# Geography Matters: International Trade Patterns and the Indirect Land Use Effects of Biofuels

Nelson Villoria 1 

### Thomas Hertel December 30, 2009

1 Corresponding 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.eduAbstract

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 thatcorn 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 1decisions 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 + βx t + Dη + ε = W δ + Dη + ε (R-1)
for i = 1 , ..., N (cross-sectional dimension) and t = 2 , ..., T (time dimension) and where yt is the dependent variable, x t is an explanatory variable, η are fixed effects, and ε i an error term, the idea is to get a correction of the biased vector parameter δ :

ˆ δ = ( W 0 AW ) − 1 A y (R-2)
where A (...) is an indempotent transformation matrix that eliminates the individual effects η . We know that ˆ δ is a biased estimator fpr δ , i.e.
E ( ˆ δ ) = Z ∞

−∞ zf ˆ δ ( z ) dz 6 = δ, (R-3) From (R-3) it is clear that  ̄ δ is an unbiased estimator for δ if it satisfies:

ˆ δ = lim J →∞ 1 J J X j =1 b δ ∗ 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 ˆ δ 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)
− 1 D 0 ( y − W  ̃ δ ) and the residuals  ̃

ε = y − W  ̄ σ − D  ̃ η . 2. Choose the number of bootstrap samples B , and proceed as follows in bootstrap 3sample 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 = W b  ̃ δ + D  ̃ η +  ̃ ε b where W b = ( y b

− 1 , x ) and with initialization y b

i 1 = yi 1 . So we condition on the initial values yi 1 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 P B

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 ˆ δ , i.e.
ω = ˆ δ

−  ̃ 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 ) = ˆ δ

−  ̃ 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) = ˆ δ
. 

### 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
1 The 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. 4exports. 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

5upper 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 : X ij = B σ o ij X j  P ij P j  − σ o
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 ). X ij are exports from country i to market j , Bij is a constant preference weight, X j is total demand in the market j , P

ij is the price charged by country i ’s suppliers in market j , and P j is the average price level in market j
. The analysis of changes in X ij 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., x ij = dXij Xi ):

x ij = xj − σo (pij − pj ) (R-5) The first term represents the growth of the overall import market for X ij . The second represents the percentage change in X ij ’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
2 For 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. 3 The derivation of the CES demand in the Armington context and other properties of the Armington model are back in Appendix A. 6swing in x ij . 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 X i is either destined for the domestic market or for exports; from now on, these markets are indexed by j . Thus, X i can be decomposed into X i,j = i , domestic consumption, and X ij , exports originating in country i destined to country j . There are n countries with potentially m = n − 1 foreign partners. Therefore:
X i = n X j X ij , i ∈ j (R-6) To guide the estimation below, some structure on how the X ij 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:
x ij = xj − σ (pij − n X k δkj p kj ) (R-7) Taking the domestic price i out of the summation yields:

x ij = xj − σ 

 pij (1

− δij )

− m

X k 6 = i δkj p kj   (R-8) using the fact that (1

− δij ) = P m k 6 = i δkj , (R-8) is further simplified as:

x ij = xj − σ 

 m X k 6 = i δkj (pij − p kj ) 

 . (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 X ij — a fact that reinforces the discussion of the previous
7section.

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

x i = n X j θij xj − σ n

X j θij   m X k 6 = i δkj (pij − p kj ) 

 , (R-10)

where θij = P ij Xij P i Xi 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:

x i = n X j θij xj − σ m

X k n X j θij δkj (pij − p kj )

. (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:

x i = n X j θij xj − σ n

X j θij δus,j (pij − pus,j )

− σ m X k 6 = US n X j θij δkj (pij − p kj )

. (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.

