World Supply and Demand of Food Commodity Calories

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1 World Supply and Demand of Food Commodity Calories THIS DRAFT: January 26, 2009 A Paper Prepared for the European Association of Environmental and Resource Economists June 2009 ABSTRACT This paper exploits weather-induced yield shocks to estimate world supply and demand for the sum of edible calories derived from corn, soybean, wheat and rice. These four crops comprise about 75% of the caloric content of food production worldwide. 1 Aggregating crops and on a caloric basis facilitates a simple yet broad-scale analysis of the supply and demand of staple food commodities. Weather-induced yield fluctuations provide a compelling naturally random source of variation to identify both supply and demand elasticities. We use these estimates to predict the price increase of food staple calories stemming U.S. ethanol policy.

2 Between the summers of 2006 and 2008, corn prices more than tripled from roughly $2.50/bushel to nearly $8.00/bushel. Prices for rice, soybeans, and wheat rose by similar or greater amounts. The exceptionally large and unanticipated rise in prices was attributed to many factors, including: (i) ethanol subsidies; (ii) commensurately rising oil prices; (iii) unexpectedly large demand growth from China and India; and (iv) weatherrelated factors, such as drought in Australia. While some have argued that the commodity price boom, much like earlier housing and stock market booms, were due to a speculative bubble, it is difficult to reconcile a bubble with an absence of inventory growth. Yet, inventories of all major commodities remained at historically low levels throughout the boom. Recently, prices have fallen precipitously, due to a large inward shift in demand stemming from the global economic slowdown. Whatever the explanation or combination of explanations, recent commodity price swings suggest a reexamination of economic models of food commodities. High prices for staple grains can cause hunger, malnutrition, and riots in developing nations. It is therefore important for policy makers to know the extent to which interventions, such as ethanol subsidies, contributed to the problem. In this paper we exploit yield shocks--deviations from country and crop-specific yield trends that are arguably due to weather--to estimate world supply and demand for the sum of edible calories derived from corn, soybean, wheat and rice. These four crops comprise about 75% of the caloric content of food production worldwide. 1 These crops are also close substitutes in production and/or demand so the per-calorie prices are similar and tend to vary synchronously over time. Aggregating crops and on a caloric basis facilitates a simple yet broad-scale analysis of the supply and demand of staple food commodities. Agricultural commodity markets are often cited as the archetypal example of competitive markets, having many price taking producers and buyers and well-developed spot and futures markets. The empirical challenge is to separate supply and demand 1

3 curves in the market s formation of prices and quantities. Correct identification requires instruments that shift one curve (supply or demand) in a way that is plausibly unrelated to shifts in the other curve. Since P.G. Wright s (1928) introduction of instrumentalvariable estimation, weather has been considered a natural instrument for supply shifts, which can be used to facilitate unbiased demand estimation. The idea is that weather shifts supply in a way that is unrelated to demand shifts. Surprisingly, the literature in agricultural economics that uses weather-based instruments for supply shocks to identify demand curves is extremely thin. We also show how weather-induced yield shocks can be used to identify the supply curve. Past weather shocks affect current inventories and thus expected future prices via storage. If past yield-shocks are bad and inventories are at low levels, then demand for new production goes up. In other words, past weather shocks exogenously shift demand for current production in a way that is plausibly unrelated to shifts in the current supply curve. A Simple Model of Supply and Demand Consider a basic model of supply and demand for food commodity calories: (1) Supply: log(s t ) = α + β log(p t-1 ) + f(t) + u t (2) Demand: log(d t ) = κ + γ log(p t ) + g(t) + v t Quantities supplied and demanded are denoted by S t and D t, respectively; P t is price; the parameters β and γ are supply and demand elasticites; α and κ are intercepts; f(t) and g(t) capture trends in supply and demand, stemming from technological change, population and income growth, and u t and v t are other unobserved factors that shift supply and demand. Note that farmers make planting decisions before a year s weather shock is realized, and hence the supply equation depends on prices expected in the current period. Prices are close to random walks and hence last period s price is a good forecast for today s expected price. Both augmented Dickey-Fuller (p-value= 0.49) and Phillips- Perron (p-value=0.30) tests fail to reject the null hypothesis of a unit root prices. 2 2

