Geography Matters: International Trade Patterns and the Indirect

Land Use Effects of Biofuels

Nelson Villoria1

Thomas Hertel

December 30, 2009

1Corresponding Author. Department of Agricultural Economics, Purdue University, 403 W. State St.

Room 567, West Lafayette, IN 47907-2056. Phone: (765) 494-4321. email: nvillori@purdue.edu
Abstract

This article investigates the relationship between bilateral international trade patterns and the

global distribution of coarse grains production responses to market developments in the United

States. Our null hypothesis is that the geographic patterns embedded in bilateral trade flows do

not affect the global production response to a change in US prices. In other words, world agricultural

markets are fully integrated. Therefore, after correcting for policy interventions and transportation

costs, farmers around the world receive a uniform price signal. The alternative to this mechanism

allows price transmission to vary with the intensity of competition between countries in specific

markets. Our main conclusion is that countries that are more exposed to competition with the US in

international markets tend to have larger supply responses to US market developments, irrespective

of their current cultivated areas and levels of production. Our work has direct implications for the

analysis of the global land use impacts of biofuel mandates where global cropland conversion is a

primary source of concern.
Reviewer’s Appendix

R-1 Background on the global coarse grains sector

Corn, sorghum, barley, oats, and rye comprise the trade category known as coarse grains. While

maize (corn) is by far the largest traded product in this category (Allen and Lutman, 2009), the

composition of the sector varies widely across countries. This can be seen in Figure R-1, which

shows the relative contribution of each individual crop to the total national area under coarse

grains for a sample of countries (the same employed in the econometric exercise below). This area

constitutes approximately 75% (average 1975-2002) of the global area harvesting coarse grains.

These countries are sorted by their average (1992-2002) hectarage (indicated within parentheses

next to each country’s name) which reveal that the US has the largest area, followed by India

(36.42 million ha), China (27.2), Brazil (12.34), Mexico (9.05), and Canada (7.21). Note that for

the US and China, the coarse grains are mostly maize, while in India, sorghum and millet dominate.

Combining its dominance in area and higher yields, the US is the largest producer of coarse grains

in the world.

During the period 1975-2002, an average of 49% of global exports originated in the US (GTAP

database documented in Gehlhar, 2005). Allen and Lutman (2009) indicated that more recently

(2003-2008), the US share of world exports averaged 60%. According to these authors:

While the United States dominates world corn trade, exports account for only a relatively small portion of demand for US corn — about 15 percent. This means that

corn prices are largely determined by supply-and-demand relationships in the US market, and the rest of the world must adjust to prevailing US prices. This makes world

corn trade and prices dependent on weather in the US Corn Belt. However, Argentina,

the second-largest corn exporter in most years, is in the Southern Hemisphere. Farmers there plant their corn after the size of the US crop is known, providing a quick,

market-oriented supply response to short US crops.

As discussed in the next section, the “large” country nature of the US is the basic argument

justifying the identification strategy of the links between price events in the US and land use

1
decisions elsewhere.

Figure R-2 compares trends in area harvested and production in the US and the rest of the

world during the period 1975-2002. The figure broadly reveals similar trends where areas have a

slow declining trend while production is increasing steadily. This is the result of yield improvements

during the last three decades. Figure R-3 plots the log of total US corn exports (in bushels) against

time. As can be seen, while the volatility of production translates into a high export volatility, the

average level of exports seems to have been relatively constant over the last three decades. Indeed,

regressing the total US corn exports on a trend variable (period 1975-2007) gives a statistically

insignificant trend coefficient of 0.002 (the straight line in the plot).

Figure R-4 shows the time distribution (1975-2002) of imports and exports of total coarse

grains in the countries in the sample (excluding the US). The dots represent mean flow values,

while the segments extend a 95% confidence interval. Imports are plotted to the left of zero and

exports to the right. The countries are sorted by their net trade position (mean exports - mean

imports). Several features of the international market for coarse grains are apparent. First, with the

exception of China (the second largest country in terms of coarse grains area), for the countries that

trade, specialization is the norm. According to the figure, France, Argentina, Australia, Canada,

China, and to a lesser extent, Hungary, South Africa, and Thailand, are the most important

exporters. Japan is by far the largest world importer, followed by Mexico, Germany, Spain and other

countries in western Europe. Second, most countries in the sample do not participate significantly

in international trade, regardless of their size (see for example, India). Likewise, countries with

large croplands such as Mexico, Brazil and China have sizable imports. Overall, the 38 countries in

the sample are responsible for 41% of global exports and 64% of global imports (average 1975-2002).

When the US is added, almost all the global exports are covered. The US is a marginal importer

with average annual imports of coarse grains of less than 2%.

2
R-2 Bootstrap based bias correction for dynamic panels

The boostrap corrected parameters are shown in Table R-3. This section is taken from Everaert

and Pozzi (2007) and is included here only as a reference. Given a model of the form:

yt = γyt−1 + βxt + Dη + ε = Wδ + Dη + ε (R-1)

for i = 1, ..., N (cross-sectional dimension) and t = 2, ..., T (time dimension) and where ytis the

dependent variable, xtis an explanatory variable, η are fixed effects, and εi an error term, the idea

is to get a correction of the biased vector parameter δ:

ˆδ = (W0AW)

−1Ay (R-2)

where A (...) is an indempotent transformation matrix that eliminates the individual

effects η. We know that ˆδ is a biased estimator fpr δ, i.e.

E(

ˆδ) = Z ∞

−∞

zfδˆ(z)dz 6= δ, (R-3)

From (R-3) it is clear that  ̄δ is an unbiased estimator for δ if it satisfies:

ˆδ = lim

J→∞

1

J

X

J

j=1

δb∗

j

(

 ̄δ) (R-4)

For practical purposes, a bias-corrected estimate for δ can be obtained by searching

over the parameter space until a vector of parameters ˆδ is found that satisfies (R-4).

This search is implemented through an iterative bootstrap procedure which simulates

the distribution of the LSDV estimator when sampling from (2) with some vector of

known parameters, say  ̃δ. This bootstrap procedure is described in the following steps:

1. Estimate the individual effect  ̃η = (T − 1)−1D0(y − W  ̃δ) and the residuals  ̃ε =

y − Wσ ̄ − Dη ̃.

2. Choose the number of bootstrap samples B, and proceed as follows in bootstrap

3
sample j, with j = 1, ..., B:

a. Obtain a bootstrap sample  ̃ε

b

from rescaled estimated residuals  ̃ε

r

(see MacKinnon,

2002).

b. Calculate a bootstrap sample y

b = Wb ̃δ + Dη ̃ +  ̃ε

b where Wb = (yb

−1

, x) and with

initialization y

b

i1 = yi1. So we condition on the initial values yi1 and on x.

c. Obtain the LSDV estimator  ̃δ

b

j = ( ̃γ

b

j

, β ̃b

j

).

3. Calculate the mean of the LSDV estimator  ̃δ

b

j

over the B bootstrap samples as

 ̃δ

b = B−1 PB

j=1

 ̃δ

b

j

(

 ̃δ).

The mean of the bootstrap distribution  ̃δ

b

can now be used to evaluate  ̃δ as an estimator

for δ. From 6 we know that for  ̃δ to be an unbiased estimator  ̄δ for δ, the mean  ̃δ

b of

the bootstrap distribution  ̃δ should equal the original biased LSDV estimates ˆδ, i.e.

ω = ˆδ −  ̃δ

b = 0. In order to find a parameter vector  ̃δ that satisfies this condition,

we iterate over the bootstrap procedure outlined in steps 1-3 and evaluate  ̃δ(k), in each

iteration k, as an estimator for δ by calculating ω(k) = ˆδ −  ̃δ

b

(k)

. If ω(k) = 0,  ̃δ(k)is taken

to be the unbiased estimate  ̄δ for δ. If ω(k) 6= 0,  ̃δ(k)is updated as  ̃δ(k+1) =  ̃δ(k) + ω(k)

and we iterate over the bootstrap procedure until this condition is satisfied. As the

biased LSDV estimator  ̄δ can be thought of as being our first guess for the vector of

population parameters δ, we initialize the algorithm by setting  ̃δ(1) = ˆδ.

R-3 Differences in output and exports under competing trade assumptions

In order to further illustrate the differences between assumptions in a comparable framework, a

numerical simulation of the effects of a sudden increase of 15% in the industrial domestic demand for

coarse grains within the US is carried out using a partial equilibrium closure in the standard GTAP

model.1 The increased demand for coarse grains in the US drives domestic prices up, discouraging

1The standard GTAP model (Hertel, 1999) and the GTAP data V.6 (Dimaranan, 2006) are used. To isolate the

substitution effects between domestic and imported sources, regional incomes, output in the non-coarse grain sectors

out of the US, and endowment prices are kept constant. This partial equilibrium closure has the effect of eliminating

income effects, decreasing the responsiveness of the coarse-grains sector by keeping resources locked in the other

sectors, and discouraging producers from substituting among production factors — and between these factors and

intermediate inputs— responding only to the expansionary effect of the increase in demand.

4
exports. The lower presence of the US in international markets offers an opportunity for other

countries to increase their market shares. One of the main markets of the US is Japan, which

absorbs around 26% of US coarse grains exports. With very low domestic production in Japan, the

US supplies around 74% of Japan’s market.

Figure R-5 plots the percentage changes of exports to Japan (on the vertical axis) from the US,

Argentina, Brazil, China, and India under different elasticities of substitution (on the horizontal

axis). When the standard GTAP parameter of 2.6 is employed, US exports decline by 0.61%.

China, Argentina, and Brazil partially fill the gap left by the US through increasing their exports

around 1.4%. As the elasticity of substitution increases, the decline in US exports becomes larger.

With a very large elasticity of substitution (σM = 100), the price increase causes a reduction of

US exports to Japan of around 14% and dramatically increases the exports of China (by 38.45%),

Argentina (21.62%), and Brazil (30.77%).

The vertical axis of the lower panel of Figure R-5 shows the percentage changes in output

associated with the increase in US industrial demand for coarse grains. Using the standard GTAP

elasticity (σM = 2.6), the largest percentage change (+11%) is in the US, the source of the shock.

As the elasticity of substitution increases, the response of the US is mitigated by the fact that it

is displaced with increasing strength by its competitors in international markets; in other words,

a higher substitutability implies that the US is more sensitive to its relative price disadvantage.

Notice that with the lowest elasticity of 2.6, Argentina has the largest output response (+0.32%)

after the US, a result consistent with the fact that Argentina is an important exporter of coarse

grains and competes with the US in many of the same foreign markets. With large elasticities of

substitution, the proportional supply response across countries becomes more even. This reasoning

explains the pattern of results obtained by Searchinger et al. (2008) who show that the US has only

a moderately larger supply response than Brazil, China, or India.

