Identifying Supply and Demand Elasticities of Agricultural

Commodities: Implications for the US Ethanol Mandate

Michael J. Roberts♣ and Wolfram Schlenker♠

Abstract

We present a new framework to identify supply elasticities of storable commodities wherepast shocks are used as exogenous price shifters. In the agricultural context, past yield shockschange inventory levels and futures prices of agricultural commodities. We use our estimatedelasticities to evaluate the impact of the 2009 Renewable Fuel Standard on commodity prices,quantities, and food consumers’ surplus for the four basic staples: corn, rice, soybeans, andwheat. Prices increase 20 percent if one third of commodities used to produce ethanol arerecycled as feedstock, with a positively skewed 95% confidence interval that ranges from 14to 35%.JEL: Q11, G13, Q42Keywords: Storable commodities, supply response, food prices, biofuel mandates.

We thank Jim Hamilton, Randall Walsh, three anonymous referees and seminar participants at Berkeley,

Cornell, Iowa State University, NBER Agricultural Economics Conference, Stanford, University of British

Columbia, University of Calgary, and the University of Maryland for very useful comments. All remaining

errors are ours. Financial support from Department of Energy Grant DE-FG02-08ER64640 and National

Science Foundation Grant SES-0962559 is thankfully acknowledged. The authors have no relevant or finan-

cial interests related to this project to disclose.

♣ Department of Agricultural and Resource Economics, North Carolina State University, Box 8109, Raleigh,

NC. Email: michael roberts@ncsu.edu.♠ School of International and Public Affairs, Columbia University, 420 West 118th Street, Room. 1308, MC

3323, New York, NY 10027. Email: wolfram.schlenker@columbia.edu.

The rapid ascent of commodity prices between late 2005 and 2008 led to renewed debate

about what drives the demand and supply for basic food commodities. Corn prices nearly

quadrupled from about $2 per bushel to almost $8 per bushel, and prices for rice, soybeans,

and wheat rose by similar amounts. These prices briefly dropped in 2009-2010 due to the

recession, but corn again broke $8 in 2011. High prices for these staple grains caused hunger,

malnutrition, and riots in a number of developing nations, as was vividly reported in the

popular press.1 The price spike was attributed to a number of factors, including the pro-

longed drought in Australia, accelerating demand growth due to the broad scale economic

development in Asia, and a shift in demand stemming from the United States ethanol policy.

The combination of ethanol subsidies, restrictions on ethanol imports, and high oil prices

caused a formerly nascent ethanol industry to quickly grow into one that consumes approxi-

mately one third of the United States corn production and about five percent of the world’s

combined caloric production of corn, soybeans, wheat and rice. Evaluating how much the

biofuel mandate contributed to higher prices requires estimates of the underlying supply and

demand elasticities.

A closely connected issue is land use change. Commodity production, pasture, and forests

sequester substantially different amounts of carbon. This has sparked a debate about the

potential benefits of using biofuels to reduce CO2 emissions. Diversion of food into fuel

raises the price of food and induces farmers to produce more. Crucial points of disagreement

concern the size and nature of this supply response, as the potential size of the CO2 effect

depends on how much additional production comes from the extensive margin. Land use

change (mainly deforestation) is thought to account for about 20 percent of worldwide CO2

emissions (IPCC 2007).2

Another discussion that requires estimates of agricultural demand and supply elasticities

involves “leakage” from carbon offset programs that pay farmers to either forestall defor-

estation or reforest land that would otherwise be used in crop production. Carbon offset

programs shift the supply of cropland inward, causing commodity prices to rise, and po-

tentially an offsetting increase in the quantity of cropland supplied elsewhere. The global

1Two examples are Fuel Choices, Food Crises and Finger Pointing on April 15, 2008 and “Across Globe,Empty Bellies Bring Rising Anger on April 18, 2008, both published in the New York Times.

2A similar concept considers market feedback in fuel consumption instead of agriculture. A standardthat limits the carbon intensity of fuels via a subsidy for low-carbon fuels increases fuel quantity demanded.Thus, CO2 emissions will decline by less than the reduction in carbon intensity. In an extreme case, sucha standard could theoretically increase total emissions. However, Stephen P. Holland, Jonathan E. Hughes& Christopher R. Knittel (2009) show that this counterintuitive result does not hold under reasonableparameter assumptions.

1

net offset can therefore be much less than the offset purchased in any particular location.

The amount of leakage depends on the size of the supply elasticity relative to the demand

elasticity.

With these applications in mind, this paper develops a new framework to empirically

identify both supply and demand elasticities of storable commodities where prices are linked

between periods via storage. We apply this framework to the world’s four most important

staple food commodities: corn, wheat, rice, and soybeans. These commodities comprise

about 75 percent of the caloric content of food production worldwide.3 While many other

commodities matter for food consumption, and the particular mix of foods varies across

locations, we limit ourselves to these four crops. The prices and quantities of other staple

food items are inextricably linked to these four commodities. As we will show below, the

prices of the four commodities tend to fluctuate closely together. In our baseline specification

we simplify matters further by aggregating these four key crops on either a caloric or value-

weighted basis.

Agricultural commodity markets, with their many price-taking producers and buyers

and well-developed spot and futures markets, are often cited as the archetype of perfect

competition. The key empirical challenge is to separate supply and demand in the market’s

formation of prices and quantities. Correct identification requires instruments that shift

prices in ways that are plausibly unrelated to unobservable shifts in each curve. Since

Philip G. Wright’s (1928) introduction of instrumental-variable estimation, weather has been

considered a natural instrument for agricultural supply shifts, which can be used to facilitate

unbiased demand estimation. The idea is that weather shifts supply in a manner that is

unrelated to unobserved demand shifts. Given this idea was established long ago we find it

surprising that the literature in agricultural economics that uses weather-based instruments

to identify demand is extremely thin.4

Here we show how yield shocks that are due to random weather shocks can also be

used to identify supply. The idea follows naturally from the theory of competitive storage:

past shocks exogenously shift inventories, which affect futures prices and the demand for

storage, which in turn cause production responses in the future. Past shocks can serve

as instruments for futures prices. The same methodology could in principle be applied to

any storable commodity, where prices are linked between periods through storage, and past

3Kenneth G. Cassman (1999) attributes two-thirds of world calories to corn, wheat, and rice. Addingsoybean calories brings the share to 75 percent.

4For example, Joshua D. Angrist, Kathryn Graddy & Guido W. Imbens (2000) use weather to instrumentthe supply of fish to the Fulton Fish market in New York.

2

shocks shift the demand to hold inventory.

Our approach to supply estimation differs from a large existing literature that stems from

the seminal work of Marc Nerlove (1958). In this literature, supply is estimated by regress-

ing quantities against uninstrumented futures prices, lagged prices, or prices predicted from

an autoregressive model. Nerlove’s approach purges endogeneity stemming from current

unanticipated supply shocks that are, for example, due to current weather shocks. How-

ever, this does not account for endogeneity stemming from anticipated supply shifts that

are unobserved to the econometrician, since futures prices reflect the intersection of antic-

ipated supply and anticipated demand. Endogeneity remains a serious concern since these

unobserved supply shifts are part of the error in a supply equation with futures prices on

the right-hand-side of the regression. This is perhaps one reason why this substantial liter-

ature on agricultural supply response finds widely varying supply elasticities that often lack

statistical significance (Hossein Askari & John Thomas Cummings 1977).

A recent example from the United States illustrates the endogeneity of futures prices

in the supply equation. In the spring of 2004 soybean rust (a fungus) was first detected

in the United States. Although soybean rust is manageable, fungicides used to control it

are expensive. In the subsequent growing season, fear of the pest caused some farmers to

switch from planting soybeans to planting corn. These supply shifts were anticipated in

advance, causing futures prices for soybeans to rise and futures prices for corn to fall, clearly

movements along the demand curves for these key crops. In other words, the planted area

did not decrease because prices went up, but prices went up because there was an unobserved

shift in supply (stemming from fear of soybeans rust) that lowered area planted and expected

harvest. In subsequent years the perceived threat of this new pest abated, causing additional

supply fluctuations as relative prices returned to normal. A naive econometrician, regressing

quantity supplied of either corn or soybeans on futures prices, would estimate a supply

elasticity biased towards zero due to the soybean rust phenomenon. While this is just one

example, it should be clear that, when using the standard approach to supply estimation,

any number of anticipated supply shifts that are either unobservable or immeasurable to the

econometrician would cause downward bias in the estimated supply response.

Our baseline approach to estimate supply and demand exploits yield shocks — devia-

tions from country and crop-specific yield trends that appear to stem mainly from random

weather shocks. A potential shortcoming of this approach is that yields themselves may be

endogenous to price. We explore this potential issue in detail and argue that any short-run

causal links going from price to yield are likely minimal. When we regress futures prices on

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past weather shocks, which are more defensibly exogenous than yield shocks, we obtain sim-

ilar point estimates that are less precisely estimated. The obvious tradeoffs between using

yield shocks and weather variables as instruments are between statistical power, endogeneity

bias and weak-instruments bias. Despite these tradeoffs, a wide variety of estimates using

different specifications and instruments show remarkable consistency, and most estimates

have strong statistical significance.

We use the demand and supply model of world commodity calories to examine the effect

of the current United States biofuel mandate on food prices. This analysis provides some

perspective on rapid price increase between 2005 and 2008 and how much of it might have

been attributable to ethanol policy. Our estimates indicate that supply is more elastic than

demand, with almost all of the supply response coming from the extensive margin, i.e.,

an expansion of land area. Both supply and demand elasticities are significantly larger,

both economically and statistically, than uninstrumented estimates derived using traditional

techniques. The estimates suggest that the US ethanol mandate increased food prices about

30 percent and increased world production area by 2 percent. The baseline estimate for the

price increase does not incorporate any recycling of the corn used to produce biofuels as

feedstock, which will reduce the predicted price increase proportionally. For example, if one

third of the calories used to produce biofuel remain in the byproduct that is fed to animals,

and this feedstock is a perfect substitute for other grains, the price increase would be 20

percent. On the other hand, if the feedstock is not a perfect substitute, the effect will lie

in between. While these predicted effects are substantial, they suggest that other factors

likely played a larger role in the 2005-2008 price boom.5 The 95% confidence interval of the

predicted price increase is positively skewed and stretches from 14% to 35% if one third of

commodities used to produce ethanol are recycled as feedstock, suggesting that significantly

larger price increases are possible even if the byproducts of ethanol generation are recycled.

At the same time, a 30 percent price increase implies an annual loss of 180 billion in

consumer surplus. While most of this is offset with an increase in producer surplus, the US

ethanol policy results in transfers from net food importers to next food exporters. Since

most developing countries are net food importers, they are especially affected. Moreover,

an increase in world food prices for a food importer is equivalent to a reduction in income,

5Catherine Hausman, Maximilian Auffhammer & Peter Berck (2012) use a vector auto-regression priceprocess to estimate how corn and soybean prices respond to shocks in the United States. They find thatUS ethanol production was responsible for roughly 27% of the recent corn price increase. Similar to Nerlove(1958), lagged variables are allowed to influence futures prices. While we follow a similar time structure ofusing lagged variables, we only use past yield shocks, not area changes, as an instrument.

4

which has been shown to increase civil conflict (Edward Miguel, Shanker Satyanath & Ernest

Sergenti 2004, Marshall B. Burke, Edward Miguel, Shanker Satyanath, John A. Dykema

& David B. Lobell 2009). The US biofuel policy therefore has significant distributional

consequences. This result is in line with earlier research about other policies that purportedly

reduce CO2 emissions. Antonio M. Bento, Lawrence H. Goulder, Mark R. Jacobsen &

Roger H. von Haefen (2009) examine the markets for new and used cars and find that

the distributional consequences of a gasoline tax crucially depend on how the revenues are

recycled. Similarly, Shanjun Li, Christopher Timmins & Roger H. von Haefen (2009) find

that higher gasoline taxes not only change the fuel economy of new cars, but also lead to

increased scrappage of old inefficient cars, which are primarily owned by the less affluent.

1 A Model of Supply and Demand

We simplify our characterization of world food commodity market by transforming quanti-

ties of corn, wheat, rice, and soybeans into caloric equivalents and then aggregating them

(Michael J. Roberts & Wolfram Schlenker 2009). In sensitivity checks we also present re-

sults for a disaggregate analysis as well as an aggregate analysis on the basis of average

price. Aggregating crops facilitates a simple yet broad-scale analysis of the supply and de-

mand of staple food commodities on a worldwide scale. A practical reason for aggregation

is that prices for all four commodities tend to vary synchronously, which seriously impedes

identification of multiple cross-price elasticities and separating cross-price elasticities from

own-price elasticities. The strong correlation of prices over time also suggests that substi-

tution possibilities are large enough that the aggregate outcomes likely characterize all four

markets reasonably well. For example, the recent Russian wildfires that impacted global

wheat production influenced corn prices almost as much as wheat prices.

1.1 Theoretical Motivation

Having reduced the staple food commodity market to a single caloric measure, we need a

model that characterizes supply, demand and inventories and how random shocks facilitate

identification of the supply and demand elasticities. The theory of competitive storage sits

at the heart of this approach. Storage is a characteristic feature of all four commodities we

consider. It allows for substitution of consumption over time by transferring commodities

from periods of relative plenty to periods of relative scarcity. Consumption is smoother than

production and prices are less variable and more autocorrelated than they would be without

5

storage opportunities. Equilibrium in each period does not require a price where supply in

the current period equals consumption demand in the current period, but a price where the

amount consumed ct equals food supply at the beginning of the period zt minus the amount

stored for the next period (denoted xt).

ct = zt − xt

An extensive literature on the rational competitive storage model characterizes demand

for inventories and the resulting price path of commodities. Our focus differs from this

literature, but we do exploit the above identity and other essential characteristics of storage

models.

Jose A. Scheinkman & Jack Schechtman (1983) and Eugenio S. A. Bobenrieth H., Juan

R. A. Bobenrieth H. & Brian D. Wright (2002) set up a model in which profit-maximizing

agricultural producers make two decisions. The first is how much to store and carry over

to the next period, xt. Storage has convex cost φ(xt). The amount not stored zt − xt is

consumed and gives consumers utility u(zt − xt). The second decision is how much “effort”

λt to put into new production, which is subject to a multiplicative i.i.d. random weather

shock ωt+1 that is unknown at the time of planting. One possible interpretation is that λt

specifies the number of acres a farmer plants and ωt+1 is the random yield, which is driven by

exogenous weather shocks. Production in the coming harvest season is λtωt+1. Production

cost g(λt) are assumed to be convex, as land of heterogeneous quality becomes progressively

more expensive to farm.

The Bellman equation for the social maximization problem is

v(zt) = maxxtλt

{u(zt − xt)− φ(xt)− g(λt) + δE [v(zt+1)]} subject to

zt+1 = xt + λtωt+1

xt ≥ 0, zt − xt ≥ 0, λt ≥ 0

Competitive price-taking producers and storers achieve the socially optimal outcome by

optimally balancing the marginal cost of effort against futures prices and the marginal cost

of storing agricultural goods against the change in futures prices. In the social planner’s

problem, price is reflected by the marginal utility of consumption. Increasing storage is

profitable in years when availability zt is sufficiently large, which causes the current price to

be low. By shifting some of the current availability into the next period, current price rises

and price in the next period falls. This process continues up to the point when the discounted

6

futures price net of storage cost equals current price. For the same reason, prices rise if

availability zt decreases. If the weather shock is sufficiently negative, inventories theoretically

may be drawn to zero, even though this is rarely observed in practice.6 Scheinkman &

Schechtman (1983) show that in a competitive equilibrium:

(i) consumption ct = zt − xt is strictly increasing in zt

(ii) storage xt is weakly increasing in zt

(iii) effort λt is weakly decreasing in zt

For our purposes, the key result from this model is that it implies exogenous shocks are

optimally divided between current consumption and inventory adjustments. We can infer

this because random shocks randomly shift zt. Thus, bad weather shocks exogenously reduce

zt and by point (i) reduce consumption and increase price. This captures movement along

the demand curve. The same negative weather shocks also draw down inventories by point

(ii), thereby increasing the price in subsequent period. When storage levels are low and

the futures price in the next period is high, farmers increase effort λt by point (iii) through

higher acreage or yields. This captures movement along the supply curve.

1.2 Empirical Model

The empirical model is

Supply: qst = αs + βspst + γsωt + fs2(t) + ut (1)

pst = δs + µs0ωt + µs1ωt−1 + fs1(t) + ǫt (2)

Demand: qdt = αd + βdpdt + fd2(t) + vt (3)

pdt = δd + µd0ωt + fd1(t) + ηt (4)

Log quantity supplied is denoted by qst = log(λt−1ωt), while log quantity demanded is

qdt = log(λt−1ωt + xt−1 − xt), which is new production minus the change in inventories. The

6In the absence of convenience yield, a stockout theoretically occurs when prices are high enough thatthe subsequent futures price change becomes negative. If, however, ωt+1 is allowed to have a mass pointat zero, i.e., a non-zero probability that the entire harvest is wiped out, and limc→0 u

′(c) = ∞, then thelong-run distribution has a finite price, inventories will be positive with probability one, and the mean ofthe price distribution is infinite (Bobenrieth H., Bobenrieth H. & Wright 2002). While low inventory levels(and high prices) will almost surely result in subsequent price declines, the futures price is still increasing.The rationale is that if another bad shock occurs, the already strained market would result in a very largeprice jump. The resulting payoff is so large that it always justifies holding positive inventories.

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supply equation uses the log of future price pst = log (pt|t−1)7, while the demand equation

uses log futures prices during the month of delivery pdt = log(pt). Intercepts αs, αd, δs, and

δd are allowed to evolve over time according to time a trend fi(t) in all of the four above

equations (i ∈ {s1, s2, d1, d2}).

Prices are the key endogenous variables on the right-hand side of both supply and de-

mand. The crux of the identification problem is that shifts in supply and demand that

are unobserved to the econometrician (ut and vt) influence prices via the equilibrium iden-

tity. Without correcting for the endogeneity of prices, the supply elasticity would be biased

negatively, since unobserved positive supply shifts (ut) would tend to reduce price all else

the same, creating a negative correlation between ut and price. A naive demand elasticity

(without correcting for the endogeneity of prices) would tend to be biased positively, since

unobserved positive demand shifts (vt) would tend to increase price all else the same, creat-

ing a positive correlation between vt and price. If unobserved supply and demand shifters

ut and vt are correlated, biases could go in either direction.8

Our baseline model uses yield deviations ξcit for crops c in country i in year t. We fit crop-

and-country specific time trends gci(t) in regressions of log yields ycit, i.e., ycit = gci(t) + ξcit.

The annual shock ωt is a weighted average of all shocks. The weights ρcit depend on predicted

yields ycit = egci(t)+σ2

2 (where σ2 is the estimated variance of the error terms), growing area

acit, and the caloric content of one production unit of crop c, κc.

ωt =

∑

c

∑

i ξcit × ycit × acit × κc∑

c

∑

i ycit × acit × κc

=∑

c

∑

i

ξcitρcit

ρcit =ycit × acit × κc

∑

c

∑

i ycit × acit × κc

In our baseline model we use the actual growing area acit. While the growing area is

endogenous, it only enters as a weighting factor of the exogenous percentage shocks ξcit that

are primarily caused by weather. If production increases in a country because of an increase

in the area but yields do not deviate from the trend, it will not be appear in our shock ωt.

Weighting by the actual area gives the accurate global exposure to exogenous shocks, which

is still a valid exogenous instrument (see appendix Section A1.1 for a formal derivation). If

7We use futures prices in December of period t − 1 with a delivery in December of year t for corn andwheat and a November delivery for soybeans and rice. We present sensitivity checks in the appendix wherewe vary the months but the results are generally robust.

8Colin A. Carter, Gordon Rausser & Aaron Smith (2011) argue that there were two big commodity pricespikes—1974 and 2008—that resulted from several correlated macro-economic factors. It is therefore crucialto use exogenous instruments.

8

one is worried about the endogeneity of the weights, we present a robustness check where we

use predicted area along the same country-and-crop-specific time trend we use in the yield

regression and get very similar results.

Another, and potentially more worrisome concern is that yields might themselves be

endogenous, which would make yield deviations an invalid instrument. We therefore present

an analysis where we replace yield shocks ξcit with observed weather outcomes: a quadratic

in average temperature and total precipitation. While these instruments are more defensibly

exogenous, they are less efficient: the point estimates for the supply elasticity remain robust,

but the first stage results are not as significant and standard errors are larger.

The price in the demand equation is identified through the exogenous shock ωt. The

exclusion restriction requires that these shocks do not directly affect demand. While it is in

principle possible that yield shocks or weather outcomes could shift tastes, hunger, or general

caloric need, it seems unlikely that these could matter in a global context. Well-established

international markets trade a significant share of production within and between regions

and nations. Thus, weather affecting crop production tends to be far removed from demand

centers. For example, most of the feed grains used for hog and poultry production in North

Carolina come from the Midwest where weather fluctuations are quite unrelated.