4 Storage is a characteristic feature of all four commodity markets. As a result, equilibrium is defined not by the prices and quantities where supply equals demand, but where supply equals demand plus the net change in storage (denoted N t ). (3) Equilibrium: S t = D t + N t In estimation, we do not focus on the theoretical underpinnings of speculative storage (a dynamic and forward looking decision), but we do account for storage and the fact that it, like prices, quantity supplied, and quantity demanded, are endogenous. And because we aggregate commodities over all countries there is no need to consider exports or imports. Prices P t are the key endogenous variables on the right-hand side of both supply and demand. The crux of the identification problem is to identify supply and demand elasticities given unobserved shifts in supply and demand (u and v) influence prices via the equilibrium identity. Without correcting for the endogeneity of prices, the supply elasticity would be biased negatively, since unobserved positive supply shifts (u) would tend to reduce price all else the same, creating a negative correlation between u and price. A naïve demand elasticity estimate would tend to be biased positively, since unobserved positive demand shifts (v) would tend to increase price all else the same, creating a positive correlation between v and price. Identification of Demand Identifying the demand elasticity γ requires an instrument that shifts supply in a way that is plausibly unrelated to unobserved shifts in demand. Technically, the instrument is a component of v plausibly unrelated to u. For short-run demand, weather-induced yield shocks are a natural choice, due to their pure economic exogeneity (farmers cannot affect the weather), near randomness (unpredictability at planting time), and because weather is likely to have little or no influence on demand, except via its influence on price. The last point stems from the fact that there are well-established international markets with a significant share traded internationally. Thus, demand is derived from 3

5 world markets comprised of firms and individuals that often reside far from the locations experiencing specific weather and production outcomes. Demand for the four basic commodities comes from various sources. These commodities are a primary source of food, especially for rice and wheat. Corn and soybeans are also used as feed for livestock and dairy operations, among many other uses. Finally, there is an emerging market for ethanol, which uses a rapidly growing share of corn production in the United States. P.G. Wright (1928) was first to use weather as an instrument for demand identification when he introduced the instrumental variables technique. A key difference from Wright is that we simultaneously consider the four key commodities that are substitutes in supply and demand. It is important to consider these crops simultaneously so coincident weather effects on crops that are substitutes in production do not confound own-price elasticities with cross-price elasticities. We aggregate the caloric value of all four crops. Future research might simultaneously estimate equations for all crops, including cross-price elasticities, but identification could be more challenging. Our proxy for weather-induced yield shocks are deviations from country-specific trends in yield (output per hectare) for each crop. Country-and-crop-specific deviations are then converted to calories and aggregated to obtain a world supply shock. Our premise is that these deviations from yield shocks are largely due to weather. This premise is supported by the fact that farm and county-level data show considerable variability in deviations from a yield trend, but have almost no autocorrelation (Roberts and Key, 2002; and Roberts, O'Donoghue and Key, 2005). Such a pattern is consistent with random weather shocks, but less consistent with structural shifts or technological innovations that would likely display a higher degree of autocorrelation. A more advanced study might rely on specific weather variables as instruments. Limited global weather data limit the practicability and statistical power of this approach at the present time. 4