To illustrate what happens to countries with low shares, consider the case of Argentina, which

has only 3.8% of the Japanese market share. Figure R-6 compares the declines in Argentinean and

US exports to Japan under comparable domestic price increases (percentage changes shown in the

5
upper horizontal axis)2 across several values of the elasticity of substitution (in the lower horizontal

axis). Starting from the lowest value of σM (2.6), the declines in the exports to Japan are larger

for the Argentina (-1.98%) than for the US (-0.61%). As discussed above, this is due to the low

market share of Argentina in the Japanese market, which is associated with the low participation of

Argentina in the Japanese CES price index. As the goods become more homogeneous (σM=100),

the same price increase implies a much larger loss of market share for Argentina (-46.75%) than for

the US (-14.49%).

R-4 Complementary notes for deriving the competition indexes

Consider the following compensated CES demand facing country i in each market j (including i

itself)3:

Xij = B

σo

ij Xj



Pij

Pj

−σo

where σo is the elasticity of substitution that, depending on the specification, could be different for

substitution between domestic products and imports (σD) and among import sources (σM). Xij

are exports from country i to market j, Bij is a constant preference weight, Xj is total demand in

the market j, Pij is the price charged by country i’s suppliers in market j, and Pj is the average

price level in market j.

The analysis of changes in Xij is facilitated by linearizing in percentage changes the CES demand

equation above. In the rest of this appendix, percentage changes are denoted using the variable

names in lower cases (i.e., xij =

dXij

Xi

):

xij = xj − σo (pij − pj ) (R-5)

The first term represents the growth of the overall import market for Xij . The second represents

the percentage change in Xij ’s share of the market, or the substitution effect. Note that the larger

the elasticity of substitution σM, the smaller the difference in price changes needed to cause a large

2For comparison purposes, the Argentinean market price of coarse grains is shocked by the same percentage

changes in the US price obtained under the demand shocks discussed above.

3The derivation of the CES demand in the Armington context and other properties of the Armington model are

back in Appendix A.

6
swing in xij . In the limit, when a product is completely homogeneous such that σM → ∞, the

slightest deviation of the changes in country i’s prices above the deviations in the changes of the

price index of country j, eliminates exporter i from j’s market.

At any point in time t, the disposition of domestically produced output Xiis either destined for

the domestic market or for exports; from now on, these markets are indexed by j. Thus, Xi can be

decomposed into Xi,j=i, domestic consumption, and Xij , exports originating in country i destined

to country j. There are n countries with potentially m = n − 1 foreign partners. Therefore:

Xi =

Xn

j

Xij , i ∈ j (R-6)

To guide the estimation below, some structure on how the Xij s behave is needed. We use the

Armington assumption. We also impose equal elasticities of substitution between domestic and

imported and among goods from different countries. Therefore, in what follows σD=σM=σ and

(R-5) is rewritten as:

xij = xj − σ(pij −

Xn

k

δkjpkj ) (R-7)

Taking the domestic price i out of the summation yields:

xij = xj − σ



pij (1 − δij ) −

Xm

k6=i

δkjpkj



 (R-8)

using the fact that (1 − δij ) = Pm

k6=i

δkj , (R-8) is further simplified as:

xij = xj − σ





Xm

k6=i

δkj (pij − pkj )



 . (R-9)

In other words, the percentage change in i’s sales to market j due to the substitution effects is a

function of the weighted sum of the changes in the prices charged by i relative to those charged by

its competitors (indexed by k), using as weights the market share of producer k in market j. For

a given change in relative prices that favors producer k, the larger the participation of k in market

j, the more pronounced the decline of Xij — a fact that reinforces the discussion of the previous

7
section.

Summing (R-9) over all the markets j yields:

xi =

Xn

j

θijxj − σ

Xn

j

θij





Xm

k6=i

δkj (pij − pkj )



 , (R-10)

where θij =

PijXij

PiXi

is the revenue share that producer i obtains from its sales to market j. Expanding

terms and rearranging them, Expression (R-10) can be rewritten as:

xi =

Xn

j

θijxj − σ

Xm

k

Xn

j

θijδkj (pij − pkj ). (R-11)

The first term in the right hand side (RHS) is the expansion effect: a revenue-share weighted sum

of the growth in each of the individual markets j catered by producers from country i. The first

summation in the second term of the RHS is over the m producers that compete with producer

i. The second summation is over destination markets, including producer i’s market. The main

message from (R-11) is that the percentage change in country i’s total output will depend on the

market share of its competitors in the destination market (δkj ), and on the importance that the

destination market has for i’s total production of coarse grains (θij ). To focus on the effects of

competition between the US and producer i we can rewrite (R-11) in the following way:

xi =

Xn

j

θijxj − σ

Xn

j

θijδus,j (pij − pus,j ) − σ

Xm

k6=US

Xn

j

θijδkj (pij − pkj ). (R-12)

The first term in the RHS of R-12 can be further decomposed into country i’s own-expansion

as well as expansion in the markets that it sells to. In the second term, the summation over n

reflects that both i and the US compete in each other’s market. This allows one to define weights

that allow one to detect competition in producer i’s own market, in the US market, and in other

markets indexed by j. The third term captures the effects of competition with other suppliers.

8
This entails rewriting (R-12) as:

xi = θiixi +

Xm

j6=i

θijxj

− σ





nX−2

j6=(i,US)

θijδus,j (pij − pus,j ) + θi,usδus,us(pi,us − pus,us) + θiiδus,i(pii − pus,i)





+ i

(R-13)

where the first term in the RHS is the own-expansion effect, the second term is the expansion effect

from trading partners, the terms within the brackets respectively capture competition between the

US and country i in country i’s own market, in the US market, and in third markets, and the last

term captures the effects on output associated with competition with other suppliers.

R-5 Variance components of the competition indexes

The price transmission parameter β in Equation 11 is identified solely on the basis of temporal

variation in the US price. The US price is a quantity weighted index of the price of coarse grains

in the most important US markets (see details in Appendix B). The index is normalized to unity

in 1975. As can be seen in Table 1, the US price index has a mean value that coincides with its

mean of 0.95 (However, this price index does not seem to be normally distributed as evidenced by

the fact that 75% of the observations are below 1 — See Q3 in Table 1 — which indicates that the

distribution of prices is skewed toward the left.) During the period 1975-2002, the US price index

has ranged from 0.63 to 1.46, suggesting that price spikes are more acute than price troughs and

also that the US price index varies significantly, providing a good basis for identifying the US price

elasticity of harvested area, β.

However, to estimate the parameters αi (i = 1..3), the competition indexes ω are included by

themselves and combined with the US price index. Because the indexes ω vary both over time (as

does the US price index) and across countries, it is informative to investigate whether the interaction

term retains enough variability to be able to identify the parameters α. To this end, in Table R1, the column “Source of variation” decomposes each interaction into its three components. For

9
instance, the variance of the interaction ln(Pust) × ωit is decomposed in the variances due to year,

country, and the interaction per se. The only case in which temporal variation has no explanatory

power is the interaction that captures the price elasticity of area due to competition within the

US market. In all cases, cross-country differences are a significant explanatory variable of the

behavior of the ωs, but they are disproportionately so in the case of interactions in third markets.

Finally, the “Interaction” component shows the variance not explained by time or cross country

variations. This portion ranges from 33% in the case of ωj to 52% in the case of ωk to 55% in the

case of ωi. This suggests that the interaction terms have enough variability to properly estimate

the parameters α.

R-6 Influential Countries

The results discussed thus far suggest that only a reduced number of countries compete with the

US The question of whether it is possible that these countries are driving the results is tackled

next. Table R-2 shows the parameters of interest obtained — βˆ from the IMW and A models

and α3 from model — estimating the restricted and unrestricted model, dropping one country at a

time. The first column of the table shows the country dropped. Starting with Argentina, when it

is dropped from the sample, the elasticity of the IWM model is reduced from 0.044 (in Table 2) to

0.037. The significance of the parameter estimate, however, is mostly unchanged. Indeed, it does

not matter which country is dropped from the sample; the elasticity βˆ of the IWM model remains

statistically significant (p-values < 0.05) at roughly 0.04.

Next, the elasticities from the Armington-D model, βˆ and ˆα3 are presented along with their

significance level. In general, it does not matter which country is dropped; βˆ loses its statistical

significance when the interaction term involving competition with the US is added to the regression. Likewise, the elasticity estimated using the interaction term, α3 remains around 0.011 and

statistically significant in all the cases (p-values < 0.03) except when Argentina is dropped that

the p-value increases to 8%, this is not a surprising result given that Argentina is the country

that competes most fiercely with the US in third markets (recall Figure 2 discussed in the Section

“empirics”).

10
Finally, the p-values obtained from an LM test identical to the one described at the beginning of

this section shows that, as before, except for the case where Argentina is dropped, there is around

a 5% probability of rejecting the null hypothesis that the exclusion restrictions associated with the

competition indexes (α1- α3 and the parameters γ attached to the ω terms) are zero given that

this was true. When Argentina is dropped, the p-value is 29%, thus, the null cannot be rejected:

this is an expected result given the large degree of competition between Argentina and the US

11
Table R-1: ANOVA of the Interaction Between the US Price and the Competitiveness Indexes

Source of variation Df Sum.Sq Mean.Sq F.value Pr..F.

Year (Pus,t × ωit) 27.00 2961.92 109.70 2.50 0.00

Country (Pus,t × ωit) 35.00 35895.29 1025.58 23.39 0.00

Interaction (Pus,t × ωit) 945.00 41440.70 43.85

Year (Pus,t × ωkt) 27.00 5.47 0.20 1.27 0.16

Country (Pus,t × ωkt) 35.00 118.74 3.39 21.29 0.00

Interaction (Pus,t × ωkt) 945.00 150.59 0.16

Year (Pus,t × ωjt) 27.00 364.08 13.48 2.55 0.00

Country (Pus,t × ωjt) 35.00 10702.92 305.80 57.92 0.00

Interaction (Pus,t × ωjt)) 945.00 4989.23 5.28

Note: The ANOVA decomposes the variability of each interaction term into its time (Year) and crosssection (Country) dimensions. The residual (Interaction) is the remainder not explained by the two included

dimensions. The ANOVA table shows for each of these components the degrees of freedom (Df), the explained

sum of squared residuals (Sum.Sq), the mean of the Sum.Sq, and an F-test that indicates whether the mean

of the different groups in Year and Country are statistically different.

