The Welfare Impacts of Commodity Price
Volatility: Evidence from Rural Ethiopia
M A R C F. B E L L E M A R E
CHRISTOPHER B. BARRETT
D AV I D R . J U S T
UNIVERSITY OF ADELAIDE
SCHOOL OF ECONOMICS
APRIL 5, 2013
Introduction
 Governments have often set commodity price stability
as a goal of economic policy (Krueger et al. 1988).
 Many policy instruments (e.g., buffer stocks,
administrative pricing, variable tariffs, marketing
boards), but price stabilization has typically met with
very limited success.
 After a period of significant research on the topic in the
1970s (Newbery and Stiglitz 1981), price stabilization
had fallen off the policy agenda by the 1990s.
Introduction
 But since the mid-1990s, commodity prices have been
reached highest level in
~30 years in 2008-10
(exact date varies by
measure).
25
FAO Real Food Price Index Volatility
20
15
10
5
0
6/1990
6/1991
6/1992
6/1993
6/1994
6/1995
6/1996
6/1997
6/1998
6/1999
6/2000
6/2001
6/2002
6/2003
6/2004
6/2005
6/2006
6/2007
6/2008
6/2009
6/2010
6/2011
6/2012
 Food price volatility
Six month lagged std dev of
FAO food price Index (2002-4 = 100)
on a rollercoaster ride (Cashin and McDermott 2002,
Roache 2010, Jacks et al. 2011).
Introduction
 Increased food price volatility – “price risk” or “price
uncertainty” – (along with higher food prices) has
rekindled popular interest in commodity price
stabilization.
 Several governments recently (re)introduced price
stabilization schemes.
 For the first time in years, international agencies are
discussing policy options for food price stabilization
(World Bank 2008, FAO 2010, IFAD 2011).
Definitional Aside
 We are concerned with price volatility, i.e., fluctuations
around a given price level, reflected in V(p).
 Many (mis)use the term “volatility” during food spikes
when they worry about high price levels. But volatility
encompasses both upward and downward spikes.
Introduction
 The impulse toward stabilization of domestic food
prices commonly arises because of three commonly
held beliefs:
Households value price stability;
2. The poor suffer disproportionately from food price
instability; and
3. Futures and options markets for hedging against
food price risk are uncommon in developing
countries and inaccessible to smallholder households
1.
Introduction
 Few would dispute point 3, but empirical tests of
points 1 and 2 are noticeably absent from the
literature.
 Given the policy importance of price stabilization, our
toolkit for understanding the relationship between
price volatility and household welfare remains
surprisingly dated and limited.
Introduction
 We address this important gap by studying whether (i)
households value price stability and (ii) the poor suffer
disproportionately from food price instability.
 We derive an estimable measure of multiple
commodity price risk aversion and the associated
willingness to pay for price stabilization.
Introduction
 We then apply this measure to rural Ethiopian
households, who can in principle both produce and
consume several commodities characterized by
uncertain prices.
 Prices in the data are highly variable, as coefficients of
variation range from 18 to 39 percent among the
commodity prices we study.
Key Findings
 The average household in the data is willing to give up
18 percent of its income to fully stabilize the prices of
the 7 most important food commodities in the data.
 Nonparametric analysis of household-specific WTP
estimates suggests that, contrary to conventional
wisdom, the welfare gains of price stabilization (as
proxied by WTP to stabilize prices) are increasing in
household income in the rural Ethiopian context.
Outline
Introduction
2. Theoretical Framework
3. Data and Descriptive Statistics
4. Empirical Framework
1.
1.
2.
5.
Estimation Results
1.
2.
3.
6.
Estimation Strategy
Identification Strategy
Marketable Surplus Equations
Price Risk Aversion Matrix
Estimated Willingness to Pay for Price Stabilization
Conclusions
Theoretical Framework
 We study the welfare implications of multiple
commodity price volatility by developing a simple,
two-period unitary agricultural household model
(Singh et al. 1986, Bardhan and Udry 1999).
 The unitary agricultural household model treats the
household as a single agent which both produces and
consumes one or more staple crops.
Theoretical Model
 Consider a representative agricultural household
whose preferences are represented by a von NeumannMorgenstern utility function U(∙) defined over
consumption of a vector co = (co1, …, coK) of K
commodities observed in the data with associated
prices p = (p01, …, p0K), a composite good cu of all
commodities not observed in the data with associated
price pu, and leisure ℓ.
 The function U(∙) is increasing and concave, and
satisfies the Inada condition at zero.
Theoretical Model
 All K goods observed in the data can, in principle, also
be produced by the household using its endowment of
land WH and its endowment of labor WL following the
production process Foi(Loi,Hoi) for all i = 1, …, K, where
Loi and Hoi denote the amount of labor and land used in
producing crop i. A similar relationship holds for the
unobservable composite good u.
 All production functions are increasing and concave.
Theoretical Model
 Without defining each variable and each constraint in
the full model, the household eventually maximizes
{H
h
oit
,H
h
ut
,H
f
ut
,H
m
t
max
m
h
, L t , L oit , H
f
oit
f
, L oit
h
, L ut
f
, L ut
E
, t }
max
{ c ot  1 , c ut  1 }
U ( c ot  1 , c ut  1 ,  t )
subject to a number of constraints.
This means that the household makes its production
decisions ex ante at time t, ahead of realized prices, but
that it takes its consumption decision ex post at time t
+ 1, after price uncertainty is realized.
Theoretical Model
 The previous maximization problem can be reduced to
a variable indirect utility function (Epstein 1975):
{H
h
oi
h
, L oi
,H
max
f
f
h
f
oi , L oi , L u , L u
,H
m
, }
EV (  , p i , y )
which is also subject to Beckerian full-income
constraint:
Y  w [ T     L   L  L  L ]  r [W   H   H
L
i
f
oi