A novelty of our approach is that we use past yield (or weather) shocks ωt−1 to identify

the supply elasticity βs in addition to the demand elasticity. As described in detail above,

this is possible because past weather-induced supply shocks affect inventories and inventories

affect futures price in subsequent periods. The key assumption for consistent identification

of the supply elasticity is that past weather-induced supply shocks have zero covariance

with unobserved supply shifters in the current period. Unobserved supply shifters might

stem from recurrent or anticipated pest problems, like the example of soybean rust in the

introduction, broad macroeconomic phenomena, governmental policies, or perhaps other

factors. One concern may be that agronomic or weather factors are correlated over time.

We address this potential concern in two ways. First, we show yields and weather shocks

display little autocorrelation.9 Second, we estimate MA models in a sensitivity check and

only use innovations in a period and the results remain robust. Third, we include current

weather shocks in the supply equation. While current shocks must be excluded from the

demand equation, including them in the supply equation increases precision by reducing the

error variance while accounting for current supply shifts that may have been associated with

9Rice is an exception; however the other three commodities and aggregate yield shocks show little auto-correlation.

9

past shocks. Thus, conditional on the current weather or yield shock, it’s not clear how or

why past weather or yield shocks might be related to unobserved supply shifters.

2 Data

World production and storage data are publicly available from the Food and Agriculture

Organization (FAO) of the United Nations (http://faostat.fao.org/) for the years 1961-2010.

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.

The last variable is only available until 2007. In our model estimates below, we stop all series

in 2007 because quantity demanded (which depends on changes in inventory) is not available

after 2007. In a sensitivity check, we also use data from the Foreign Agricultural Service

(FAS) by the United States Department of Agriculture (http://http://www.fas.usda.gov/)

that has data for 1961-2010 for all variables, including stocks.10 Variables are converted into

edible calories using conversion factors by Lucille Williamson & Paul Williamson (1942),

which specify edible calories per output quantity of various crops. Consumption (quantity

demanded) is calculated as production minus the net change in inventories.

Data on quantities are displayed in Figure 1. The top panel displays the number of people

that could be fed on a 2000 calories-per-day basis, and how much each of the four commodities

contributed to total caloric production. Maize has the biggest share while soybeans has the

smallest share. Wheat and rice are in the middle and have roughly equal shares. One

noteworthy fact is that overall year-to-year fluctuations (top line) are predominantly due to

fluctuations in corn. More than half of all corn, sometimes also called maize, was traditionally

produced in the United States and the bulk of that production is geographically concentrated

in one region, the Midwestern corn belt.11 Other crops are less geographically concentrated

and local weather shocks average close to zero when summed over the whole world. Maize

may contribute a larger share of world caloric variability simply because its production is

more geographically concentrated and therefore more likely to experience correlated weather

outcomes.

The bottom panel of Figure 1 shows production and consumption quantities. Two fea-

tures are noteworthy: First, production and consumption have been steadily trending up-

ward, almost linearly. Both appear trend stationary. Second, fluctuations around trend

10FAS reports production for marketing years. The exact procedure how marketing years are linked tocalendar years is given in Section A2.1 of the Appendix.

11Today, the US still accounts for roughly 40 percent of world maize production.

10

production are small in proportion to the trend. Consumption fluctuations are even smaller

due to smoothing from storage accumulation and depletion. The FAO series on stock vari-

ation, necessary for derivation of consumption, ends in 2007 and hence so does our demand

estimate.

Yield shocks in our baseline model are calculated by taking jackknifed residuals from

fitting separate yield trends for each crop in each country. Trends and shocks were estimated

separately for each country with an average of 0.5 percent or more of world production for a

given crop.12 Remaining rest-of-world yields were pooled and treated as a single country for

each crop. Yield shocks in the baseline model were derived from a trend that is approximated

by a restricted cubic spline with 3 knots,13 i.e., two variables.14

Our premise is that these deviations from yield trends are exogenous as they largely due

to random weather. One potential concern is that yields themselves might be a function of

prices. For example, higher prices could induce farmers to choose higher sowing densities,

thereby increasing average yields. On the other hand, higher prices might induce farmers to

expand their production to marginal, less productive, land, thereby lowering average yields.

It is a priori unclear which way the bias would go. We believe that endogenous yield responses

are not important in our paper for two stylized facts. First, if yields were responsive to price

levels, we would observe that yield shocks are correlated between various countries in a

given year, as all countries face the same world price.15 Idiosyncratic yield shocks for various

countries get averaged out in aggregate except when regions that account for a significant

share of production get hit by the same shock. Accordingly, aggregate shocks vary much less

than country-and-crop-specific shocks. Our baseline log deviations vary between -0.057 and

0.044 in the FAO data.16 A value of -0.05 implies that global production was roughly 5%

below predicted yields.

Second, aggregate yield shocks ωt have almost no autocorrelation, while prices have a

12The average share of world production between 1961-2010 in both the FAO and FAS data are listedin Appendix Tables A1-A2. Countries that on average produced at least 0.5% of a crop are shown in thebottom map in Appendix Figures A1-A4.

13The fitted trends and residuals are displayed in Appendix Figures A5-A7.14Restricted cubic splines are more flexible than quadratic time trends. To access the sensitivity of the

results to the chosen trend specification, Table A15 in the appendix fits yield trends ranging from a lineartime trend to splines with 5 knots with little effect on the estimated results. Wile we use generated variablesas instruments, Jeffrey M. Wooldridge (2002, p.117) points out that this will still give consistent estimatesof the standard errors in the second stage.

15Figure A8 in the appendix shows scatter plots of yield deviations for the two biggest exporters for eachof our four commodities. These plots show no systematic correlation, one even has a negative correlationcoefficient.

16Shocks vary between -0.070 and 0.051 in the FAS data, which averages over fewer countries.

11

high degree of autocorrelation.17 If yields endogenously respond to prices, than aggregate

yield shocks would show autocorrelation as well. While some endogenous yield response is

likely present, these stylized facts suggest it is small relative to variation induced by weather.

To further address the concern of endogenous yield responses, we conduct a sensitivity

check where we replace yield shocks with observed weather variables. Since global production

and consumption data are annual aggregates, we construct annual weather aggregates for a

quadratic in average temperature as well as total precipitation. Weather data from Center

for Climatic Research at the University of Delaware (version 2.01) gives monthly temperature

and precipitation readings on a 0.5 degree grid for the entire world for the years 1901-2008.

Weather outcomes in a country are the area-weighted average of all grids that fall in a

country. See appendix A2.2 for a more detailed description. The weather for corn in the US

is therefore different for rice in the US in a given year as they are grown in different areas

and different time periods. The global average is simply the area weighted average of all

crops and countries. Since the FAS data provides production quantities for all countries with

significant production, we take the weighted average of each weather variable and country

for all countries in the FAS data, i.e., we omit small countries in the FAO data as they tend

to add noise to the measure.

We obtain two price series. Our baseline model uses futures prices from the Chicago

Board of Trade with a delivery month of December for maize and wheat, and November for

soybeans and rice.18 We construct the demand price pdt as the log of the average futures

price during the month when delivery occurred, e.g., in December of the delivery year for

corn. Futures price in the supply equation pst = pt|t−1 is the log of the average futures price

in December one year prior to delivery.19 All prices are deflated by the Consumer Price

Index.20 Prices for each commodity are converted to their caloric equivalent, with the world

calorie price taken as world production-weighted averages of the four commodities.21

17The Durbin-Watson statistic when we regress our baseline shock ωt on various time trends in Tables 1(FAO data) and Table A8 (FAS data) is 1.68-1.87, suggesting there is no autocorrelation. On the otherhand, the statistic is 0.43-0.99 if we use prices, which is below the critical value at the 1% level.

18We use futures price for “No. 2 yellow” for corn, “No. 1 yellow” for soybeans, “No. 2 soft red” forwheat, and “Rough Rice #2” for rice. Rice futures did not trade before 1986, so we prorate the price of riceby the change in rice spot data. For example, if the spot data in 1980 was 70% of 1986, we set the futuresprice data in 1980 as 70% of the futures price in 1986. Since the price data is interpolated for rice, we donot use it when we derive the average price of all crops.

19In some cases the time series of a contract does not extend back to the previous December so we takethe average price in months closest to previous December.

20We deflate prices before we take logs. We use the CPI for all urban consumers:ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt

21For most commodities one cannot reject a unit root using standard tests (Dabin Wang & William G.

12

A second price series with longer temporal coverage are those received by US farmers,

publicly available from the US Department of Agriculture. Figure 2 displays real price

(annual cost of a 2000 calories per day diet in 2010 dollars). There has been a general

downward trend of food prices. Prices per calorie move together for all four commodities,

most notably maize, wheat and soybeans.22 This is not surprising, given that those three are

close substitutes in production and consumption. For example, maize and soybeans (and to

some degree wheat) are used as feed for livestock. If one were cheaper per calorie than the

others, profit-maximizing farmers should switch to the cheaper input. Price fluctuations are

proportionately much larger than quantity fluctuations in Figure 1. This fact suggests that

both demand and supply are inelastic.

3 US Ethanol Subsidies and Mandates

Ethanol has a long history as a car fuel. Ford’s Model-T was designed to run both on

ethanol and petroleum, or arbitrary mixes of the two. Declining petroleum prices led to a

slow phase out of ethanol as a fuel. Recent concerns about anthropogenic CO2 emissions

have renewed interest in ethanol as a fuel substitute, even though the net effect is highly

debated (Timothy Searchinger, Ralph Heimlich, R. A. Houghton, Fengxia Dong, Amani

Elobeid, Jacinto Fabiosa, Simla Tokgoz, Dermot Hayes & Tun-Hsiang Yu 2008). Ethanol is

currently being mixed with traditional petroleum in ratios up to 10 percent. Most cars can

run on such fuel mixes. Modern flex-fuel cars are designed to run on fuel that is up to 85

percent ethanol.

The US ethanol mandate may have a measurable influence on world food prices since it

diverts a sizable amount of global production into the fuel market. Since 1960, the US share

of combined world caloric production for the four key commodities was about 23 percent

(bottom left panel of Appendix Figure A11), and the majority came from maize. Any

Tomek 2007), but nor can one reject the null hypothesis of a stationary series with significant autocorrelation,as implied by storage theory. The same is true for our data: Augmented Dickey-Fuller tests do not rejecta unit root for the price series. On the other hand, the first stage of Cochrane-Orcutt regressions of priceson a time trend predict autocorrelation coefficients between 0.50 and 0.81 dependent on whether we useFAO or FAS data and how many spline knots we include to model the time trend. Given that productionis clearly trend stationary (a unit root can be rejected), and that production and prices are linked betweenperiods through storage, the evidence points towards a stationary time series with high autocorrelation.Nevertheless, we present a sensitivity check where we control for lagged prices in both the first and secondstage, but the results remain robust.

22In a sensitivity check we do not use the caloric conversion ratios of Williamson & Williamson (1942),but instead derive them implicitly by forcing the average price of each commodity in 1961-2010 to equal theone for maize. The rescaled price series is shown in Appendix Figure A9.

13

mandate that diverts a sizable share of US production into fuel will also be sizable from a

global perspective due to the US market share in calorie production.

Ethanol production has risen rapidly over the last couple of years as shown in Appendix

Figure A10. An ethanol tax credit was established in 2005, but it was phased out in January

2012. Mandates, however, are still in effect. The 2005 US Energy Policy Act mandated

7.5 billion gallons of ethanol be used by 2012. The 2007 Energy Independence and Security

Act instituted a long-term mandate of using 36 billion by 2022, but limited the share that

could be derived from corn-based ethanol. It also accelerated the short-term mandate. In

2009, the US Renewable Fuels Standard (RFS) required refiners and fuel blenders to blend

roughly 11 billion gallons of ethanol into gasoline. We examine the effect of the 2009 RFS on

world food prices. Currently, nearly all of U.S. ethanol is produced from corn, and 11 billion

gallons of ethanol would require roughly 4.07 billion bushels of corn assuming an average

of 2.7 gallons of ethanol per bushel of corn (D. Rajagopal, E. Sexton, D. Roland-Holst &

D. Zilberman 2007). This translates into roughly one third of US maize production in 2010

(12.4 billion bushels), or about 5 percent of world caloric production in 2010. Recall that

the largest negative historic production shocks was -0.057, so the annual impact of the US

ethanol mandate is roughly equivalent to the worst production shock on record, except that

the mandate is permanent, not transitory like the weather.

A byproduct from corn ethanol production, called distiller’s grains, can be used as feed

for livestock. While estimates vary, up to one third of the caloric input is said to be re-

coverable, but the nutritional content is debated and generally thought to be inferior. We

therefore present two estimates: our baseline model assumes that five percent of world caloric

production is diverted into ethanol generation as well as a scenario where we assume that

one third of the calories is recycled as feed stock.

While 5 percent of world caloric production would be required for 11 billion gallons

of ethanol, the average daily US motor gasoline consumption is 0.39 billion barrels per

day.23 Supplying approximately 8 percent of United States gasoline consumption requires

approximately 5 percent of world caloric food production.

4 Empirical Results

Here we report results using FAO data. Appendix Section A4 reports results using FAS

data, which are generally comparable.

23Energy Information Administration: http://www.eia.doe.gov/basics/quickoil.html

14

4.1 Main Results

We summarize the main results in Table 1. Results include IV and 3SLS estimates, each with

multiple specifications of the time trend. Elasticity estimates are reasonably stable across

models, varying between 0.087 and 0.116 for supply and -0.028 and -0.066 for demand. F-

statistics for first-stage instruments, lagged yield shocks ωt−1 for the case of supply and

concurrent yield shocks ωt for the case of demand, are given at the bottom of the table. All

F-values are greater than 10, an accepted standard for strong instruments. Comparison of

the coefficients on ωt−1 in the futures-price regression (panel A) and ωt in the current-price

regression (panel B) imply shocks affect futures prices nearly as much as current prices.

This is consistent with storage theory wherein transitory shocks are smoothed over time,

giving rise to autocorrelation in prices. It is also interesting that ωt is statistically significant

in some of the futures price regression. This indicates that shocks are at least partially

forecastable.24

There is a tradeoff between the two estimation methods (IV or 3SLS). For IV specifica-

tions we report robust standard errors throughout the paper (unless noted otherwise) that

account for arbitrary forms of heteroscedasticity and autocorrelation in the error term. The

3SLS results are more efficient than IV estimates, but 3SLS standard errors may be biased

if the error terms are not iid. An exercise reported in the appendix (Table A12) suggests

that 3SLS standard errors may be reasonable approximations. That exercise reports two

sets of standard errors for the IV results: uncorrected and robust standard errors. While

prices show significant autocorrelation, yield shocks do not: Table A12 presents tests for

conditional heteroscedasticity as well as autocorrelation for the yield shocks ωt, which all

fail to reject the null that they are iid. Note that the second-stage elasticity estimates, the

main parameters of interest, have similar standard errors whether or not they are corrected

for heteroscedasticity and autocorrelation. This suggests that multi-stage standard errors

are mainly sensitive to whether the instrument is iid.

Table 1 also includes implied effects of the US ethanol mandate on world commodity

prices. A shift in demand ∆q changes equilibrium price by ∆q

βs−βd. We therefore define a

price multiplier 1

βs−βd

using point estimates for the supply and demand elasticity, which

translates outward shifts in demand (changes in quantities) into price changes. Multipliers

range from 5.75 to 7.73, which imply that a 5% shift in demand food into fuels increase price

of the four staple commodities by 29%-39%. Our preferred estimate uses the more efficient

24Partial forecastability of current shocks does not create bias in the supply equation because currentshocks are not excluded from the second stage.

15

three-stage least squares estimator and more flexible time trends to account for the repeated

spikes in the data: the baseline estimate is an approximately 30% price increase, which is

on the conservative end of the range.

An unbiased estimate of the price increase needs to adjust for the fact that the expectation

of an inverse of a random variable does not equal the inverse of its expectation. To find

the expected price increase we take one-million random draws from the estimated joint

distribution of estimated supply and demand elasticities and find the price multiplier for each

one.25 Expected price changes, taken as the average of the one-million simulated multipliers,

are larger, because the price multiplier is a convex function of the sum of two elasticities,

and the expected value of a convex function is larger than the function evaluated at the

argument’s expected level. For the same reason, the 95% confidence interval of the multiplier

is positively skewed.

An estimated price increase of 30% implies a decline in food consumers’ surplus equal

to 180 billion dollars annually. We obtain this number assuming (i) expected supply (along

the trend line) is the equivalent of feeding 7.92 billion people per year on 2000 calories per

day of raw grains and oilseed; (ii) prices in 2010 were 77 dollars per person per year; and

(iii) the ethanol mandate increases prices by 30%. About two thirds of ethanol production

comes from new production and about one third comes from reduced food consumption, i.e.,

1.67% of global production, given the supply elasticity tends to be about twice the size of

the estimated demand elasticity. The reduction in food consumption is equivalent to the

annual caloric requirement of about 132 million people.

There might also be an offsetting increase in producer surplus. Some argue that the

ethanol mandate increases fuel supply, thereby lowering fuel cost, which in turn benefits

consumers (Rajagopal et al. 2007). Alternatively, if past ethanol subsidies were insufficient

to achieve the current mandate, it could increase the cost of gasoline production. A full

welfare analysis would require an account of this supply shift, plus assumptions about the

elasticities of supply and demand of fuels, which is beyond the scope of this paper. Otherwise,

if the net effect on fuel costs is small, in the agricultural market the policy largely amounts

to a shift from consumer surplus to producer surplus.

The baseline scenario assumes byproducts from ethanol production are not fed to animals.

We report estimates assuming zero recycling because studies differ in what fraction can be

recycled, and the demand shift can be easily adjusted to any assumed recycling ratio. For

25Another approach would be to use shrinkage estimators to obtain more efficient estimates of the inverseratio. Since the elasticities are interesting in their own right, we decided to stick with standard OLS estimates,as a shrinkage estimator would result in biased estimates of these elasticities.

16

example, if one third of the calories could be recovered as feed stock, the demand shift and

price increase would be multiplied by two-thirds, dropping the price increase to 20% rather

than 30%. For our preferred 3SLS estimates in Table 1, the positively skewed 95% confidence

interval ranges from 14 to 35 percent.

4.2 Using Weather as an Instrument

While an absence of autocorrelation in aggregate yield shocks and an absence of correlation

in shocks between countries suggests that random weather component is much larger than

possible endogenous yield responses to price, a more defensibly exogenous instrument is

weather itself. In Table 2 we present results when weather variables rather than yield shocks

are used as instruments. We now use four instruments instead of one: a quadratic in both

average temperature and total precipitation.26 Coefficients from the log quantity regressions

are given in columns (a), while results from the log price regressions are given in columns

(b). Significance levels decrease in both the first stage and the second stage. Coefficients

on the instruments in the supply equation seem reasonable. For example, the quadratic in

average temperature is hill-shaped with an optimal growing season average of 19◦C or 67◦F.

Instruments in the demand equation are neither individually nor jointly significant and the

demand elasticities should hence be interpreted with caution.27 While past weather shocks

are more defensible as an instrument, our baseline regression uses past yield shocks due to

the large increase in efficiency.

4.3 Response on Extensive and Intensive Margins

Searchinger et al. (2008) and others argue that ethanol production drives up food commodity

prices, which, in turn, causes greater conversion of forest and pasture into crop production.

Because land use conversion (mainly deforestation) already accounts for up to 20% of global

CO2 emissions, these indirect land-use changes might offset or even reverse apparent CO2

emission savings derived from substituting ethanol for traditional gasoline. Thus, an in-

26These weather variables are weighted averages of the University of Delaware gridded weather data, wherewe weight grids in a county over the areas a crop is grown and the time during which it is grown. Annualweather variables for each country and crop are aggregated using the growing area in a country. See theData Appendix A2.2 for more detail.

27There are two reasons why it is empirically more challenging to estimate demand elasticities. First, thebottom panel of Figure 1 shows that consumption is much smoother through time than production. Second,these small changes in consumption are only indirectly derived using changes in inventories, which are harderto obtain than production numbers.

17

teresting policy question is whether new corn ethanol supply comes from the intensive or

extensive margin. We investigate this issue in Table 3. The first three columns regress the log

of growing area (for maize, rice, soybeans, and wheat) on the instrumented price to measure

responses on the extensive margin. The last three columns use the log of total fertilizer, one

of the major inputs that can be adjusted to increase production on the intensive margin.28

The regressions are identical to the IV regression in our baseline model, except log growing

area or log fertilizer use replaces log quantity. The estimated area elasticity is 0.07-0.08,

while there is no significant response for fertilizer use—the point estimate is negative. This

suggests that new supply likely comes from the extensive, not the intensive margin.

The estimated land-area elasticity is slightly smaller than the overall supply elasticity.