12
Table R-2: Parameter Estimates and Hypotheses Tests Dropping one Country at a Time

Country βˆ IWM p-value βˆ Arm-D p-value.1 α3 Arm-D p-value.2 LM p-value

Argentina 0.04 0.04 0.03 0.12 0.01 0.07 0.29

Australia 0.04 0.02 0.03 0.11 0.01 0.01 0.03

Austria 0.04 0.02 0.02 0.14 0.01 0.01 0.05

Bulgaria 0.05 0.01 0.03 0.11 0.01 0.01 0.06

Brazil 0.05 0.01 0.03 0.09 0.01 0.01 0.06

Canada 0.04 0.03 0.02 0.16 0.01 0.01 0.05

Switzerland 0.04 0.02 0.02 0.14 0.01 0.01 0.05

Chile 0.04 0.04 0.02 0.23 0.01 0.01 0.04

China 0.04 0.02 0.03 0.13 0.01 0.01 0.05

Colombia 0.05 0.01 0.03 0.06 0.01 0.01 0.06

Spain 0.05 0.02 0.03 0.12 0.01 0.01 0.05

France 0.05 0.02 0.03 0.12 0.01 0.01 0.04

Greece 0.04 0.02 0.03 0.13 0.01 0.01 0.05

Hungary 0.05 0.01 0.03 0.10 0.01 0.01 0.06

Indonesia 0.04 0.02 0.02 0.14 0.01 0.01 0.05

India 0.04 0.02 0.03 0.13 0.01 0.01 0.05

Italia 0.05 0.02 0.03 0.12 0.01 0.01 0.05

Japan 0.05 0.01 0.03 0.09 0.01 0.01 0.04

Sri Lanka 0.05 0.01 0.03 0.09 0.01 0.01 0.05

Morocco 0.04 0.03 0.02 0.18 0.01 0.01 0.04

Madagascar 0.05 0.01 0.03 0.12 0.01 0.01 0.05

Mexico 0.04 0.02 0.02 0.16 0.01 0.01 0.05

New Zealand 0.04 0.03 0.02 0.16 0.01 0.02 0.08

Peru 0.05 0.01 0.03 0.09 0.01 0.01 0.06

Philippines 0.05 0.02 0.03 0.12 0.01 0.01 0.05

Poland 0.04 0.02 0.03 0.13 0.01 0.01 0.05

Portugal 0.04 0.02 0.03 0.13 0.01 0.01 0.04

Thailand 0.04 0.04 0.02 0.15 0.01 0.02 0.11

Turkey 0.04 0.02 0.02 0.14 0.01 0.01 0.05

Uganda 0.05 0.01 0.03 0.11 0.01 0.01 0.06

Uruguay 0.04 0.02 0.02 0.14 0.01 0.01 0.04

Venezuela 0.06 0.00 0.04 0.03 0.01 0.01 0.07

Vietnam 0.05 0.01 0.03 0.11 0.01 0.01 0.05

South Africa 0.05 0.01 0.03 0.11 0.01 0.01 0.06

Zambia 0.04 0.02 0.02 0.17 0.01 0.01 0.04

Zimbabwe 0.04 0.02 0.02 0.13 0.01 0.01 0.04

Note:The parameter estimates shown in the columns, as well as the LM comparing the restricted

(IWM) and unrestricted (A) models are estimates n times, where n is the number of countries.

Each time, one country is excluded. The exclude country is shown in the rows.

13
Table R-3: Bootstrap Corrected Parameters

Variable IWM A

ln(Ai,t−1), ˆγ0 0.864 *** 0.859 ***

ln(TMPit), ˆγ1 -0.101 -0.072

ln(P REit), ˆγ2 0.016 * 0.017 *

P

θii,t−1 ln GDPi,t−1, ˆγ3 -0.018 * -0.018

m

j6=i

θij,t−1 ln GDPj,t−1, ˆγ4 -0.001 ** -0.001 **

ln RERi,us,t−1, ˆγ5 0.006 0.005

ln(Pus,t−1), βˆ 0.043 ** 0.019

ω

3−yr−ma

i,t−1

, ˆγ6 0.001 *

ω

3−yr−ma

us,t−1

, ˆγ7 0.008

ω

3−yr−ma

j,t−1

, ˆγ8 0.001

ω

3−yr−ma

i,t−1

ln(Pus,t−1), ˆα1 -0.000

ω

3−yr−ma

us,t−1

ln(Pus,t−1), ˆα2 0.052

ω

3−yr−ma

j,t−1

ln(Pus,t−1), ˆα3 0.011 **

Note: Parameter estimates corrected using bootstrap algorithm by Everaert and Pozzi (2007).*** p ≤ 0.01,

** p ≤ 0.05, * p ≤ 0.10

14
Sri Lanka (0.04)

Japan (0.06)

Switzerland (0.09)

New Zealand (0.1)

Madagascar (0.18)

Chile (0.2)

Uruguay (0.22)

Portugal (0.34)

Greece (0.41)

Austria (0.53)

Peru (0.55)

Venezuela (0.62)

Vietnam (0.63)

Zambia (0.67)

Colombia (0.75)

Bulgaria (0.85)

Uganda (1.25)

Thailand (1.36)

Italia (1.55)

Hungary (1.65)

Zimbabwe (1.72)

Morocco (2.56)

Philippines (2.72)

Indonesia (3.42)

France (3.63)

Argentina (4)

Poland (4.02)

South Africa (4.14)

Spain (4.41)

Turkey (4.42)

Australia (4.86)

Canada (6.84)

Mexico (9.55)

Brazil (12.64)

China (27.37)

India (30.81)

USA (35.71)

barley maize millet oats rye sorghum

0.00.20.40.60.81.0

Figure R-1: Composition of the Area Devoted to Coarse Grains in Selected Countries.

Note: The percentages are based on harvested areas of individual crops averaged over 1992:2002.

Countries are ranked according to their total harvested area averaged during the same period. The

total area, in parentheses is in million hectares. Source: FAO.

15
1975 1980 1985 1990 1995 2000

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Index 1975=1

ROW Production

US Production

ROW Area

US Area

Figure R-2: Production and Harvested Area of Coarse Grains in the US and in the Rest of the

World (ROW).

Note: The four series are relative to 1975. Source: Allen and Lutman (2009).

16
0 5 10 15 20 25 30

21.0 21.2 21.4 21.6

Year (1975=1)

Log of total US exports (in bushels)

Figure R-3: US Exports of Coarse Grains are Volatile in the Short Run but Relatively Stable Over

Time.

Note: The straight line in the plot is obtained by regressing the total log of exports on a trend

variable. The obtained equation is (standard errors in parentheses): log(exportst) = 21.315(0.06)+

0.002T(0.003). Source: Allen and Lutman (2009).

17
Trade flows (imports < 0 and exports > 0) in million US$

Japan (0.06)

Mexico (9.55)

Spain (4.41)

Italia (1.55)

Portugal (0.34)

Poland (4.02)

Venezuela (0.62)

Colombia (0.75)

Brazil (12.64)

Peru (0.55)

Switzerland (0.09)

Greece (0.41)

Morocco (2.56)

Turkey (4.42)

Indonesia (3.42)

Philippines (2.72)

Chile (0.2)

Zambia (0.67)

India (30.81)

Sri Lanka (0.04)

Zimbabwe (1.72)

Uganda (1.25)

Uruguay (0.22)

Vietnam (0.63)

Madagascar (0.18)

Bulgaria (0.85)

New Zealand (0.1)

Austria (0.53)

South Africa (4.14)

Hungary (1.65)

Thailand (1.36)

China (27.37)

Canada (6.84)

Australia (4.86)

Argentina (4)

France (3.63)

−2500 −2000 −1500 −1000 −500 0 500 1000 1500

● ●

● ●

●●

●●

● ●

● ●

● ●

● ●

● ●

● ●

● ●

● ●

● ●

● ●

●●

●●

● ●

● ●

●

●●

●

● ●

●●

● ●

●●

● ●

● ●

● ●

● ●

●

●●

● ●

●●

● ●

●●

●●

Figure R-4: Imports, Exports, and Area of Selected Countries.

Note: The midpoints are averages 1975-2002 while the segments extend to the lower and upper

95% confidence interval of the annual distribution of trade flows. Countries are ordered by their

net trading position (exports - imports) using the averages 1975-2002. The trade data is in millions

US$. Sources: GTAP V6 inGehlhar (2005).

18
Argentina

Brazil

China

India

USA

% Change in Exports to Japan

−20

0 20 40 60

% Change in Coarse Grains Output

0

2

4

6

8 10

σ=2.6 σ=25 σ=50 σ=75 σ=100

Figure R-5: Supply Response and the Elasticity of Substitution.

Note: The upper panel shows, for selected countries, the percentage change in exports to Japan

following a 15% increase in the US industrial demand of US coarse grains under different values of

the elasticity of substitution between import sources, σM. The experiments were performed using

a partial equilibrium closure (income, factor prices, and output in the non-coarse grains sector

are held fixed) in the standard GTAP model (Hertel et al., 2007) using version 6 of the database

(Dimaranan, 2006). The lower panel shows, for the same experiment, the percentage changes in

output.

19
2.6 25 50 75 100

USA

Argentina

Elasticity of substitution σ

% Change in Exports to Japan

−40 −30 −20 −10

0

% Change in market price of coarse grains

0.85 1.29 1.04 0.89 0.80

Figure R-6: Market Shares and the Elasticity of Substitution.

Note: For the same change in prices, the exports of Argentina to Japan suffer a larger reduction

than those of the US due to the fact that the US has a much larger market share (74%) of the

Japanese market than Argentina (approx. 4%).

20
Growing concerns about global environmental issues have brought a renewed interest in the interdependence of global agricultural supply responses. A good example of this interest is given by

the debate surrounding the release of greenhouse gases (GHG) owing to indirect land use-changes

(iLUC) associated with biofuel expansion in the US and elsewhere. iLUC are the consequence of

adjustments in global agricultural production in response to higher crop prices resulting from an

increase in demand for biofuel crops in a given region. It turns out that, when the GHG emissions

of iLUC are taken into account, current-technology crop-based biofuels are likely to be more damaging than conventional fossil fuels (Searchinger et al., 2008; Hertel et al., 2010). Current iLUC

estimates are the subject of much dispute due to the uncertainties involved in their estimation

(Wang and Haq, 2008; ACE, 2009). A particularly contentious point is where these iLUC will take

place (Keeney and Hertel, 2009; Hertel et al., 2010). The geography of iLUC matters due to differences in yields, which determine how much land conversion is necessary to achieve a given level

of production, and land cover types, which determine the GHG emissions of the newly converted

land. Hence, a critical issue for better understanding the environmental effects of biofuel policies

is the geography of international agricultural trade.