i

h
oi
f
u
h
u
H
f
oi
i
i
h
oi
H u  H u ]
f
h
i
p i Foi ( L oi , H oi )  Fu ( L u , H u )  I
with FONCs modified to incorporate uncertain prices.
Theoretical Framework
 This allows summarizing the household’s demand and
supply of each crops into a single variable, i.e., the
household’s marketable surplus Mi for each crop, equal
to the difference of production less consumption:
M iklt  Fi ( L iklt , H iklt )  c iklt
 For each crop (i), a household (k) in village (l) and
period (t) can be a net seller, autarkic, or a net buyer,
and a household’s position vis-à-vis the market often
changes within a given year (e.g., “buy high, sell low”).
Theoretical Framework
 The effects of price volatility on producers are well
known (Baron 1970, Sandmo 1971): output price
uncertainty means firms employ fewer inputs, forgoing
expected profits to hedge against price volatility.
 This has been extended to consumers (Waugh 1944,
Deschamps 1973, Hanoch 1977, Turnovsky et al. 1980,
Newbery & Stiglitz 1981) who are thought to be price
risk loving for a specific commodity when the budget
share of that commodity is not too large.
Theoretical Framework
 But recall that agricultural households are both
producers and consumers.
 Thus, it is entirely possible for some households to be
price risk averse, for others to be price risk neutral,
and for yet others to be price risk loving.
 So it is impossible to determine a priori whether
agricultural households – who may be net buyers or
sellers or autarkic – are hurt by price volatility.
Theoretical Framework
 Ultimately, we derive a matrix of price risk aversion:
 A11

A 21

A
 

 AK1
A12

A 22



AK 2

A1 K 

A2 K

 

A KK 
Each element of A is a price risk aversion coefficient,
analogous to Arrow-Pratt income risk aversion coefficients.
For example, A11 denotes aversion to variance in the price
of commodity 1, and A12 denotes aversion to covariance
between the prices of commodities 1 and 2.
Theoretical Framework
 In matrix A,
Aij > 0 indicates that the household is price risk averse over
commodities i and j, i.e., the household is hurt by a positive
covariance between those two prices.
 Aij = 0 indicates that the household is price risk neutral over
commodities i and j, i.e., the household is unaffected by the
covariance between those two prices.
 Aij < 0 indicates that the household is price risk loving over
commodities i and j, i.e., the household benefits from a
positive covariance between those two prices.

