Assessing the Land Use Changes and Greenhouse Gas Emissions of Biofuels: Elucidating the Crop Yield Effects

The Specification of Agricultural Supplies

The agricultural supply side is fully described by Keeney and Hertel (2009). This paper recalls, below, the most important assumptions. There exists a representative producer in each agricultural sector and region. These mono-product farmers maximize their profits subject to technical, market (prices), and political (subsidies/taxes) constraints. The agricultural supply response to output price shocks and its decomposition between yield and land responses are calibrated by two types of structural parameters: the substitution elasticities between inputs, and the elasticities of transformation governing the mobility of inputs between sectors. The latter elasticities determine the supply elasticities of these inputs to each agricultural sector.

For the substitution elasticities, I first note that in the GTAP-BIO model five types of inputs are distinguished in each agricultural production technology: land, labor, capital, energy products, and other inputs. It is theoretically possible to specify 10 free substitution elasticities in each agricultural technology; in practice, only 2 substitution elasticities are specified, due to the imposed separability assumptions. More precisely, each agricultural technology is specified with a nested CES production structure. At the lowest level of the production structure, the substitution between the capital and energy products is specified with a first CES function. At the intermediate level, a second CES function defines the substitution among land, labor, and an aggregate comprising capital and energy products. Finally, at the upper level of the production structure, a third CES function defines the substitution between the value-added composite and the other inputs. It is furthermore assumed that the second and third CES functions share the same elasticity of substitution.

The supply elasticities of inputs to each agricultural sector (captured by the elasticities of transformation) differ according to the horizon considered for the analysis. Most analyses consider a long-run horizon that is relevant when computing the net GHG emissions of biofuels (the 30-year period of amortization). All inputs are assumed to be perfectly elastic in the long run. The only exception is land, where total land is assumed to be fixed. Its allocation among the different crop sectors, pasture, forest, and other uses is governed by a nested constant elasticity of transformation (CET) structure. In particular, a first CET allocates cropland to each crop sector.

In mathematical terms, these different assumptions lead to the following system of land and production responses to an output price shock in a given agricultural sector:

[1]

[2]

[3]

where q, l, p_q, and p_l are the percentage changes of production, land use, output price, and land rental price; σ and are the substitution and land supply elasticities, respectively; and s_l is the initial share of land in production cost. Equation [1] is the derived demand of land, equation [2] is the zero profit condition that implicitly determines the optimal production levels, and equation [3] is the land supply condition. These equations are adapted from Keeney and Hertel (2009) to account for the constant Allen Uzawa elasticity of substitution across pairs of inputs.

From these three equations, we can compute the ex ante elasticities of output, land and yields with respect to the output price:

[4]

[5]

[6]

The output elasticity (equation [4]) is thus composed of two terms, the land elasticity (equation [5]) and the yield elasticity (equation [6]). It appears that the last equation depends only on the substitution elasticity. This substitution elasticity is calibrated in the GTAP-BIO to target a given yield elasticity. Above all, these equations make clear that the calibration of yield elasticity is made independently of the calibration of the output elasticity. If the elasticity of land supply or the share of land in production cost is low, then the land response is high (equation [5]). As a result, a high output elasticity is obtained even if the yield elasticity is low, which implies that ex ante an output price increase will lead mostly to land use changes and a modest yield effect.

The Calibration Results

Table 1 reports these ex ante elasticities for major countries producing corn using initial land shares from the GTAP-BIO database and an elasticity of 0.5 for the CET function allocating cropland. This table also provides the resulting substitution elasticities for later discussion. The world production elasticity is a production-weighted sum of regional production elasticities in order to take into account the different regional corn prices. Finally, we compute the contribution of yield elasticities in the output elasticities. This table is divided into two parts. The first part provides the results when the targeted yield elasticity equals 0.2; the second part provides the same results when the target yield elasticity equals 0.4. These two figures are those retained in the final CARB analysis.

The results show that in all countries, the initial yield elasticity is much lower than the output elasticity. For instance, when the targeted yield is 0.2, the initial U.S. production elasticity is 2.67. Hence, the ex ante yield effects represent only 7.5% of the production effects. At the world level, the initial yield elasticity is slightly larger than the targeted elasticity (0.32 compared to 0.2) due to an aggregation effect (initial yields differ greatly across regions). However, the fact remains that the initial yield elasticity is small compared with the output elasticity by representing only 8.1%.