8This entails rewriting (R-12) as:

x i = θii x i + m

X j 6 = i θij xj

− σ   n − 2 X j 6 =( i,US ) θij δus,j (pij − pus,j ) + θi,us δus,us (pi,us − pus,us ) + θii δus,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 α i ( 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

9instance, the variance of the interaction ln( P ust ) × 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 ω s, 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 ω k 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 — ˆ β from the IMW and A models and α 3 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 ˆ β of the IWM model remains statistically significant ( p -values < 0
. 05) at roughly 0.04. Next, the elasticities from the Armington-D model, ˆ β and ˆ α 3 are presented along with their significance level. In general, it does not matter which country is dropped; ˆ β loses its statisticalsignificance when the interaction term involving competition with the US is added to the regression. Likewise, the elasticity estimated using the interaction term, α 3 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”).

10Finally, 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 ( α 1 - α 3 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

11Table 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 ( P

us,t × ω it ) 27.00 2961.92 109.70 2.50 0.00 Country ( P

us,t × ω it ) 35.00 35895.29 1025.58 23.39 0.00 Interaction ( P

us,t × ω it ) 945.00 41440.70 43.85 Year ( P

us,t × ω kt ) 27.00 5.47 0.20 1.27 0.16 Country ( P

us,t × ω kt ) 35.00 118.74 3.39 21.29 0.00 Interaction ( P

us,t × ω kt ) 945.00 150.59 0.16 Year ( P

us,t × ωjt ) 27.00 364.08 13.48 2.55 0.00 Country ( P

us,t × ωjt ) 35.00 10702.92 305.80 57.92 0.00 Interaction ( P

us,t × ωjt )) 945.00 4989.23 5.28Note: 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.

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

β IWM p-value ˆ

β Arm-D p-value.1 α 3 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.

13Table R-3: Bootstrap Corrected Parameters Variable IWM A ln( A i,t

− 1 ), ˆ

γ0 0.864 *** 0.859 *** ln( TMP

it ), ˆ γ 1 -0.101 -0.072 ln( P REit ), ˆ

γ2 0.016 * 0.017 * θ ii,t

− 1 ln GDP

i,t

− 1 , ˆ γ3 -0.018 * -0.018 P m j 6 = i θ ij,t

− 1 ln GDP j,t

− 1 , ˆ γ4 -0.001 ** -0.001 ** ln RERi,us,t

− 1 , ˆ

γ5 0.006 0.005 ln( P us,t

− 1 ), ˆ β 0.043 ** 0.019 ω 3

− yr − ma i,t

− 1 , ˆ

γ6 0.001 * ω 3

− yr − ma us,t

− 1 , ˆ

γ7 0.008 ω 3

− yr − ma j,t

− 1 , ˆ

γ8 0.001 ω 3

− yr − ma i,t

− 1 ln( P

us,t

− 1 ), ˆ α 1 -0.000 ω 3

− yr − ma us,t

− 1 ln( P

us,t

− 1 ), ˆ α 2 0.052 ω 3

− yr − ma j,t

− 1 ln( P

us,t

− 1 ), ˆ α 3 0.011 ** Note: Parameter estimates corrected using bootstrap algorithm by Everaert and Pozzi (2007).*** p ≤ 0
. 01, ** p ≤ 0
. 05, * p ≤ 0
. 10

14Figure 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.

15Figure 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).

16Figure 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 ( exports t ) = 21

. 315(0

. 06)+ 0
. 002 T (0

. 003). Source: Allen and Lutman (2009).

17Figure 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).

18Figure 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.

19Figure 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%).