There will be less than a one-to-one relationship between output increases and land area

increases if higher-productivity countries happen to be more responsive to prices than low-

productivity countries. For example, if total land area increases by 5%, but areas with

higher-than-average yield increase area by 6% and areas with less-than-average yield increase

by 4%, total supply will increase by more than 5%. We therefore replicate the analysis for

individual countries and find different sensitivities to world caloric shocks and world prices.

Major producers and exporters like the United States and Brazil show much larger elasticities

than the global average.

Although our land area elasticity for Brazil is comparable to Kanlaya J. Barr, Bruce A.

Babcock, Miguel Carriquiry, Andre Nasser & Leila Harfuch (2010) in magnitude, our esti-

mate for the US is significantly larger. Agricultural programs of the US government have

historically driven the US area response. In times of low prices, farmers received subsidies in

exchange for setting previously cropped land idle (called set asides). At the same time, the

US government scaled up programs that pay farmers to idle land for purposes of reducing soil

erosion and protecting wildlife, water quality, and addressing other environmental concerns.

During periods of high prices, set asides and conservation programs have been scaled back.

When we regress the log of the growing area plus government-mandated set-asides and land-

retirement programs on instrumented price (panel C of Table 3), the estimated US elasticity

drops sharply. Thus, much of the land supply response in the US derives partly, and perhaps

mainly, from agricultural policy responding to prices. During the recent price spike, however,

conserved lands declined only modestly.29 Given the relatively subdued responses of recent

28FAO does not provide crop-specific fertilizer use. The data is hence for all crops, not just the four staples.The data is limited to 1961-2002 since reporting practices changed in 2003.

29Set asides ended with the Federal Agriculture Improvement and Reform Act of 1996. Since the firstRenewable Fuel Standards in 2005, land enrolled in the Conservation Reserve Program has fallen from about

18

US agricultural policy and that the US figures so prominently in world production of sta-

ple grains and oilseeds, supply response today might be somewhat less than our estimates,

which would make the price and welfare impacts larger. However, land in US set aside and

conservation programs is thought to be significantly inferior to land under cultivation, so it

is not clear how much smaller the supply elasticity may be.

Using our estimated elasticities, total caloric production would increase by roughly 3.3

percent, or 190 trillion calories. In 2010, worldwide planting area for the four commodities

was 1.6 billion acres. Using the average elasticity of 0.077 from Table 3 on the predicted

30 percent price change, total acreage is predicted to have increased by 2.3 percent, or 36

million acres, which is the size of the total land area (not agricultural area) of the US state

of Iowa.

4.4 Comparison to Traditional Methods

We compare the new estimates to other approaches without a first stage in Table 4. The

first three columns report elasticity estimates using OLS, while the last three columns uses

seemingly unrelated regressions (SUR). These models use uninstrumented price and futures

prices, not predicted price in the spirit of Nerlove (1958). The SUR regressions do account for

the correlation of innovations ut and vt. We include this regression mainly to illustrate likely

endogeneity bias in comparison to IV and 3SLS estimates in Table 1. The OLS regressions

give extremely inelastic estimates of supply and demand, 0.02 for supply if we include 4

spline knots and -0.018 for demand. The estimates also become much more sensitive to the

flexibility of the time controls. While the demand elasticity is statistically significant at the

10% level if we include 4 spline knots, the standard errors are small and (if assumptions are

accepted, which is dubious) rule out elasticities less than -0.038 with 97.5 percent confidence.

The supply is statistically significant if we use 3 spline knots, which rules out elasticities

greater than 0.106 with 97.5 percent confidence, or even smaller quantities for other time

controls. The predicted price increase of the ethanol mandate (diverting 5 percent of world

production) would be much larger, as the price multiplier is at least 25, or 4 times the

baseline. For the seemingly unrelated regressions (SUR), the price multiplier is at least

three times as large. Instrumenting prices with yield shocks is therefore crucial; otherwise

the predicted price increase would likely be too large. Our concern with the traditional

approach is that both futures prices and lagged prices incorporate anticipated area responses

and are hence endogenous.

37 million acres in 2008 to about 29 million acres today (Daniel Hellerstein & Scott Malcolms 2011).

19

4.5 World Versus Local Prices

Our baseline model sums over all countries in the world. ADM, Bunge, and Carghill are

internationally operating arbitrageurs that work to equate possible price differentials between

countries, subject to transportation costs. Prices in countries that have a port seem to be

strongly associated with one another. For example, Paul L. Fackler & Huseyin Tastan

(2008) test whether the law of one price holds for soybeans in the United States, Brazil,

and Europe and cannot reject that markets are cointegrated. While landlocked countries

might have prices that differ from the world market as arbitrage between prices becomes

more costly, most large producers used in this study (see appendix Tables A1 and A2) do

have ports.

We use price data from the US Chicago Board of Trade, and one might wonder how

appropriate it is as a global measure. Table 5 disaggregates yield shocks into those in the

US and the rest of the world (RW). Shocks in both regions are rescaled using the ratio of the

predicted production in the region divided by predicted global production. For brevity, the

table presents only elasticities and the predicted commodity price increase, while individual

coefficients for both the US and the rest of the world are given in Appendix Table A4.

Panel C presents a test whether the coefficients on the instruments derived from US yield

deviations equal those for the rest of the world. In no case can we reject that the coefficients

are equal at any conventional significance level; all p-values are above 0.2. In other words, a

production shock in Brazil does not have a significantly different effect on US futures prices

than an equally sized shock in the US. The estimated elasticities are also comparable to

what we obtained in Table 1.

4.6 Long-Run Response to Price

Identification of our supply response relies on exogenous price variation that is driven by

production shocks in the previous period. One concern is whether we are estimating a

short-run elasticity that is a lower bound for the long-run elasticity.30 Two observations

speak against this: first, prices are both volatile and show a large degree of persistence,

30It is also possible that the long-run elasticity is smaller than the short-run elasticity. This could happenif, in the short run, farmers respond to higher prices by using practices that boost output temporarily to thedetriment of long-run productivity. Specifically, long-run supply response could be diminished by (a) over-extracting from aquifers and thereby increasing future costs of irrigation; (b) accumulation of pest problemsfrom an expanded monoculture; (c) reduced soil quality, especially if land that is newly cultivated in responseto higher prices is marginal, has thin topsoil and cannot be cropped continuously. Such challenges are wellknown and have long been pervasive in agriculture.

20

so farmers can expect temporary production shocks to have long-run price effects. There

has been an active debate following Angus Deaton & Guy Laroque (1996) surrounding

apparently excessive autocorrelation in prices. While our variation stems from short-run

weather shocks, farmers can expect price changes from these weather shocks to persist. This

persistence is also manifested in the relationship between crop and farmland prices. The

run-up in commodity prices resulted in an almost proportional increase in farmland prices in

2005-2008. Since farmland prices are forward looking, this is only efficient if farmers expect

commodity prices to stay high, which would seem unlikely if a longer-run supply response

were to erode the price shock. Second, our estimate of the longer-run supply response is

consistent with our short-run estimates (Table 6). This longer run analysis includes two

lags in the supply equation, where prices are again instrumented with the previous period’s

weather shock. The table displays the coefficients on the futures price in the current period

βs,t and lagged futures prices (βs,t−1, βs,t−2) as well as the sum of the three coefficients, which

is the combined long-run impact. The sum of coefficients is slightly larger, but very close to

our baseline estimate in Table 1 where we only consider futures prices in the current period.

4.7 Multicrop Systems

Our baseline estimates pooled all four basic staples (maize, rice, soybeans, and wheat) while

ethanol production relies almost exclusively on maize. If the four commodities are not

perfect substitutes, the mandate could cause corn prices to rise more than the other three

crops.31 We therefore consider a 2x2 system of supply and demand equations, where the two

commodities are maize and the sum of the other three crops (Table 7). We present results for

the specification with 4 spline knots, akin to column (2b) of Table 1. The first two columns,

(1a) and (1b), as well as the last two columns, (2a) and (2b), are from a single regression. The

only difference is that the last two columns impose symmetry of the cross-price elasticities,

which cannot be rejected in the unrestricted version of the model (a p-value of 0.87). Own-

price supply elasticities are positive, but only statistically significant if we impose symmetry.

Cross-price supply elasticities are never significant, but these have large standard errors. We

cannot rule out the possibility that the cross-price elasticity equals the own-price elasticity.32

31Appendix Table A5 pool quantities and prices for all four commodities, but separate yield shocks foreach of the four commodities. The bottom of the tables present tests whether the coefficients on the twoshocks are the same, and equality cannot be rejected except if we model the time trend least flexible as arestricted cubic spline in time with 3 knots.

32In our view, substitutability is reasonably large for relatively small variations in adjustments to globalcrop mix. For example, wheat, corn and soybeans are substitutable over many parts of the MidwesternUnited States. In other parts of the world, e.g., India and China, some land is substitutable between wheat

21

Own-price demand elasticities are negative and significant. The size is larger than what we

observe when we aggregate all four commodities. This is deceptive as the cross-price demand

elasticities are quite large in magnitude, and significant if we impose symmetry. Consumers

or agricultural producers that use commodities as inputs (e.g., feedlots) have the option to

switch between commodities as relative prices change. Studies that focus on one commodity

might therefore obtain an elasticity that is too high.

To derive price implications of this model, let q be the (2x1) column vector of the quantity

of maize and three-crop aggregate commodity and let p be corresponding vector of prices.

The demand system is q = βdp and the supply system is q = βsp.33 The effect of the US

ethanol mandate, which diverted 5% of world caloric production of the four commodities,

or 14% of the world’s maize production into ethanol, is hence [βs − βd]−1 [1 0]′ ∆q. For

the same price increase, the multiplier will be lower as the mandate diverts 14% of maize

production compared to 5% of world caloric production, which is larger by a factor of 2.8.

Panel C of Table 7 displays (i) the multiplier that uses the point estimates of the own-price

and cross-price elasticities as well as (ii) the expected multiplier and (iii) the 95% confidence

interval if we sample one million draws from the joint distribution of the parameters. The

predicted price increase for corn is 51% (3.63 × 0.14), while the predicted price increase

for the other commodities is 27% (1.95 × 0.14). Although the own-price effect for corn is

statistically significant at the 95% confidence level and 50% larger than the cross-price effect

for the other commodities, the two multipliers are not significantly different from one another

due to the lack of precision in the 2x2 system.34 The price increases are smaller using FAS

data.

We are mainly interested is the ethanol-induced increase in overall expenditures for com-

modity calories. The baseline model implicitly assumes the four commodities are perfect sub-

stitutes, with the overall effect embodied by the price increase of the aggregate commodity,

calories. For the disaggregate analyses, the overall price increase is the production-weighted

average of individual commodity price increases. Multipliers that translate changes in aggre-

gate demand into predicted changes in the overall price are given in the notes to Table 7.35

and rice. Especially since aggregate shocks are small and buffered by storage, a chain of substitutions couldmake aggregate substitutability quite large, at least over the range of aggregate weather shocks. But sinceprices consequently move together, it is difficult to precisely identify cross-price elasticities.

33For a more detailed model, see Appendix Section A1.2.34Results using both 4 and 5 spline knots are shown in appendix Table A6 for FAO data and appendix

Table A10 for the FAS data.35We take the production-weighted average of the individual multipliers, where the production weights

are the average fraction of world caloric production in 2005-2010 for each of the crops. We then divide theaverage multiplier by the maize share to transfer units into multiplies of aggregate demand instead of maize

22

These multipliers are 8.37 in the unrestricted system and 7.21 if we impose symmetry, which

is slightly higher than the baseline multiplier of roughly 6 in the pooled analysis.36 The 95%

confidence interval increases to (4.8, 12.6) under the more efficient estimate where we impose

symmetry, and increases significantly more to (0.6, 31.5) in the less efficient unrestricted sys-

tem. Since confidence intervals are positively skewed, the upper bound increases more than

the lower bound decreases.

Table 8 reports results if we disaggregate the analysis further and estimate a 4x4 system of

supply and demand for each of the commodities. Prices of each commodity are instrumented

with past yield shocks (supply) or concurrent yield shocks (demand) for each of the four

commodities. We switch to using the FAS data, which has three more observations, as the

analysis already has limited degrees of freedom. Prices of the four commodities move closely

together, which makes it is difficult to identify them separately. Instruments are weak and

results should be interpreted with care. While the point estimates for the price multipliers

are roughly comparable to the 2x2 system, the 95% confidence interval includes zero for each

of the four commodities due to the large standard errors. We take the table as suggestive

evidence that our pooled analysis gives number that are roughly comparable to a 4x4 system.

The predicted price increase for maize is 59% (4.21 × 0.14) in the unrestricted system

and 36% (2.54 × 0.14) if we impose symmetry of cross-price elasticities. At the same time,

predicted price increases for other commodities are lower. The multipliers for translating

shifts in aggregate demand into changes in the overall price of calories are 7.53 and 3.25,

respectively, which is again reasonably similar to our baseline estimate of 6.37 Since the

estimates are less precise, the 95% confidence interval increase to (-6.6, 14.5) if we impose

symmetry and (-43.8, 61.6) in the unrestricted system.

In summary, even if we relax the assumption of perfect substitutability, the predicted

price increase in the overall expenditures for the four commodities remains relatively robust

around a multiplier of 6. At the same time, we cannot rule out a maize price increase that

is twice as large as the overall increase for calories. But this larger price increase for corn

is counterbalanced by lower prices increases for other commodities. Since the multi-crop

systems are more flexible and less precisely estimated, the 95% confidence intervals increase,

with the upper bound rising significantly more than lower bound declines due to positive

skewness.

demand.36The multipliers are 5.48 and 5.19 if we use the FAS data in Table A10.37The multipliers are 6.63 and 4.26 if we use the FAO data in Table A7.

23

4.8 Further Robustness Checks

An online appendix reports a number of additional sensitivity checks that we briefly sum-

marize here. Results are generally robust in the sense that the price multiplier is around 6

in most specifications.

The 2009 Renewable Fuel Standard (RFS) changed fuel supply and gasoline prices, and

thereby influenced agricultural production costs.38 If this shift in supply were large enough,

it would confound our estimated elasticities. One way to ensure this is not the case is

to re-estimate the model using only data before the introduction of the ethanol mandate.

Table A13 limits the analysis to 1961-2003 or 1961-2005, so the data set stops before the

recent run-up in prices and the implementation of the 2007 or 2009 Renewable Fuel standards.

Results are similar.

Table A14 varies the timing at which we evaluate futures prices. Final results of a year’s

production shock are not fully revealed before December. On the other hand, planting

decisions for next year’s harvest of winter wheat are made in September in the northern

hemisphere. We therefore consider futures prices in September of the previous year (Panel

A), or March of the concurrent year (Panel B), because production shocks in the Southern

hemisphere are resolved by March of the concurrent year. Panel C again evaluates prices at

the end of the year, but uses the spot price in the demand equation instead of the futures

price during the month of delivery. Results are similar in all cases.

To check the sensitivity of our estimates to the derivation of yield shocks, Table A15

replicates the analysis using linear time trends, restricted cubic splines with 4 knots (3

variables), or restricted cubic splines with 5 knots (4 variables) in the derivation of the yield

shocks. Our baseline specification used 3 spline knots (2 variables). The results are again

insensitive to the chosen time trend in the derivation of yield shocks.

Table A16 further examines the derivation of yield shocks. Panel A replicates the analysis

by using yield shocks that are not jackknifed as in our baseline. Panels B and C allow yields

to be autocorrelated, which may arise from technological break-throughs or if weather has

autocorrelation. We fit models up to MA(1) or MA(3), respectively, for each country and

crop. For example, in panel C, we fit four models.39 The model with the lowest BIC is

38The RFS, which might nominally be considered an implicit cost or tax on gasoline production, formerlyincluded a large subsidy for ethanol production. Now that ethanol plants are in place (fixed costs are largelysunk), it is not clear whether current and past RFS ultimately served to subsidize or tax fuel. Anothercomplicating feature is the substantial size of US demand for gasoline. Since ethanol displaced about 10percent of oil formerly used in gasoline production, the biofuel mandate may have reduced world oil prices.

39MA(0), MA(1), MA(2), and MA(3).

24

chosen, and yield deviations are the innovations in a given period, i.e., the new information

that has been revealed. Results remain robust.

Table A17 reports results from three further sensitivity checks. Given that prices show a

high degree of persistence, we include the second lag of prices in panel A. Log futures prices

for period t that are traded at the end of t−1 are instrumented with the yield shock in ωt−1,

while controlling for the second lag of the dependent variable, i.e., log futures prices with a

maturity in t− 1 that are traded in t− 2. Panel B uses two lagged shocks ωt−1 and ωt−2 to

instrument futures prices. The panel also presents results from overidentification tests as we

now include two instruments, but none of them have p-values below 0.40. Panel C rescales

the caloric conversion ratios so the average price in 1961-2010 of all four crops equals that of

maize.40 The original as well as the rescaled price series are shown in Figure A9. We do this

as the average price of rice is highest, and shifts in production between crops hence alters

the overall price. However, the results are insensitive to this rescaling.

5 Conclusions

Our analysis makes two contributions to the literature. We first introduce a new framework

on how to identify supply elasticities for storable commodities and apply it in the agricultural

setting: weather-induced yield shocks can facilitate estimation of both supply and demand

of agricultural commodities. In applying this idea to the available data we found it more

practical to use yield shocks (deviations from time trends of output per land unit) instead

of using weather directly, which gives a weaker first stage as global annual production has

to be linked to aggregate annual weather measures. We obtain similar point estimates using

both weather and yield shocks. The 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.

While the idea of using weather to identify demand is an old idea, it has rarely been

applied, and to our knowledge, has never been applied on a global scale. Our approach

of using past shocks to identify supply is new and results in estimates that are far more

elastic than those obtained using traditional methods. 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

40In other words, the price series of wheat, soybeans and rice are each multiplied by a constant so theaverage price equals the maize average price.

25

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 computational 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.

The second contribution is to estimate elasticities for caloric energy from the world’s most

predominant food commodities. With this perspective in mind, we consider price and quan-

tity predictions stemming from the rapid and largely policy-induced expansion of ethanol

demand. The 2009 Renewable Fuels Standard diverted approximately 5 percent of world

caloric production of the four staple crops into ethanol production. Since commodities are

storable and current ethanol production levels were largely anticipated since the Energy Pol-

icy 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 30 percent if none of the corn

used for biofuel production can be recycled. If the distillers’ grains, a byproduct from corn

used in ethanol production, are recycled as feed stock, the price increase would be scaled

back accordingly. For example, if one third of the calories can be recovered as feedstock,

the price increase would be lowered to 20 percent. These predicted price increases are far

smaller than those obtained using a SUR model that does not account for the endogeneity

of prices. Our prediction is slightly larger than the USDA projected price increase made for

corn in 2007, and would suggest that the ethanol mandate had some role in the four-fold

price increase, but by no means can account for all of it.

It is also important to consider uncertainty surrounding these baseline estimates. The

95% confidence bands around the induced price increase have a large, positive skew. Even

taking distillers grains into account, the ethanol-induced price increase for food commodities

as a whole may be as low as 14 percent, just 6 percentage points below the baseline of 20%;

but it may also be as large as 35 percent, a full 15 percentage points above the baseline.41

Multi-crop models relax the perfect substitutability between the four crops. Price increases

may vary across crops, but the point estimates for the increase in total expenditures for the

four crops remains comparable. These estimates are less precise, and the 95% confidence

bands increase more on the upper end than the lower end due to the positive skewness.

41Using the 3SLS results in Table 1.

26

Our analysis suggests factors besides the US ethanol policy likely contributed strongly

to the rapid price rise between 2005 and 2008. These factors may include rapid growth in

the demand for basic calories from emerging economies like China. This demand growth has

accelerated through demand for meat and other animal-based foods, which are highly income

elastic. While population doubled in China between 1961 and 2006, meat consumption grew

33-fold (FAO), and comprised a little less than a third of the world’s meat consumption in

2007. Meat requires between 5-10 times the agricultural area to obtain the same amount of

calories as a vegetarian diet. This demand growth resumed as the world economy recovers

from the financial crisis and subsequent recession and corn prices jump to new highs in

2011. Another reason for the large price increase is a decrease in supply due to detrimental

weather, such as prolonged drought in Australia, coupled with low worldwide inventories.

The implications of increases in demand coupled with the potential of production shortfalls

in the face of changing climate will likely add further upward pressure on future prices.

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Figure 1: World Production and Consumption of Calories (FAO Data)

01

23

45

67

8B

illio

n P

eopl

e (2

000

calo

ries/

day)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010year

Maize Wheat Rice Soybeans

23

45

67

8B

illio

n P

eopl

e (2

000

calo

ries/

day)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Consumption Production

Notes: The top panel shows world production of calories from maize, wheat, rice, and soybeans for 1961-

2010. The bottom panel shows combined production and consumption. Storage allows consumption to be

smoothed over periods. The y-axis in both panels gives the number of people who could be fed on a 2000

calories/day diet by hypothetically only consuming the four commodities.

