the year book agricultural statistics of Bangladesh,
conducting by the Bangladesh Bureau of Statistics (BBS) every year. The dependent variable, rice production
and other independent variables such as area, the amount of seed, the amount of fertilizer, rainfall, wage rate
per labor without food and wage rate of bullock pair for each crop are collected from yearly book of
agriculture statistics of Bangladesh. For this study we consider 29 time periods from 1980-1981 to 20082009.The meteorological data such as rainfall, temperature and humidity are collected from the meteorological
department in Bangladesh. The yearly distributions of fertilizer data for each rice crop (Boro, Aus and Aman)
are collected from Bangladesh Agriculture Development Corporation.
2.1.2 Descriptions of the Variables
Dependent Variable
Production (Y): Total Boro (Local, HYV and Hybrid Boro), Aus (Local and HYV Aus) and Aman (broadcast,
local transplant and HYV Aman) have been estimated at thousand metric tons.
Independent Variables
Area: The total areas of Boro, Aus and Aman rice have been estimated at hectares. Here we considered the
total area of cultivated land where specifically Boro are cultivated crop. In this study we considered all the
varieties of each crop.
Seed: Seed is the very important input to increase rice production. Therefore it is required that the farmers
must use pure, healthy seeds as per the minimum certification standards which have standard percentage. In
fact the seeds are foundation of farming; the high good quality seeds are those which have genetic purity,
physical purity, health standards and moisture percentage in accordance with the minimum seed certification
standards. For this study the amount of seed is considered of each crop and it is measured in thousand metric
tons.
Fertilizer in Urea: Fertilizer in Urea is a kingpin in enhancing crop production. No country has been able to
increase agricultural productivity without expanding the use of chemical industry. The total amount of
fertilizer in urea is used in each crop separately and the unit of fertilizer in urea is in metric tons.
Fertilizer in TSP: Triple supper phosphate (TSP) is the major fertilizer which is applied in agricultural land in
various proportions for rice production system in Bangladesh. For this study, the unit of fertilizer in TSP is in
metric tons.
Rainfall: The primary source for agriculture production for most of the world is rainfall. For this study the
total rainfall is considered for Boro rice in millimeter during February-July session. Similarly the total rainfall
is considered for Aus and Aman rice during March-June and July-December respectively.
Explanatory Variable
Temperature: Rice crop is influenced by seasonal characteristics and different variables of climate such as
temperature. Extreme temperature due to climate change usually affects livestock. High temperature affects
livestock in a number of ways: causes great discomfort as in the case of human, decreases feed intake and
alters nutrient metabolism leading to high loss of energy and the combined effects of discomfort and nutrient
metabolism reduces their productivity, resulting in financial loss of the farmers. Here we took the average
monthly temperature (in Celsius) in each rice crop session.
Humidity: Humidity is a measure of the amount of water vapor in a body of air at a certain temperature.
Humidity is an important measure in agriculture because it has an effect on evaporation rates. Where there is
high humidity, animals may get stressed, and moulds, mildews and fungus may grow which is indirectly effect
in agriculture especially in rice production. For this study we considered average humidity in percentage in
each crop.
Daily average wage rate of labour without food: The wage rate is important factor which has an indirect
impact in the production of rice. In this study, the average daily wage rate per man without food is considered
and it is measured in taka.
Wage rate of Bullock pair in a day: Most of the cultivation areas in Bangladesh are in rural where the
improved agriculture technology is not available. The farmer is depended on the traditional method to prepare
their land for cultivation. Wage rate of bullock pair is considered in a day.