20Growing 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 emissionsof 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 takeplace (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
1that 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, grainconsumption, 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,
221% 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 coarsegrains 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 changes 1

. 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

3GHG 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 A it . A lagged area term A it

− 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( A it ) = ln( P

it

− 1 ) β + Z it Γ (1)
where P

it

− 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
4to 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( A it

− 1 ) and ln(  ̄

A i ) respectively. National prices P it are not available over the time period in question 2 . The strategy is therefore to proxy domestic relative returns to land in each country i with a world reference price denoted by P kt . Therefore, the relationship between domestic prices and the world price can be formalized using: P it = RERikt P

kt τ it (2) where RERikt is the real exchange rate in local currency units (LCU/$) in country i , and τ it 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( A it ) = ln( P k,t

− 1 ) β + [ Z it , Z i , 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 , X i , is either destined for the domestic market or for exports to country j . Thus, X i can be

5decomposed into X i,j = i , domestic consumption, and X i,j 6 = 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 :

x ij = 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. x ij 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 x ij . 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 shares 4

. Algebraically, pj = P n i δij pij , where δij = P ij Xij P j X j is the budget share that market j expends on products from supplier i . Substituting the linearized price index pj in Equation (4), taking the

6domestic price i out of the summation, and using the fact that (1

− δij ) = P m k 6 = i , yields 5 :

x ij = xj − σ 

 m X k 6 = i δkj (pij − p kj ) 

 . (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 x ij . Summing Equation (5) over all the markets j , expanding terms and rearranging them, yields 6 :

x i = n X j θij xj − σ m

X k n X j θij δkj (pij − p kj )

. (6)

where θij = P ij Xij P i Xi 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:

x i = n X j θij xj − σ n

X j θij δus,j (pij − pus,j )

− σ m X k 6 = US n X j θij δkj (pij − p kj )

. (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

7sales and imports as follows:

x i = θii x i + m

X j 6 = i θij xj

− σ   n − 2 X j 6 =( i,US ) θij δus,j (pij − pus,j ) + θi,us δus,us (pi,us − pus,us ) + θii δus,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 = θii δus,i , ωus = θi,us δus,us , and ωj = P n − 2 j 6 =( i,US ) θij δus,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

8is 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( A it ) = β ln( P

us,t

− 1 ) + α 1 [ωi,t ln( P

us,t

− 1 )] + α 2 [ωus,t ln( P us,t

− 1 )] + α 3 [ωj,t ln( P us,t

− 1 )] +[ Z it , Z i
. t

− 1 ] Γ + ηit , (9)

where β , α 1 , α 2 , α 3 , and Γ are parameters to be estimated. The error term ηit is a disturbance that is further decomposed in a country-specific fixed effect ( μ i ) and a remainder disturbance ε it assumed to be identically and independently distributed, centered around zero, uncorrelated over time, and with constant variances. The matrices Z it , Z i,t

− 1 contain all the covariates from the structural equations behind the empirical model (i.e., total land endowment  ̄ A i , lagged area ln( A it

− 1 ), exogenous shifters such as temperature and precipitation, real exchange rates ln( RERi,us,t

− 1 ), the expansion terms from (8), θiit X

it and P m

j 6 = i θijt X

jt , and the ω indexes that also capture trade costs τ it ). 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:
H 0 : [α 1 , α 2 , α 3 ] = 0 H A : [α 1 , α 2 , α 3 ] 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
9countries 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 δ jjt . 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 δ jj . 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 ( ω kt ). 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

10competition 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 used 8

. 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 A it is a function of ηit = μ i + ε it , where μ i is a country specific fixed effect. As μ i does not change over time, it turns out that the lagged area term A it

− 1 is also a function of μ i , thus inducing correlation between A it

− 1 and ηit . Using a fixed effect estimator alleviates this problem by explicitly controlling for μ i . However, the underlying within-transformation is based on the differences in A it

− 1 and ε it from their respective means. In calculating the mean value, ε i. , ε it

− 1 is used, and thus, by construction, A it

− 1 is correlated with ε i. (Nickell, 1981). The bias induced by correlation between A it

− 1 and ε i. 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,

11the 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-season 9 , mean temperature ( TMP it ) and precipitation ( P RE it ); 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( A it ) = μ i + γ0 ln( A i,t