Theoretical Framework
 Each element Aij of matrix A is such that
A ij  
Mi
pj

j
( j  R )   ij

where Mi is the marketable surplus of commodity i, pj is
the price of commodity j, j is the budget share of
commodity j, ηj is the income elasticity of the
marketable surplus of commodity j, R is the
household’s coefficient of relative risk aversion, and εij
is the elasticity of the marketable surplus of
commodity i relative to price j.
Theoretical Framework
 We then derive the hh’s willingness to pay (WTP) to
stabilize prices – the welfare it would derive from
stable prices, expressed as a percentage of its income.
 Our measure of WTP to stabilize prices is such that
WTP 
1
 
2
K
K
i 1
j 1
 ij Aij
where ij denotes the covariance between prices i and j
and Aij are elements of the A matrix of price risk
parameters.
Data and Descriptive Statistics
 We use four rounds (1994a, 1994b, 1995, and 1997) of
the Ethiopian Rural Household Survey (ERHS) data.
 Each round includes up to three seasons. The full
sample includes 8,518 hh-season observations, with a
mean of 5.7 seasonal observations per household.
 The data includes households across 16 districts
(woreda) with an attrition rate of 2 percent across the
four rounds selected for analysis (Dercon and
Krishnan, 1998).
Data and Descriptive Statistics
 We focus on coffee, maize, beans, barley, wheat, teff,
and sorghum: 7 most traded commodities in the data.
 The average household is a net buyer of each, but
much variation in marketable surplus positions, with
median=0 for all crops but coffee.
Data and Descriptive Statistics
 Considerable variation in prices of those 7 products.
Also control for other food prices (all in real Eth birr).
Data and Descriptive Statistics
 Households have very low income (avg = US$376/yr).
 18% have zero-valued income observations due to
crop failure, unemployment, etc.
 Lots of variation in commodity budget shares
Mean
Income
Income (Birr)
Nonzero Income (Birr)
Std. Dev.
886.17
1087.35
Budget Shares of Marketable Surpluses
Budget Share of Coffee
-0.15
Budget Share of Maize
-0.13
Budget Share of Beans
-0.07
Budget Share of Barley
-0.12
Budget Share of Wheat
-0.11
Budget Share of Teff
-0.21
Budget Share of Sorghum
-0.06
(9869.70)
(10922.88)
(1.07)
(0.41)
(0.17)
(0.53)
(0.44)
(0.70)
(0.33)
Median
271.62
403.32
-0.09
0.00
0.00
0.00
0.00
0.00
0.00
Min
Max
0.00 820625.80
0.64 820625.80
-0.99
-1.00
-1.00
-1.00
-0.99
-0.99
-1.00
0.99
0.99
0.91
0.99
0.96
0.99
1.00
Empirical Framework
 Recall that each element Aij of matrix A is such that
A ij  
Mi
pj

j
( j  R )   ij

 Mi (marketable surplus, or production remaining to be
sold after consumption) and pj are both directly
observable in the data, and parameter j can be
computed directly from the data as well.
 Parameters ηj and εij can be estimated from marketable
surplus equations. More on this in a second.
Empirical Framework
 Ideally, the coefficient of relative risk aversion R would
be elicited in the field using experimental methods.
 Not available in ERHS, so we assume R = 1, which is
well within the range of credible estimated values in
the literature.
 Have replicated w/other values. Qualitative results
unchanged as estimates scale monotonically w/R.
Empirical Framework
 We estimate seven (one for each of the seven
commodities retained for analysis) of the following
marketable surplus equations by SUR:
M
*
ik  t
  i i y
*
kt
  ij 
7
j 1
p j t   i d k   i d  t   ik  t
*
where subscripts denote crop i for household k in
district ℓ in round t.
 M is marketable surplus, y is income, p is a price, dk is a
household fixed effect, dlt is a district-round fixed
effect, and  is an error term with mean zero.
Brief technical aside
M
*
ik  t
  i i y
*
kt
  ij 
7
j 1
p j t   i d k   i d  t   ik  t
*
An asterisk (*) denotes an inverse hyperbolic sine (IHS)
transformation:
x  sinh
*
1
x  log( x 
x  1)
2
This allows us to keep zero- and negative-valued
observations without having to add a distortionary factor
to all observations. Plus can interpret coefficient
estimates s as elasticities (Burbidge et al. 1988,
MacKinnon and Magee 1990, Pence 2006).
Empirical Framework
So we compute the Aij estimates from the estimated
marketable surplus equations as follows:
M
*
ik  t
  i i y
*
kt
  ij 
A ij  
Mi
pj