30

Figure 2: Commodity Prices

010

020

030

040

050

0P

rice

of 2

000

Cal

orie

s P

er D

ay (

$201

0/pe

rson

/yea

r)

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010Year

Maize Wheat Rice Soybeans

Notes: Figure shows caloric prices over time for maize, wheat, rice, and soybeans for 1913-2010. The y-axis

gives the annual cost of 2000 calories per day. Price series is taken from National Agricultural Statistics

Service.

31

Table 1: Supply and Demand Elasticity (FAO Data)

Instrumental Variables Three Stage Least Squares(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: Supply EquationSupply Elast. βs 0.102∗∗∗ 0.096∗∗∗ 0.087∗∗∗ 0.116∗∗∗ 0.112∗∗∗ 0.097∗∗∗

(0.025) (0.025) (0.020) (0.019) (0.020) (0.019)Shock ωt 1.184∗∗∗ 1.229∗∗∗ 1.211∗∗∗ 1.249∗∗∗ 1.279∗∗∗ 1.241∗∗∗

(0.146) (0.138) (0.105) (0.111) (0.101) (0.091)First Stage ωt−1 -3.901∗∗∗ -3.628∗∗∗ -3.824∗∗∗ -3.546∗∗∗ -3.113∗∗∗ -3.226∗∗∗

(1.145) (0.945) (0.910) (0.800) (0.704) (0.731)First Stage ωt -2.918∗ -2.276∗ -2.372∗ -2.885∗∗∗ -2.350∗∗∗ -2.420∗∗∗

(1.647) (1.294) (1.279) (0.967) (0.815) (0.819)

Panel B: Demand EquationDemand Elast. βd -0.028 -0.055∗∗ -0.054∗∗ -0.034 -0.062∗∗∗ -0.066∗∗∗

(0.021) (0.024) (0.022) (0.023) (0.022) (0.021)First Stage ωt -5.564∗∗∗ -4.655∗∗∗ -4.770∗∗∗ -5.354∗∗∗ -4.445∗∗∗ -4.332∗∗∗

(1.489) (1.300) (1.249) (1.384) (1.210) (1.186)

Panel C: Effect of Demand ShiftMultiplier 1

βs−βd

7.73 6.63 7.06 6.65 5.75 6.12

Exp. Multiplier 8.39 7.08 7.42 6.90 5.92 6.31(95% Conf. Int.) (5.2,15.3) (4.6,12.2) (5.0,12.0) (4.9,10.4) (4.3,8.5) (4.6,9.1)

F1st-stage Supply 11.61 14.73 17.66F1st-stage Demand 13.97 12.81 14.60Observations 46 46 46 46 46 46Spline Knots 3 4 5 3 4 5

Notes : Tables show regression results for the supply and demand of calories. The first three columns

(1a)-(1b) use instrumental variables, while columns (2a)-(2c) use three stages least squares. Columns (a),

(b), and (c) include restricted cubic splines in time with 3, 4, and 5 knots, respectively. Panel A gives

results for the supply equations (1) and (2), i.e., coefficients above the vertical line give the results for log

quantity, while coefficients below the line give first stage results of log price. Similarly, panel B gives results

for demand equations (3) and (4). Coefficients on time trends are suppressed. Panel C gives the effect of

a demand shift on commodity prices: multipliers translate percentage changes in demand into percentage

changes in equilibrium price. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

32

Table 2: Supply and Demand Elasticity - Weather as Instrument (FAO Data)

(1a) (1b) (2a) (2b) (3a) (3b)log Q log P log Q log P log Q log P

Panel A: Supply Equation

Supply Elast. βs 0.085∗ 0.089 0.091∗

(0.048) (0.055) (0.053)Temperature Tt−1 3.252∗∗∗ 3.080∗∗∗ 3.050∗∗∗

(0.863) (0.738) (0.768)Temperature T2

t−1 -0.084∗∗∗ -0.080∗∗∗ -0.078∗∗∗

(0.022) (0.019) (0.019)Precipitation Pt−1 2.937 2.597 3.174

(2.249) (1.923) (2.097)Precipitation P2

t−1 0.130 -0.193 -0.497(1.072) (0.922) (0.982)

Temperature Tt 0.037 1.776∗∗ -0.015 1.413∗∗ -0.041 1.259∗

(0.184) (0.750) (0.201) (0.669) (0.195) (0.691)Temperature T2

t -0.002 -0.045∗∗ -0.000 -0.035∗∗ 0.000 -0.031∗

(0.005) (0.019) (0.005) (0.017) (0.005) (0.018)Precipitation Pt 0.547 2.274 0.498 1.952 0.610∗ 2.847

(0.332) (1.805) (0.363) (1.611) (0.371) (1.742)Precipitation P2

t -0.426∗∗∗ -0.694 -0.431∗∗∗ -0.952 -0.464∗∗∗ -1.233(0.143) (0.829) (0.156) (0.737) (0.157) (0.763)

Panel B: Demand Equation

Demand Elast. βd -0.014 -0.056∗∗ -0.047∗

(0.025) (0.028) (0.025)Temperature Tt 1.282 1.099 1.305

(1.209) (1.003) (1.038)Temperature T2

t -0.034 -0.030 -0.035(0.030) (0.025) (0.026)

Precipitation Pt 1.991 1.636 0.759(3.227) (2.675) (2.853)

Precipitation P2t 1.075 0.705 1.015

(1.460) (1.211) (1.266)

Panel C: Effect of Demand Shift

Multiplier 1

βs−βd

10.07 6.91 7.25

Exp. Multiplier 14.13 9.35 7.71(95% Conf. Int.) (4.8,52.9) (3.8,25.7) (4.0,27.4)

Observations 46 46 46 46 46 46Spline Knots 3 3 4 4 5 5

Notes : Table replicates the three-stage least square results in Table 1 except that prices are instrumented

with weather (quadratic in average temperature and precipitation) instead of yield shocks. Column pairs (a)

and (b) present results from one joint regression, where columns (a) give results for the quantity regression,

and columns (b) the results for the price regressions. Columns (1a-b), (2a-b), and (3a-b) include restricted

cubic splines in time with 3, 4, and 5 knots, respectively. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%;∗ : 10%.

33

Table 3: Growing Area and Fertilizer Use As a Function of Instrumented Prices (FAO Data)

Log Growing Area Log Fertilizer(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: WorldFutures Price pt|t−1 0.082∗∗∗ 0.078∗∗∗ 0.071∗∗∗ -0.070 -0.071 -0.066

(0.021) (0.023) (0.017) (0.094) (0.073) (0.063)

Panel B: USFutures Price pt|t−1 0.289∗∗∗ 0.278∗∗∗ 0.278∗∗∗ 0.026 0.021 0.097

(0.075) (0.075) (0.071) (0.173) (0.095) (0.079)

Panel C: US Growing Area + Set-AsidesFutures Price pt|t−1 -0.071 -0.050 -0.095∗∗

(0.065) (0.055) (0.045)

Panel D: BrazilFutures Price pt|t−1 0.261∗ 0.217 0.174 -0.150 -0.166 -0.041

(0.141) (0.142) (0.111) (0.506) (0.262) (0.260)Observations 46 46 46 41 41 41Spline Knots 3 4 5 3 4 5

Notes : Table presents IV regression results. The regressions are equivalent to the IV results in Table 1

except that the second-stage dependent variable is different: columns (1a)-(1c) use log growing area and

columns (2a)-(2c) log fertilizer. Columns (a), (b), and (c) include restricted cubic splines in time with 3, 4,

and 5 knots, respectively. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

34

Table 4: Comparison to Uninstrumented Regressions (FAO Data)

OLS SUR(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: ElasticitiesSupply Elast. βs 0.051∗ 0.020 0.023 0.065∗∗∗ 0.039 0.040∗

(0.028) (0.031) (0.029) (0.020) (0.025) (0.024)Demand Elast. βd 0.012 -0.018∗ -0.016∗ 0.023∗∗ -0.011 -0.010

(0.011) (0.010) (0.009) (0.009) (0.009) (0.008)

Panel B: Effect of Demand ShiftMultiplier 1

βs−βd

25.59 26.19 25.55 23.64 19.89 20.04

Exp. Multiplier 55.05 22.85 15.26 77.51 37.23 15.51(95% Conf. Int.) (-206,248) (-227,262) (-205,247) (12,120) ( 8,122) ( 9,118)

Observations 46 46 46 46 46 46Spline Knots 3 4 5 3 4 5

Notes : Table replicates Table 1 except that prices are not instrumented. Columns (1a)-(1c) give results for

OLS regressions, and columns (2a)-(2c) from Seemingly Unrelated Regressions (SUR). Columns (a), (b), and

(c) include restricted cubic splines in time with 3, 4, and 5 knots, respectively. Stars indicate significance

levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

35

Table 5: Supply and Demand Elasticity - Separating Shocks in US from Rest of World (FAOData)

Instrumental Variables Three Stage Least Squares(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: ElasticitiesSupply Elast. βs 0.107∗∗∗ 0.089∗∗∗ 0.083∗∗∗ 0.112∗∗∗ 0.105∗∗∗ 0.091∗∗∗

(0.022) (0.025) (0.020) (0.019) (0.020) (0.018)Demand Elast. βd -0.021 -0.053∗∗ -0.053∗∗ 0.003 -0.049∗∗ -0.051∗∗∗

(0.020) (0.022) (0.021) (0.017) (0.019) (0.017)

Panel B: Effect of Demand ShiftMultiplier 1

βs−βd

7.84 7.07 7.39 9.14 6.50 7.05

Exp. Mult. (s.e.) 8.35 7.44 7.78 9.62 6.71 7.28(95% Conf. Int.) (5.3,14.7) (4.8,13.3) (5.2,12.6) (6.5,15.5) (4.9,9.8) (5.3,10.6)

Panel C: P-value on Equal CoefficientsS1st-stage ωt−1 equal 0.20 0.56 0.77 0.81 0.50 0.61D1st-stage ωt equal 0.42 0.24 0.27 0.77 0.36 0.38Observations 46 46 46 46 46 46Spline Knots 3 4 5 3 4 5

Notes : Table replicates Table 1 except caloric shocks for the United States and the Rest of the World are

considered separately. Both shocks are normalized by the predicted fraction of global production to make

the shocks comparable in size. Panel C presents p-values from tests for whether the shock coefficients are

the same when used as instruments for price. Coefficients for the US and the Rest of the World (RW) are

given in Appendix Table A4. Columns (a), (b), and (c) include restricted cubic splines in times with 3, 4,

and 5 knots, respectively. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

36

Table 6: Supply and Demand Elasticity - Lagged Supply Price (FAO Data)

Instrumental Variables Three Stage Least Squares(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: Supply EquationSupply: βs,t 0.066∗ 0.059 0.060∗∗ 0.074∗∗ 0.086∗∗∗ 0.079∗∗∗

(0.039) (0.037) (0.031) (0.031) (0.030) (0.027)Supply: βs,t−1 0.030 0.024 0.028 0.023 0.004 0.013

(0.048) (0.042) (0.035) (0.031) (0.027) (0.024)Supply: βs,t−2 0.041 0.039 0.031 0.025 0.029∗ 0.026∗

(0.037) (0.033) (0.030) (0.016) (0.017) (0.015)Combined

∑

τ=0 βs,t−τ 0.137∗∗∗ 0.121∗∗∗ 0.118∗∗∗ 0.123∗∗∗ 0.119∗∗∗ 0.118∗∗∗

(0.018) (0.020) (0.015) (0.016) (0.021) (0.019)

Panel B: Demand EquationDemand Elast. βd -0.019 -0.059∗∗ -0.055∗∗ -0.028 -0.051∗∗∗ -0.051∗∗∗

(0.021) (0.025) (0.026) (0.020) (0.017) (0.017)

Panel C: Effect of Demand ShiftMultiplier 1

βs−βd

6.41 5.53 5.75 6.63 5.90 5.91

Exp. Multiplier 6.63 5.73 5.94 12.61 7.86 8.20(95% Conf. Int.) (4.8,9.8) (4.1,8.6) (4.3,8.7) (5.9,28.2) (5.0,13.9) (5.2,14.4)

Observations 44 44 44 44 44 44Spline Knots 3 4 5 3 4 5

Notes : Table replicates Table 1 except that it includes two lags of the price in the supply equation. Columns

(a), (b), and (c) include restricted cubic splines in time with 3, 4, and 5 knots, respectively. Stars indicate

significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

37

Table 7: Supply and Demand Elasticity - Two Crop System (FAO Data)

Unrestricted System Symmetry ImposedLog Log Log Log

Maize Other Maize Other(1a) (1b) (2a) (2b)

Panel A: Supply SystemLog Maize Price 0.086 -0.024 0.136∗ -0.001

(0.118) (0.078) (0.070) (0.047)Log Other Price 0.040 0.105∗ -0.001 0.088∗∗

(0.088) (0.058) (0.047) (0.036)

Panel B: Demand SystemLog Maize Price -0.271∗∗ 0.221∗ -0.269∗∗∗ 0.240∗∗

(0.123) (0.124) (0.099) (0.102)Log Other Price 0.248∗ -0.336∗∗ 0.240∗∗ -0.361∗∗∗

(0.136) (0.132) (0.102) (0.113)

Panel C: Effect of Maize Demand ShiftMultiplier 4.14 2.31 3.63 1.95Exp. Multiplier 4.58 2.57 4.08 1.90(95% Conf. Int.) (1.7,15.6) (-1.0,9.1) (2.6,7.1) (0.5,3.6)

P-val (symmetry) 0.870 . . .Observations 46 46 46 46Spline Knots 4 4 4 4

Notes : Table replicates 3SLS results with 4 knots from Table 1, except that calories from the four crops

are split into a 2x2 system: maize (M) and all other crops (O). Columns (a) and (b) present results from

one joint regression, where columns (a) give the results for the maize regression and columns (b) the results

for the aggregated crop (rice, soybeans, and wheat). The first two columns do not impose symmetry, while

the last two do. The multiplier gives the price increase for a 1% outward shift in demand for maize, while

baseline results give the multiplier on aggregate demand for maize, rice, soybeans, and wheat. To make

the multiplier comparable to the pooled analysis, we derive the production-weighted average multiplier of

all commodities, which is 8.37 in the unrestricted system and 7.21 if we impose symmetry. Stars indicate

significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

38

Table 8: Supply and Demand Elasticity - Four Crop System (FAS Data)

Unrestricted System Symmetry Imposed

Log Log Log Log Log Log Log Log

Maize Rice Soybeans Wheat Maize Rice Soybeans Wheat

(1a) (1b) (1c) (1d) (2a) (2b) (2c) (2d)Panel A: Supply System

Log Maize Price 0.207∗ -0.019 -0.734 -0.123 0.270∗∗∗ -0.016 -0.303∗ 0.107∗

(0.121) (0.043) (0.546) (0.163) (0.101) (0.065) (0.168) (0.061)Log Rice Price 0.043 0.048 0.350 0.111 -0.016 0.032 0.078 0.036

(0.094) (0.033) (0.426) (0.127) (0.065) (0.076) (0.145) (0.050)Log Soybeans Price -0.252 0.085 0.705 0.010 -0.303∗ 0.078 0.554 -0.163

(0.177) (0.062) (0.761) (0.240) (0.168) (0.145) (0.452) (0.127)Log Wheat Price 0.088 -0.019 -0.229 0.059 0.107∗ 0.036 -0.163 0.100

(0.099) (0.035) (0.417) (0.135) (0.061) (0.050) (0.127) (0.063)

Panel B: Demand System

Log Maize Price -0.244∗∗∗ 0.153∗∗∗ 0.227 -0.065 -0.287∗∗∗ 0.141∗∗∗ 0.078 0.068(0.078) (0.054) (0.193) (0.083) (0.066) (0.032) (0.068) (0.045)

Log Rice Price 0.061 0.007 -0.145 0.014 0.141∗∗∗ -0.017 -0.114∗∗∗ -0.071∗∗

(0.046) (0.031) (0.131) (0.051) (0.032) (0.031) (0.038) (0.030)Log Soybeans Price -0.008 -0.081 -0.329 0.043 0.078 -0.114∗∗∗ -0.236∗∗ -0.039

(0.107) (0.075) (0.238) (0.110) (0.068) (0.038) (0.109) (0.065)Log Wheat Price 0.199∗∗ -0.152∗∗∗ -0.063 -0.109 0.068 -0.071∗∗ -0.039 -0.095

(0.079) (0.055) (0.183) (0.083) (0.045) (0.030) (0.065) (0.060)

Panel C: Effect of Maize Demand Shift

Multiplier 4.21 1.99 3.11 0.94 2.54 -1.18 1.70 1.21Exp. Multiplier 3.00 5.41 1.34 1.07 2.77 3.48 1.98 -3.52

(95% Conf. Int.) (-20.1,28.1) (-33.4,40.0) (-19.7,24.3) (-17.0,18.9) (-5.2,11.5) (-16.6,16.1) (-3.4,7.1) (-13.3,14.5)P-val (symmetry) 0.201 . . . . . . .Observations 49 49 49 49 49 49 49 49Spline Knots 5 5 5 5 5 5 5 5

Notes : Table replicates 3SLS results with 5 knots from Table 1 except that each of the four crops is modeled separately. Columns (a)-(d)

present results from one joint regression. The first four columns do not impose symmetry, while the last four do. The multiplier gives the price

increase for a 1% outward shift in demand for maize, while baseline results give the multiplier on aggregate demand for maize, rice, soybeans,

and wheat. To make the multiplier comparable to the pooled analysis, we derive the production-weighted average multiplier of all commodities,

which is 7.53 in the unrestricted system and 3.25 if we impose symmetry. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

39

Identifying Supply and Demand Elasticities of Agricultural

Commodities: Implications for the US Ethanol Mandate

Michael J. Roberts♣ and Wolfram Schlenker♠

Online Appendix

♣ Department of Agricultural and Resource Economics, North Carolina State University, Box 8109, Raleigh,

NC. Email: michael roberts@ncsu.edu.

♠ School of International and Public Affairs, Columbia University, 420 West 118th Street, Room. 1308, MC

3323, New York, NY 10027. Email: wolfram.schlenker@columbia.edu.

A1 Model

A1.1 Validity of ωt as Instrument

Our baseline model uses log yield deviations ξcit for crops c in country i and year t. We

are fitting crop-and-country specific time trends gci(t) in regressions of log yields ycit, i.e.,

ycit = gci(t) + ξcit.The annual shock ωt is a weighted average of all shocks. The weights ρcit

depend on predicted yields ycit = egci(t)+σ2

2 (where σ2 is the estimated variance of the error

terms), growing area acit, and the caloric content of one production unit of crop c, κc.

ωt =

∑

c

∑

i ξcit × ycit × acit × κc∑

c

∑

i ycit × acit × κc

=∑

c

∑

i

ξcitρcit

ρcit =ycit × acit × κc

∑

c

∑

i ycit × acit × κc

Here we show that ωt is exogenous despite the endogeneity of ρcit, given:

(i) E[ξcit] = 0, which is true by construction of the shocks

(ii) ξcit is exogenous, which is otherwise assumed and defended in the text

(iii) ξcit is independent of the weight ρcit, which may be a stronger assumption, but follows

if yield shocks follow from weather experienced after planting decisions are made.

Assumption (iii) is testable: when we regress country-and-crop specific weights ρcit on

the shocks ξcit, the p-value is never below 0.69 regardless whether we use FAO or FAS

data and whether we include country-by-crop specific fixed effects or not.

A valid instruments requires that ut is orthogonal to ωt, or COV (ut, ωt) = 0. We have

COV (ut, ωt) = COV

(

ut,∑

c

∑

i

ξcitρcit

)

= E

[

ut

∑

c

∑

i

ξcitρcit

]

− E [ut]︸ ︷︷ ︸

=0

E

[∑

c

∑

i

ξcitρcit

]

= E

[∑

c

∑

i

ξcit

]

E

[∑

c

∑

i

utρcit

]

= 0

A1

The second line uses the definition of the covariance, the third line use the fact that ξcit is

exogenous (orthogonal to ut) and independent of ρcit. Finally, the fourth line uses E[ξcit] = 0.

A1.2 Price Effect in Muti-crop System

In the main paper we estimate the effect of new biofuel demand on price using a model that

aggregates the four major food commodities based on caloric content. Here we present the

algebra for modeling price effects on n commodities. Denote the log demand for commodity

i by qi, the log price by pi, and the elasticity of demand for commodity i with respect to

price of commodity j as βd,ij. We have:

q1

q2...

qn

︸ ︷︷ ︸

q

=

αd,1

αd,2

...

αd,n

︸ ︷︷ ︸

αd

+

βd,11 βd,12 . . . βd,1n

βd,21 βd,22 . . . βd,2n

......

. . ....

βd,n1 βd,n2 . . . βd,nn

︸ ︷︷ ︸

βd

p1

p2...

pn

︸ ︷︷ ︸

p

= αd + βdp

Similar, the supply system is given by:

q1

q2...

qn

︸ ︷︷ ︸

q

=

αs,1

αs,2

...