6 Identification of Supply A novelty of our approach is that we use weather (yield shocks) to identify the supply elasticity β in addition to the demand elasticity. We can do this by looking at inventory levels and storage, which links demand for new production with past weather shocks. Negative yield-shocks reduce supply and inventories while increasing the price, thereby shifting demand for new production. These past weather shocks are unlikely to be associated with current supply shifters, such as pest infestations or technological change. Put another way, past weather-induced yield shocks, via storage, exogenously shift demand for future production, allowing for clear identification of supply. As mentioned above, weather-induced yield shocks, show considerable variability but have almost no autocorrelation, which aids identification of demand. Commodity price shocks, on the other hand, are well known to have a large degree of persistence that stems from storage (Deaton and Laroque, 1992, 1996; Williams and Wright, 1991). Price autocorrelation, however, may also stem from factors besides storage, such as persistent demand shocks (e.g., global income growth). Within the aggregate supply and demand framework above, past weather shocks affect future price by changing future inventories via storage (N t ). Thus, we can think of these past weather shocks, not as a component of the raw demand shifters (v), but as shifters in the demand for current supply, (D t + N t ), the right-hand side of the equilibrium condition. Because N t is linked to past yield shocks, demand for current supply (and expected prices) shifts with past yield shocks. Using past yield shocks as an instrument for current expected prices would seem to be a useful improvement over the standard method (stemming from Nerlove, 1956), that estimates supply response using futures prices, the lagged prices, or time-series forecasted prices as a proxy for expected prices at planting time. The problem with the standard approach is that expected prices are still confounded by non-weather 5

7 components of unobserved supply shifters (u). Anticipated supply shocks affect expected prices so expected prices remain endogenous to supply. The use of past yield shocks as an instrument for expected price may pose some potential problems. Pest infestations or technology shocks that persist for multiple years may shift both expected prices and future supply. However, the fact that both farm-level data as well as aggregated data show little or no autocorrelation in yields suggests that in practice such problems are likely small (Roberts and Key, 2002; and Roberts, O'Donoghue and Key, 2005). Supply response occurs largely via acreage changes, not yield changes. Moreover, small locally persistent yield shocks are likely dominated by aggregate transitory variation in weather. Data World production and storage data are publicly available from the Food and Agriculture Organization (FAO) of the United Nations ( The data include production, area harvested, yields (ratio of total production divided by area harvested), and stock variation (change in inventories) for each of the four key crops. These variables are converted into edible calories using conversion factors by Williamson and Williamson (1942). Consumption (quantity demanded) is calculated as production minus the net change in inventories. Yield shocks were calculated by taking jackknifed residuals from fitting separate yield trends for each crop in each country. 3 Trends and shocks were estimated for any country with an average of one percent or more of world production and remaining restof-world yields were pooled and treated as a single country for each crop. Yield shocks were derived from both linear and quadratic trends and showed small and statistically insignificant autocorrelation. Shocks derived from both linear and quadratic trends give similar results so we only report data and results from quadratic trends. 6

8 We derived caloric shocks for each country and crop using the product of (i) country-and-crop-specific yield shocks, (ii) hectares harvested, and (iii) the ratio of calories per production unit. The world caloric shock is simply the sum of all countryspecific shocks. Aggregating country and crop specific yield shocks purges production variation stemming from endogenous land expansion or contraction. The world caloric shocks were scaled relative to the world trend in total caloric production. 4 Prices are those received by U.S. farmers in the month of December of each year, publicly available from the U.S. Department of Agricultural ( which were then deflated by the Consumer Price Index. Prices for each commodity are converted to their caloric equivalent with the world calorie price taken as worldproduction-weighted averages of the four commodities. Data on quantities and prices are displayed in figure 1 for the years The FAO series on stock variation, necessary for derivation of consumption, ends in Four features are of note: (1) production and consumption have been trending up steadily; (2) fluctuations around the trend in production are small in proportion to the trend and consumption fluctuations are even smaller, due to the smoothing from storage accumulation and depletion; (3) price fluctuations are proportionately much larger than quantities; (4) prices fluctuate negatively in comparison to quantities produced. Features (2) and (3) suggest that both supply and demand are inelastic. Feature (4) suggests production fluctuations have a lot to do with the weather, with exogenous supply shifts causing movement along the demand curve. Also indicative of weather, deviations around the production trend also show little autocorrelation. It may be tempting to use deviations from the trend in world production as a proxy for aggregate weather shocks. Such an approach can be misleading because it still confounds supply and demand responses to price, such as adjustments in growing area. While weather-induced yield shocks are arguably random, expansion in the production areas anticipate prices and are known before harvest is realized. Our constructed world 7