7
*
j 1
j
p j t   i d k   i d  t   ik  t
( j  R )   ij

j


p jM
y
j
Empirical Framework
M
*
ik  t
  i i y
*
kt
  ij 
A ij  
Mi
pj

7
*
j 1
j
p j t   i d k   i d  t   ik  t
( j  R )   ij

j


p jM
y
j
Empirical Framework
M
*
ik  t
  i i y
*
kt
  ij 
A ij  
Mi
pj

7
*
j 1
j
p j t   i d k   i d  t   ik  t
( j  R )   ij

j


p jM
y
j
Empirical Framework
M
*
ik  t
  i i y
*
kt
  ij 
A ij  
Mi
pj

7
*
j 1
j
p j t   i d k   i d  t   ik  t
( j  R )   ij

j


p jM
y
j
Empirical Framework
M
*
ik  t
  i i y
*
kt
  ij 
A ij  
Mi
pj

7
*
j 1
j
p j t   i d k   i d  t   ik  t
( j  R )   ij

j


p jM
y
j
Empirical Framework
 What about statistical identification? In an ideal world, we
would randomly assign prices and income levels to each
household in each time period.
 Unfortunately, we do not live in that ideal world, and we
have to rely on observational data. This is intrinsic to the
nature of the problem.
 The identification here comes from our use of longitudinal
data, and thus of household and district-round fixed effects
to purge much, but not all, prospective endogeneity due to
unobserved heterogeneity or reverse causality.
Empirical Framework
 Household fixed effects control for the systematic, time
invariant way in which households form their price
expectations and earn their income.
 Use village-level prices to avoid hh-level price endogeneity
 District-round fixed effects control for departures from the
systematic way in which each household forms its price
expectations by accounting for the price information
available to each household in a given district in a given
time period.
Empirical Framework
 Still, fixed effects are not a panacea, so we caution
against interpreting our estimates as strictly causal.
 We run a battery of robustness checks to ensure the
core, qualitative results hold up to other reasonable
estimation approaches.
 But we equally caution against ignoring crucial policy
questions for which perfect identification is just not
feasible. Too important an issue not to weigh in as
best as we can with the tools available to us.
Estimation Results
 Results appear sensible: reasonable signs/magnitudes.
Table 5: Seasonal Marketable Surplus Equation Estimates
(1)
(2)
(3)
(4)
Variables
Coffee
Maize
Beans
Barley
Dependent Variables: Marketable Surplus of Each Commodity
Price of Coffee
0.536**
3.340***
0.656**
-1.692***
(0.230)
(0.444)
(0.290)
(0.417)
Price of Maize
-0.330
4.330***
0.545
0.316
(0.460)
(0.889)
(0.581)
(0.835)
Price of Beans
-0.697
-4.414***
0.933
2.571**
(0.578)
(1.117)
(0.731)
(1.049)
Price of Barley
-2.013***
0.365
0.361
1.835**
(0.469)
(0.905)
(0.592)
(0.850)
Household Income
0.115***
0.180***
0.015
0.215***
(0.009)
(0.017)
(0.011)
(0.016)
Observations
8,518
8,518
8,518
8,518
R-squared
0.174
0.171
0.098
0.157
Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. Includes household and
district-round fixed effects, controls for other commodity prices.
Estimation Results
 Except for wheat, the own-price elasticities are
positive (coffee, maize, barley) or not significant
(beans, teff, sorghum).
 This means that as the price of a commodity increases,
households produce (consume) more (less) of them.
 For wheat, this is likely because of the profit effect
(Singh et al. 1986): as wheat price increases, the
household might make so much profit as to decrease
its quantity sold.
Estimation Results
 Except for beans, whose income elasticity is not
significant, income elasticities are all positive.
 This means that as household income increases, a
household produces (consumes) more (less) of those
crops.