αs,n

︸ ︷︷ ︸

αs

+

βs,11 βs,12 . . . βs,1n

βs,21 βs,22 . . . βs,2n

......

. . ....

βs,n1 βs,n2 . . . βs,nn

︸ ︷︷ ︸

βs

p1

p2...

pn

︸ ︷︷ ︸

p

= αs + βsp

The equilibrium is given by equating demand and supply

αd + βdp = αs + βsp ⇔ [αd −αs] = [βs − βd]p

And hence the equilibrium prices are

p = [βs − βd]−1 [αd −αs]

If biofuels shift out the demand by ∆αd,1 for commodity 1, the resulting effect on equilibrium

prices is

∆p = [βs − βd]−1 [∆αd,1 0 . . . 0]′

A2

Note that all prices adjust, even though the demand for only one commodity increases

because the prices are linked through cross-price elasticities. Uncertainty of the estimate

is derived by drawing one million random draws from the estimated joint distribution of

the βd,ij and βs,ij, inverting the matrix [βs − βd]−1, and derive the predicted price increase

[βs − βd]−1 [∆αd,1 0 . . . 0]′ for each commodity on each draw.

If there is just one commodity, this simplifies to the baseline case: ∆p =∆αd,1

βs,11−βd,11.

A2 Data Appendix

A2.1 Agricultural Production Data

Yield data for the four staple commodities, maize, rice, soybeans, and wheat, were obtained

from two data sources. The baseline model uses data from the Food and Agriculture Or-

ganization (FAO) of the United Nations (http://faostat.fao.org/) for the years 1961-2010.

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.

Production and area are assigned to the calendar year given by FAO. Demand is annual

production plus the change in inventory, which is given by the negative of the “Stock Varia-

tion” variable in the FAO data. The last variable is only available until 2007, so the baseline

regression uses data for the 47 years from 1961 to 2007. Since most regressions include one

lag of yield shocks, those using FAO data generally have 46 observations.

In a sensitivity check, we use data from the Foreign Agricultural Service (FAS) by the

United States Department of Agriculture (http://http://www.fas.usda.gov/) that has data

for 1961-2010 for all variables, including stocks. FAS reports production for marketing years,

i.e., the 12-month period between the last harvest and the next harvest, when the amount

produced is being sold. To be consistent with the FAO data, we assign production data to

calendar years based on the year when the marketing year starts. We adjust the year for

Argentina maize and Romanian soybeans, as they seem to be off by one year. Consumption

quantities are set equal to production plus the inventory levels at the beginning of the

marketing year minus inventory levels at the end of the marketing year, which are given in

the data.

The FAS data does not provide production data for soybeans before 1964, so we manu-

ally fill in production numbers from USDA. Soybeans were a small share of overall calorie

production at that time, and the US produced a dominant share of global production, so the

omitted countries should have little influence. The FAS data does not give an estimate for

A3

the world total. Instead we simply sum the numbers for all countries in the data to get the

total production of all major producers. Since the FAS data does exclude countries that are

not major producers, consumption estimates tend to be smaller than production estimates.

We model yields in each country that on average account for at least 0.5% of global

production and sum the remaining countries as “Rest of the World.” Countries that produce

at least 0.5% of any of the four commodities are given in Tables A1 and A2. The geographic

location of these countries is shown in the bottom panels of Figures A1-A4. Individual yield

observations in our baseline model using FAO data as well as time trends using restricted

cubic spline with 3 knots are shown in Figures A5-A7.A1 The knots are 1963, 1984, and

2005. Regressions with 4 spline knots use the knots 1962, 1976, 1992, and 2006. Regressions

with 5 spline knots use the knots 1962, 1973, 1984, 1995, and 2006.

Figure A8 shows the correlation of annual yield shocks of the two biggest exporters for

each of the four commodities. The two largest exporters are engaged in the world market

and farmers should respond to changes in world prices. If yields are endogenous to price,

yield shocks between the two largest producers should be correlated as they both respond

to the same price shock. However, the figure shows little correlation between the shocks.

A2.2 Weather Data

Weather data from Center for Climatic Research at the University of Delaware (version

2.01) gives monthly temperature and precipitation readings on a 0.5 degree grid for the

entire world for the years 1901-2008.A2 Weather outcomes for a particular crop in a country

are the area-weighted average of all grids that fall in a country over the growing season.

The crop-specific area weights from Chad Monfreda, Navin Ramankutty & Jonathan A.

Foley (2008) are displayed in the top panels of Appendix Figures A1-A4. The authors provide

the fraction of each 5 minute grid cell that is used for various crops.A3 Fraction greater than

1 indicate double cropping.

The growing season for each crop and country was obtained from W. J. Sacks, D. Deryng,

J.A. Foley & N. Ramankutty (2010). The authors provide planting and harvest dates on a 5

minute grid.A4 We include the entire months between planting and harvest. For example, if

average planting is on April 8th and harvest on September 12th, we use weather data from

A1We use STATA’s command mkspline to obtain restricted cubic splines with three knots. This gives twovariables, which captures a trend in a more flexible way than using a quadratic time trend.

A2http://climate.geog.udel.edu/∼climate/A3http://www.geog.mcgill.ca/landuse/pub/Data/175crops2000/NetCDF/ (accessed November 2008).A4http://www.sage.wisc.edu/download/sacks/crop calendar.html (accessed January 2010).

A4

April through September.

A2.3 Price Data

Our baseline model uses futures prices during the month of delivery (December for maize

and wheat and November for rice and soybeans) in the demand equation and futures prices

as they are traded in the previous December in the supply equation. Prices are converted

into dollars per calorie by using the conversion ratios of Williamson & Williamson (1942)

that list the edible amount of calories in each production unit.

Since futures data are only available since 1960s, Figure 2, which shows a longer history

of prices converted to the real annual cost of a 2000 calories/day, uses annual prices received

by farmers as reported by the National Agricultural Statistics Service.A5 Food commodity

prices have declined over the long run, except for price spikes during World War II, in the

1970s, and the recent run-up. Despite the recent run-up, prices are still low relative to most

of history. The top panel of Figure A9 replicates this time series for the time frame of our

analysis 1961-2010.

The bottom panel of Figure A9 no longer uses the conversion ratios of Williamson &

Williamson (1942), but backs them out implicitly by assuming the average price of a calorie

is the same for all crops. This calibration tracks relative changes in prices over time. In

effect, the bottom panel shows each price series multiplied by a constant such that the

average prices of rice, soybeans and wheat in 1961-2010 equal that of maize.

A2.4 Ethanol Production

Renewable fuel standards and ethanol tax credits have led to a rapid expansion of the US

ethanol production capacity as shown in the top panel of Figure A10. As a result, the United

States produces far more than 50% of the global production capacity in 2010, followed by

South America (primarily Brazil), which accounted for roughly one-third. Production shares

are shown in the botttom panel of Figure A10.

A5www.nass.usda.gov

A5

Table A1: Countries Used to Derive Maize and Soybean Yield ShocksData from FAO Data from FAS

Production Share Years in Data Production Share Years in Data

Country Avg Min Max N Min Max Avg Min Max N Min Max

Panel A: Maize Yields

United States of America 41.76 30.55 48.11 50 1961 2010 45.09 32.98 50.50 50 1961 2010China 15.96 7.95 21.72 50 1961 2010 17.03 9.77 23.56 50 1961 2010Brazil 5.29 3.45 7.49 50 1961 2010 5.71 3.66 7.79 50 1961 2010USSR 3.52 1.98 8.35 31 1961 1991 3.96 2.11 8.66 26 1961 1986Mexico 3.00 2.02 3.94 50 1961 2010 3.06 1.66 4.41 50 1961 2010Yugoslav SFR 2.47 1.39 3.25 31 1961 1991 2.65 1.48 3.46 31 1961 1991Argentina 2.35 1.03 3.52 50 1961 2010 2.53 1.11 3.78 50 1961 2010France 2.29 0.91 3.65 50 1961 2010 . . . . . .Romania 2.08 0.49 3.29 50 1961 2010 2.61 1.37 3.73 38 1961 1998South Africa 1.98 0.61 3.62 50 1961 2010 2.12 0.66 3.88 50 1961 2010India 1.93 1.26 2.82 50 1961 2010 2.09 1.35 3.02 50 1961 2010Italy 1.51 0.96 1.93 50 1961 2010 . . . . . .Hungary 1.37 0.51 2.10 50 1961 2010 1.57 0.80 2.19 38 1961 1998Indonesia 1.31 0.72 2.17 50 1961 2010 1.14 0.76 1.79 49 1961 2010Canada 1.16 0.36 1.71 50 1961 2010 1.23 0.38 1.84 50 1961 2010Serbia And Montenegro 0.89 0.50 1.19 14 1992 2005 0.95 0.55 1.20 14 1992 2005Egypt 0.89 0.70 1.09 50 1961 2010 0.95 0.78 1.16 49 1961 2010Ukraine 0.80 0.27 1.42 19 1992 2010 1.03 0.29 2.34 24 1987 2010Philippines 0.77 0.59 1.10 50 1961 2010 0.83 0.61 1.23 50 1961 2010Thailand 0.67 0.29 1.16 50 1961 2010 0.71 0.30 1.23 50 1961 2010Nigeria 0.65 0.12 1.34 50 1961 2010 0.71 0.32 1.44 50 1961 2010Spain 0.58 0.34 0.89 50 1961 2010 . . . . . .North Korea 0.52 0.14 0.89 50 1961 2010 . . . . . .Bulgaria 0.50 0.04 0.96 50 1961 2010 0.64 0.18 1.03 38 1961 1998Kenya . . . . . . 0.53 0.28 0.78 50 1961 2010Rest Of World 9.09 6.95 12.04 50 1961 2010 8.22 6.30 11.64 50 1961 2010

Panel B: Soybeans Yields

United States of America 55.55 33.17 73.48 50 1961 2010 58.22 32.88 100.00 50 1961 2010Brazil 15.11 1.01 27.23 50 1961 2010 17.29 1.59 29.59 46 1965 2010China 12.63 5.77 27.26 50 1961 2010 11.83 5.64 27.47 47 1964 2010Argentina 7.31 0.00 21.61 50 1961 2010 8.05 0.05 22.03 46 1965 2010India 1.79 0.02 4.99 50 1961 2010 1.89 0.03 4.27 42 1969 2010Paraguay 1.09 0.01 2.85 50 1961 2010 1.11 0.03 2.75 46 1965 2010Canada 1.07 0.44 1.90 50 1961 2010 1.09 0.44 1.85 47 1964 2010USSR 0.94 0.46 1.75 31 1961 1991 0.89 0.48 1.61 23 1964 1986Indonesia 0.94 0.27 1.63 50 1961 2010 0.91 0.24 1.65 47 1964 2010Italy . . . . . . 0.76 0.01 1.69 10 1981 1990Rest Of World 3.93 2.52 6.72 50 1961 2010 3.25 0.01 5.84 48 1963 2010

Notes: Tables displays countries used to derive yield deviations, sorted from largest producer to smallest producer. The first

six columns summarize the data from FAO, the last six columns from FAS. Within each data set, the first three give average,

minimum, and maximum annual share of global production, respectively, while the last three give the number of years for

which we have data as well as the first and last year, respectively.

A6

Table A2: Countries Used to Derive Wheat and Rice Yield ShocksData from FAO Data from FAS

Production Share Years in Data Production Share Years in Data

Country Avg Min Max N Min Max Avg Min Max N Min Max

Panel A: Wheat Yields

USSR 21.23 12.68 31.10 31 1961 1991 26.54 15.35 35.94 26 1961 1986China 14.23 6.43 20.10 50 1961 2010 17.25 7.71 24.52 50 1961 2010United States of America 11.91 7.60 16.86 50 1961 2010 14.52 10.00 19.90 50 1961 2010India 8.73 3.42 13.04 50 1961 2010 10.58 4.01 16.92 50 1961 2010Russian Federation 7.07 4.55 9.33 19 1992 2010 8.96 5.54 11.99 24 1987 2010France 5.35 3.72 6.78 50 1961 2010 . . . . . .Canada 4.75 2.78 8.44 50 1961 2010 5.80 3.46 10.25 50 1961 2010Turkey 3.44 2.60 4.37 50 1961 2010 3.42 2.56 4.12 50 1961 2010Australia 3.14 1.70 4.67 50 1961 2010 3.84 2.03 5.87 50 1961 2010Germany 2.94 1.99 4.02 50 1961 2010 . . . . . .Ukraine 2.76 0.64 3.87 19 1992 2010 3.85 0.81 6.12 24 1987 2010Pakistan 2.54 1.29 3.80 50 1961 2010 3.09 1.51 4.74 50 1961 2010Argentina 2.20 1.25 4.19 50 1961 2010 2.70 1.74 5.10 50 1961 2010United Kingdom 2.02 1.06 2.92 50 1961 2010 . . . . . .Italy 2.00 0.92 3.79 50 1961 2010 . . . . . .Kazakhstan 1.88 0.80 3.23 19 1992 2010 2.44 0.96 3.85 24 1987 2010Iran 1.56 0.98 2.59 50 1961 2010 1.89 1.14 3.23 50 1961 2010Poland 1.38 0.93 1.79 50 1961 2010 1.62 1.10 2.16 38 1961 1998Yugoslav SFR 1.29 0.90 1.78 31 1961 1991 1.55 1.08 2.16 31 1961 1991Romania 1.25 0.44 2.25 50 1961 2010 1.64 0.64 2.79 38 1961 1998Spain 1.14 0.58 2.09 50 1961 2010 . . . . . .Czechoslovakia 1.05 0.66 1.41 32 1961 1992 1.25 0.81 1.71 31 1961 1991Hungary 0.96 0.45 1.44 50 1961 2010 1.24 0.64 1.76 38 1961 1998Bulgaria 0.76 0.31 1.11 50 1961 2010 1.00 0.37 1.37 38 1961 1998Egypt 0.73 0.35 1.37 50 1961 2010 0.90 0.43 1.76 49 1961 2010Uzbekistan 0.68 0.16 1.03 19 1992 2010 0.69 0.08 1.26 24 1987 2010Mexico 0.67 0.37 1.04 50 1961 2010 0.77 0.50 1.06 50 1961 2010Czech Republic 0.66 0.47 0.80 18 1993 2010 . . . . . .Afghanistan 0.57 0.25 1.02 50 1961 2010 0.70 0.33 1.23 50 1961 2010Brazil 0.56 0.17 1.21 50 1961 2010 0.64 0.05 1.45 50 1961 2010Morocco 0.56 0.20 1.05 50 1961 2010 0.66 0.23 1.34 50 1961 2010Serbia And Montenegro . . . . . . 0.51 0.31 0.74 14 1992 2005Syria . . . . . . 0.56 0.19 1.10 50 1961 2010Rest Of World 7.04 4.67 9.83 50 1961 2010 4.94 2.86 6.96 50 1961 2010

Panel B: Rice Yields

China 34.08 26.07 39.13 50 1961 2010 34.74 25.61 39.66 50 1961 2010India 20.59 16.77 24.81 50 1961 2010 20.59 16.52 24.33 50 1961 2010Indonesia 7.61 4.68 9.88 50 1961 2010 7.64 5.35 9.03 50 1961 2010Bangladesh 5.56 4.66 7.34 50 1961 2010 5.58 4.63 7.40 50 1961 2010Thailand 4.33 3.32 5.17 50 1961 2010 4.15 3.27 4.70 50 1961 2010Vietnam 4.08 2.54 6.03 50 1961 2010 4.03 2.50 5.86 50 1961 2010Japan 3.55 1.55 7.49 50 1961 2010 3.83 1.72 7.71 50 1961 2010Myanmar 3.23 2.39 4.94 50 1961 2010 2.50 2.12 3.11 50 1961 2010Brazil 2.06 1.33 2.98 50 1961 2010 2.07 1.47 2.87 49 1961 2010Philippines 1.90 1.48 2.47 50 1961 2010 1.84 1.36 2.43 50 1961 2010South Korea 1.55 0.86 2.26 50 1961 2010 1.68 0.96 2.41 50 1961 2010United States of America 1.44 1.01 2.02 50 1961 2010 1.52 1.05 2.16 50 1961 2010Pakistan 1.09 0.72 1.51 50 1961 2010 1.08 0.71 1.54 50 1961 2010Egypt 0.76 0.44 1.07 50 1961 2010 0.75 0.41 1.14 50 1961 2010Nepal 0.68 0.43 0.98 50 1961 2010 0.69 0.44 0.96 49 1961 2010Cambodia 0.65 0.14 1.23 50 1961 2010 0.63 0.13 1.18 50 1961 2010North Korea 0.58 0.25 0.90 50 1961 2010 0.59 0.31 0.77 50 1961 2010Madagascar 0.53 0.41 0.71 50 1961 2010 0.50 0.40 0.68 50 1961 2010Taiwan . . . . . . 0.70 0.22 1.34 49 1961 2010Rest Of World 5.74 4.54 7.16 50 1961 2010 4.98 3.87 6.42 50 1961 2010

Notes: Table displays countries used to derive yield deviations, sorted from largest producer to smallest producer. The first

six columns summarize the data from FAO, the last six columns from FAS. Within each data set, the first three give average,

minimum, and maximum annual share of global production, respectively; the last three give the number of years for which we

have data as well as the first and last available year. A7

Figure A1: Maize Growing Area and Countries in Study

Notes: Top panel displays the fraction of each grid cell in Monfreda, Ramankutty & Foley (2008) used to

grow maize (note the nonlinear scale on the right). Numbers greater than 1 indicate double cropping. The

bottom panel displays countries that on average produce at least 0.5% of global production. Colors indicate

whether this is the case in both the FAO and FAS data (red), only the FAS data (orange), or only the FAO

data (yellow).

A8

Figure A2: Rice Growing Area and Countries in Study

Notes: Top panel displays the fraction of each grid cell in Monfreda, Ramankutty & Foley (2008) used to

grow rice (note the nonlinear scale on the right). Numbers greater than 1 indicate double cropping. The

bottom panel displays countries that on average produce at least 0.5% of global production. Colors indicate

whether this is the case in both the FAO and FAS data (red), only the FAS data (orange), or only the FAO

data (yellow).

A9

Figure A3: Soybeans Growing Area and Countries in Study

Notes: Top panel displays the fraction of each grid cell in Monfreda, Ramankutty & Foley (2008) used to

grow soybeans (note the nonlinear scale on the right). Numbers greater than 1 indicate double cropping.

The bottom panel displays countries that on average produce at least 0.5% of global production. Colors

indicate whether this is the case in both the FAO and FAS data (red), only the FAS data (orange), or only

the FAO data (yellow).

A10

Figure A4: Wheat Growing Area and Countries in Study

Notes: Top panel displays the fraction of each grid cell in Monfreda, Ramankutty & Foley (2008) used to

grow wheat (note the nonlinear scale on the right). Numbers greater than 1 indicate double cropping. The

bottom panel displays countries that on average produce at least 0.5% of global production. Colors indicate

whether this is the case in both the FAO and FAS data (red), only the FAS data (orange), or only the FAO

data (yellow).

A11

Figure A5: Country-Level Yields and Yield Trends for Maize and Soybeans

Panel A: Maize Yields

1.4

1.6

1.8

22.

22.

4Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

United States of America

0.5

11.

52

Log

Mai

ze Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

China

0.2

.4.6

.81

Log

Mai

ze Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Rest Of World (FAO)

0.5

11.

5Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Brazil

.4.6

.81

1.2

1.4

Log

Mai

ze Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

USSR

0.5

11.

5Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Mexico

.6.8

11.

21.

41.

6Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Yugoslav SFR

.51

1.5

2Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Argentina

.51

1.5

22.

5Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

France

.51

1.5

Log

Mai

ze Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Romania

−.5

0.5

11.

5Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

South Africa

−.2

0.2

.4.6

.8Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

India

11.

52

2.5

Log

Mai

ze Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Italy

.51

1.5

2Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Hungary

−.5

0.5

11.

5Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Indonesia

1.4

1.6

1.8

22.

2Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Canada

.81

1.2

1.4

1.6

1.8

Log

Mai

ze Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Serbia And Montenegro

11.

52

2.5

Log

Mai

ze Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Egypt

.81

1.2

1.4

1.6

Log

Mai

ze Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Ukraine

−.5

0.5

1Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Philippines

0.5

11.

5Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Thailand

−.5

0.5

1Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Nigeria

.51

1.5

22.

5Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Spain

0.5

11.

52

Log

Mai

ze Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

North Korea

.51

1.5

2Lo

g M

aize

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Bulgaria

Panel B: Soybean Yields

.4.6

.81

1.2

Log

Soy

bean

s Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

United States of America

−.5

0.5

1Lo

g S

oybe

ans

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Brazil

−.4

−.2

0.2

.4.6

Log

Soy

bean

s Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

China

0.2

.4.6

.81

Log

Soy

bean

s Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Argentina

−.4

−.2

0.2

.4.6

Log

Soy

bean

s Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Rest Of World (FAO)

−.8

−.6

−.4

−.2

0.2

Log

Soy

bean

s Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

India

.2.4

.6.8

11.

