The Welfare Impacts of Commodity Price Volatility: Evidence from Rural Ethiopia

M A R C F. B E L L E M A R EC H R I S T O P H E R B . B A R R E T T

D AV I D R . J U S T

U N I V E R S I T Y O F A D E L A I D ES C H O O L O F E C O N O M I C S

A P R I L 5 , 2 0 1 3

The Welfare Impacts of Commodity Price Volatility: Evidence from Rural Ethiopia

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 on a rollercoaster ride (Cashin and McDermott 2002, Roache 2010, Jacks et al. 2011).

Food price volatility reached highest level in~30 years in 2008-10(exact date varies by measure).

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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:

1. Households value price stability; 2. The poor suffer disproportionately from food price

instability; and3. Futures and options markets for hedging against

food price risk are uncommon in developing countries and inaccessible to smallholder households

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

1. Introduction2. Theoretical Framework3. Data and Descriptive Statistics4. Empirical Framework

1. Estimation Strategy2. Identification Strategy

5. Estimation Results1. Marketable Surplus Equations2. Price Risk Aversion Matrix3. Estimated Willingness to Pay for Price Stabilization

6. 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 Neumann-Morgenstern 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

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.

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Theoretical Model

The previous maximization problem can be reduced to a variable indirect utility function (Epstein 1975):

which is also subject to Beckerian full-income constraint:

with FONCs modified to incorporate uncertain prices.

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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:

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”).

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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.


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.


Ultimately, we derive a matrix of price risk aversion:

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.

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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.


Each element Aij of matrix A is such that

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.

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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

where ij denotes the covariance between prices i and j and Aij are elements of the A matrix of price risk parameters.

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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).


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.


Considerable variation in prices of those 7 products. Also control for other food prices (all in real Eth birr).


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 Std. Dev. Median Min Max

Income Income (Birr) 886.17 (9869.70) 271.62 0.00 820625.80

Nonzero Income (Birr) 1087.35 (10922.88) 403.32 0.64 820625.80

Budget Shares of Marketable Surpluses Budget Share of Coffee -0.15 (1.07) -0.09 -0.99 0.99

Budget Share of Maize -0.13 (0.41) 0.00 -1.00 0.99 Budget Share of Beans -0.07 (0.17) 0.00 -1.00 0.91 Budget Share of Barley -0.12 (0.53) 0.00 -1.00 0.99 Budget Share of Wheat -0.11 (0.44) 0.00 -0.99 0.96 Budget Share of Teff -0.21 (0.70) 0.00 -0.99 0.99 Budget Share of Sorghum -0.06 (0.33) 0.00 -1.00 1.00

Empirical Framework

Recall that each element Aij of matrix A is such that

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.

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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:

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.

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Brief technical aside

An asterisk (*) denotes an inverse hyperbolic sine (IHS) transformation:

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).

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Empirical Framework

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Empirical Framework

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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 sensibleTable 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 -1.865 -4.854 -17.834 -10.862 38.506 -21.604

(1.528) (0.229) (0.306) (1.607) (0.829) (2.544) (1.709)

Maize 40.283 619.379 -291.741 37.066 -269.469 194.685 210.238

(1.450) (20.738) (9.414) (1.810) (9.594) (6.615) (7.506)

Beans 2.951 19.307 31.923 18.214 128.988 -22.697 -96.824

(0.109) (0.548) (0.936) (0.750) (3.363) (0.714) (2.471)

Barley -9.887 27.202 127.682 227.309 219.168 -117.312 -372.571

(0.528) (1.895) (5.700) (10.612) (10.098) (5.323) (16.955)

Wheat 2.235 -239.443 -42.106 -37.143 23.787 229.359 94.698

(0.147) (14.714) (1.982) (2.769) (5.973) (11.204) (5.048)

Teff 13.812 305.788 2.280 -24.684 81.363 102.842 -166.878

(0.530) (11.756) (0.541) (1.809) (3.273) (5.234) (6.243)

Sorghum 2.144 11.641 -9.884 85.849 -62.620 -6.230 45.352

(0.135) (0.961) (0.661) (4.459) (3.522) (0.753) (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

Ignoring Including Covariances,

Covariances Row-Based

Commodity WTP (Std. Err.) WTP (Std. Err.) Coffee 0.091 *** (0.019) 0.107 *** (0.019)

Maize 0.042 *** (0.001) 0.052 *** (0.002)

Beans 0.003 *** (0.000) -0.019 *** (0.001)

Barley 0.018 *** (0.001) 0.015 *** (0.001)

Wheat 0.001 *** (0.000) 0.007 *** (0.001) Teff 0.008 *** (0.000) 0.024 *** (0.001) Sorghum 0.004 *** (0.000) -0.008 *** (0.001)

Total 0.167 *** (0.019) 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

The Welfare Impacts of Commodity Price Volatility: Evidence from Rural Ethiopia

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