9 yield shocks, derived from individual countries and crops, have a much stronger (negative) association with price than aggregate production. Table 1 reports summary statistics on caloric prices, production, consumption, our constructed world aggregate yield shocks, and yield shocks interacted with inventories. In figure 2 we plot prices and yield shocks over time. In our model estimates below, we stop all series in 2003 for consistency (because quantity demanded is not available after 2003) and because it precedes the recent boom and bust in commodity prices. Estimating Equations We estimate the system of two equations using standard two-stage-least squares. In the first stage we regress the natural log of price against current and lagged yield shocks, plus a polynomial time trend. In place of the raw yield shocks we use yield shock interacted with inventory levels. Prices are well known to be more volatile when inventories are low as compared to when they are high. This follows from both storage theory and evidence. Prominent examples include the recent price spike and the one in the 1970s, both of which occurred in an environment with unusually low inventories. Interacting aggregate yield shocks with aggregate inventory levels therefore increases the statistical power of the instrument. If yield shocks are linearly independent of other supply or demand shifters then multiplying yield shocks with inventory levels is also linearly independent of those shifters. Several models with different numbers of yield-shock lags and different orders of the trend polynomial. We denote the yield shock in year t, whether interacted with inventories or not, by W t. Stage-one regression model: (4) log(p t ) = ρ 0 + ρ 1 W t + ρ 2 W t-1 + ρ 3 W t µ 1 t + µ 2 t 2 + ε t. We consider both the raw yield shocks and yield shocks interacted with pre-shock inventory levels. Both give similar results but standard errors are smaller when shocks 8

10 interacted with inventories, so those are the results we report below. Results using the raw shocks are available upon request. In the second stage we estimate the structural equations 1 and 2, substituting the predicted values of price from the first stage in place of actual prices. For equation 1 (supply), we regress the natural log of production quantity against predicted price, a polynomial time trend as a proxy for f(t) and the observed supply shifter, the current yield shock (W t ). Stage 1 variables excluded from the stage-two supply equation are the instruments, lagged yields shocks as described above. Stage-two regression model of supply: (5) log(s t ) = α + β + f 0 t + f 1 t h W t + u t. For equation 2 (demand) we regress the natural log of quantity consumed (S t - N t, the quantity produced minus the net-change in storage) on predicted price, a polynomial time trend as a proxy for g(t) and the observed demand shifter, past yield shocks (W t-i ). The stage 1 variable excluded from the stage two demand equation is the current supply shock (W t ), as described above. Stage-two regression model of demand: (6) log(s t -N t ) = κ + γ + g 0 t + g 1 t z 0 W t-1 + z 1 W t-2 + v t. Results Regression results are summarized in table 2. Columns 1-3 use two-stage least squares and lagged price as a proxy for expected price. These columns differ by the number of lagged yield shocks and order of the polynomial time trend used as a control. Elasticity estimates are reasonably stable across model, varying between and for supply and and for demand. 9

11 We most prefer estimates in column 1 because the additional variables used in other estimates are statistically insignificant, first-stage F-statistics for the instrumental variables are strongest, and small-sample bias is known to be smallest in 2SLS when there are fewer instruments. The estimates for the model in column indicate a supply elasticity of and approximate 95 percent confidence interval of (0.044, 0.168) and a demand elasticity of and approximate 95 percent confidence interval of (-0.081, 0.003). We do not report coefficients on the time trend. Unsurprisingly, the trend estimates show demand has grown more slowly than supply, which accords with the general trend down in prices. Additional specifications (not reported), which include lagged prices as controls or yield shocks without inventory interactions as instruments, also give results similar to those reported in columns 1-3. If we limit the sample so that it begins in 1978, after the last major spike in prices, supply and demand estimates are still similar but become somewhat more inelastic. Also, if we include the predicted current price in the supply equation instead of predicted lagged price, the supply elasticity is no longer significant even though the point estimate greatly increases. This is likely due to weak instruments in the supply equation when using current price (the first-stage F-statistic is about 1), which creates bias in addition to the large standard error (e.g., Nelson and Startz, 1990). The last column reports elasticity estimates from seemingly unrelated regressions (SUR) without a first stage. That is, these models use raw endogenous price, not predicted price, in equations 5 and 6, but account for observed supply and demand shifters and the correlation of unobserved supply and demand innovations, u t and v t. We include this regression mainly to illustrate likely endogeneity bias in comparison to 2SLS estimates. The regressions include a quadratic trend and two lagged yield shocks. The SUR regression gives extremely inelastic estimates of supply and demand, for supply and for demand. While the demand elasticity is not statistically significant, the standard errors are small and (if assumptions are accepted, which is dubious) rules out 10