2Lo

g S

oybe

ans

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Paraguay

.4.6

.81

1.2

Log

Soy

bean

s Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Canada

−1.

5−

1−

.50

.5Lo

g S

oybe

ans

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

USSR

−.4

−.2

0.2

.4Lo

g S

oybe

ans

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Indonesia

Notes: Figure displays yields in FAO data as well as trends (restricted cubic spline with 3 knots). Countries

are sorted from largest producer to smallest producer.

A12

Figure A6: Country-Level Yields and Yield Trends for Rice

.51

1.5

2Lo

g R

ice

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

China

.2.4

.6.8

11.

2Lo

g R

ice

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

India

.51

1.5

Log

Ric

e Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Indonesia

.6.8

11.

2Lo

g R

ice

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Rest Of World (FAO)

.4.6

.81

1.2

1.4

Log

Ric

e Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Bangladesh

.4.6

.81

1.2

Log

Ric

e Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Thailand

.51

1.5

2Lo

g R

ice

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Vietnam

1.5

1.6

1.7

1.8

1.9

Log

Ric

e Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Japan

.4.6

.81

1.2

1.4

Log

Ric

e Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Myanmar

0.5

11.

5Lo

g R

ice

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Brazil

0.5

11.

5Lo

g R

ice

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Philippines

1.2

1.4

1.6

1.8

2Lo

g R

ice

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

South Korea

1.4

1.6

1.8

22.

2Lo

g R

ice

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

United States of America

.4.6

.81

1.2

Log

Ric

e Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Pakistan

1.6

1.8

22.

22.

4Lo

g R

ice

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Egypt

.4.6

.81

1.2

Log

Ric

e Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Nepal

−.5

0.5

1Lo

g R

ice

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Cambodia

11.

52

Log

Ric

e Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

North Korea

.4.6

.81

1.2

Log

Ric

e Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Madagascar

Notes: Figure displays yields in FAO data as well as trends (restricted cubic spline with 3 knots). Countries

are sorted from largest producer to smallest producer.

A13

Figure A7: Country-Level Yields and Yield Trends for Wheat

−.5

0.5

1Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

USSR

−.5

0.5

11.

5Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

China

.4.6

.81

1.2

Log

Whe

at Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

United States of America

−.5

0.5

1Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

India

.2.4

.6.8

1Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Russian Federation

0.5

1Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Rest Of World (FAO)

11.

52

Log

Whe

at Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

France

−.5

0.5

1Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Canada

0.5

1Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Turkey

−.2

0.2

.4.6

.8Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Australia

11.

52

Log

Whe

at Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Germany

.4.6

.81

1.2

1.4

Log

Whe

at Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Ukraine

−.5

0.5

1Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Pakistan

0.5

11.

5Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Argentina

1.2

1.4

1.6

1.8

22.

2Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

United Kingdom

.6.8

11.

21.

4Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Italy

−.6

−.4

−.2

0.2

Log

Whe

at Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Kazakhstan

−.5

0.5

1Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Iran

.6.8

11.

21.

4Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Poland

.51

1.5

Log

Whe

at Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Yugoslav SFR

.2.4

.6.8

11.

2Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Romania

0.5

11.

5Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Spain

.81

1.2

1.4

1.6

1.8

Log

Whe

at Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Czechoslovakia

.51

1.5

2Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Hungary

.51

1.5

Log

Whe

at Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Bulgaria

.51

1.5

2Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Egypt

0.5

11.

5Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Uzbekistan

.51

1.5

2Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Mexico

1.4

1.5

1.6

1.7

1.8

Log

Whe

at Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Czech Republic

−.4

−.2

0.2

.4.6

Log

Whe

at Y

ield

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Afghanistan

−1

−.5

0.5

1Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Brazil

−1

−.5

0.5

1Lo

g W

heat

Yie

ld

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Morocco

Notes: Figure displays yields in FAO data as well as trends (restricted cubic spline with 3 knots). Countries

are sorted from largest producer to smallest producer.

A14

Figure A8: Correlation of Shocks of Two Biggest Exporters (FAO Data)

−.4

−.2

0.2

.4Lo

g Y

ield

Res

idua

ls (

Arg

entin

a)

−.3 −.2 −.1 0 .1 .2Log Yield Residuals (United States of America)

Maize

−.1

5−

.1−

.05

0.0

5.1

Log

Yie

ld R

esid

uals

(U

nite

d S

tate

s of

Am

eric

a)

−.2 −.1 0 .1Log Yield Residuals (Thailand)

Rice

−.3

−.2

−.1

0.1

.2Lo

g Y

ield

Res

idua

ls (

Bra

zil)

−.2 −.1 0 .1 .2Log Yield Residuals (United States of America)

Soybeans

−.6

−.4

−.2

0.2

.4Lo

g Y

ield

Res

idua

ls (

Aus

tral

ia)

−.2 −.1 0 .1 .2Log Yield Residuals (United States of America)

Wheat

Notes: Figure shows scatter plots of log yield residuals (deviations from the trend, which is modeled using

restricted cubic splines with 3 knots) of the two largest exporters of each crop in 1961-2010. The correlation

coefficients are 0.002 for maize, 0.40 for rice, -0.16 for soybeans, and 0.19 for wheat. For wheat, the second

largest exporter is Canada, but since the growing area is adjacent to the United States, the largest exporter,

we instead use the third largest exporter (Australia).

A15

Figure A9: Commodity Prices

010

020

030

040

050

0P

rice

of 2

000

Cal

orie

s P

er D

ay (

$201

0/pe

rson

/yea

r)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Maize Wheat Rice Soybeans

050

100

150

200

Pric

e of

200

0 C

alor

ies

Per

Day

($2

010/

pers

on/y

ear)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Maize Wheat Rice Soybeans

Notes: Figure displays caloric prices over time for maize, wheat, rice, and soybeans in the years 1961-2010.

The y-axis are the annual cost for 2000 calories per day. The bottom panel rescales prices by a constant so

the average price in 1961-2010 is the same as for maize.A16

Figure A10: US Ethanol Production Capacity Over Time and as Share of World Capacity

02

46

810

1214

US

Eth

anol

Pro

duct

ion

(bill

ion

gallo

ns)

1980 1985 1990 1995 2000 2005 2010Year

11.31%

31.04%57.65%

United States South America Rest of World

Notes: Top panel shows ethanol production capacity in billion gallons 1980-2011. The bottom panel shows

the US share of global capacity in 2010, South America, and the rest of the world. Data is taken from:

http://www.ethanolrfa.org/pages/statisticsA17

A3 FAO Data - Additional Results

This section presents additional results that were omitted from the main paper due to space

constraints.

Table A3 weighs crop and country-specific shocks by predicted area (using the same

restricted cubic spline with 3 knots in a regression of log area, i.e., using the same setup that

was used to derive predicted yield), but the results remain robust.

Table A4 presents the coefficients on US yield shocks as well as yield shocks for the

rest of the world. Table 5 in the main paper listed the elasticities as well as test results

whether the coefficients on the instruments are equal, but not the coefficients themselves.

Note that the coefficients are close in magnitude: a shock outside the US moves futures

prices by a similar amount as shocks in the US. We normalize shocks by the fraction of

global production (according to predicted yields) to make the shocks comparable: Since the

US produces around 23% of global calories, the US shock is multiplied by roughly 0.23, while

the shock on the rest of the world is multiplied by 0.77. To get the effect of 1% shock in the

US on world prices, one simply has to divide the first-stage parameter by roughly one-fourth.

The first-stage instrument in the supply equation is around -4, which implies that a negative

1% yield shock in the US increase global commodity prices in the next period by 1%. The

coefficient in the demand equation is slightly larger in magnitude (around -5), suggesting

that a negative 1% yield shock in the US increase global commodity prices in the current

period by 1.25%.

Similarly, Table A5 splits overall shocks, our instrument, into each of the four commodi-

ties. The coefficients on the different instruments are not significantly different except when

we use 3 spline knots as the time trend in the IV regression (column 1a) or 3SLS regres-

sion (column 2a). Since we are using one “combined” price (production-weighted average of

maize, soybeans, and wheat, where we use predicted yields along the trend), this regression

should be interpreted with caution as the weighted price basket will be related to all four

commodity shocks even if they only impact the price of one crop.

Table A6 replicates Table 7 of the main paper but shows results not only for time trends

that are modeled as restricted cubic splines with 4 knots but also 5 knots.

Table A7 estimates a 4x4 system using FAO data similar to Table 8 in the main paper

that uses FAS data.

A18

Table A3: Supply and Demand Elasticity: Weighting Yield Schocks by Predicted GrowingArea (FAO Data)

Instrumental Variables Three Stage Least Squares(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: Supply EquationSupply Elast. βs 0.107∗∗∗ 0.102∗∗∗ 0.092∗∗∗ 0.122∗∗∗ 0.119∗∗∗ 0.102∗∗∗

(0.026) (0.027) (0.020) (0.019) (0.020) (0.018)Shock ωt 1.178∗∗∗ 1.216∗∗∗ 1.202∗∗∗ 1.237∗∗∗ 1.266∗∗∗ 1.232∗∗∗

(0.147) (0.145) (0.102) (0.107) (0.099) (0.086)First Stage ωt−1 -3.748∗∗∗ -3.519∗∗∗ -3.740∗∗∗ -3.453∗∗∗ -3.054∗∗∗ -3.165∗∗∗

(1.162) (0.945) (0.903) (0.782) (0.683) (0.713)First Stage ωt -2.801∗ -2.211∗ -2.326∗ -2.788∗∗∗ -2.283∗∗∗ -2.380∗∗∗

(1.633) (1.283) (1.260) (0.956) (0.804) (0.806)

Panel B: Demand EquationDemand Elast. βd -0.028 -0.054∗∗ -0.054∗∗ -0.033 -0.058∗∗∗ -0.063∗∗∗

(0.021) (0.023) (0.021) (0.024) (0.022) (0.020)First Stage ωt -5.362∗∗∗ -4.533∗∗∗ -4.674∗∗∗ -5.219∗∗∗ -4.406∗∗∗ -4.345∗∗∗

(1.487) (1.271) (1.205) (1.364) (1.190) (1.168)

Panel C: Effect of Demand ShiftMultiplier 1

βs−βd

7.41 6.41 6.87 6.49 5.65 6.07

Exp. Multiplier 8.01 6.83 7.18 6.73 5.81 6.24(95% Conf. Int.) (5.0,14.4) (4.4,11.7) (4.9,11.3) (4.8,10.1) (4.3,8.3) (4.6,8.9)

F1st-stage Supply 10.41 13.86 17.15F1st-stage Demand 13.01 12.73 15.06Observations 46 46 46 46 46 46Spline Knots 3 4 5 3 4 5

Notes : Table replicates Table 1 except that log yield residuals are not averaged using actual area but area

as given by a restricted cubic spline with 3 knots (same trend used in the derivation of the yield shocks).

Columns (a), (b), and (c) include restricted cubic splines in time with 3, 4, and 5 knots, respectively. Stars

indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A19

Table A4: Supply and Demand Elasticity - Separating Shocks in US from Rest of World(FAO Data)

Instrumental Variables Three Stage Least Squares(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: Supply EquationSupply Elast. βs 0.107∗∗∗ 0.089∗∗∗ 0.083∗∗∗ 0.112∗∗∗ 0.105∗∗∗ 0.091∗∗∗

(0.022) (0.025) (0.020) (0.019) (0.020) (0.018)Shock ωt,US 1.481∗∗∗ 1.383∗∗∗ 1.374∗∗∗ 1.342∗∗∗ 1.429∗∗∗ 1.396∗∗∗

(0.145) (0.167) (0.130) (0.111) (0.123) (0.108)Shock ωt,RW 0.922∗∗∗ 1.007∗∗∗ 0.995∗∗∗ 0.973∗∗∗ 1.040∗∗∗ 1.018∗∗∗

(0.155) (0.133) (0.105) (0.143) (0.132) (0.119)First Stage ωt−1,US -2.619∗∗ -4.218∗∗∗ -4.086∗∗∗ -3.163∗∗∗ -3.660∗∗∗ -3.610∗∗∗

(1.244) (1.107) (1.064) (1.159) (1.062) (1.084)First Stage ωt−1,RW -4.935∗∗∗ -3.033∗ -3.551∗∗ -3.570∗∗∗ -2.544∗∗ -2.753∗∗

(1.610) (1.587) (1.498) (1.171) (1.098) (1.133)First Stage ωt,US -1.157 -2.751 -2.549 -1.629 -2.770∗∗ -2.659∗∗

(2.518) (2.239) (2.223) (1.355) (1.207) (1.218)First Stage ωt,RW -4.234∗∗∗ -1.918 -2.258∗ -4.346∗∗∗ -2.025 -2.386∗

(1.513) (1.235) (1.240) (1.331) (1.260) (1.259)

Panel B: Demand EquationDemand Elast. βd -0.021 -0.053∗∗ -0.053∗∗ 0.003 -0.049∗∗ -0.051∗∗∗

(0.020) (0.022) (0.021) (0.017) (0.019) (0.017)First Stage ωt,US -4.696∗∗ -5.855∗∗∗ -5.871∗∗∗ -5.517∗∗∗ -5.787∗∗∗ -5.741∗∗∗

(1.915) (1.460) (1.366) (1.939) (1.625) (1.569)First Stage ωt,RW -6.438∗∗∗ -3.248∗ -3.498∗ -6.305∗∗∗ -3.707∗∗ -3.897∗∗

(1.821) (1.896) (1.879) (1.952) (1.658) (1.558)

Panel C: Effect of Demand ShiftMultiplier 1

βs−βd

7.84 7.07 7.39 9.14 6.50 7.05

Exp. Mult. (s.e.) 8.35 7.44 7.78 9.62 6.71 7.28(95% Conf. Int.) (5.3,14.7) (4.8,13.3) (5.2,12.6) (6.5,15.5) (4.9,9.8) (5.3,10.6)

Panel D: P-value on Equal CoefficientsS1st-stage ωt−1 equal 0.20 0.56 0.77 0.81 0.50 0.61D1st-stage ωt equal 0.42 0.24 0.27 0.77 0.36 0.38F1st-stage Supply 5.74 9.73 10.19F1st-stage Demand 7.17 8.57 9.92Observations 46 46 46 46 46 46Spline Knots 3 4 5 3 4 5

Notes : Table list all coefficient estimates of Table 5 in the main paper. Columns (a), (b), and (c) include

restricted cubic splines in time with 3, 4, and 5 knots, respectively. Stars indicate significance levels:∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A20

Table A5: Supply and Demand Elasticity - Separating Shocks of Four Crops (FAO Data)

Instrumental Variables Three Stage Least Squares

(1a) (1b) (1c) (2a) (2b) (2c)Panel A: Supply Equation

Supply Elast. βs 0.113∗∗∗ 0.099∗∗∗ 0.086∗∗∗ 0.118∗∗∗ 0.109∗∗∗ 0.094∗∗∗

(0.023) (0.023) (0.017) (0.020) (0.020) (0.018)Shock ωt,M 1.787∗∗∗ 1.685∗∗∗ 1.539∗∗∗ 1.541∗∗∗ 1.686∗∗∗ 1.542∗∗∗

(0.188) (0.192) (0.158) (0.162) (0.167) (0.158)Shock ωt,R 1.022∗∗∗ 1.415∗∗∗ 0.996∗∗∗ 1.130∗∗∗ 1.454∗∗∗ 1.042∗∗∗

(0.348) (0.321) (0.286) (0.285) (0.284) (0.273)Shock ωt,S -0.210 -0.060 0.702 0.308 0.027 0.721

(0.724) (0.640) (0.569) (0.543) (0.545) (0.557)Shock ωt,W 0.982∗∗∗ 0.934∗∗∗ 0.976∗∗∗ 0.990∗∗∗ 0.991∗∗∗ 1.012∗∗∗

(0.173) (0.156) (0.151) (0.179) (0.176) (0.163)First Stage ωt−1,M -0.831 -1.834 -0.617 0.205 -0.125 0.232

(1.527) (1.475) (1.530) (1.502) (1.497) (1.637)First Stage ωt−1,R -6.933∗ -4.790 -4.605 -4.411∗ -2.517 -2.845

(3.420) (3.601) (3.846) (2.560) (2.630) (2.630)First Stage ωt−1,S -10.736∗∗ -7.811 -12.694∗∗ -10.104∗ -8.342 -10.037∗

(5.144) (5.176) (6.072) (5.236) (5.137) (5.895)First Stage ωt−1,W -3.963∗∗ -3.963∗∗ -5.112∗∗∗ -4.397∗∗∗ -4.563∗∗∗ -5.142∗∗∗

(1.909) (1.817) (1.612) (1.385) (1.303) (1.430)First Stage ωt,M 0.036 -0.702 0.253 1.406 -0.557 0.420

(2.179) (2.431) (2.347) (1.737) (1.757) (1.799)First Stage ωt,R -7.072 -4.633 -3.812 -8.486∗∗∗ -5.447∗ -4.218

(4.282) (4.085) (4.203) (2.613) (2.919) (2.962)First Stage ωt,S -3.799 -1.761 -6.580 -5.725 -1.177 -5.796

(6.328) (6.396) (8.848) (5.574) (5.611) (6.263)First Stage ωt,W -3.752∗∗ -3.782∗∗∗ -4.802∗∗∗ -4.459∗∗∗ -4.636∗∗∗ -5.465∗∗∗

(1.499) (1.339) (1.711) (1.664) (1.630) (1.699)

Panel B: Demand Equation

Demand Elast. βd 0.000 -0.062∗∗∗ -0.056∗∗∗ 0.009 -0.067∗∗∗ -0.061∗∗∗

(0.019) (0.024) (0.021) (0.015) (0.019) (0.017)First Stage ωt,M -4.506∗∗ -6.910∗∗∗ -6.763∗∗ -5.098∗ -7.601∗∗∗ -7.063∗∗∗

(2.054) (2.475) (2.824) (2.757) (2.259) (2.328)First Stage ωt,R -14.164∗∗∗ -5.859 -5.822 -14.012∗∗∗ -7.823∗∗ -5.706

(3.042) (4.141) (4.439) (3.483) (3.345) (3.498)First Stage ωt,S -5.574 0.661 0.098 -4.367 8.889 4.427

(8.268) (9.669) (12.006) (9.177) (6.742) (7.585)First Stage ωt,W -3.559 -2.768 -3.069 -3.601 -2.166 -2.954

(2.613) (2.457) (2.247) (2.498) (1.835) (1.903)

Panel C: Effect of Demand Shift

Multiplier 1

βs−βd

8.88 6.21 7.05 9.23 5.66 6.45

Exp. Mult. (s.e.) 9.71 6.51 7.33 9.74 5.80 6.62(95% Conf. Int.) (5.9,18.4) (4.4,10.4) (5.1,11.2) (6.5,15.9) (4.4,8.0) (5.0,9.3)

Panel D: P-value on Equal Coefficients

S1st-stage ωt−1 equal 0.16 0.70 0.20 0.10 0.25 0.19D1st-stage ωt equal 0.01 0.70 0.77 0.08 0.10 0.59F1st-stage Supply 4.44 4.56 5.79F1st-stage Demand 7.75 4.69 4.76Observations 46 46 46 46 46 46Spline Knots 3 4 5 3 4 5

Notes : Table replicates Table 1 except that it includes separate shocks for each of the four crops: maize (M),

rice (R), soybeans (S), and wheat (W). Shocks are normalized by the predicted fraction of global production

to make them comparable. Panel D presents p-values from tests whether the coefficients on the shocks used

as instruments are jointly the same. Columns (a), (b), and (c) include restricted cubic splines in time with

3, 4, and 5 knots, respectively. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A21

Table A6: Supply and Demand Elasticity - Two Crop System (FAO Data)

Unrestricted 2x2 System 2x2 System with Symmetry ImposedLog Log Log Log Log Log Log Log

Maize Other Maize Other Maize Other Maize Other(1a) (1b) (2a) (2b) (3a) (3b) (4a) (4b)

Panel A: Supply SystemLog Maize Price 0.086 -0.024 0.085 0.002 0.136∗ -0.001 0.106 0.006

(0.118) (0.078) (0.141) (0.090) (0.070) (0.047) (0.081) (0.058)Log Other Price 0.040 0.105∗ 0.024 0.068 -0.001 0.088∗∗ 0.006 0.064

(0.088) (0.058) (0.109) (0.070) (0.047) (0.036) (0.058) (0.046)

Panel B: Demand SystemLog Maize Price -0.271∗∗ 0.221∗ -0.164 0.111 -0.269∗∗∗ 0.240∗∗ -0.158∗∗ 0.134

(0.123) (0.124) (0.120) (0.101) (0.099) (0.102) (0.078) (0.086)Log Other Price 0.248∗ -0.336∗∗ 0.146 -0.244∗∗ 0.240∗∗ -0.361∗∗∗ 0.134 -0.274∗∗∗

(0.136) (0.132) (0.139) (0.119) (0.102) (0.113) (0.086) (0.104)

Panel C: Effect of Maize Demand ShiftMultiplier 4.14 2.31 4.82 1.67 3.63 1.95 4.64 1.76Exp. Multiplier 4.58 2.57 3.12 0.95 4.08 1.90 3.22 2.15(95% Conf. Int.) (1.7,15.6) (-1.0,9.1) (-23.6,36.8) (-12.1,17.1) (2.6,7.1) (0.5,3.6) (2.6,16.1) (-3.4,5.2)

P-val (symmetry) 0.870 . 0.964 . . . . .Observations 46 46 46 46 46 46 46 46Spline Knots 4 4 5 5 4 4 5 5

Notes : Table replicates Table 7 using restricted cubic splines with both 4 as well as 5 knots to model the time trend. The multiplier gives

the price increase for a 1% outward shift in demand for maize, while baseline results give the multiplier on aggregate demand for maize, rice,

soybeans, and wheat. To make the multiplier comparable to the pooled analysis, we derive the production-weighted average multiplier of all

commodities, which are 8.37, 7.88, 7.21, and 7.86, respectively, in the four 2x2 systems. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%;∗ : 10%.