− 1 ) + β ln( P us,t

− 1 ) + α 1 [ω 3

− yr − ma i,t

− 1 ln( P

us,t

− 1 )] + α 2 [ω 3

− yr − ma

us,t

− 1 ln( P

us,t

− 1 )] + α 3 [ω 3

− yr − ma

j,t

− 1 ln( P

us,t

− 1 )] + γ1 ln( TMP

it ) + γ2 ln( P RE

it ) + γ3 θii,t

− 1 ln GDP i,t

− 1 + γ

4 m X j 6 = i θij,t

− 1 ln GDP

j,t

− 1 + γ5 ln RERi,us,t

− 1 + γ6 ω 3

− yr − ma i,t

− 1 + γ7 ω 3

− yr − ma

us,t

− 1 + γ8 ω 3

− yr − ma

j,t

− 1 + ε it . (11)



## Results and Discussion To test the null hypothesis (geography of trade does not matter for production decisions), the restrictions α 1 = α 2 = α 3 = 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

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

constant variance (within and across countries) and are serially uncorrelated 10 . 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 ˆ α 2 and ˆ α 3 are less than half the traditional ones. In the case of ˆ α 2 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 R 2 in the middle panel of Table 2). The coefficient of the lagged area term (ˆ γ0 ) is large and highly significant, evidencing the persistence of harvested areas over time. The coefficient on temperature (ˆ γ1 ) is negative and large, but the precision of the estimates is low. The coefficient on precipitation (ˆ γ2 ) is quite small and insignificant. The terms associated with country size — own-GDP weighted by output consumed at home (ˆ γ3 ) and the revenue-share-weighted average of the GDPs of the trading partners (ˆ γ 4 ) — 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 higher 11 . In line with expectations, a depreciation of the real exchange rate (ˆ γ5 ) 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, ˆ β 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,

ˆ β , 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

13is 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 R 2 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, α 1 , α 2 , α 3 , 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) models 12 yield three general conclusions. First, the LSDV parameter

ˆ γ0 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 )
− 1 β 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

14article 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 ˆ γ7 , ˆ γ8 ,

ˆ α 1 , and ˆ α 2 — 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 ˆ

β 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 ˆ β for all the estimated models. The VIF indicates the proportion by which the variance of ˆ β 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, ˆ β loses its significance. This is a relatively low VIF. If for example the standard error of ˆ

β 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 ˆ β regains its significance; however, in model D, the VIF is lower (1.09), and ˆ β is insignificant. This seems to reinforce the notion that, in these regressions, higher VIFs are disconnected from the significance of ˆ β
. The results discussed thus far suggest that only a reduced number of countries compete with the US. We conducted a robustness test 13 in which the restricted and unrestricted model are estimated

15dropping 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

16yields 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 predictions 14

. 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

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

changes in production, for a given US price shock 15 . 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 18across 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. 2 FAO has some data on domestic producer prices; however, the series are available only for limited periods of time. 3 The 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., x ij = dX ij X i ). 4 Ibidem 3. 5 See derivation details in Section R-4 of the Reviewer’s Appendix. 6 Ibidem 5. 7 See 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. 9 We follow Lobell and Field (2007) in defining global growing seasons. See more details in Appendix B. 10 To 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. 11 Documented in Section R-1 of the Reviewer’s Appendix. 12 Results are available from the authors upon request (Section R-2 of the Reviewer’s Appendix). See original article for details of the bootstrap correction. 13 Results available from the authors upon request, and in section R-6 of the Reviewer’s Appendix 14 See Appendix C for details 15 Unfortunately, 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