In the agricultural economics literature there are two traditional paradigms guiding the modeling

of international trade flows. One, assumes the existence of an integrated world market (IWM)

cleared by a single price. This paradigm is widely used in agricultural policy analysis (Fabiosa

et al., 2008). Under this assumption, when the relative prices charged by different suppliers change,

countries easily adjust their trading patterns by shifting to the lowest cost provider. Such arbitrage

ensures a single world market price for each commodity. However, in the near term, in which debates

such as biofuels are framed, and for which the actual location of predicted effects is fundamental, it

is common to observe that trade patterns do not respond to changes in relative prices as would be

expected under the IWM hypothesis (Hillberry et al., 2005). On the contrary, because of the size

of initial trade flows, as well as preferences and tastes, we observe a significant degree of persistence

in trade flows, a phenomenon that we refer to here as the geography of trade. This view of the

world is typically implemented by using the so called Armington (1969) assumption which assumes

1
that goods are differentiated by their place of origin.

The main implication of the IWM hypothesis is that the origin of the biofuels impacts is

irrelevant. After correcting for border frictions and differences in supply elasticities, the assumption

of a single world price causes countries with the largest areas to have the greatest changes in land

use given a change in relative prices (more on this below). In contrast, and as we show below,

under the product differentiation hypothesis, the intensity with which supply and demand shocks

are transmitted to different regions varies with the degree of competition with the source of the

shock. The specific question that we ask is which of the two trade assumptions better explains the

historical response of coarse grains area across countries to changes in the US price market. The

significance of this research question extends beyond the iLUC of biofuels. Any national policy can

modify global land-use patterns in unintended ways, and so the ability to understand how supply

and demand shocks propagate throughout interdependent economies is important.

Our empirical strategy is to nest the two alternative models outlined above within a standard

land demand equation. Using three decades worth of country level data on harvested areas, grain

consumption, and bilateral trade flows, we test the hypothesis that the IWM view is an appropriate way of modeling the global transmission of a shock in the supply/demand of coarse grains.

Motivated by the literature examining the iLUC associated with US biofuel policy, we focus on

the transmission of price changes in the US coarse grains sector to the productive sectors of other

countries. Our findings reject the IWM hypothesis in favor of a model that explicitly takes into

account the geographic patterns of trade flows. We show that adoption of this alternative model

has important distributional implications in terms of the global area and production responses to

US biofuel policies.

Trade Assumptions and Global Land Use Predictions

Searchinger et al. (2008) offer the most influential study of global iLUC associated with biofuels

expansion. This study utilizes the FAPRI model of global agriculture which embeds the IWM

hypothesis. These authors find that out of the new 10,817 thousand hectares (26,729 ’000 acres)

needed to accommodate a 55.92 billion liter (14.77 billion gallons) increase in US corn ethanol,

2
21% are located in the US, 26% in Brazil, 10% in China, and 11% in India. Although the FAPRI

model does take into account cross-country differences in supply elasticities, as well as in price

transmission due to policies (Fabiosa et al., 2008), these results evidence that the greatest changes

are predicted to happen in the largest producing countries of the world, and that the pre-shock

trading behavior is largely irrelevant to these impacts. (While the US and Brazil are active traders,

China and India have historically been relatively closed to trade.)

As advanced in the introduction, observed trade patterns tend to be highly persistent over time

and space. Armington (1969) rationalizes this persistence by assuming that changes in quantities

(consumed, produced, and traded) of each product following a change in relative prices will depend

on the ease with which consumers can substitute among the different origins of a given good, as

captured by a constant elasticity of substitution (CES). Econometric estimates from Hertel et al.

(2007) based on the cross-country variability in bilateral trade costs give a CES value for coarse

grains of 2.6 (std. error 1.1), suggesting that coarse grains indeed do behave as differentiated products. This estimate is much lower than those obtained by the same authors for other commodities,

such as rice, wheat, and oilseeds. Drawing on this elasticity, a recent analysis of the importance of

the different assumptions employed in assessing the iLUC of biofuels by Keeney and Hertel (2009)

reveals that out of the land needed to satisfy an increase of 1 billion gallons of ethanol in the US,

56% is located in the US, 4% in Brazil, 6% in China, and a negligible amount in India. While

these results are not directly comparable to those of Searchinger et al. (2008), the strength of these

differences is enough to hint that the IWM and Armington models of competition lead to very

different conclusions about global iLUC changes1.

The GHG released from the iLUC of biofuels are a function of existing land cover (which in turn

determine GHG emissions) and agricultural yields (which determine the amount of land needed to

make up for the US output diverted to biofuel production). To the extent that both yields and land

cover widely vary across countries, the differences in the location of the predicted supply response

can translate into sharp differences in the size of the estimated GHG emissions. For example, while

Searchinger et al. (2008) calculated that current biofuels mandates, implemented over a period of

30 years, would need more than 100 years to recoup their carbon debt, Hertel et al. (2010) obtained

3
GHG values that suggest a 28 year payback period. A factor partially explaining these differences is

the use of different trade assumptions: IWM in the case of Searchinger et al. (2008) and Armington

in the case of Hertel et al. (2010).

Conceptual Framework

To see which of the two trade assumptions has better support in the historical data, this section

proposes a land demand equation that links land use decisions to the price of coarse grains and

then develops an alternative price transmission mechanism driven by the intensity of competition

in international markets. This model serves to formalize the differences between the IWM and the

Armington assumptions. We close by establishing the hypotheses to be tested.

The Derived Demand for Land

From a standard profit maximization problem, Shumway, Pope, and Nash (1984) show that, given

a set of crop choices and a fixed amount of land A ̄, the optimal demands for land are a function of

output and input prices, the total endowment of land, and a vector of exogenous shifters, Z. Our

analysis focuses on the cross-country land use decisions for a single crop composite of coarse grains

production, hence we assume that the optimal land demands apply at the country level. We index

countries by i, and denote land demands at time t by Ait. A lagged area term Ait−1, capturing

the sluggish adjustment due to costs of crop rotation, clearing of new land, and other year-to-year

adjustment costs, is added to the RHS of the land demand equation. We further assume that

farmers price expectations in the current year are based on the price of the previous year. The

relationship between optimal land allocations and its determinants is assumed to be log-linear,

given rise to the following relationship:

ln(Ait) = ln(Pit−1)β + ZitΓ (1)

where Pit−1 is a measure of the relative return to land capturing the price of coarse grains relative

to the prices of competing crops and inputs, β is the elasticity of area to changes in relative return

4
to lands, and Γ is the vector of parameters relating the rest of the exogenous variables contained

in matrix Z which is now augmented with the exogenous variables, lagged and total area, denoted

by ln(Ait−1) and ln(A ̄

i) respectively.

National prices Pit are not available over the time period in question2. The strategy is therefore

to proxy domestic relative returns to land in each country i with a world reference price denoted

by Pkt. Therefore, the relationship between domestic prices and the world price can be formalized

using:

Pit = RERiktPktτit (2)

where RERikt is the real exchange rate in local currency units (LCU/$) in country i, and τit is a

term (in power-of-the-tax form) that collects the myriad of transaction costs that foreign products

face when entering i’s market — these costs will be discussed in more detail below. Expression (2)

is a classical price transmission equation of the type used to study the Law of One Price which has

been widely tested in agricultural and commodity markets (e.g. Mundlak and Larson, 1992).

Substituting (2) into (1) yields the land response equation in terms of the one year lagged

reference price:

ln(Ait) = ln(Pk,t−1)β + [Zit, Zi,t−1]Γ (3)

where the matrix of exogenous covariates Z, and its corresponding parameter vector Γ, now include

the one year lagged real exchange rate and the trade cost terms from Equation (2).

Equation (3) is consistent with an integrated world market in which farmers uniformly respond,

other things held constant, to a unique world price. This equation is the basis of the econometric

estimation below. To accomplish the goal of contrasting the IWM and the Armington hypotheses

an alternative theory of international price formation based on product differentiation is next

developed.

International Trade and Price Transmission

At any point in time t, the disposition of domestically produced output of coarse grains in country

i, Xi, is either destined for the domestic market or for exports to country j. Thus, Xi can be

5
decomposed into Xi,j=i

, domestic consumption, and Xi,j6=i, exports originating in country i destined

to country j. There are n countries with potentially m = n − 1 foreign partners.

Following the widely used Armington model we have the following linearized version of a compensated CES demand facing country i in each market j (including i itself)3

:

xij = xj − σ (pij − pj ) (4)

where σ is the elasticity of substitution that we assume here to be equal for substitution between

domestic products and imports and among import sources. xij is the percentage change in exports

from country i to market j. xj is total change in demand in the market j, also known as the

expansion effect. pij is the percentage change in the price charged by country i’s suppliers in

market j and pj is the change in the average price level in market j. Collectively, the second term

in the RHS of Equation (4) is the substitution effect, capturing the extent to which, for example,

foreign suppliers displace US coarse grains as US prices rise in the wake of biofuels growth.

Note that the larger the elasticity of substitution σ, the smaller the difference in price changes

needed to cause a large swing in xij . In the limit, when a product is completely homogeneous such

that σ → ∞, the slightest deviation of the changes in country i’s prices, say, above the deviations

in the changes of the price index of country j, eliminates exporter i from j’s market. This case is

equivalent to the IWM hypothesis, whereby regions readily change their suppliers if prices deviate

from the single world price that clears the world markets.

With a finite σ, there is some stickiness in the trade relationship. In this case, the ability of

consumers to substitute away from a given supplier is a function, not only of the price elasticity

of demand (Armington, 1969, p.174-175), but also, of budget shares. To see why, we use the fact

that, at the optimal shares, the percentage change in the CES price index in market j equals the

weighted sum of the prices charged by each of its suppliers, using as weights, j’s budget shares4.

Algebraically, pj =

Pn

i

δijpij , where δij =

PijXij

PjXj

is the budget share that market j expends on

products from supplier i. Substituting the linearized price index pj in Equation (4), taking the

6
domestic price i out of the summation, and using the fact that (1 − δij ) = Pm

k6=i

, yields5:

xij = xj − σ





Xm

k6=i

δkj (pij − pkj )



 . (5)

In words, the percentage change in i’s sales to market j due to the substitution effects is a function

of the weighted sum of the changes in the prices charged by i relative to those charged by its

competitors (indexed by k), using as weights the market share of producer k in market j. For a

given change in relative prices that favors producer k, the larger the participation of k in market j

the more pronounced the decline of xij .

Summing Equation (5) over all the markets j, expanding terms and rearranging them, yields6

:

xi =

Xn

j

θijxj − σ

Xm

k

Xn

j

θijδkj (pij − pkj ). (6)

where θij =

PijXij

PiXi

is the revenue share that producer i obtains from its sales to market j. Now

the expansion effect (the first term in the RHS) is the revenue-share weighted sum of the growth

in each of the individual markets j served by producers from country i. The second RHS term,

or substitution effect, now includes i’s revenue shares. This substitution effect indicates that the

percentage change in country i’s total output will depend on the market share of its competitors

in the destination market (δkj ), and on the importance that the destination market has for i’s

total production of coarse grains (θij ). To focus on the effects of competition between the US and

producer i we can rewrite (6) in the following way:

xi =

Xn

j

θijxj − σ

Xn

j

θijδus,j (pij − pus,j ) − σ

Xm

k6=US

Xn

j

θijδkj (pij − pkj ). (7)

The first term in the RHS of Equation 7 can be further decomposed into country i’s ownexpansion as well as expansion in the markets that it sells to. In the second term, the summation

over n reflects that both i and the US compete in each other’s market. The third term captures

the effects of competition with other suppliers. Finally, rewrite Equation (7) to break out domestic

7
sales and imports as follows:

xi = θiixi +

Xm

j6=i

θijxj

− σ





nX−2

j6=(i,US)

θijδus,j (pij − pus,j ) + θi,usδus,us(pi,us − pus,us) + θiiδus,i(pii − pus,i)





+ i.