When the targeted yield elasticity increases to 0.4, we find, as expected, larger substitution elasticities and output elasticities (see equations [6] and [4]). All output elasticities increase by 0.2, while the land elasticities remain constant. At the world level, the yield elasticity now represents 12.5% of the output elasticity.

However, the available information suggests that the introduction of yield effects is ex ante much more consequent with the FAPRI model. Table 2 also reports the output, land, and yield elasticities specified in this model. In its standard version, the yield elasticities are assumed to be zero. They are positive in the variant described by Dumortier et al. (2011). Land elasticities are taken from the FAPRI website² for all countries excluding the United States, where a more sophisticated modeling of farm supply is specified and prevents direct computation. The world aggregate reported in Table 2 excludes the U.S. figures. The world aggregate is a weighted sum using production and acreage observed in 2009.

The yield elasticity for corn introduced in the FAPRI model is thus lower than in the CARB analysis using the GTAP-BIO model (approximately 0.12 compared with a range between 0.2 and 0.4). However, the contributions of yield responses to output responses are much higher. For instance, they are 65.2% for Europe and 45.8% for China. By comparison, these contributions are lower than 12% with the GTAP-BIO framework. At the world level, the contribution of yield in output response is 38.0% with the FAPRI model compared to, at most, 12.5% with the GTAP-BIO model. Accordingly, one may already understand why the impacts of crop yield effects on the land use changes and the net GHG emissions induced by biofuels are different across the two frameworks.

The foregoing analysis focuses on the ex ante effects of corn prices on yield and land use change effects. It should be added that the final price effects are endogenous in both models and also depend on the demand responses. The ex ante price and land change effects following a biofuel demand shock (denoted below by Δ^D) are given by

[7]

[8]

where is the own price demand elasticity.

These expressions are identical to those of Hertel (2011) and make clear that the ratio of the yield elasticity to the land elasticity matters more than the absolute value of the yield elasticity. With larger crop yield responses, the output responses are increased considerably with the FAPRI model and more marginally with the GTAP-BIO model. This means that the resulting price effects (and food displacement effects) may become less significant in the former compared with the latter. Hence, the final impacts of the crop yield calibration on these GHG results are much more complex than the foregoing ex ante analysis focusing on the corn supply side only would suggest. Additional complexities come from the fact that in the GTAP-BIO model, the output, land, and yield elasticities are not constant but rather evolve with, for example, input cost shares (see equations [4] to [6]). Moreover, there are cross product effects (from other arable crop markets), size effects (shocks do not always imply small price effects), and regional effects (for instance, the corn price may change in different proportions in different countries due to trade instruments). For this reason, I now turn to simulations using the GTAP-BIO model with a different calibration of crop yield elasticities.

The Alternative Calibrations

I first analyze the biofuel shock with the standard parameters of the GTAP-BIO model (particularly regarding the mobility of factors between sectors). The targeted yield elasticity is assumed to be 0.2. This first version allows understanding of the ex post contribution of crop yield responses in production responses for different countries. I then explore two alternative calibrations of the crop yield responses while maintaining ex ante land effects. That is, I proceed as in the CARB analysis and adopt a long-run horizon in the benchmark.

To make the results as comparable as possible to the FAPRI results, I consider in the first alternative no ex ante crop yield responses.³ The resulting ex ante elasticities are provided in the first part of Table 3. In the second alternative, I consider larger ex ante crop yield responses. I emphasize, as do many other authors, that the choice of precise yield elasticities is delicate. All biofuel analyses recognize that there is limited knowledge on the extent of crop yield and production elasticities with respect to output prices. Keeney and Hertel (2009) and the expert work group on elasticities requested by the CARB (Babcock, Gurgel, and Stowers 2010) devote significant efforts to gathering econometric evidence on the yield elasticities. Unfortunately, most econometric papers focus only on the yield elasticities without simultaneously considering the production (and land) elasticities. The exception is the recent analysis by Huang and Khanna (2010), which develops a reduced form econometric analysis. These authors estimate crop yield elasticities of 0.06, 0.15, and 0.43 for soybeans, corn, and wheat, respectively. They also estimate crop land elasticities that acknowledge cross price effects. Thus, it is impossible to consistently compute the production elasticities using their reduced form approach. Let us ignore the cross price elasticities on land use estimated by these authors, so that the following computed production elasticities overestimate the true ones. The resulting production elasticities are 0.55, 0.66, and 0.50 for soybeans, corn, and wheat, respectively. Accordingly, the contribution of crop yield elasticities in production elasticities is certainly greater than 11%, 23%, and 86% for soybeans, corn, and wheat, respectively. The percentage for corn is much higher than the ex ante percentage assumed in the GTAP-BIO model for U.S. corn (13.9% when the target yield elasticity is 0.4).