2.2.1Analytical Framework
In this framework, the output (rice production) is treated as a stochastic production process and is defined as
the specification of Battese and Coelli (1995) model specification may be expressed as:
𝑌𝑖𝑡 = 𝐸𝑋𝑃(𝑋𝑖𝑡 𝛽+𝑉𝑖𝑡 − 𝑈𝑖𝑡 )
(1)
Where 𝑌𝑖𝑡 represent the production at the t-th observation (t = 1,2,..., T) for the i-th firm (i = 1,2,..., N); 𝑋𝑖𝑡 = a
(1 X k) vector of values of known functions of inputs of production in rice and other explanatory variables
associated with the i-th firm at the t-th observation ,  is a vector of unknown parameters for the stochastic
frontier. 𝑣𝑖𝑡 assumed to be iid N (0, 𝜎𝑣2 ) random errors, independently distributed of the 𝑈𝑖𝑡 , 𝑈𝑖𝑡 represents
non-negative random variables, associated with technical inefficiency of production, which are assumed to be
independently distributed, such that 𝑈𝑖𝑡 is obtained by truncation (at zero) of the normal distribution with
mean, 𝑍𝑖𝑡 𝛿 , and varianc 𝜎 2 ; 𝑍𝑖𝑡 is a (1 X m) vector of explanatory variables associated with technical
inefficiency of production of overtime and
𝛿 represents (m x 1) vector of unknown coefficient to be estimated. Since Rice producing always operates
under uncertainty, again the present study employs a stochastic production frontier approach introduced. In this
framework we add the following assumption that 𝑈𝑖𝑡 ’s are non-negative random variables which are assumed
to account for technical inefficiency in production and to be independently distributed as truncations at zero of

the N  ,  u
2
 distribution; where
𝑈𝑖𝑡 = 𝑍𝑖𝑡 𝛿 where 𝑍𝑖𝑡 is a 1  p  vector of explanatory variables which
may influence the inefficiency of rice producing in Bangladesh and  is a  p  1 vector of parameters to be
estimated 𝑈𝑖𝑡 = 𝑍𝑖𝑡 𝛿 + 𝑊𝑖𝑡 ……………………(2)
Where, the random variable 𝑊𝑖𝑡 follows truncated normal distribution with mean zero and variance  2 , such
that the point of truncation is −𝑍𝑖𝑡 𝛿 .Parameters of the stochastic frontier given by equation (1) and
inefficiency model given by equation (2) are simultaneously estimated by using maximum likelihood
estimation. After obtaining the estimates of 𝑈𝑖𝑡 the technical efficiency of the t-th observation (t = 1, 2... T) in
the i-th rice producing or farmers is given by:
𝑇𝐸𝑖𝑡 = 𝐸𝑋𝑃(−𝑈𝑖𝑡 ) = 𝐸𝑋𝑃(−𝑍𝑖𝑡 𝛿 − 𝑊𝑖𝑡 )
(3)
2.2.2Empirical Stochastic Frontier Model
There are several functional forms for estimating the relationship between inputs and output. Since the CobbDouglas functional form is preferable to other forms if there are three or more independent variables in the
model (Hanley and Spash 1993), the Cobb-Douglas production function with five independent variables was
applied in this study. Following Battese and Coelli (1995) the model (1) can be expressed into the Cobb-
Douglas stochastic frontier production functional form with logarithm. The empirical Stochastic Cobb-Douglas
frontier production model for technical inefficiency effect on Boro rice production can be expressed equation
(1) as follows
𝑙𝑛𝑌𝑖𝑡 = 𝛽0 + 𝛽1 ln( 𝑋1𝑖𝑡 ) + 𝛽2 ln( 𝑋2𝑖𝑡 )+ 𝛽3 ln(𝑋3𝑖𝑡 ) + 𝛽4 ln( 𝑋4𝑖𝑡 )+ 𝛽5 ln(𝑋5𝑖𝑡 ) + + 𝑉𝑖𝑡 − 𝑈𝑖𝑡
i=1, 2, 3;
t=1, 2, 3……..29
(4)
Where
𝑌𝑖𝑡 = production in the i-th rice (Boro, Aus and Aman) with t-th period.
𝑋1𝑖𝑡 = Area in the i-th rice with t-th period
𝑋2𝑖𝑡 = The quantity of seed of the -th rice in the i-th rice with t-th period
𝑋3𝑖𝑡 =The amount of Urea is used in the i-th rice with t-th period
𝑋4𝑖𝑡 =the amount of TSP is used in the i-th rice with t-th period
𝑋5𝑖𝑡 =the Amount of rainfall in the i-th rice with t-th period
𝛽0 , 𝛽1 , 𝛽2 , , 𝛽3 , 𝛽4 𝑎𝑛𝑑 𝛽5 =unknown parameter to be estimated
𝑙𝑛 = Refers to the natural logarithm
i=the number of rice (Boro, Aus and Aman)
t = time period
2.2.3 Technical Inefficiency Effect Model
The technical inefficiency effects model (2), 𝑈𝑖 are defined as
𝑈𝑖𝑡 = 𝛿0 + 𝛿1 𝑍1𝑖𝑡 + 𝛿2 𝑍2𝑖𝑡 + 𝛿3 𝑍3𝑖𝑡 + 𝛿4 𝑍4𝑖𝑡 + 𝑊𝑖𝑡
(5)
Where 𝑈𝑖𝑡 𝑖 ’s are non-negative random variables, assumed to be independently distributed such that the
technical inefficiency effect for the ith farmer, 𝑈𝑖𝑡 , were obtained by truncation of normal distribution with
mean zero and variance,  u2 such that
𝑍1𝑖𝑡 = the average temperature in the i-th rice with t-th period
𝑍2𝑖𝑡 = the average humidity in the i-th rice with t-th period
𝑍3𝑖𝑡 = in the i-th rice with t-th period the average wage rate of human labour without food.