(8)

Here the first term in the RHS is the own-expansion effect, the second term is the expansion effect

from trading partners, the terms within the brackets respectively capture competition between the

US and country i in third markets, in the US market, and in country i’s own market, and the last

term captures the effects on output associated with competition with other suppliers.

In what follows, the product shares within the bracketed term in Equation (8) are referred

as to competition indexes and they are denoted by ωi = θiiδus,i, ωus = θi,usδus,us, and ωj =

Pn−2

j6=(i,US)

θijδus,j . A handy feature of these indexes is that they also capture bilateral trade barriers

that can be used to construct average trade costs such as those in Equation (2). This is explained

in Appendix B which shows that the ωj s capture the variability of trade costs across partners (and

over time), and the indexes ωi and ωus capture the barriers faced by the US when entering country

i and the barriers faced by country i when entering the US

To summarize, note that, to the extent that yields of coarse grains can be treated as exogenous,

changes in total output map one-to-one with changes in area. This means that area decisions are a

function of market growth (the expansion effect) and differences in relative prices (the substitution

effect), and as such, global land use decisions are a function of the relative importance of foreign

markets vis `a vis other competitors. Next we translate these concepts into testable hypotheses.

Hypotheses to be tested

To test whether the elasticity of harvested area to changes in the reference price varies with the

degree of competition in international markets, it is useful to note that both (3) and (8) propose

that changes in area harvested are a function of relative returns to land. The important difference

8
is that, while (3) postulates a unique channel of transmission between the reference price and the

area decisions, (8) proposes that the price transmission will depend on competition intensity, and

also on whether competition takes place in the domestic or international markets. To make the

integrated world market and Armington equations (3) and (8) compatible, we focus only on changes

in the US price, thus imposing on (8) the restriction pij = 0 for all i 6= US.

The empirical model is given by combining the ω indexes with the US price:

ln(Ait) =β ln(Pus,t−1)

+α1[ωi,t ln(Pus,t−1)] + α2[ωus,t ln(Pus,t−1)] + α3[ωj,t ln(Pus,t−1)]

+[Zit, Zi.t−1]Γ + ηit,

(9)

where β, α1, α2, α3, and Γ are parameters to be estimated. The error term ηit is a disturbance that is

further decomposed in a country-specific fixed effect (μi) and a remainder disturbance εit assumed to

be identically and independently distributed, centered around zero, uncorrelated over time, and with

constant variances. The matrices Zit, Zi,t−1 contain all the covariates from the structural equations

behind the empirical model (i.e., total land endowment A ̄

i

, lagged area ln(Ait−1), exogenous shifters

such as temperature and precipitation, real exchange rates ln(RERi,us,t−1), the expansion terms

from (8), θiitXit and Pm

j6=i

θijtXjt, and the ω indexes that also capture trade costs τit).

The null hypothesis is that geography does not matter. In other words, the integrated world

market hypothesis is an accurate depiction of how harvested areas around the world respond to US

price changes. The alternative hypothesis is that geographic patterns of trade influence planting

decisions in individual countries. Formally:

H0 : [α1, α2, α3] = 0

HA : [α1, α2, α3] 6= 0

(10)

Data and empirical implementation

Table 1 presents summary statistics for all the variables used in the regressions. The dependent

variable is the sum of the annual area harvested for barley, oats, maize, and sorghum for 35

9
countries for the period 1975-2002, sourced from FAO (2009). These countries, including the US,

cover approximately 75% (average 1975-2002) of the global harvested area of coarse grains, are

responsible for 90% of global exports (of which almost half come out of the US), and 64% of global

imports (average 1975-2002)7.

Key variables for this study are the competition indexes based on the market shares of exporters

in different importing countries. From the modeling framework, two types of shares are needed.

When a given country is seen as an exporter (and thus indexed by i) the relevant share is θijt: the

share of country i’s exports of coarse grains to country j in country i’s total coarse grains output at

time t — we will refer to this share as a sales share. When the same country is seen as an importer

(and thus indexed by j), the needed share is δijt, the share of coarse grains originating in country

i in the total consumption of coarse grains in country j at time t — a budget share.

In both cases, domestic sales are considered; thus, the first step is to obtain the own-sales

shares θiit and own-budget shares δjjt. Details about the procedures and sources used to build

these shares and the competition indexes discussed below are reported in Appendix B. Figure 1

plots the domestic budget shares θii (horizontal axis) against the domestic sales shares δjj . In the

upper left corner is Argentina, whose domestic needs are completely satisfied by domestic output,

but for which, at the same time, the domestic market is just a small fraction of total sales, leaving

large amounts of excess supplies for exports. Other countries with large productions and excess

supplies are Thailand, France, South Africa, and Hungary. In the opposite corner at the bottom

right is Japan. This country has a very large demand for coarse grains relative to production, and

its limited production goes entirely to its feed industry. As we move toward the upper right corner,

countries become self-sufficient and have fewer excess supplies to export, as in the case of India.

The market shares just described are used to calculate the competition indexes between a given

country i with the US in third markets (ωjt), in country i’s own market (ωit), and in the US market

(ωkt). These variables, bounded by [0, 1] (they are the product of two different shares), are shown

in the three panels of Figure 2, which shows, for each country, a box-plot describing the temporal

distribution of the different competition indexes. Starting with the leftmost panel, from bottom

to top, Argentina shows the largest median value (thick black bar inside the box) of the index of

10
competition with the US in third markets. Moreover, going from the minimum value (vertical bar

at the end of the left whisker) to the maximum value (vertical bar at the end of the right whisker),

it can be seen that the intensity of competition varies through time over a range spanning almost

20 percentage points.

The leftmost panel of Figure 2 shows that most countries do not compete significantly with

the US in third markets. The largest competitors (judging by the median values) are Argentina,

Thailand, Zimbabwe, Australia, France, and Germany. The second panel gives similar information,

but this time the interest is in competition with US imports in each country’s own market. Ranking

the countries using the medians, Japan’s coarse grains sector faces the highest competition of

imports from the US. In general, the US plays an active role as a supplier of several of the individual

markets. Finally, the third panel (rightmost), shows competition with the US in the US market.

Only for Canada, Argentina, and Chile, is this factor important, and even then, the value of the

index is low. The time variation of the indexes is a potential source of endogeneity (current market

shares may influence land decisions); thus, in the estimation, one-year lags of 3 year moving averages

are used8.

Another potential source of endogeneity bias is the presence of a lagged dependent variable on

the right hand side of (9). This is because the dependent variable Ait is a function of ηit = μi + εit,

where μiis a country specific fixed effect. As μi does not change over time, it turns out that the

lagged area term Ait−1 is also a function of μi, thus inducing correlation between Ait−1 and ηit.

Using a fixed effect estimator alleviates this problem by explicitly controlling for μi. However, the

underlying within-transformation is based on the differences in Ait−1 and εit from their respective

means. In calculating the mean value, εi., εit−1 is used, and thus, by construction, Ait−1 is correlated

with εi. (Nickell, 1981). The bias induced by correlation between Ait−1 and εi. decreases with the

time dimension of the dataset. Our panel consists of 35 countries with observations ranging from

7 to 25 years due to missing values of the RER; thus, it is sensible to assume the time dimension

of the panel to be fixed. To deal with this potential bias, several suggestions have been offered

(Baltagi, 2008, p.147-148). Our method of choice is a bootstrap correction due to Everaert and Pozzi

(2007). This is because, with the small sample in both the time and cross-sectional dimensions,

11
the bootstrap correction satisfactorily approximates analytical corrections and, as shown in the

Monte Carlo experiments of Everaert and Pozzi (2007), is more efficient than commonly used

GMM estimators.

To control for differences in total land endowment we include country-specific fixed effects.

These also capture cross-country differences in agricultural policies that are relatively sluggish over

time. As explained in Appendix B, the US price index is constructed using export prices and

exported quantities; weather is controlled for by including country-specific, growing-season9, mean

temperature (TMPit) and precipitation (P REit); changes in demand are considered by including

the GDP of both exporters and importers. Following the Armington specification in Equation 8,

the own and partner’ GDPs are weighted by revenue and bilateral market shares, respectively.

Sources for GDPs and the data and procedures employed in the construction of the real exchange

rates, are also detailed in Appendix B.

Th final equation to be estimated takes the following form:

ln(Ait) = μi + γ0 ln(Ai,t−1) + β ln(Pus,t−1)

+α1[ω

3−yr−ma

i,t−1

ln(Pus,t−1)] + α2[ω

3−yr−ma

us,t−1

ln(Pus,t−1)] + α3[ω

3−yr−ma

j,t−1

ln(Pus,t−1)]

+γ1 ln(TMPit) + γ2 ln(P REit) + γ3θii,t−1 ln GDPi,t−1 + γ4

Xm

j6=i

θij,t−1 ln GDPj,t−1

+γ5 ln RERi,us,t−1 + γ6ω

3−yr−ma

i,t−1 + γ7ω

3−yr−ma

us,t−1 + γ8ω

3−yr−ma

j,t−1

+εit.

(11)

Results and Discussion

To test the null hypothesis (geography of trade does not matter for production decisions), the

restrictions α1 = α2 = α3 = 0 are imposed on Equation (11). Then, both the restricted and

unrestricted models are estimated using least squares with country-specific dummy variables (LSDV

estimation), and a Lagrange Multiplier (LM) test is used to compare them.

The estimates of the restricted model are shown in the first column of Table 2 under the heading

IWM. For each variable, three values are stacked. The first is the LSDV parameter estimate. The

12
second is a traditional standard error calculated assuming that the regression residuals have a

constant variance (within and across countries) and are serially uncorrelated10. The third value in

each stacked group is a standard error robust to both heteroskedasticity and serial autocorrelation.

Interestingly, in many cases, the robust errors tend to overstate the degree of significance of the

parameter estimates relative to their traditional counterparts. This is particularly worrying in

the case of the unrestricted model A, for which the robust errors of ˆα2 and ˆα3 are less than half

the traditional ones. In the case of ˆα2 the robust standard errors make the coefficient appear

statistically significant. It is preferable to err on the conservative side of less significance, so the

rest of this discussion is based on the traditional standard errors.