## References

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room. Armington, P.S. 1969. “A Theory of Demand for Products Distinguished by Place of Production.” Staff Papers - International Monetary Fund 16:159–178. Baltagi, B.H. 2008. Econometric Analysis of Panel Data , 4th ed. New York: John Wiley. Dimaranan, B. 2006. Global Trade, Assistance, and Production: The GTAP 6 Data Base . West Lafayette, IN: Center for Global Trade Analysis, Purdue University. Everaert, G., and L. Pozzi. 2007. “Bootstrap-based bias correction for dynamic panels.” Journal of Economic Dynamics and Control 31:1160–1184. Fabiosa, J.F., J.C. Beghin, F. Dong, A. Elobeid, S. Tokgoz, and T.E. Yu. 2008. “Land Allocation Effects of the Global Ethanol Surge: Predictions from the International FAPRI Model.” Working Paper No. 08005, Iowa State University, Department of Economics, Ames, IA. FAO. 2009. “FAOSTAT.” http://faostat.fao.org/. Gehlhar, M. 2005. “Chapter 15.B: Reconciling Merchandise Trade Data.” In GTAP 6 Data Base Documentation . GTAP Center, pp. 15–B–1–11. Hertel, T., A. Golub, A. Jones, M. O’Hare, R. Plevin, and D. Kammen. 2010. “Global Land Use and Greenhouse Gas Emissions Impacts of U.S. Maize Ethanol: The Role of Market-Mediated Responses.” BioScience Forthcoming (March Issue). 21Hertel, T., D. Hummels, M. Ivanic, and R. Keeney. 2007. “How confident can we be of CGE-based

assessments of Free Trade Agreements?” Economic Modelling 24:611–635. Hertel, T.W. 1999. Global trade analysis . Cambridge University Press.Heston, A., R. Summers, and B. Aten. 2006. “Penn World Table Version 6.2, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania.” http://pwt.econ.upenn.edu/php site/pwt index.php. Hillberry, R.H., M.A. Anderson, E.J. Balistreri, and A.K. Fox. 2005. “Taste Parameters as Model Residuals: Assessing the ”Fit” of an Armington Trade Model.” Review of International Economics 13:973–984. Keeney, R., and T.W. Hertel. 2009. “The Indirect Land Use Impacts of United States Biofuel Policies: The Importance of Acreage, Yield, and Bilateral Trade Responses.” American Journal of Agricultural Economics 91:895–909. Lobell, D., and C. Field. 2007. “Global scale climatecrop yield relationships and the impacts of recent warming.” Environmental Research Letters 2. Mitchell, T.D., and P.D. Jones. 2005. “An improved method of constructing a database of monthly climate observations and associated high-resolution grids.” International Journal of Climatology 25:693–712.Monfreda, C., N. Ramankutty, and J.A. Foley. 2008. “Farming the planet: 2. Geographic distribution of crop areas, yields, physiological types, and net primary production in the year 2000.” Global Biogeochemical Cycles , Mar., pp. 1:19. Mundlak, Y., and D.F. Larson. 1992. “On the Transmission of World Agricultural Prices.” The World Bank Economic Review 6:399–422. Nickell, S. 1981. “Biases in Dynamic Models with Fixed Effects.” Econometrica 49:1417–1426.

22Pesaran, M.H., and Z. Zhao. 1998. “Bias Reduction in Estimating Long-run Relationships from

Dynamic Heterogenous Panels.” In Analysis of Panels and Limited Dependent Variables: A Volume in Honour of G.S. Maddala . Cambridge: Cambridge University Press, pp. 297–321. Searchinger, T., R. Heimlich, R.A. Houghton, F. Dong, A. Elobeid, J. Fabiosa, S. Tokgoz, D. Hayes, and T. Yu. 2008. “Use of U.S. Croplands for Biofuels Increases Greenhouse Gases Through Emissions from Land-Use Change.” Science 319:1238–1240. Shumway, C.R., R.D. Pope, and E.K. Nash. 1984. “Allocatable Fixed Inputs and Jointness in Agricultural Production: Implications for Economic Modeling.” American Journal of Agricultural Economics 66:72. Stock, J.H., and M.W. Watson. 2008. “Heteroskedasticity-Robust Standard Errors for Fixed Effects Panel Data Regression.” Econometrica 76:155–174.The World Bank. 2009. “World Development Indicators Online.” urlhttp://go.worldbank.org/6HAYAHG8H0. USDA. 2009. “ERS/USDA Data - Feed Grains Database.” http://www.ers.usda.gov/data/feedgrains/. Wang, M., and Z. Haq. 2008. “Ethanol’s Effects on Greenhouse Gas Emissions (E-letter to Searchinger et al.).” http://www.sciencemag.org/cgi/eletters/319/5867/1238#10977. Wooldridge, J.M. 2001. Econometric Analysis of Cross Section and Panel Data , 1st ed. The MIT Press. —. 2002. Introductory Econometrics: A Modern Approach , 2nd ed. South-Western College Pub.