This discussion demonstrates the issue of choosing a particular value for crop yield elasticities independently of the production elasticities. The calibration procedure ensures that the value of one elasticity is fulfilled, but without controlling for the others. In this paper, I do not want to claim to choose the true values for all elasticities. Rather, I want to make the sensitivity analysis of crop yields from the GTAP-BIO model comparable to that of the FAPRI model. Accordingly, I define the value of the corn yield elasticity such that its ex ante contribution to the production response equals the FAPRI one defined at the world level (38%). The resulting value is rounded to 2. The second part of Table 3 reports the corresponding ex ante elasticities. Applying the same corn yield elasticity to all countries, we find that the ex ante shares of yield effects in production effects become closer to the FAPRI shares, particularly for China. These shares remain lower for Europe and greater for Brazil.

Above all, this much higher calibrated yield elasticity implies much higher substitution elasticities between inputs (approximately 0.4, depending on the country). These figures appear more consistent with available econometric estimates than the initial GTAP-BIO implied values (all lower than 0.1). For instance, Abler (2001) conducts an extensive literature review of these elasticities for the United States, Canada, and Mexico. Considering all studies, he finds that for the U.S. the average elasticity of substitution between land and other farmer-owned inputs equals 0.3 and that the average elasticity of substitution between land and purchased inputs equals 0.5. Salhofer (2001) performs a similar review for European countries. He finds that the average elasticity of substitution between land and other primary factors lies between 0.1 and 0.3 and that the average elasticity of substitution between land and other inputs lies between 1.6 and 2.7.

In other words, here the absolute value of the crop yield elasticity is certainly high compared with the available econometric estimates. However, this value is more credible when considered relative to the production elasticities and when compared with available econometric evidence on substitution elasticities.

Results

This discussion first focuses on the main results for corn markets obtained from the three calibrations of yield elasticities. Let us begin with the initial calibration (ex ante yield elasticity of 0.2) retained in the CARB analysis (the middle part of Table 4). Unsurprisingly, the results show an increase in U.S. corn production of 16.38%. It appears that this production increase is obtained by a greater increase of the corn harvested area (by 17.10%).⁴ Hence, with the initial calibration there is a slight decrease of U.S. corn yield. Impacts on other countries are quite modest compared with the United States. The production impacts amount to 2.09% in Brazil and only 0.54% in Europe. This is explained by the modest price transmission implied by the so-called Armington modeling of trade flows.⁵ At the world level, there is an increase of production by 4.32% and an increase of harvested area by 2.78%. Corn yield at the world level thus increases by 1.54%, contributing to 36% of the production increase. This result is mainly explained by an aggregation effect: the corn production increases most in the United States, where the initial yield is greater than in other countries. In all countries and at the world level, the ex post elasticities are quite different from the ex ante elasticities. For instance, the ex post U.S. production elasticity is lower than one (precisely 16.38/ 17.08), while its ex ante level is 2.67. Nevertheless, it is interesting to note that the ex post world yield elasticity (0.34) is close to its calibrated value (0.32). Having explained the major effects of the biofuel shock for a given calibration, I can now examine the impact of modifying the calibration of crop yield elasticities.

I first consider the results when the ex ante yield elasticity is zero (first part of Table 4). As expected, there are now lower yield effects. For instance, the U.S. corn yield decreases by 3.57 compared with a decrease of 0.72 with the previous calibration. By contrast, the land use changes are greater: the U.S. harvested area increases by 18.33% (compared with 17.10%). We also find greater price effects because the corn production becomes less price sensitive. For the same biofuel demand shock, the production values increase less, and thus other demands (for feed and food) adjust more. Again, the production effects are quite modest in other countries due to the imperfect price transmission. Corn yields increase only in China. At the world level, we find lower yield effects and greater land use changes: the world corn harvested area increases by 3.21% compared with 2.78% with the previous calibration.