Returning to the IWM regression shown in Table 2, the included regressors explain around 66%

of the temporal cross-country variation in harvested areas (see adjusted R2in the middle panel of

Table 2). The coefficient of the lagged area term (ˆγ0) is large and highly significant, evidencing the

persistence of harvested areas over time. The coefficient on temperature (ˆγ1) is negative and large,

but the precision of the estimates is low. The coefficient on precipitation (ˆγ2) is quite small and

insignificant. The terms associated with country size — own-GDP weighted by output consumed at

home (ˆγ3) and the revenue-share-weighted average of the GDPs of the trading partners (ˆγ4) — are

significant and negative. A possible explanation for this is that the income variables are capturing

the downward trend of global harvested areas as yields trend higher11. In line with expectations, a

depreciation of the real exchange rate (ˆγ5) has a positive effect on output (doubling the RER leads

to approx. 1% increase in harvested area). The elasticity of area with respect to the US price, βˆ is

statistically significant and plausibly sized. With a value of 0.04, this elasticity implies that if the

US price were to double, areas harvested in the non-US regions would increase by 4.4%.

The next column shows the unrestricted model labeled “A.” The two models are similar, with

two important exceptions. First, the coefficient on the real exchange rate lost its significance due

to a slight reduction in the size of the estimate. More importantly, the coefficient on the US price,

βˆ, is no longer significant. However, the interaction term between degree of competition overseas

(ωj ) and the US price is highly significant. This suggests that a price increase in the US will affect

areas harvested by the proportion 0.011 × ω

3−yr−ma

j,t−1

, and thus, the size of the national elasticity

13
is contingent on the importance of output of country i exposed to markets where the US is an

important supplier.

To investigate whether model A explains the temporal cross-country variability of areas harvested better than the IWM model, the residuals of the restricted model are regressed on all the

covariates of model A. The sample size and the R2 of this regression are used to compute an LM

statistic that in turn is distributed Chi-squared (Wooldridge, 2002, p. 186). The null hypothesis

is that the excluded parameters, α1, α2, α3, and the parameters on the ω terms, are uncorrelated

with the residuals of the restricted model, for if they are, the restricted parameter estimates are

inconsistent. The lowest panel of table 2 (row “LM test”) shows the probability (p-values) of rejecting this null hypothesis given that the excluded restrictions are indeed zero. This probability

is 3.7% in the comparison of models A and IWM, so the null hypothesis of the LM test is rejected

at the 5% level of significance. In other words, the inclusion of the interaction terms represents a

model improvement relative to the IWM model.

Before further exploring what is driving the apparent superiority of model A over the IWM

model, we assess how severe is the so called Nickell (1981) bias mentioned before. As indicated

we use a bootstrap correction due to Everaert and Pozzi (2007). The results for the restricted

(IWM) and unrestricted (A) models12 yield three general conclusions. First, the LSDV parameter

γˆ0 is severely biased downward in both models. Second, the rest of the parameter estimates are

virtually identical. Third, the pattern of significance based on the bootstrap sample confirms the

pattern of significance observed using traditional standard errors (as opposed to the robust ones),

thus supporting the earlier choice of using them as the basis of inference.

The most consequential finding of the bootstrap correction relates to the estimation of long run

elasticities, (1 − γ0)

−1β for the IWM model or its counterpart for the Armington model, which will

be evidently biased if the LSDV estimates are employed in their calculation. Pesaran and Zhao

(1998) point out that simply using the bootstrap corrected parameter will not solve the problem

due to the nonlinearities involved in the long run elasticity. They compare four different methods,

including a bootstrap correction and conclude that “none of the estimators seem to be effective

when the coefficient of the lagged dependent variable is around 0.8.” Due to this limitation, this

14
article will not further pursue the calculation of long run elasticities. Moreover, due to the similarity

between the bootstrap-corrected and the LSDV estimates, the rest of the discussion will continue

focusing on the latter.

In Table 2, a puzzling feature of model A is that, although the addition of the interaction terms

is an improvement over the restricted model, the exclusion restrictions — with parameters ˆγ7, ˆγ8,

αˆ1, and ˆα2 — are statistically zero. To investigate whether they are zero because of interactions

with the other price terms or simply because they do not add any additional explanatory power

to the restricted model, columns B, C, and D report regressions keeping one price interaction at

a time. Just as before, the lowest portion of Table 2 shows LM and LR tests for the pairwise

comparison of the IWM model against these models. This exercise gives evidence that neither

competition in country i’s own market (model B including ωi and its interaction with the US price)

nor competition with the US (model C including ωus interacted with the US price) improve the

IWM formulation (with a p-value of 0.085, the LM test rejects the IWM model only marginally in

the case of model B). In contrast, model D, which retains competition in third markets reiterates

the significance of the interaction term and also rejects, albeit in a weaker fashion, the IWM model.

The fact that βˆ is statistically insignificant in model A prompts the question of whether this

is because of multicollinearity with the interaction terms. To investigate this possibility, the lower

panel of Table 2 shows the variance inflation factors (VIF) of βˆ for all the estimated models. The

VIF indicates the proportion by which the variance of βˆ is inflated due to the addition of the

exclusion restrictions. In model IWM, the VIF is 1.016, indicating that there are no other variables

collinear with the US price term. When all the exclusion restrictions are added, the VIF jumps to

1.275, and as noted before, βˆ loses its significance. This is a relatively low VIF. If for example the

standard error of βˆ in model A were reduced by 30%, the parameter estimate would still not be

significant. In model B, the VIF reduces to 1.169, and βˆ regains its significance; however, in model

D, the VIF is lower (1.09), and βˆ is insignificant. This seems to reinforce the notion that, in these

regressions, higher VIFs are disconnected from the significance of βˆ.

The results discussed thus far suggest that only a reduced number of countries compete with the

US. We conducted a robustness test13 in which the restricted and unrestricted model are estimated

15
dropping one country at a time and found that the parameter values are virtually unchanged.

Regarding the LM test, we reject the IWM model in favor of the Armington specification in all

cases, except for the case where Argentina is dropped. This is not surprising given the large degree

of competition between Argentina and the US in third markets.

Implications

Are the differences in the prediction of harvested areas, at the national and global levels, large

enough to matter? Do the conclusions regarding area carry over to production levels? If so, does

this have any consequences for the estimates of the iLUC-induced GHG emissions? We address

these questions here.

One approach to answering this question would be to compare historical changes over the recent

biofuels boom period to predictions based on a model excluding the biofuels effect. However, to

do so would entail decomposing the price impact of biofuels from that of all the other forces at

work over this period, including weather, economic and population growth, etc. This is a daunting

task (Abbot, Hurt, and Tyner, 2008). Instead, we choose to focus on a natural experiment which

occurred in 1993, and which rivals the impact of biofuels in magnitude. Specifically, Babcock

(2007) reports that the year 1993 was a year of excess rain and no heat and as a consequence corn

production in the US fell significantly; according to USDA data, from 1992 to 1993: area harvested

of coarse grains fell by 14% (-5.46 million ha); production of coarse grains fell by 32% (corn output

fell from 9,476.7 to 6,337.7 million bushels — 240 to 160 million MT); exports of coarse grains fell

by 22% (corn exports decreased from 1,663.28 to 1328.32 million bushels — 41.58 to 33.21 million

MT); and the coarse grains index price increased by 15%.

To appreciate the effect of a 15% increase in the US price from 1992 to 1993, we use the data

values of 1994 (recall that producers look at 1-year lagged prices, so in our model the effects of a

price shock in 1993 are realized in 1994) and for each model, we predict two sets of harvested areas

by country. The first set of predictions uses the data as observed, and thus, captures the price

increase from 1992 to 1993. The second set of predictions assume that the US price did not change

between 1992 and 1993. For each country and model, the difference between these two predictions

16
yields an estimate of how much additional area is incorporated by a 15% increase in the US price,

relative to an scenario in which the US price does not change. Because these values are based on

model predictions, they inherit the uncertainty attached to the estimated parameters. We take

account of this uncertainty to bootstrap confidence intervals around the land use predictions14.

These confidence intervals, in turn, allow us to examine whether the mean values of the two sets

of predictions are statistically distinct.

Figure 3 plots the area predictions for the estimated IWM and Armington model. The countries

are sorted by the predicted changes in area. The thick dot represents the mean prediction while

the segments depict the 95% confidence interval. If the confidence intervals of the two models do

not overlap, we conclude that the model have statistically different predictions. Three conclusions

can be drawn from Figure 3. First, for 22 of the 35 countries, we find no significant difference

between the predictions from the IWM and the Armington model. Second, in 8 of the 13 countries

where we detect significant differences, the IWM model tends to predict larger changes in area

than the Armington model — in other words, the IWM predictions are biased upward. Note that

these countries include India, Brazil, and Mexico, which are large countries in terms of harvested

area. Conversely, for China, Canada, Argentina, and Australia, the IWM predictions are biased

downward. The three last countries, in particular, are large exporters with high yields. These

differences in the geographic pattern of response to US prices could well translate into differences

in global area changes, a question to which we now turn.

Summing each bootstrapped vector of predictions yields an average of 1,018,030 hectares for the

IWM model and an average of 985,436 hectares for the Armington model. The confidence intervals

around these predictions reveal that they are not statistically different. To see how this translates

into production, we combine country-level yields (index for coarse grains taken from FAO) with the

predicted harvested areas. The IWM predicts 2.66 million MT while the Armington model predicts

3.16 million MT, and this time, these means are statistically different. This suggests that for the

same amount of land, the Armington model predicts a larger quantity produced. Intuitively, if yields

were randomly distributed across countries, we should not expect differences in total production.

However, because the countries that are more productive are also the ones that are more exposed

17
to US prices in the international markets, the Armington model is predicting significantly larger

changes in production, for a given US price shock15. Alternatively, this implies that, for a given

reduction in US supplies to the world market, less area in the rest of the world must be converted

to “fill the gap”.

Conclusions

The analysis of indirect land use change owing to biofuels programs in the US and Europe has

become an important policy issue generating significant demand for agricultural economic analysis.

Large-scale economic models have been used for this task; however such models have resulted in

widely differing predictions of where the land-use changes will occur, partly, because of differences

in the treatment of the interaction between bilateral trade and supply behavior. This article

investigates which of the two competing views of this interaction — an integrated world market vs.

products differentiated by place of origin — has better grounding in the historical data.

We use a reduced form land demand equation that nests the two pricing mechanisms characterizing the afore-mentioned trade assumptions. The focus is on the changes in the harvested areas

of coarse grains triggered by changes in the US price of these products. We derive competition

indexes that combine the share of a country’s output in a given market with the importance of

the US as a supplier of that market. Using data for a cross section of countries representative of

global production and trade covering the period 1975-2002 we reject the integrated world market in

favor of the Armington model. Our main results are robust to the correction of the bias generated

by the presence of a lagged dependent variable, potential multicollinearity of price terms, and to

variations in the countries included in the sample.