A22

Table A7: Supply and Demand Elasticity - Four Crop System (FAO Data)

Unrestricted System Symmetry Imposed

Log Log Log Log Log Log Log Log

Maize Rice Soybeans Wheat Maize Rice Soybeans Wheat

(1a) (1b) (1c) (1d) (2a) (2b) (2c) (2d)Panel A: Supply System

Log Maize Price 0.196 0.016 -0.588∗∗∗ -0.089 0.232∗∗ 0.026 -0.224∗∗∗ 0.031(0.231) (0.051) (0.185) (0.240) (0.101) (0.047) (0.085) (0.072)

Log Rice Price -0.121 0.019 -0.121 0.220 0.026 0.000 -0.054 0.081∗

(0.297) (0.066) (0.243) (0.310) (0.047) (0.059) (0.067) (0.046)Log Soybeans Price -0.121 0.017 0.530∗ -0.085 -0.224∗∗∗ -0.054 0.549∗∗∗ -0.035

(0.351) (0.077) (0.278) (0.362) (0.085) (0.067) (0.143) (0.086)Log Wheat Price 0.100 0.022 0.297 0.029 0.031 0.081∗ -0.035 0.015

(0.250) (0.055) (0.195) (0.257) (0.072) (0.046) (0.086) (0.082)

Panel B: Demand System

Log Maize Price -0.356∗∗∗ 0.203∗∗∗ -0.414∗∗∗ 0.038 -0.117∗∗ 0.150∗∗∗ -0.060 0.039(0.084) (0.045) (0.119) (0.080) (0.051) (0.030) (0.047) (0.039)

Log Rice Price 0.334∗∗∗ -0.100∗∗∗ 0.184∗∗ 0.007 0.150∗∗∗ -0.103∗∗∗ -0.058∗ -0.069∗∗

(0.057) (0.032) (0.086) (0.057) (0.030) (0.028) (0.033) (0.031)Log Soybeans Price 0.241∗∗∗ -0.127∗∗∗ 0.506∗∗∗ -0.028 -0.060 -0.058∗ 0.172∗∗ -0.023

(0.092) (0.049) (0.125) (0.085) (0.047) (0.033) (0.068) (0.052)Log Wheat Price -0.171∗∗ -0.057 -0.169 -0.135∗ 0.039 -0.069∗∗ -0.023 -0.089

(0.084) (0.044) (0.113) (0.076) (0.039) (0.031) (0.052) (0.059)

Panel C: Effect of Maize Demand Shift

Multiplier 3.43 1.20 2.41 1.94 2.68 -2.46 1.32 3.87Exp. Multiplier 1.15 0.73 0.24 0.89 3.45 1.08 0.95 2.19

(95% Conf. Int.) (-10.0,14.8) (-8.1,10.7) (-11.3,13.2) (-6.0,10.1) (-6.1,12.9) (-18.3,16.3) (-6.6,9.8) (-9.5,15.1)P-val (symmetry) 0.025 . . . . . . .Observations 46 46 46 46 46 46 46 46Spline Knots 5 5 5 5

Notes : Table replicates Table 8 except that it uses FAO data instead of FAS data. The multiplier gives the price increase for a 1% outward

shift in demand for maize, while baseline results give the multiplier on aggregate demand for maize, rice, soybeans, and wheat. To make the

multiplier comparable to the pooled analysis, we derive the production-weighted average multiplier of all commodities, which is 6.63 in the

unrestricted system and 4.26 if we impose symmetry. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A23

A4 FAS Data

Results in the main paper used data from FAO. This section replicates the analysis using

a different data set from the Foreign Agricultural Service of USDA. Each data set has

advantages: On the one hand data from FAO gives production estimates for the entire

world, while FAS only covers the biggest countries. Figure A11 shows total production for

FAO in the top left column and for FAS in the top right column, which is lower as several

countries are missing in the latter database. On the other hand, data for FAS is available

until 2010, i.e., including the recent run-up in prices.

The advantage of the FAS data is the longer temporal coverage. The disadvantage of the

FAS data is the smaller spatial coverage. Yield shocks for the biggest producers will still

be a valid instrument. The larger concern relates to derived consumption quantities, which

depend on changes in inventory levels for the largest producers, which are an incomplete

proxy for overall changes.

The main paper relies on FAO data except for the four-crop system that has so many

parameters that any additional data point (year) seems important. This section replicates

Tables of the main paper and generally finds similar results using FAO or FAS data.

The baseline supply and demand elasticity for calories (Table 1 in the main paper using

FAO data) is replicated in Table A8 using FAS data.

Table 2 in the main paper used weather shocks instead of yield shocks as instruments.

Table A9 replicates the analysis using FAS data.

Table 7 in the main paper estimated a two-crop system splitting crops into maize as well

as the sum of the other three: rice, soybeans and wheat. Table A10 replicates this analysis

using FAS data and presents results using both 4 and 5 spline knots to capture overall time

trends.

Finally, Table A11 presents the results when we separate yield shocks of each of the four

commodities are included. The coefficients are not significantly different from another (see

Panel D) except when the time trend is modeled with only three spline knots.

A24

Figure A11: World Production of Calories (FAO and FAS Data)

01

23

45

67

8B

illio

n P

eopl

e (2

000

calo

ries/

day)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010year

Maize Wheat Rice Soybeans

01

23

45

67

8B

illio

n P

eopl

e (2

000

calo

ries/

day)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010year

Maize Wheat Rice Soybeans

05

1015

2025

3035

US

Fra

ctio

n of

Wor

ld P

rodu

ctio

n (P

erce

nt)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

05

1015

2025

3035

US

Fra

ctio

n of

Wor

ld P

rodu

ctio

n (P

erce

nt)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Year

Notes: Figure displays world production of calories from maize, wheat, rice, and soybeans for 1961-2010

(top row) and the fraction of calories produced in the US (bottom row). The left column uses FAO data,

and the right column uses FAS data. The y-axis in the top row gives the number of people who could be fed

on a 2000 calories/day diet if they hypothetically only consumed the four commodities. In the bottom row,

the y-axis is the percent of global production.

A25

Table A8: Supply and Demand Elasticity (FAS Data)

Instrumental Variables Three Stage Least Squares(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: Supply EquationSupply Elast. βs 0.129∗∗∗ 0.103∗∗∗ 0.106∗∗∗ 0.119∗∗∗ 0.111∗∗∗ 0.112∗∗∗

(0.032) (0.034) (0.032) (0.022) (0.026) (0.026)Shock ωt 1.148∗∗∗ 1.195∗∗∗ 1.186∗∗∗ 1.114∗∗∗ 1.209∗∗∗ 1.197∗∗∗

(0.166) (0.131) (0.126) (0.114) (0.096) (0.096)First Stage ωt−1 -3.399∗∗∗ -2.645∗∗∗ -2.709∗∗∗ -2.802∗∗∗ -2.535∗∗∗ -2.595∗∗∗

(1.159) (0.921) (0.948) (0.840) (0.776) (0.776)First Stage ωt -2.480 -1.557 -1.627 -2.578∗∗ -1.557∗ -1.630∗

(1.628) (1.199) (1.239) (1.121) (0.888) (0.880)

Panel B: Demand EquationDemand Elast. βd -0.034 -0.093∗∗ -0.087∗∗ -0.031 -0.094∗∗ -0.088∗∗

(0.034) (0.038) (0.038) (0.037) (0.043) (0.039)First Stage ωt -4.642∗∗∗ -3.489∗∗∗ -3.532∗∗∗ -4.709∗∗∗ -3.464∗∗∗ -3.512∗∗∗

(1.415) (1.170) (1.178) (1.356) (1.106) (1.080)

Panel C: Effect of Demand ShiftMultiplier 1

βs−βd

6.15 5.12 5.18 6.69 4.89 5.00

Exp. Multiplier 6.96 3.95 5.65 7.20 5.25 5.32(95% Conf. Int.) (3.9,14.2) (3.4,10.6) (3.4,10.5) (4.5,12.9) (3.3,9.2) (3.5,9.0)

F1st-stage Supply 8.60 8.25 8.17F1st-stage Demand 10.76 8.89 9.00Observations 49 49 49 49 49 49Spline Knots 3 4 5 3 4 5

Notes : Table replicates Table 1 except that it uses FAS data instead of FAO data, which runs through 2010.

Columns (a), (b), and (c) include restricted cubic splines in time with 3, 4, and 5 knots, respectively. Stars

indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A26

Table A9: Supply and Demand Elasticity - Weather as Instrument (FAS Data)

(1a) (1b) (2a) (2b) (3a) (3b)log Q log P log Q log P log Q log P

Panel A: Supply Equation

Supply Elast. βs 0.092∗ 0.086 0.086(0.048) (0.059) (0.057)

Temperature Tt−1 3.443∗∗∗ 3.147∗∗∗ 3.149∗∗∗

(0.847) (0.728) (0.762)Temperature T2

t−1 -0.090∗∗∗ -0.082∗∗∗ -0.082∗∗∗

(0.021) (0.018) (0.019)Precipitation Pt−1 2.432 2.823 2.996

(2.239) (1.913) (2.053)Precipitation P2

t−1 0.599 -0.150 -0.263(1.075) (0.928) (0.986)

Temperature Tt 0.051 2.039∗∗∗ 0.039 1.617∗∗ 0.011 1.564∗∗

(0.201) (0.750) (0.222) (0.692) (0.218) (0.717)Temperature T2

t -0.002 -0.052∗∗∗ -0.002 -0.041∗∗ -0.001 -0.039∗∗

(0.005) (0.019) (0.006) (0.018) (0.006) (0.018)Precipitation Pt 0.344 2.367 0.513 2.230 0.644 2.724

(0.351) (1.819) (0.389) (1.671) (0.399) (1.798)Precipitation P2

t -0.381∗∗ -0.546 -0.500∗∗∗ -0.698 -0.551∗∗∗ -0.871(0.149) (0.836) (0.165) (0.764) (0.168) (0.793)

Panel B: Demand Equation

Demand Elast. βd -0.004 -0.068∗ -0.071∗

(0.029) (0.036) (0.037)Temperature Tt 1.269 0.819 0.965

(1.167) (0.948) (0.962)Temperature T2

t -0.033 -0.021 -0.025(0.029) (0.023) (0.024)

Precipitation Pt 0.947 -0.582 -1.231(3.198) (2.584) (2.649)

Precipitation P2t 1.655 1.631 1.839

(1.455) (1.176) (1.192)

Panel C: Effect of Demand Shift

Multiplier 1

βs−βd

10.43 6.46 6.36

Exp. Multiplier 7.38 9.63 7.48(95% Conf. Int.) (4.7,58.9) (3.5,25.0) (3.6,23.0)

Observations 47 47 47 47 47 47Spline Knots 3 3 4 4 5 5

Notes : Table replicates Table 2 except that it uses FAS data instead of FAO data. The sample runs through

2008 as the weather data set ends in 2008. Columns (a), (b), and (c) include restricted cubic splines in time

with 3, 4, and 5 knots, respectively. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A27

Table A10: Supply and Demand Elasticity - Two Crop System (FAS Data)

Unrestricted 2x2 System 2x2 System with Symmetry ImposedLog Log Log Log Log Log Log Log

Maize Other Maize Other Maize Other Maize Other(1a) (1b) (2a) (2b) (3a) (3b) (4a) (4b)

Panel A: Supply SystemLog Maize Price 0.061 -0.046 0.055 -0.054 0.124 -0.013 0.135 -0.020

(0.123) (0.069) (0.132) (0.074) (0.089) (0.056) (0.092) (0.060)Log Other Price 0.044 0.139∗∗∗ 0.051 0.148∗∗∗ -0.013 0.115∗∗ -0.020 0.125∗∗

(0.090) (0.051) (0.099) (0.056) (0.056) (0.046) (0.060) (0.049)

Panel B: Demand SystemLog Maize Price -0.532∗∗ 0.183 -0.444∗∗ 0.091 -0.382∗∗∗ 0.369∗∗ -0.315∗∗ 0.285∗

(0.226) (0.162) (0.225) (0.136) (0.132) (0.164) (0.123) (0.153)Log Other Price 0.610∗∗ -0.363∗ 0.506∗ -0.233 0.369∗∗ -0.617∗∗∗ 0.285∗ -0.496∗∗

(0.288) (0.207) (0.290) (0.176) (0.164) (0.216) (0.153) (0.205)

Panel C: Effect of Maize Demand ShiftMultiplier 2.99 1.36 3.06 1.16 3.25 1.69 3.33 1.63Exp. Multiplier 7.23 3.61 4.02 1.54 3.71 1.81 3.70 1.73(95% Conf. Int.) (0.7,13.1) (-1.8,7.0) (-4.4,18.1) (-5.1,9.4) (2.2,7.5) (0.6,4.0) (2.2,8.2) (-0.0,3.9)

P-val (symmetry) 0.223 . 0.221 . . . . .Observations 49 49 49 49 49 49 49 49Spline Knots 4 4 5 5 4 4 5 5

Notes : Table replicates Table 7 except that it uses FAS data and uses restricted cubic splines with both 4 as well as 5 knots to model the time

trend. The multiplier gives the price increase for a 1% outward shift in demand for maize, while baseline results give the multiplier on aggregate

demand for maize, rice, soybeans, and wheat. To make the multiplier comparable to the pooled analysis, we derive the production-weighted

average multiplier of all commodities, which are 5.48, 5.19, 6.35, and 6.33, respectively, in the four 2x2 systems. Stars indicate significance

levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A28

Table A11: Supply and Demand Elasticity - Separating Shocks of Four Crops (FAS Data)

Instrumental Variables Three Stage Least Squares

(1a) (1b) (1c) (2a) (2b) (2c)Panel A: Supply Equation

Supply Elast. βs 0.162∗∗∗ 0.113∗∗∗ 0.112∗∗∗ 0.155∗∗∗ 0.120∗∗∗ 0.118∗∗∗

(0.036) (0.037) (0.036) (0.027) (0.026) (0.026)Shock ωt,M 1.474∗∗∗ 1.436∗∗∗ 1.415∗∗∗ 1.136∗∗∗ 1.430∗∗∗ 1.400∗∗∗

(0.208) (0.165) (0.150) (0.190) (0.154) (0.155)Shock ωt,R 0.955 1.715∗∗∗ 1.385∗∗ 1.129∗∗ 1.745∗∗∗ 1.470∗∗∗

(0.659) (0.414) (0.568) (0.512) (0.373) (0.443)Shock ωt,S 1.296∗ 1.309∗∗ 1.446∗∗∗ 1.236∗∗ 1.313∗∗∗ 1.370∗∗∗

(0.743) (0.523) (0.462) (0.555) (0.440) (0.448)Shock ωt,W 1.038∗∗∗ 0.880∗∗∗ 0.879∗∗∗ 0.958∗∗∗ 0.917∗∗∗ 0.910∗∗∗

(0.207) (0.174) (0.181) (0.195) (0.167) (0.166)First Stage ωt−1,M 0.047 -0.962 -1.307 1.086 -0.017 -0.197

(2.026) (1.676) (1.732) (1.424) (1.483) (1.574)First Stage ωt−1,R -10.353∗∗ -4.151 -4.745 -4.651 0.045 -0.847

(4.856) (4.937) (5.019) (3.680) (3.922) (4.003)First Stage ωt−1,S -9.453 -4.586 -2.812 -8.844∗∗ -5.164 -4.086

(7.901) (6.833) (7.472) (3.981) (4.128) (4.495)First Stage ωt−1,W -3.097∗ -3.431∗∗ -3.466∗∗ -3.377∗∗ -4.131∗∗∗ -4.258∗∗∗

(1.719) (1.681) (1.692) (1.441) (1.445) (1.489)First Stage ωt,M 1.136 0.607 0.573 1.928 0.790 0.802

(2.801) (2.508) (2.468) (1.910) (1.744) (1.764)First Stage ωt,R -8.147 -2.644 -3.646 -11.912∗∗∗ -4.338 -4.129

(5.688) (5.946) (5.825) (4.074) (4.215) (4.717)First Stage ωt,S -7.815 -3.904 -3.016 -7.961 -3.658 -3.522

(8.408) (6.951) (6.919) (4.937) (4.549) (4.758)First Stage ωt,W -3.090∗∗ -3.437∗∗ -3.406∗∗ -3.868∗∗ -3.987∗∗ -4.143∗∗

(1.441) (1.371) (1.408) (1.854) (1.694) (1.747)

Panel B: Demand Equation

Demand Elast. βd 0.036 -0.096∗∗∗ -0.082∗∗ 0.043∗∗ -0.099∗∗∗ -0.076∗∗∗

(0.029) (0.037) (0.035) (0.019) (0.029) (0.026)First Stage ωt,M -3.472 -4.896∗∗ -5.204∗∗∗ -3.374 -4.964∗∗∗ -5.557∗∗∗

(2.264) (1.978) (1.914) (2.396) (1.646) (1.771)First Stage ωt,R -19.207∗∗∗ -6.327 -8.208 -19.284∗∗∗ -6.114∗ -5.735

(3.752) (4.264) (5.538) (4.384) (3.529) (4.533)First Stage ωt,S -7.708 -1.933 -0.249 -7.711 -3.381 -3.724

(7.569) (6.587) (6.264) (6.450) (3.891) (4.543)First Stage ωt,W -2.216 -1.889 -1.841 -2.201 -1.228 -1.486

(2.077) (1.950) (1.871) (2.256) (1.353) (1.503)

Panel C: Effect of Demand Shift

Multiplier 1

βs−βd

7.94 4.78 5.13 8.94 4.58 5.15

Exp. Mult. (s.e.) 9.98 5.16 5.61 9.97 4.73 5.34(95% Conf. Int.) (4.5,26.8) (3.2,9.4) (3.4,10.4) (5.9,18.5) (3.4,6.9) (3.8,8.0)

Panel D: P-value on Equal Coefficients

S1st-stage ωt−1 equal 0.17 0.73 0.70 0.08 0.36 0.45D1st-stage ωt equal 0.00 0.65 0.47 0.01 0.29 0.36F1st-stage Supply 2.40 1.72 1.55F1st-stage Demand 9.93 3.15 2.99Observations 49 49 49 49 49 49Spline Knots 3 4 5 3 4 5

Notes : Table replicates Table A5 except that it uses FAS data. It includes separate shocks for each of

the four crops: maize (M), rice (R), soybeans (S), and wheat (W). Shocks are normalized by the predicted

fraction of global production to make them comparable. Panel D presents p-values from tests whether the

coefficients on the shocks are jointly the same. Columns (a), (b), and (c) include restricted cubic splines in

time with 3, 4, and 5 knots, respectively. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A29

A5 Sensitivity Checks

Table A12 presents two sets of standard errors for the IV regressions: one that is uncorrected

as well as one that accounts for heteroscedasticity and serial correlation of unknown form.

The estimates are generally similar in the second stage, suggesting that heteroscedasticity

and serial correlation are not important in the estimated standard errors of the elasticities of

interest. The remainder therefore presents results using three stage least square estimates,

which are more efficient.

Table A13 limits the analysis to 1961-2003 or 1961-2005, so the data set stops before

the recent run-up in prices and the implementation of the 2007 or 2009 Renewable Fuel

standards, but results are similar.

Table A14 varies the timing at which we evaluate futures prices. Final results of a year’s

production shock are not fully revealed before December. On the other hand, planting

decisions for the next year’s harvest of winter wheat are made in September in the northern

hemisphere. We therefore consider futures prices in September of the previous year (Panel

A), or March of the concurrent year (Panel B), because production shocks in the Southern

hemisphere are resolved by March of the concurrent year. Panel C again evaluates prices at

the end of the year, but uses the spot price in the demand equation instead of the futures

price during the month of delivery. Results are similar in all cases.

To check the sensitivity of our estimates to the derivation of yield shocks, Table A15

replicates the analysis using linear time trends, restricted cubic splines with 4 knots (3

variables), or restricted cubic splines with 5 knots (4 variables) in the derivation of the yield

shocks. Our baseline specification used 3 spline knots (2 variables). The results are again

insensitive to the chosen time trend in the derivation of yield shocks.