Finally, let us consider the third calibration. The direction of results is perfectly symmetrical. As expected, the production and yield effects are now greater, while the land use and price effects are lower. At the world level, there is an increase of corn harvested area amounting to 1.40%, which represents 44% of the impact obtained when the ex ante crop yield effects are null. This does not imply that the total land use changes and GHG emissions also decrease by the same percentage; the impacts on other arable crop markets must also be taken into account. Table 5 provides the main results for the other grain, oilseed, and sugar crop markets at the world level.

As expected, we find that the positive price impacts on these other arable crops decrease with the price responsiveness of crop yields. We also find that the ex post yield effects tend to increase when the ex ante yield elasticities increase. The exception is for the other grains market (the world yield increases by only 0.79 with the third calibration) because the own price effect vanishes. Finally, we find that the land use tends to decrease when the ex ante yield elasticities increase. This is particularly the case for oilseeds. When the ex ante yield elasticity is zero, the world oilseed harvested area increases by 0.63%. This results mainly from a reduction in the U.S. oilseed production compensated for by increases in countries such as Canada, the European Union, and Sub-Saharan Africa countries with initially lower yields. In contrast, when the ex ante yield elasticity is 2, then the world oilseed harvested area decreases by 0.49%. We thus find, as did Golub and Hertel (2012), that these crop market effects are also dramatic.

The final impacts in terms of cropland converted, reduction of forest and pasture land, and the land use change carbon intensity (as computed by the CARB) are reported in Table 6. We find that the increase of cropland is much reduced when the ex ante yield elasticity increases in relative terms, as in the FAPRI analysis: from 8.81 million ha when the ex ante crop elasticity is zero to 1.17 million ha when it is 2. The reduction of forest land and pasture land due to the biofuel shock are both significantly altered. Finally, we find that the land use change carbon intensity is dramatically reduced from 68.6 to 10.8 gCO₂eq/MJ. Although not the same as the FAPRI results, they are much closer to them. The calibration of yield elasticities relative to production elasticities thus matters greatly: it crucially determines the potential efficiency of the biofuel policy in mitigating carbon emissions.

Sensitivity Analysis to the Length of Run

Thus far, I have considered a long-run horizon where all primary factors of production are fully mobile across sectors. The only exception was land. This implies quite large production and land elasticities. In the preceding analysis, I increase the crop yield elasticities without changing these land elasticities and factor mobilities. To check the robustness of the previous results and to adopt production elasticities that are more consistent with available econometric evidence, I now assume, like Keeney and Hertel (2009), that labor and capital are not perfectly mobile across sectors, and adopt a unitary elasticity of mobility.

The issue in this case is that there is no longer a direct correspondence between the substitution elasticity and the crop yield elasticity. This is because an output price increase translates into an increase in the land (rental) price and an increase in the labor/capital (rental) prices as well. To illustrate, let us temporarily assume that only the labor supply is imperfectly elastic. In this case, the ex ante elasticities of output, land, and yields with respect to the output price are given by

[9]

[10]

[11]

where the subscript n stands for labor. Equation [11] makes clear that the ex ante yield elasticity depends on the relative supply elasticities of land and labor. It is also the same ratio of factor supply elasticities that now appears in the ex ante land elasticities (equation [10]): if the labor supply is imperfectly elastic, then the ex ante land (and production) elasticity is lower than it was previously.

In this sensitivity analysis, I vary the substitution elasticities, picking those adopted previously and justified by econometric evidence for the higher elasticities. Table 7 reports the ex ante production, land, and yield elasticities for corn at the world level. This table also reports the ex post impacts of the biofuel shock on the corn price and the land use change carbon intensity.

By definition, the ex ante production and land elasticities are now lower. For instance, when no substitution is allowed between land and other inputs, the world ex ante production elasticity for corn amounts to 1.67 (compared with 3.76). When the substitution elasticity is taken from the previous third calibration, the world production elasticity amounts to 2.12 (compared with 5.76 previously). In this case, the world ex ante yield elasticity amounts to 0.74 and thus represents 35% of the production elasticities. This value remains quite close to the share computed from the FAPRI analysis.

The simulation results show, as expected, greater price impacts than those obtained so far. The simple reason for this result is that the supply side of the corn market is less price-responsive. More importantly, the carbon intensity is also provided. We again find a very significant impact of allowing ex ante crop yield effects: the level of reduction is more in line with the FAPRI results.