12 elasticities less than with 95% confidence. The supply is statistically significant and the high end of the 95% confidence interval is Recall that when using SUR endogeneity of prices biases the supply elasticity negatively and demand elasticity positively. This is because unobserved demand shifters are positively correlated with price and unobserved supply shifters are negatively correlated with price. The 2SLS estimates are designed to correct this bias. As expected, all 2SLS elasticity estimates are greater in magnitude, by a factor of two for the demand elasticity and by a factor of five for the supply elasticity. Discussion We have two basic goals with this analysis. The first is to demonstrate how yield shocks (deviations from a trend), which are likely attributable to random weather fluctuations, can facilitate estimation of both supply and demand of agricultural commodities. The second objective is to estimate approximate elasticities for caloric energy from the world s most predominant food commodities. Our model is simple. By aggregating crops and countries we obscure the likely importance of many important factors, especially the imperfect substitutability of crops, transportation costs, tariffs, trade restrictions and agricultural subsidies. But what the model lacks in complexity it gains in transparency. We see these estimates as a complement to larger and more sophisticated models wherein local supply and demand responses are either assumed or estimated individually, and transportation and trade restrictions are carefully accounted for. Our estimates provide a useful reality check for whether micro complexities add up to patterns that are observable in the aggregate data. With this perspective in mind, we consider price and quantity predictions stemming from the rapid and largely policy-induced expansion of ethanol demand. This policy has diverted (or will soon divert) approximately half of US corn production to ethanol production. Given that the U.S. grows about 40% of the world s corn and given 11

13 that corn accounts for about a quarter of the calories among the four key crops, the policy equals approximately a 5 percent shift in the world demand for calories. Since commodities are storable and the current ethanol production trend was largely anticipated since the Energy Policy Act of 2005, it is reasonable to expect that futures prices would have quickly incorporated the shift in demand, even though it has taken several years for ethanol production growth to be realized. Using our preferred estimated supply and demand elasticities, a shift of this magnitude would cause an estimated increase in price equal to 0.05 / ( ) = 34.5%. This prediction is slightly larger than the USDA projected price increase made for corn in 2007 and would suggest that the ethanol subsidy had a minor role in the 3-fold price increase. However, within our model, this prediction would also apply to prices for wheat, soybeans, and rice. Because the elasticities are uncertain and the price increase corresponds to their inverse, the expected price increase is greater than one over the expected sum of price elasticities (due to Jensen s inequality). A non-parametric bootstrap of the parameter estimates utilizing 1000 re-samples gave an estimated average price increase of 37.5 percent with a 95 percent confidence interval of 23.5 to 66.0 percent. This suggests USDA projections may have been mildly optimistic. The more inelastic SUR estimates (which are likely biased) could rationalize price increases up to percent. It is surprising that research in agriculture economics has not made greater use of weather-based instruments. One possible reason is difficulty of linking weather variables to agricultural outcomes, like crop yields. We have circumvented this difficulty by summing local yield deviations from trend. In theory, such deviations might be part of the supply response function and therefore endogenous; in practice, however, this appears to be a small issue. Nevertheless, use of weather variables instead of yield shocks may be a promising direction for future research. To make such an approach viable will require rich weather data and a parsimonious model linking weather to yield. Recent empirical research in the U.S. suggests such an approach may be feasible (Schlenker and Roberts). 12