𝑍4𝑖𝑡 = The wage rate of bullock pair in daily in the i-th rice with t-th period,
𝛿0 , 𝛿1 , 𝛿2, 𝛿3 𝑎𝑛𝑑 𝛿4 are parameters to be estimated
𝑊𝑖𝑡 were unobservable random variables or classical disturbance term, which are assumed to be independently
distributed, obtained by truncation of the normal distribution with mean zero and unknown variance,  u2 , such
that 𝑈𝑖𝑡 𝑖 is non- negative. The β, and δ coefficients are unknown parameters to be estimated, together with the
𝜎2
variance parameters which are expressed in terms of 𝜎 2 = 𝜎𝑣2 + 𝜎𝑢2 , 𝛾 = 𝜎𝑢2 , γ is the ratio of variance of farm
specific technical efficiency to the total variance of output and has a value between zero and one. The
estimates for all parameters of the inefficiency model (5) were estimated by using the Maximum Likelihood
(ML) method. The econometric computer software package FRONTIER 4.1 (Coelli, 1996) was applied to
estimate the parameters of stochastic frontier models using the ML method.
3 Results and Discussions
3.1.1Maximum-Likelihood Estimates of Stochastic Cobb-Douglas Frontier Production Model
The estimated parameters of technical efficiency (TE) model were reported in the Table 1. In the TE model, a
positive coefficient indicates the improvement of technical efficiency and vice-versa. In the result, seed and
area are found significant with positive coefficient. That is these variables have direct influence to increase the
level of efficiency. Again it was observed that coefficient of seed, fertilizer (urea) and area are significant these
indicated that these inputs are directly related with the TE. The negative coefficient of rainfall, fertilizer (urea)
and fertilizer (TSP) are indicated that over rainfall and more fertilizer will be cause of decreasing TE.
The value of γ (0.8430) is positive and significant at 1% level of significance. It can be interpreted as follows:
84 percent of random variation around in rice production due to inefficiency and 1 percent due to stochastic
random error. the estimated value of σ is (0.0019) was significantly different from Zero, indicate a good fit.
In inefficiency effects model, a positive coefficient indicates the decrease of technical efficiency and viceversa. The coefficient of temperature is positive and significant at 1 percent level of significance which is
indicated that is temperature has direct influence on rice production. Hence from the result, it was observed
that humidity and wage rate of labor were found decreasing the level of inefficiency. Hence the variable
humidity does not play any contributors role in producing rice production. The coefficient of wage rate of
labor was found negative but significant which indicated that farmers are unable to pay high rate of wage.
3.1.2 Year wise Efficiencies of Rice in Bangladesh
The year wise efficiency of three rice crop (Boro, Aus, Aman) in Bangladesh was displayed in Table 2: and
Figure 1. From this investigation we observed that the highest efficiency was in 2008 for Boro rice and the
lowest efficiency was in 1980 for each crop. The mean efficiency of three rice crops was found 0.86, .0.79 and
0.82 for Boro, Aus and Aman respectively. Hence the mean efficiency of Boro rice is better than others. Time
had an important effect in increasing efficiency. It was also revealed that the technical efficiency of the Aman
rice during the period 1980to 2008 was found to be 0.82. This implied that 82 percent of potential output was
being realized by the rice production that the technical efficiency had increased over time. From the figure, the
overall situation of three types of rice crops is to be clearly understood. Boro is most efficient (86 percent)
followed by the Aman rice was second most efficient (82 percent). These findings are in line with the
argument that included in Boro rice is superior as it is regular. Aman and Aus rice were relatively less efficient
than Boro rice. So it can be concluded that technical efficiency of Boro rice was improved more than Aus and
Aman over time. The result can interpret as government may give more attention to support in rice production
care in rice production providing technical support in the context of agricultural sector. From the figure it was
clear that but sometimes the Te are ups and down. Last five year from 2004 to 2008, the technical efficiency
was found higher and maintained almost same.