The dominance of the differentiated products model has important consequences for the global

distribution of land response following a shock to the US price. Simple predictions using the

parameter estimates of the two competing models show that, allowing competition in third markets

leads to dramatic differences in the predictions of changes in area, especially for the largest producers

of the world. Moreover, the results highlight that by taking competition into account, the total

estimates of production of the two models are quite different due to differences in productivity

18
across countries. Our results support the notion that the geography of trade is an important

factor explaining the global distribution of agricultural production responses to national biofuels

programs.

19
Notes

1

In Section R-3 of the Reviewer’s Appendix, we report on the results of using the GTAP model to compare changes

in exports and output under the two sets of assumptions. The comparison reinforces the point made in this section

— however, we prefer to present here a comparison of published results.

2FAO has some data on domestic producer prices; however, the series are available only for limited periods of

time.

3The CES utility, the derivation of the CES demand in the Armington context, and other properties of the

Armington model are in Appendix A. The algebraic details of the derivation of the competition indexes discussed

below are in Section R-4 of the Reviewer’s Appendix. In the rest of this article, percentage changes are denoted using

the variable names in lower cases (i.e., xij =

dXij

Xi

).

4

Ibidem 3.

5See derivation details in Section R-4 of the Reviewer’s Appendix.

6

Ibidem 5.

7See Section R-1 in the Reviewer’s Appendix for a fuller discussion of the representativeness of this sample in

terms of area covered and international trade.

8

In Section R-5 of the Reviewer’s Appendix we present further evidence on the variance of these measures.

9We follow Lobell and Field (2007) in defining global growing seasons. See more details in Appendix B.

10To verify whether these two assumptions hold, the bottom panel of Table 2 shows the p-values of a BreuschPagan test for heteroskedasticity and a test for serial autocorrelation due to Wooldridge (2001, p.275). In general,

homoskedasticity is rejected at the 1% significance level, while the null hypothesis of non-autocorrelation cannot be

rejected (with the exceptions of models A and D, which will be discussed shortly). In principle, it would be natural

to fix the standard errors to be robust to the presence of heteroskedasticity. However, in panels with fixed T and

large N, the conventional White estimator is inconsistent (Stock and Watson, 2008), so it is advised to use errors that

are robust to both heteroskedasticity and serial autocorrelation, which are shown for each parameter underneath the

traditional standard errors.

11Documented in Section R-1 of the Reviewer’s Appendix.

12Results are available from the authors upon request (Section R-2 of the Reviewer’s Appendix). See original article

for details of the bootstrap correction.

13Results available from the authors upon request, and in section R-6 of the Reviewer’s Appendix

14See Appendix C for details

15Unfortunately, at the time of this writing there are not available (to us) GHG emission factors at the level of

detail required by our comparisons, but in light of this discussion, it seems plausible to expect that the distributional

effects associated with persistent patterns of trade reflect on global GHG estimates.

20
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23
Table 1: Descriptive Statistics

mean Std.Dev. min Q1 median Q3 max

Area (Mill Ha) 4.10 7.41 0.03 0.50 1.49 4.30 43.88

Temperature (C) 19.22 5.47 5.70 16.39 20.00 23.17 28.05

Precipitation (ml) 93.21 78.84 0.00 29.56 71.42 141.37 420.72

GDP (Billion 2000 US$) 274.06 640.44 2.12 27.89 87.86 256.08 4680.00

US Price (Index) 0.95 0.16 0.63 0.84 0.95 1.00 1.46

ωi 0.05 0.12 0.00 0.00 0.00 0.03 0.86

ωus 0.00 0.01 0.00 0.00 0.00 0.00 0.12

ωj 0.01 0.04 0.00 0.00 0.00 0.00 0.41

Note: Q1 and Q3 are the first and third quartile of the distribution of each variable. The terms ω

are competition indexes between any country i in the sample and the US in country i’s own market,

the US market, or in third markets (j).

24
Table 2: Regression Results, Diagnosis, and Comparisons

IWM A B C D

ln(Ai,t−1, ˆγ0 0.787 0.783 0.783 0.789 0.784

(0.021)*** (0.021)*** (0.021)*** (0.021)*** (0.021)***

(0.040)*** (0.040)*** (0.039)*** (0.040)*** (0.041)***

ln(TMPit), ˆγ1 -0.111 -0.091 -0.087 -0.111 -0.116

(0.083) (0.083) (0.083) (0.083) (0.083)

(0.065)* (0.066) (0.065) (0.065)* (0.066)*

ln(P REit), ˆγ2 0.015 0.016 0.015 0.015 0.016

(0.010) (0.010) (0.010) (0.010) (0.010)

(0.011) (0.010) (0.011) (0.011) (0.010)

θii,t−1 ln GDPi,t−1, ˆγ3 -0.025 -0.025 -0.026 -0.025 -0.024

(0.010)** (0.012)** (0.010)** (0.010)** (0.012)**

P

(0.009)*** (0.013)* (0.009)*** (0.009)*** (0.013)*

m

j6=i

θij,t−1 ln GDPj,t−1, ˆγ4 -0.001 -0.001 -0.001 -0.001 -0.001

(0.001)** (0.001)*** (0.001)*** (0.001)** (0.001)**

(0.001)* (0.001)** (0.001)** (0.001)* (0.001)*

ln RERi,us,t−1, ˆγ5 0.009 0.008 0.007 0.009 0.010

(0.005)* (0.005) (0.005) (0.005)* (0.005)*

(0.007) (0.007) (0.007) (0.007) (0.007)

ln(Pus,t−1), βˆ 0.044 0.021 0.048 0.035 0.026

(0.020)** (0.026) (0.024)** (0.021)* (0.022)

(0.024)* (0.021) (0.023)** (0.024) (0.024)

ω

3−yr−ma

i,t−1

, ˆγ6 0.001 0.001

(0.001)** (0.001)*

(0.000)*** (0.000)***

ω

3−yr−ma

us,t−1

, ˆγ7 0.006 0.007

(0.010) (0.010)

(0.006) (0.006)

ω

3−yr−ma

j,t−1

, ˆγ8 0.001 0.001

(0.002) (0.002)

(0.001) (0.001)

ω

3−yr−ma

i,t−1

ln(Pus,t−1), ˆα1 -0.001 -0.001

(0.002) (0.002)

(0.002) (0.002)

ω

3−yr−ma

us,t−1

ln(Pus,t−1), α2 0.050 0.057

(0.035) (0.035)

(0.016)*** (0.012)***

ω

3−yr−ma

j,t−1

ln(Pus,t−1), ˆα3 0.011 0.012

(0.005)** (0.005)**

(0.002)*** (0.002)***

N 894.000 894.000 894.000 894.000 894.000

SSR 8.501 8.373 8.454 8.468 8.444

Adj R2 0.656 0.658 0.657 0.656 0.657

Log likelihood 812.488 819.250 814.958 814.240 815.482

VIF of βˆ 1.016 1.275 1.169 1.045 1.090

Heteroskedasticity (p-values) 0.000 0.002 0.000 0.000 0.000

Autocorrelation (p-values) 0.129 0.084 0.131 0.104 0.097

LM test (p-values) 0.000 0.037 0.085 0.174 0.051

LR test (p-values) 0.000 0.035 0.085 0.173 0.050

Note: The dependent variable is the log of annual area harvested in each country. The number of years included for each

country vary between 7 up to a maximum of 28 (1975-2002). Standard errors, traditional and robust to heteroskedasticity and

serial autocorrelation of general form (Stock and Watson, 2008) are underneath each parameter estimate. The middle panel

presents some measures of goodness of fit. The lowest panel is a diagnosis of the regression. First, the variance inflation factor

(VIF) of the US price coefficient is presented. Then, the last four rows show the probability (p-values) of not rejecting the

following null hypotheses: 1) the LSDV residuals are homoskedastic (Breusch-Pagan test for heteroskedasticity); 2) the LSDV

residuals are serially uncorrelated (test for short panels by Wooldridge (2001, p.275)); and 3) the omitted terms in the “Base”

model but present in models A to D add no explanatory power to the former equation. These tests are a Lagrange Multiplier

(LM) distributed Chi-square..

*** p ≤ 0.01, ** p ≤ 0.05, * p ≤ 0.10

25
0.5 0.6 0.7 0.8 0.9 1.0

0.0 0.2 0.4 0.6 0.8 1.0

Share of the domestic market in total sales (θii)

Domestic budget share δjj

ARG AUS

AUTBGR

BRA

CAN

CHE CHL

CHN

COL

ESP

FRA

GRC

HUN

IDN

IND

ITA

JPN

LKA

MAR

MDG

MEX

NZL

PER

PHL

POL

PRT

THA

TUR

UGAURY

VEN

VNM

ZAF

ZMB

ZWE

Figure 1: The Ability of Domestic Production to Supply Domestic Markets.

Note: The shares are averages over the period 1975-2002.

26
ARG

AUS

AUT

BGR

BRA

CAN

CHE

CHL

CHN

COL

ESP

FRA

GRC

HUN

IDN

IND

ITA

JPN

LKA

MAR

MDG

MEX

NZL

PER

PHL

POL

PRT

THA

TUR

UGA

URY

VEN

VNM

ZAF

ZMB

ZWE

0.000.050.100.150.200.250.30

Third Markets (ωjt)

ARG

AUS

AUT

BGR

BRA

CAN

CHE

CHL

CHN

COL

ESP

FRA

GRC

HUN

IDN

IND

ITA

JPN

LKA

MAR

MDG

MEX

NZL

PER

PHL

POL

PRT

THA

TUR

UGA

URY

VEN

VNM

ZAF

ZMB

ZWE

0.00.10.20.30.40.5

Own Market (ωit)

ARG

AUS

AUT

BGR

BRA

CAN

CHE

CHL

CHN

COL

ESP

FRA

GRC

HUN

IDN

IND

ITA

JPN

LKA

MAR

MDG

MEX

NZL

PER

PHL

POL

PRT

THA

TUR

UGA

URY

VEN

VNM

ZAF

ZMB

ZWE

0.000.010.020.03

The US Market (ωkt)

Competition with the U.S. in...

Figure 2: Competition of the Sample Countries with the US in Third Markets, Their Own Markets,

and US Markets.

Note: The box-plots show the distribution of the indexes over 1975-2002. The units of the indexes

are between zero and unity.