14 References Cassman, Kenneth G. Ecological intensification of cereal production systems: Yield potential, soil quality, and precision agriculture, Proceedings of the National Academy of Sciences, 96, 1999, pp Deaton, A and G. Laroque, On the Behavior of Commodity Prices, Review of Economic Studies, 59, 1992, pp Deaton, A and G. Laroque, Competitive Storage and Price Dynamics, Journal of Political Economy, 4(5), 1996, pp Nelson, C. R. and R. Startz, Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator, Econometrica, 58 (4) 1990, pp Nerlove, M. The Dynamics of Supply: Estimation of Farmers Response to Price, Baltimore: John Hopkins University Press, Roberts M. J. and N. Key, Does Liquidity Matter to Agricultural Production, in Just and Pope Eds., A Comprehensive Assessment of the Role of Risk in U.S. Agriculture, Kluwer Academic Publishers, Roberts, M. J., Nigel Key and Erik O Donoghue, Estimating the Extent of Moral Hazard in Crop Insurance Using Administrative Data, Review of Agricultural Economics 28 (3), 2006, pp Schlenker, W. and M. J. Roberts, Estimating the Impact of Climate Change on Crop Yields: The Importance of Nonlinear Temperature Effects, NBER Working Paper, No , Williams, J and B. D. Wright, Storage and Commodity Markets, Cambridge University Press, Wright, Philip G, The Tariff on Animal and Vegetable Oils, New York: MacMillan,

15 Footnotes 1. Cassman (1999) attributes two-thirds of world calories to corn, wheat, and rice. Adding soybean calories brings the share to 75 percent. 2. A common econometric model of agricultural supply follows Nerlove (1958), which derives supply response as an adaptive function of expected price, and where expected price follows from an autoregressive process. The reduced form of the Nerlove model regresses quantity against lagged price and two lags of quantity. In our application, lagged quantities are far from statistically significant so the Nerlove model reduces to our model. The difference is that we account for the endogeneity of lagged prices. 3. OLS residuals give biased estimates of the errors. Jackknifed residuals, derived by excluding the current observation when determining the current residual, give unbiased estimates of the error. 4. We divide world yield shocks and inventories by the trend in production, estimated non-parametrically using penalized regression splines. The estimated trend is very nearly linear. Table 1. Summary Statistics of Key Variables Mean SD Min Max Log Quantity Produced (S t ) (log million kcal) Log Quantity Consumed (S t -N t ) (log million kcal) Log Price (P t ) (log dollar/mil. kcal) Weather Shock -1e Weather Shock X Inventory (W t )

16 Table 2. Summary of Regression Model Estimates Model 2SLS (1) 2SLS (2) 2SLS (3) SUR (4) Supply elasticity (standard error) (0.029) (0.031) (0.031) (0.014) Demand elasticity (standard error) (0.021) (0.025) (0.026) (0.011) Time trend polynomial 2nd order 3rd order 4th order 2nd order Weather shock lags Use lagged price for supply Yes Yes Yes Yes 1st-Stage F-stat for supply instruments 1st-Stage F-stat for demand instrument NA NA Adjusted-R 2 Supply/Demand / / / / Cross-equation correlation of residuals Expected percent price increase with 5% outward shift in demand (95% Confidence Interval) 37.6 (23.3, 66.0) 36.7 (22.1, 69.9) 35.5 (21.4, 66.9) 91.5 (52.6, 177.8) 15

17 Notes: Data on production and consumption were derived from production and stock variation data reported by the Food and Agricultural Organization of the United Nations. Total calories sum those from corn, soybean, wheat, and rice. Caloric conversion rates were taken from Williamson and Williamson (1947). For quantities, the unit of analysis, a million kcal, is enough to satisfy the caloric need of approximately 1.3 individuals for a year if the commodities are consumed directly. Prices are in U.S dollars. 16

18 Notes: Data on prices are the natural log of those plotted in figure 1. Yield shocks are derived from aggregating yield shocks from individual crops and countries using data from FAO. Crops included are corn, soybeans, wheat and rice. Countries included are all those averaging 1% or more of world production in a given crop. Production from the rest of the world was pooled for each crop and separate yield trend and shocks were derived. All yield shocks were converted to calories and summed. The figure shows the yield shock divided by the trend in world caloric production. This variable, interacted with the inventory-to-trendproduction ratio, is the instrument for price used in the regression models. 17

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