Conclusion
The results of this study show that the rice related productive factor included in the inefficiency effects model
have had significant influences upon the technical inefficiency. The impact of climate condition on rice
production will depend on actual patterns of climatic factors change in rice growing regions. From the study
we conclude that the agricultural input factor such as area, seed and fertilizer are responsible factor in rice
production system. The inefficiency effects model we observed that the climatic conditions are playing an
important role in our rice production i.e. the effects of maximum temperature would drastically reduce total
rice production and humidity indicates the decreasing the level of inefficiency. So, the effects of changing
climatic conditions on rice production give the higher technical inefficiency rate and we lost a significant
amount of rice production may hamper for only effects of those climatic conditions. In this regards proper
management practices (should be proper distribution and application of seed and fertilizer on the basis of area)
would also help to meet the food demand and achieve our desire rice production target under changing climatic
condition in future. Public awareness of the impact of climate conditions on the agricultural production
systems deserves priority consideration, and mitigating technologies must be developed, which will require
increased public and private investment. .
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Tables :
Table 1: Maximum-Likelihood estimates of stochastic frontier production by model in rice production
in Bangladesh.
VARIABLE
PARAMETER
Coefficient
2.4431*
CONSTANT
𝛽0
AREA
𝛽1
SEED
𝛽2
0.8377
0.1409*
FERU
𝛽3
-0.5501*
*
MODEL (2)
S.E
0.4510
T-Ratio
5.4164
0.0361
23.1537
0.0191
7.3501
0.0381
-14.4129
@
0.0114
-1.4788
0.0931
-0.4031
FERT
𝛽4
-0.1694
RANF
𝛽5
-0.3756@
Inefficiency effects model
CONSTANT
𝛿0
TEM
𝛿1
HUM
𝛿2
WRR
𝛿3
Coefficient
S.E
T-Ratio
-0.5956@
1.8197*
0.6821
0.6350
-0.8732
2.8652
-0.4297@
-0.8378*
0.4120
-1.0431
.11866
-7.0608
0.11952
1.233
.000325
0.0682
5.8614
12.344
@
WBR
𝛿4
0.1474
Sigma
Gamma
Ln- likelihood
𝜎2
𝛾
0.0019*
0.8430*
164.0921
Mean Efficiency
0.8289
*,**,** * Significance level at 1 0 0 , 5 0 0 , 10 0 0 , consecutively
Error
@ Means insignificant , S.E. = Standard
Table 2: Year wise Efficiencies of Boro, Aus, Aman Rice of Bangladesh
YEAR
1980-1981
1981-1982
1982-1983
1983-1984
1984-1985
1985-1986
1986-1987
1987-1988
1988-1989
1989-1990
1990-1991
1991-1992
1992-1993
1993-1994
1994-1995
1995-1996
1996-1997
1997-1998
1998-1999
1999-2000
2000-2001
2001-2002
2002-2003
2003-2004
2004-2005
2005-2006
2006-2007
2007-2008
2008-2009
Mean
Combined mean efficiency
BORO RICE
EFFICIENCY
0.6568
0.6555
0.6813
0.7056
0.7307
0.7366
0.7485
0.7756
0.7835
0.8526
0.8482
0.8643
0.8113
0.8703
0.8411
0.8733
0.9063
0.8956
0.9470
0.9494
0.9747
0.9670
0.9820
0.9865
0.9948
0.9908
0.9933
0.9973
0.9954
0.86259
AUS RICE
EFFICIENCY
0.5904
0.5990
0.5913
0.6390
0.6636
0.6552
0.6875
0.7195
0.7178
0.7014
0.7164
0.7550
0.7834
0.7667
0.7636
0.7980
0.8395
0.7788
0.8033
0.8810
0.9387
0.9533
0.9419
0.9563
0.9372
0.9806
0.9845
0.9916
0.9933
0.79751
0.8289
AMAN RICE
EFFICIENCY
0.6213
0.5806
0.5983
0.6243
0.6747
0.6768
0.7846
0.7124
0.7183
0.8007
0.7952
0.8346
0.8390
0.8292
0.8220
0.8488
0.8699
0.8208
0.8316
0.9092
0.9549
0.9552
0.9577
0.9868
0.9739
0.9871
0.9922
0.9879
0.9919
0.826893
1980-1981
1981-1982
1982-1983
1983-1984
1984-1985
1985-1986
1986-1987
1987-1988
1988-1989
1989-1990
1990-1991
1991-1992
1992-1993
1993-1994
1994-1995
1995-1996
1996-1997
1997-1998
1998-1999
1999-2000
2000-2001
2001-2002
2002-2003
2003-2004
2004-2005
2005-2006
2006-2007
2007-2008
2008-2009
Technical Efficiency
1.2
1
0.8
0.6
0.4
Boro
Aus
0.2
Aman
0
Year
Figure 1: Comparison of Year wise technical Efficiency of Boro, Aus and Aman Rice in Bangladesh