 This makes sense for staples, since they are usually
inferior goods (Bennett 1941).
Estimation Results
 Price risk aversion estimates likewise look sensible
Table 6a: Estimated Matrix of Price Risk Aversion for Relative Risk Aversion R = 1 (N = 8518)
Coffee
Maize
Beans
Barley
Wheat
Teff
Sorghum
Coffee
7.200
(1.528)
40.283
(1.450)
2.951
(0.109)
-9.887
(0.528)
2.235
(0.147)
13.812
(0.530)
2.144
(0.135)
Maize
-1.865
(0.229)
619.379
(20.738)
19.307
(0.548)
27.202
(1.895)
-239.443
(14.714)
305.788
(11.756)
11.641
(0.961)
Beans
-4.854
(0.306)
-291.741
(9.414)
31.923
(0.936)
127.682
(5.700)
-42.106
(1.982)
2.280
(0.541)
-9.884
(0.661)
Barley
-17.834
(1.607)
37.066
(1.810)
18.214
(0.750)
227.309
(10.612)
-37.143
(2.769)
-24.684
(1.809)
85.849
(4.459)
Wheat
-10.862
(0.829)
-269.469
(9.594)
128.988
(3.363)
219.168
(10.098)
23.787
(5.973)
81.363
(3.273)
-62.620
(3.522)
Teff
38.506
(2.544)
194.685
(6.615)
-22.697
(0.714)
-117.312
(5.323)
229.359
(11.204)
102.842
(5.234)
-6.230
(0.753)
Sorghum
-21.604
(1.709)
210.238
(7.506)
-96.824
(2.471)
-372.571
(16.955)
94.698
(5.048)
-166.878
(6.243)
45.352
(2.173)
Estimation Results
 Note that, in decreasing order of price risk aversion,
the average household is averse to fluctuations in the
price of maize, barley, teff, sorghum, beans, wheat, and
coffee (for equivalent variances).
 This is roughly what one would expect: staples
“matter” most.
Estimation Results
 WTP is perhaps more interesting and policy-relevant.
This turns on A estimates but also price covariances.
As conventional wisdom predicts, mean WTP>0.
Table 7: Estimated WTP for Price Stabilization
Commodity
Coffee
Maize
Beans
Barley
Wheat
Teff
Sorghum
Total
WTP
0.091
0.042
0.003
0.018
0.001
0.008
0.004
0.167
Ignoring
Covariances
(Std. Err.)
***
(0.019)
***
(0.001)
***
(0.000)
***
(0.001)
***
(0.000)
***
(0.000)
***
(0.000)
***
(0.019)
Including Covariances,
Row-Based
WTP
(Std. Err.)
0.107 ***
(0.019)
0.052 ***
(0.002)
-0.019 ***
(0.001)
0.015 ***
(0.001)
0.007 ***
(0.001)
0.024 ***
(0.001)
-0.008 ***
(0.001)
0.179 ***
(0.019)
Estimation Results
 But contrary to conventional wisdom, WTP appears to
increase significantly in hh income. So in this context
price stabilization appears distributionally regressive.
Conclusions
 Two contributions to the literature:
1.
First, we derive an estimable matrix of price risk aversion
coefficients over multiple commodities in a general
(AHM) framework, and provide an empirical illustration
using panel data from rural Ethiopia.
2.
Second we look at the welfare impacts of price volatility
(and thus of price stabilization) in data. This provides the
first empirical tests of conventional wisdom about price
stabilization policy based on household data.
Conclusion
Key take-away findings:
The average rural Ethiopian household would be
willing to pay 18% of its income to stabilize completely
stabilize the seven key food commodity prices.
Though virtually all households favor stable prices, it is
the wealthier households who gain (lose)
disproportionately from price stabilization (volatility).
Conclusion
 In other words, price stabilization would yield net welfare
gains in these data, but regressively so.
 This is consistent with Lindert’s (1991) “developmental
paradox,” the empirical regularity whereby price
stabilization policies become increasingly common as
countries develop. Anderson (2010): “poor countries tax
farmers, rich countries subsidize them.”
 Our findings clash with conventional wisdom, which posits
that food price volatility disproportionately hurts the poor.
Thank you for your interest and comments