Table A16 further examines the derivation of yield shocks. Panel A replicates the analysis

by using yield shocks that are not jackknifed as in our baseline. Panels B and C allow yields

to be autocorrelated, which may arise from technological breakthroughs or if weather has

autocorrelation. We fit models up to MA(1) or MA(3), respectively, for each country and

crop. For example, in panel C, we fit four models.A6 The model with the lowest BIC is

chosen, and yield deviations are the innovations in a given period, i.e., the new information

that has been revealed. Results remain robust.

Table A17 reports results from three further sensitivity checks. Given that prices show a

high degree of persistence, we include the second lag of prices in panel A. Log futures prices

A6MA(0), MA(1), MA(2), and MA(3).

A30

for delivery in period t that are traded at the end of t − 1 are instrumented with the yield

shock in ωt−1, while controlling for the second lag of the dependent variable, i.e., log futures

prices with a maturity in t− 1 that are traded in t− 2. Panel B uses two lagged shocks ωt−1

and ωt−2 to instrument futures prices. The panel also presents results from overidentification

tests as we now include two instruments, but none of them have p-values below 0.40. Panel C

rescales the caloric conversion ratios so the average price in 1961-2010 of all four crops equals

that of maize.A7 The original as well as the rescaled price series are shown in Figure A9. We

do this as the average price of rice is highest, and shifts in production between crops hence

alters the overall price. However, the results are insensitive to this rescaling.

A7In other words, the price series of wheat, soybeans and rice are each multiplied by a constant so theaverage price equals the maize average price.

A31

Table A12: Supply and Demand Elasticity (Standard vs Robust Errors)

FAO Data FAS Data

(1a) (1b) (1c) (2a) (2b) (2c)Panel A: Supply Equation

Supply Elast. βs 0.102∗∗∗ 0.096∗∗∗ 0.087∗∗∗ 0.129∗∗∗ 0.103∗∗∗ 0.106∗∗∗

[0.024] [0.023] [0.019] [0.033] [0.032] [0.031](0.025) (0.025) (0.020) (0.032) (0.034) (0.032)

Shock ωt 1.184∗∗∗ 1.229∗∗∗ 1.211∗∗∗ 1.148∗∗∗ 1.195∗∗∗ 1.186∗∗∗

[0.127] [0.106] [0.092] [0.143] [0.102] [0.102](0.146) (0.138) (0.105) (0.166) (0.131) (0.126)

First Stage ωt−1 -3.901∗∗∗ -3.628∗∗∗ -3.824∗∗∗ -3.399∗∗∗ -2.645∗∗∗ -2.709∗∗∗

[1.016] [0.853] [0.877] [1.202] [0.944] [0.945](1.145) (0.945) (0.910) (1.159) (0.921) (0.948)

First Stage ωt -2.918∗∗∗ -2.276∗∗ -2.372∗∗ -2.480∗∗ -1.557 -1.627∗

[1.031] [0.876] [0.891] [1.202] [0.949] [0.951](1.647) (1.294) (1.279) (1.628) (1.199) (1.239)

Panel B: Demand Equation

Demand Elast. βd -0.028 -0.055∗∗ -0.054∗∗∗ -0.034 -0.093∗∗ -0.087∗∗

[0.024] [0.022] [0.020] [0.040] [0.043] [0.039](0.021) (0.024) (0.022) (0.034) (0.038) (0.038)

First Stage ωt -5.564∗∗∗ -4.655∗∗∗ -4.770∗∗∗ -4.642∗∗∗ -3.489∗∗∗ -3.532∗∗∗

[1.461] [1.290] [1.291] [1.445] [1.169] [1.155](1.489) (1.300) (1.249) (1.415) (1.170) (1.178)

Panel C: Effect of Demand Shift

Multiplier 1

βs−βd

7.73 6.63 7.06 6.15 5.12 5.18

Exp. Mult. [s.e.] 8.39 6.99 7.38 9.31 5.63 5.66[95% Conf. Int.] [5.1,15.8] [4.7,11.4] [5.1,11.5] [3.8,16.0] [3.3,11.0] [3.4,10.6]

Exp. Mult. (s.e.) 8.39 7.08 7.42 6.96 3.95 5.65(95% Conf. Int.) (5.2,15.3) (4.6,12.2) (5.0,12.0) (3.9,14.2) (3.4,10.6) (3.4,10.5)

Panel D: Test whether ωt is i.i.d.

Autocorr. (p-val) 0.303 0.406 0.402 0.523 0.659 0.649Heterosc. (p-val) 0.724 0.410 0.537 0.766 0.715 0.659Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Notes : Table replicates IV regressions of Tables 1 and A8 but displays two sets of errors: standard errors

in square brackets [] are unadjusted, and standard errors in round brackets () adjust for heteroscedasticity

and autocorrelation of an arbitrary form. The first three columns (1a)-(1b) use data from FAO, while

columns (2a)-(2c) use data from FAS. Panel D regresses ωt on the time controls given in the last row and

tests whether the residuals exhibit autocorrelation or heteroscedasticity. Columns (a), (b), and (c) include

restricted cubic splines in time with 3, 4, and 5 knots, respectively. Stars indicate significance levels and are

based on standard errors in squared brackets: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A32

Table A13: Supply and Demand Elasticity - Sensitivity to Years

FAO Data FAS Data(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: Years 1961-2003Supply Elast. βs 0.117∗∗∗ 0.120∗∗∗ 0.097∗∗∗ 0.116∗∗∗ 0.117∗∗∗ 0.109∗∗∗

(0.019) (0.020) (0.019) (0.023) (0.025) (0.025)Demand Elast. βd -0.041∗ -0.056∗∗ -0.076∗∗∗ -0.052∗ -0.082∗∗ -0.081∗∗∗

(0.022) (0.023) (0.021) (0.029) (0.033) (0.030)Multiplier 1

βs−βd

6.33 5.68 5.77 5.93 5.03 5.28

Exp. Multiplier 6.55 5.85 5.93 6.21 5.26 5.50(95% Conf. Int.) (4.7,9.7) (4.3,8.5) (4.4,8.4) (4.2,9.8) (3.6,8.3) (3.8,8.5)

Observations 42 42 42 42 42 42Spline Knots 3 4 5 3 4 5

Panel B: Years 1961-2005Supply Elast. βs 0.116∗∗∗ 0.114∗∗∗ 0.094∗∗∗ 0.117∗∗∗ 0.114∗∗∗ 0.107∗∗∗

(0.020) (0.020) (0.019) (0.022) (0.025) (0.024)Demand Elast. βd -0.043∗ -0.061∗∗∗ -0.072∗∗∗ -0.051 -0.086∗∗∗ -0.082∗∗∗

(0.024) (0.023) (0.020) (0.031) (0.032) (0.030)Multiplier 1

βs−βd

6.29 5.70 6.03 5.93 5.00 5.28

Exp. Multiplier 6.54 5.88 6.21 6.22 5.22 5.50(95% Conf. Int.) (4.6,9.9) (4.3,8.5) (4.6,8.9) (4.2,9.9) (3.6,8.1) (3.9,8.4)

Observations 44 44 44 44 44 44Spline Knots 3 4 5 3 4 5

Panel C: Years 1961-2007 and 1961-2010 (Baseline)Supply Elast. βs 0.116∗∗∗ 0.112∗∗∗ 0.097∗∗∗ 0.119∗∗∗ 0.111∗∗∗ 0.112∗∗∗

(0.019) (0.020) (0.019) (0.022) (0.026) (0.026)Demand Elast. βd -0.034 -0.062∗∗∗ -0.066∗∗∗ -0.031 -0.094∗∗ -0.088∗∗

(0.023) (0.022) (0.021) (0.037) (0.043) (0.039)Multiplier 1

βs−βd

6.65 5.75 6.12 6.69 4.89 5.00

Exp. Multiplier 6.90 5.92 6.31 7.20 5.25 5.32(95% Conf. Int.) (4.9,10.4) (4.3,8.5) (4.6,9.1) (4.5,12.9) (3.3,9.2) (3.5,9.0)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Notes : Table replicates 3SLS regressions in Table 1 and Table A8 except that different years are used in

the regression. The first three columns (1a)-(1b) use data from FAO, while columns (2a)-(2c) use data from

FAS. Columns (a), (b), and (c) include restricted cubic splines in time with 3, 4, and 5 knots, respectively.

Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A33

Table A14: Supply and Demand Elasticity - Sensitivity to Month of Price

FAO Data FAS Data(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: Supply Price in September of Previous YearSupply Elast. βs 0.110∗∗∗ 0.107∗∗∗ 0.092∗∗∗ 0.113∗∗∗ 0.108∗∗∗ 0.109∗∗∗

(0.019) (0.020) (0.018) (0.023) (0.027) (0.026)Demand Elast. βd -0.034 -0.062∗∗∗ -0.066∗∗∗ -0.031 -0.094∗∗ -0.088∗∗

(0.023) (0.022) (0.021) (0.037) (0.043) (0.039)Multiplier 1

βs−βd

6.95 5.91 6.33 6.93 4.95 5.09

Exp. Multiplier 7.23 6.10 6.52 7.56 5.32 5.44(95% Conf. Int.) (5.1,11.1) (4.4,8.9) (4.8,9.4) (4.6,14.0) (3.4,9.5) (3.5,9.3)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Panel B: Supply Price in MarchSupply Elast. βs 0.125∗∗∗ 0.120∗∗∗ 0.105∗∗∗ 0.127∗∗∗ 0.119∗∗∗ 0.121∗∗∗

(0.020) (0.021) (0.019) (0.027) (0.030) (0.030)Demand Elast. βd -0.034 -0.062∗∗∗ -0.066∗∗∗ -0.031 -0.094∗∗ -0.088∗∗

(0.023) (0.022) (0.021) (0.037) (0.043) (0.039)Multiplier 1

βs−βd

6.29 5.50 5.84 6.33 4.69 4.79

Exp. Multiplier 6.51 5.66 6.00 6.80 5.13 5.10(95% Conf. Int.) (4.7,9.6) (4.2,8.1) (4.4,8.5) (4.3,12.2) (3.2,8.8) (3.3,8.7)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Panel C: Spot Price in Demand EquationSupply Elast. βs 0.109∗∗∗ 0.111∗∗∗ 0.096∗∗∗ 0.117∗∗∗ 0.107∗∗∗ 0.112∗∗∗

(0.022) (0.022) (0.019) (0.028) (0.030) (0.029)Demand Elast. βd -0.059∗∗ -0.088∗∗∗ -0.094∗∗∗ -0.043 -0.120∗∗∗ -0.106∗∗∗

(0.024) (0.021) (0.018) (0.035) (0.038) (0.035)Multiplier 1

βs−βd

5.97 5.03 5.28 6.27 4.41 4.59

Exp. Multiplier 6.10 5.12 5.37 6.48 4.53 4.72(95% Conf. Int.) (4.6,8.4) (4.0,6.7) (4.2,7.1) (4.7,9.5) (3.3,6.5) (3.5,6.7)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Notes : Table replicates 3SLS regressions in Table 1 and Table A8 except for the month at which futures

prices are evaluated. The first three columns (1a)-(1b) use data from FAO, while columns (2a)-(2c) use

data from FAS. Columns (a), (b), and (c) include restricted cubic splines in time with 3, 4, and 5 knots,

respectively. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A34

Table A15: Supply and Demand Elasticity - Sensitivity to Specification of Yield Trend inDerivation of Yield Shocks

FAO Data FAS Data(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: Linear Yield TrendSupply Elast. βs 0.128∗∗∗ 0.124∗∗∗ 0.094∗∗∗ 0.122∗∗∗ 0.120∗∗∗ 0.116∗∗∗

(0.022) (0.022) (0.019) (0.028) (0.026) (0.025)Demand Elast. βd -0.033 -0.056∗∗ -0.068∗∗∗ -0.088 -0.089∗∗ -0.084∗∗

(0.025) (0.022) (0.021) (0.067) (0.039) (0.035)Multiplier 1

βs−βd

6.22 5.56 6.18 4.77 4.78 4.99

Exp. Multiplier 6.47 5.73 6.37 5.40 5.07 5.25(95% Conf. Int.) (4.5,9.9) (4.2,8.3) (4.6,9.2) (2.8,14.6) (3.3,8.4) (3.5,8.5)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Panel B: Yield Trend with 4 Spline KnotsSupply Elast. βs 0.104∗∗∗ 0.091∗∗∗ 0.092∗∗∗ 0.121∗∗∗ 0.118∗∗∗ 0.118∗∗∗

(0.021) (0.021) (0.020) (0.026) (0.027) (0.026)Demand Elast. βd -0.059∗∗ -0.081∗∗∗ -0.073∗∗∗ -0.082 -0.097∗∗ -0.090∗∗

(0.027) (0.025) (0.022) (0.061) (0.041) (0.038)Multiplier 1

βs−βd

6.15 5.82 6.06 4.93 4.65 4.80

Exp. Multiplier 6.42 6.04 6.27 5.93 4.96 5.06(95% Conf. Int.) (4.4,10.0) (4.3,9.1) (4.5,9.3) (3.0,12.7) (3.2,8.5) (3.4,8.3)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Panel C: Yield Trend with 5 Spline KnotsSupply Elast. βs 0.100∗∗∗ 0.086∗∗∗ 0.083∗∗∗ 0.080∗∗ 0.074∗ 0.077∗∗

(0.026) (0.025) (0.024) (0.035) (0.038) (0.036)Demand Elast. βd -0.072∗∗ -0.089∗∗∗ -0.085∗∗∗ -0.076 -0.107∗∗ -0.100∗∗

(0.031) (0.026) (0.024) (0.065) (0.052) (0.048)Multiplier 1

βs−βd

5.85 5.72 5.93 6.41 5.52 5.63

Exp. Multiplier 6.20 5.99 6.21 9.10 7.44 6.52(95% Conf. Int.) (4.1,10.4) (4.1,9.5) (4.3,9.8) (3.2,30.7) (3.2,17.7) (3.4,15.9)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Notes : Table replicates 3SLS regressions in Table 1 and Table A8 except that various time trends are used

to derive yield deviations. The first three columns (1a)-(1b) use data from FAO, while columns (2a)-(2c)

use data from FAS. Columns (a), (b), and (c) include restricted cubic splines in time with 3, 4, and 5 knots,

respectively. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A35

Table A16: Supply and Demand Elasticity - Sensitivity to Derivation of Yield Shocks

FAO Data FAS Data(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: Residuals (Not Jackknifed)Supply Elast. βs 0.118∗∗∗ 0.113∗∗∗ 0.098∗∗∗ 0.119∗∗∗ 0.110∗∗∗ 0.112∗∗∗

(0.019) (0.020) (0.018) (0.022) (0.026) (0.025)Demand Elast. βd -0.035 -0.063∗∗∗ -0.067∗∗∗ -0.030 -0.096∗∗ -0.090∗∗

(0.023) (0.023) (0.021) (0.036) (0.043) (0.040)Multiplier 1

βs−βd

6.57 5.69 6.06 6.70 4.86 4.97

Exp. Multiplier 6.82 5.87 6.24 7.16 5.19 5.29(95% Conf. Int.) (4.8,10.2) (4.3,8.5) (4.6,9.0) (4.5,12.7) (3.3,9.2) (3.4,9.0)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Panel B: Innovations in MA(1) Yield ModelSupply Elast. βs 0.117∗∗∗ 0.114∗∗∗ 0.076∗∗ 0.135∗∗∗ 0.134∗∗∗ 0.130∗∗∗

(0.034) (0.036) (0.033) (0.037) (0.042) (0.040)Demand Elast. βd -0.055 -0.064∗ -0.086∗∗ -0.093 -0.102∗ -0.100∗

(0.046) (0.036) (0.036) (0.088) (0.058) (0.054)Multiplier 1

βs−βd

5.83 5.60 6.20 4.38 4.25 4.33

Exp. Multiplier 6.82 6.20 7.03 6.16 5.02 4.52(95% Conf. Int.) (3.5,16.2) (3.6,12.9) (3.9,15.2) (2.2,20.9) (2.6,12.0) (2.7,11.2)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Panel C: Innovations in MA(3) Yield ModelSupply Elast. βs 0.119∗∗∗ 0.118∗∗∗ 0.078∗∗ 0.136∗∗∗ 0.136∗∗∗ 0.131∗∗∗

(0.036) (0.037) (0.034) (0.041) (0.043) (0.040)Demand Elast. βd -0.056 -0.061 -0.082∗∗ -0.102 -0.103∗ -0.103∗

(0.054) (0.038) (0.038) (0.097) (0.059) (0.056)Multiplier 1

βs−βd

5.71 5.60 6.27 4.19 4.18 4.28

Exp. Multiplier 6.95 5.55 7.21 5.91 5.28 4.79(95% Conf. Int.) (3.2,20.2) (3.5,13.5) (3.8,16.5) (1.9,23.8) (2.5,11.9) (2.6,11.2)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Notes : Table replicates 3SLS regressions in Table 1 and Table A8 except that yield deviations are from

standard regressions (not jackknifed) or more general MA(1) or MA(3) models. The preferred model is

selected using the BIC criteria, and yield residuals are innovations for the model in question. The first three

columns (1a)-(1b) use data from FAO, while columns (2a)-(2c) use data from FAS. Columns (a), (b), and

(c) include restricted cubic splines in time with 3, 4, and 5 knots, respectively. Stars indicate significance

levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%. A36

Table A17: Supply and Demand Elasticity - Price Rescale and Lag Structure

FAO Data FAS Data(1a) (1b) (1c) (2a) (2b) (2c)

Panel A: Include Lagged PricesSupply Elast. βs 0.104∗∗∗ 0.099∗∗∗ 0.100∗∗∗ 0.134∗∗∗ 0.117∗∗∗ 0.121∗∗∗

(0.014) (0.015) (0.014) (0.015) (0.016) (0.015)Demand Elast. βd -0.039 -0.055∗∗∗ -0.053∗∗∗ -0.019 -0.101∗∗ -0.090∗∗

(0.026) (0.017) (0.017) (0.039) (0.043) (0.040)Multiplier 1

βs−βd

6.97 6.51 6.51 6.57 4.59 4.74

Exp. Multiplier 7.29 6.66 6.63 -4.93 4.82 4.96(95% Conf. Int.) (5.0,11.5) (5.1,9.1) (5.1,8.9) (4.2,15.1) (3.3,7.7) (3.4,7.8)

Observations 45 45 45 48 48 48Spline Knots 3 4 5 3 4 5

Panel B: Two Lags of Shocks in SupplySupply Elast. βs 0.132∗∗∗ 0.127∗∗∗ 0.118∗∗∗ 0.140∗∗∗ 0.127∗∗∗ 0.130∗∗∗

(0.018) (0.021) (0.018) (0.020) (0.026) (0.025)Demand Elast. βd -0.027 -0.055∗∗∗ -0.057∗∗∗ -0.026 -0.063∗∗ -0.063∗∗

(0.022) (0.020) (0.020) (0.036) (0.031) (0.030)Multiplier 1

βs−βd

6.29 5.48 5.73 6.02 5.28 5.18

Exp. Multiplier 6.48 5.63 5.87 6.41 5.58 5.46(95% Conf. Int.) (4.7,9.4) (4.2,7.9) (4.4,8.2) (4.2,10.9) (3.7,9.3) (3.7,8.8)

Overid. (p-value) 0.553 0.409 0.367 0.833 0.705 0.756Observations 45 45 45 48 48 48Spline Knots 3 4 5 3 4 5

Panel C: Caloric Conversion to Equate Avg. PriceSupply Elast. βs 0.113∗∗∗ 0.097∗∗∗ 0.091∗∗∗ 0.124∗∗∗ 0.107∗∗∗ 0.111∗∗∗

(0.017) (0.018) (0.017) (0.020) (0.023) (0.022)Demand Elast. βd -0.016 -0.069∗∗∗ -0.067∗∗∗ 0.001 -0.089∗∗ -0.080∗∗

(0.015) (0.022) (0.019) (0.022) (0.038) (0.034)Multiplier 1

βs−βd

7.72 6.03 6.32 8.12 5.11 5.25

Exp. Multiplier 7.94 6.21 6.49 8.47 5.41 5.50(95% Conf. Int.) (5.9,11.2) (4.6,8.9) (4.8,9.2) (5.9,13.2) (3.6,8.8) (3.8,8.7)

Observations 46 46 46 49 49 49Spline Knots 3 4 5 3 4 5

Notes : Table replicates 3SLS regressions in Table 1 and Table A8 except for caloric conversion factors and

how many lags are included. Panel B also includes overidentification tests for the supply equation, which

includes two instruments. The first three columns (1a)-(1b) use data from FAO, while columns (2a)-(2c) use

data from FAS. Columns (a), (b), and (c) include restricted cubic splines in time with 3, 4, and 5 knots,

respectively. Stars indicate significance levels: ∗∗∗ : 1%; ∗∗ : 5%; ∗ : 10%.

A37