23Table 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 ω i 0.05 0.12 0.00 0.00 0.00 0.03 0.86 ω us 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 ).

24Table 2: Regression Results, Diagnosis, and Comparisons

IWM A B C D ln( A i,t

− 1 , ˆ

γ0 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( TMP

it ), ˆ γ 1 -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 ), ˆ

γ2 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) θ ii,t

− 1 ln GDP

i,t

− 1 , ˆ γ3 -0.025 -0.025 -0.026 -0.025 -0.024

(0.010)** (0.012)** (0.010)** (0.010)** (0.012)** (0.009)*** (0.013)* (0.009)*** (0.009)*** (0.013)* P m j 6 = i θ ij,t

− 1 ln GDP j,t

− 1 , ˆ γ4 -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 , ˆ

γ5 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( P us,t

− 1 ), ˆ β 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 , ˆ

γ6 0.001 0.001 (0.001)** (0.001)* (0.000)*** (0.000)*** ω 3

− yr − ma us,t

− 1 , ˆ

γ7 0.006 0.007 (0.010) (0.010) (0.006) (0.006) ω 3

− yr − ma j,t

− 1 , ˆ

γ8 0.001 0.001 (0.002) (0.002) (0.001) (0.001) ω 3

− yr − ma i,t

− 1 ln( P

us,t

− 1 ), ˆ α 1 -0.001 -0.001 (0.002) (0.002) (0.002) (0.002) ω 3

− yr − ma us,t

− 1 ln( P

us,t

− 1 ), α 2 0.050 0.057 (0.035) (0.035) (0.016)*** (0.012)*** ω 3

− yr − ma j,t

− 1 ln( P

us,t

− 1 ), ˆ α 3 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 R 2 0.656 0.658 0.657 0.656 0.657 Log likelihood 812.488 819.250 814.958 814.240 815.482 VIF of ˆ β 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 25Figure 1: The Ability of Domestic Production to Supply Domestic Markets.

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

26Figure 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.

27Figure 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 ( X j ) using a constant elasticity of substitution (CES) function:

X j = n X i Bij X 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 X ij 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 ( E

j ) yields bilateral demands of the form:
X ij = B σ

ij E j P − σ ij P n i B σ ij P 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 E j yields the expenditure function:

E ( P ij , X

j ) = X

i B σ ij P 1

− σ ij ! 1

1

− σ X j (A-3) Where the first term on the right hand side is the CES price index P j . Substituting E ( P ij , X j ) for E j in (A-2) and using the definition of the CES price index yields the Hicksian or compensated

29CES demands used in the text: X ij = B σ ij X j  P ij P j  − 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 P j can be also expressed as a linear function of bilateral prices P ij . 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:
P j  ∂X

j ∂X ij 
= P

ij , ∀i. (A-5) Meanwhile, given that (A-1) is linearly homogeneous, Euler’s theorem allows decomposing X j as:
X j = n X i ∂X j ∂X ij X ij . (A-6) Solving (A-5) for the price ratio P ij P j , and substituting into (A-6) yields:

X j = n X i P ij P j X ij , (A-7) which we can solve again for P j to obtain:

P j = n X i X ij X j P ij . (A-8) So, the price index P j is the sum of the bilateral prices P ij weighted by the share of optimal bilateral demand X ij on total import demand X j . Totally differentiating (A-8) gives:
dP j = n X i X ij X j dP ij + n X i d  X

ij X j  P ij (A-9) which, after multiplying the first and second RHS terms by P ij /P ij and X

ij X j /X ij X j , respectively,

30and dividing trough by P j becomes:
dP j P j = n X i P ij X ij P j X j dP ij P ij + n X i P ij X ij P j X j d  Xij X j   Xij X j  . (A-10) The second RHS term in (A-10) is zero because is a weighted average of percentage changes in market shares. Letting δij = P ij Xij P j X j , and using lowercases to denote percentage changes, Expression (A-10) becomes: pj = n X i δij pij . (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 31seen 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 δ jjt given by: θiit = P iit X iit P it Y it , δ

jjt = P

jjt X jjt P jt X jt (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 = P

ijt X ijt P it X it ≡ P j 6

= i P ijt X ijt P it X it P

ijt X ijt P j 6 = i P ijt X ijt ≡ (1

− θiit ) V

ijt (B-2)
where: (1

− θiit ) = P j 6 = i P ijt X ijt P it X it (B-3) is the proportion of country i ’s output that goes to foreign markets, and
V ijt = P

ijt X ijt P j 6 = i P ijt X ijt (B-4) is the share of country i ’s exports to country j in country i ’s total coarse grains exports. The data
on V ijt comes from the GTAP database, Version 6 (Gehlhar, 2005). Likewise, δijt can be decomposed and rewritten as follows:

δijt = P

ijt X ijt P jt X jt ≡ P i 6

=j P ijt X ijt P jt X jt P

ijt X ijt P i 6 =j P ijt X ijt ≡ (1

− δ

jjt ) V ijt (B-5)

32where V ijt was defined before, and (1

− δ jjt ) 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 = P n − 2

j 6 =( i,k ) θij δkj ω k = θik δkk ωi = θii δki (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 τ ij , so P

ij = P i τ ij . τ ij can be thought of as a comprehensive measure of tariffs, sanitary barriers, shipping costs, etc. This allows rewriting ωj as:

ωj = n − 2 X j 6 =( i,US ) θij δus,j = n − 2

X j 6 =( i,US ) P

ij X ij P i X i P us,j X us,j P us X us = n − 2 X j 6 =( i,US ) τ

ij X ij X i τ us,j X us,j X us (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,us δus,us = P i,us X i,us P i X i P us,us X us,us P us X us = τ

i,us X i,us X i X us,j X us (B-8)
where τ

i,us are the barriers faced by suppliers in country i when entering the US market, and
τ us,us = 1. Likewise, for For ωi :

ωi = θi,i δus,i = P i,i X i,i P i X i P us,i X us,i P us X us = X

i,i X i τ us,i X us,i X us (B-9)

33where τ us,i are the barriers faced by US suppliers when entering market i , and τ i,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 I

us,t CP I i,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 ) = ˆ

ΓX + ˆ ε (C-1)

34where log( A ) is the vector of areas harvested by country in 1994, ˆ Γ is the vector of parameter estimates of either model, X is the matrix of regressors in 1994, and ˆ ε are the estimated residuals. Fitted values are defined by d log( A ) = ˆ

ΓX
.

• Obtain R random samples with replacement of the vector of residuals ˆ ε and denote each sample by ˆ

ε r with r = 1 , ..., R
.

• Get R bootstrapped vectors of the dependent variable log( A ) r = d log( A ) + ˆ

ε r
.

• Regress each vector log( A ) r on X to get the r th vector of parameter estimates ˆ Γ r

• Using the values of X for 1994, calculate a vector of R predictions using d log( A ) r = ˆ

Γ r X 1994 ; 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 d log( A ) ∗ r = ˆ

Γ r X ∗ 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