27
Hectares

Sri Lanka Japan

Switzerland

New Zealand

Madagascar Uruguay

Chile

Venezuela Portugal

Peru

Greece

Zambia

Austria

Colombia

Bulgaria

Uganda Italy

Thailand

Hungary

Zimbabwe

Morocco

Indonesia

Philippines

Spain

Turkey

Poland

South Africa

France

Australia

Mexico

Brazil Argentina

Canada

India

China

0 50000 100000 150000 200000 250000

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IWM

Armington

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Figure 3: Confidence intervals (95%) for the differences between the mean harvested areas predicted

by the IWM and the Armington model, by country.

28
Appendices

A The Armington specification of trade flows

Start with some notation. Exporting countries are indexed by i, markets are indexed by j. There are

n countries trading among themselves. Armington (1969) assumes separable utilities for different

groups of goods. Goods are assumed to be differentiated by place of origin. Given changes in relative

prices, consumers substitute among origins according to an elasticity of substitution assumed to be

invariant to the share of each good in total consumption and equal across countries. This allows

aggregating total consumption of coarse grains in market j (Xj ) using a constant elasticity of

substitution (CES) function:

Xj =

 Xn

i

BijX

ρ

ij!1

ρ

, ρ = 1 −

1

σ

(A-1)

where Bij is a constant bilateral preference weight, σ is the elasticity of substitution and Xij are

market j’s imports from each origin i, including itself; thus, the summation above includes all n

countries.

Maximization of (A-1) subject to the budget constraint implied by the budgetary allocation to

coarse grains (Ej ) yields bilateral demands of the form:

Xij =

Bσ

ijEjP

−σ

ij

Pn

i Bσ

ijP

1−σ

ij

(A-2)

Substituting these Marshallian or uncompensated demands in the CES aggregate (A-1) yields the

indirect utility function. Solving the indirect utility function for Ej yields the expenditure function:

E(Pij, Xj ) = X

i

B

σ

ijP

1−σ

ij ! 1

1−σ

Xj (A-3)

Where the first term on the right hand side is the CES price index Pj . Substituting E(Pij, Xj )

for Ej in (A-2) and using the definition of the CES price index yields the Hicksian or compensated

29
CES demands used in the text:

Xij = B

σ

ijXj



Pij

Pj

−σ

(A-4)

A.1 The CES price index as a weighted sum of bilateral price changes

Given the optimal demands (A-4), the CES price index Pj can be also expressed as a linear function

of bilateral prices Pij . This function must satisfy the condition that the value of the marginal utility

of a given product equals that product’s price (Armington, 1969, p.165). Formally:

Pj



∂Xj

∂Xij 

= Pij , ∀i. (A-5)

Meanwhile, given that (A-1) is linearly homogeneous, Euler’s theorem allows decomposing Xj as:

Xj =

Xn

i

∂Xj

∂Xij

Xij . (A-6)

Solving (A-5) for the price ratio Pij

Pj

, and substituting into (A-6) yields:

Xj =

Xn

i

Pij

Pj

Xij , (A-7)

which we can solve again for Pj to obtain:

Pj =

Xn

i

Xij

Xj

Pij . (A-8)

So, the price index Pj is the sum of the bilateral prices Pij weighted by the share of optimal

bilateral demand Xij on total import demand Xj . Totally differentiating (A-8) gives:

dPj =

Xn

i

Xij

Xj

dPij +

Xn

i

d



Xij

Xj



Pij (A-9)

which, after multiplying the first and second RHS terms by Pij/Pij and XijXj/XijXj , respectively,

30
and dividing trough by Pj becomes:

dPj

Pj

=

Xn

i

PijXij

PjXj

dPij

Pij

+

Xn

i

PijXij

PjXj

d



Xij

Xj





Xij

Xj

 . (A-10)

The second RHS term in (A-10) is zero because is a weighted average of percentage changes in

market shares. Letting δij =

PijXij

PjXj

, and using lowercases to denote percentage changes, Expression (A-10) becomes:

pj =

Xn

i

δijpij . (A-11)

which is the expression used in the main text.

B Data description

B.1 Climate variables

The climate variables are calculated aggregating the climate data of the Climate Research Unit

(Mitchell and Jones, 2005) from the grid cell level (30 min resolution) up to the national level using

as weights the production value of each grid cell calculated using Monfreda, Ramankutty, and

Foley (2008)’s productivity data and FAO (2009) prices. These growing seasons are the contiguous

months within the growing seasons for the major growing regions (Lobell and Field, 2007). These

are July-Aug. (maize), May-Aug. (barley) and Aug. (sorghum). Besides these crops, millet, oats,

and rye are included to better match the GTAP trade category “gro.” Also for the aggregated

“gro,” with growing seasons differing across crops, the monthly climate value of each grid-cell is

weighted by the fraction of the production value corresponding to the crops grown in the grid-cell

during that month.

B.2 Shares and competition indexes

From the modeling framework, two types of shares are needed. When a given country is seen as an

exporter (which is indexed by i) the relevant share is θijt, the share of country i’s exports of coarse

grains to country j in country i’s total coarse grains output at time t. When the same country is

31
seen as an importer (and thus indexed by j), the needed share is δijt, the share of coarse grains

originating in country i in the total consumption of coarse grains in country j at time t. In both

cases, domestic sales are considered; thus, the first step is to obtain the shares θiit and δjjt given

by:

θiit =

PiitXiit

PitYit

, δjjt =

PjjtXjjt

PjtXjt

(B-1)

Obtaining data on prices or value terms for total output, consumption, and domestic sales

proved difficult without compromising the country and time coverage of the sample. Fortunately,

the equality of the price terms in the numerators and denominators of the shares in (B-1) allows

the obtaining of shares using quantity values, which are readily available from FAO (2009). A small

difficulty is that it would not be appropriate to add quantities of corn, sorghum, etc., to get the

aggregated coarse grains: the empirical choice was to calculate the own-country shares using data

on maize, which for most countries, comprises the bulk of produced and traded coarse grains.

This implies that the bilateral share θijt can be decomposed in the following way:

θijt =

PijtXijt

PitXit

≡

P

j6=i PijtXijt

PitXit P

PijtXijt

j6=i PijtXijt

≡ (1 − θiit)Vijt (B-2)

where:

(1 − θiit) =

P

j6=i PijtXijt

PitXit

(B-3)

is the proportion of country i’s output that goes to foreign markets, and

Vijt = P

PijtXijt

j6=i PijtXijt

(B-4)

is the share of country i’s exports to country j in country i’s total coarse grains exports. The data

on Vijt comes from the GTAP database, Version 6 (Gehlhar, 2005).

Likewise, δijt can be decomposed and rewritten as follows:

δijt =

PijtXijt

PjtXjt

≡

P

i6=j PijtXijt

PjtXjt P

PijtXijt

i6=j PijtXijt

≡ (1 − δjjt)Vijt (B-5)

32
where Vijt was defined before, and (1 − δjjt) is the proportion of country j’s consumption that

comes from overseas.

The shares θijt and δijt are used to obtain the competition indexes:

ωj =

Pn−2

j6=(i,k)

θijδkj

ωk = θikδkk

ωi = θiiδki

(B-6)

which stand for competition between country i and country k in country j’s market, in k’s market

and in country i’s market.

These indexes also capture bilateral trade barriers that can be used to construct average trade

costs such as those in Equation (2). This can be seen by writing the price that country i charges

in market j as the product of the market price in i times bilateral trade cost τij , so Pij = Piτij .

τij can be thought of as a comprehensive measure of tariffs, sanitary barriers, shipping costs, etc.

This allows rewriting ωj as:

ωj =

nX−2

j6=(i,US)

θijδus,j =

nX−2

j6=(i,US)

PijXij

PiXi

Pus,jXus,j

PusXus

=

nX−2

j6=(i,US)

τijXij

Xi

τus,jXus,j

Xus

(B-7)

which shows that the ωj s capture the variability of trade costs across partners, and although the

subscript t is omitted to avoid clutter, over time. By the same logic, the indexes ωi and ωus capture

the barriers faced by the US when entering country i and the barriers faced by country i when

entering the US For ωus:

ωus = θi,usδus,us =

Pi,usXi,us

PiXi

Pus,usXus,us

PusXus

=

τi,usXi,us

Xi

Xus,j

Xus

(B-8)

where τi,us are the barriers faced by suppliers in country i when entering the US market, and

τus,us = 1. Likewise, for For ωi:

ωi = θi,iδus,i =

Pi,iXi,i

PiXi

Pus,iXus,i

PusXus

=

Xi,i

Xi

τus,iXus,i

Xus

(B-9)

33
where τus,i are the barriers faced by US suppliers when entering market i, and τi,i = 1.

B.3 US price index of coarse grains

The US price index uses export quantity weights to combine price information obtained from USDA

(2009) on the following markets:

• Corn, No. 2, Yellow at Gulf ports, Louisiana Gulf, barge delivered IN $ per bushel

• Oats, No. 2 heavy white at Minneapolis IN $ per bushel

• Barley, No. 2 or better, feed at Market: Duluth IN $ per bushel

• Sorghum, No. 2, Yellow at Gulf ports, Louisiana Gulf, barge delivered IN $ per cwt

The period covered is 1975-2002.

B.4 Macroeconomic variables

The data on GDPs are in 2000 US$ and come from The World Bank (2009). The real exchange

rates (RERit) denominated in dollars and based on the year 2000 are constructed using consumer

price indexes The World Bank (2009), and nominal exchange rates from the Penn World Tables

(Heston, Summers, and Aten, 2006) using the formula:

RERit =

NERit

NERi,2000

CP Ius,t

CP Ii,t

(B-10)

C Bootstrap algorithm

The specifics of the bootstrap are as follows:

• Consider the following generalization of either the IWM or the Armington regression model:

log(A) = ΓXˆ + ˆε (C-1)

34
where log(A) is the vector of areas harvested by country in 1994, Γˆ is the vector of parameter

estimates of either model, X is the matrix of regressors in 1994, and ˆε are the estimated

residuals. Fitted values are defined by log(dA) = ΓXˆ .

• Obtain R random samples with replacement of the vector of residuals ˆε and denote each

sample by ˆε

r with r = 1, ..., R.

• Get R bootstrapped vectors of the dependent variable log(A)

r = log(dA) + ˆεr

.

• Regress each vector log(A)

r on X to get the rth vector of parameter estimates Γˆr

• Using the values of X for 1994, calculate a vector of R predictions using log(dA)

r = ΓˆrX1994;

these predictions incorporate the weather shock described above. Then, reduce the US price

in 1994 by 15% to get the matrix X∗, and obtain R vectors of predictions log(dA)

∗r = ΓˆrX∗

1994;

these predictions assume that were not changes between 1992 and 1993.

• So for each country and model we have 2 sets of R predicted land values: one with the US price

shock and another without it. For each replica r we compute the difference between these

two predictions, thus getting the R estimates of the additional harvested area associated with

an increase in the US price. This distribution of additional harvested areas allows calculating

means and confidence intervals for each model.

35