Global market integration increases likelihood thata future African Green Revolution could increasecrop land use and CO2 emissionsThomas W. Hertela,1, Navin Ramankuttyb,2, and Uris Lantz C. Baldosa

aDepartment of Agricultural Economics, Purdue University, West Lafayette, IN 47907; and bDepartment of Geography, McGill University, Montreal, QC,Canada H3A 0B9

Edited by B. L. Turner, Arizona State University, Tempe, AZ, and approved August 8, 2014 (received for review February 25, 2014)

There has been a resurgence of interest in the impacts of agriculturalproductivity on land use and the environment. At the center of thisdebate is the assertion that agricultural innovation is land sparing.However, numerous case studies and global empirical studies havefound little evidence of higher yields being accompanied by reducedarea. We find that these studies overlook two crucial factors:estimation of a true counterfactual scenario and a tendency to adopta regional, rather than a global, perspective. This paper introducesa general framework for analyzing the impacts of regional andglobal innovation on long run crop output, prices, land rents, landuse, and associated CO2 emissions. In so doing, it facilitates a rec-onciliation of the apparently conflicting views of the impacts ofagricultural productivity growth on global land use and environ-mental quality. Our historical analysis demonstrates that the GreenRevolution in Asia, Latin America, and the Middle East was unam-biguously land and emissions sparing, compared with a counterfac-tual world without these innovations. In contrast, we find that theenvironmental impacts of a prospective African Green Revolutionare potentially ambiguous. We trace these divergent outcomes torelative differences between the innovating region and the rest ofthe world in yields, emissions efficiencies, cropland supply response,and intensification potential. Globalization of agriculture raises thepotential for adverse environmental consequences. However, if sus-tained for several decades, an African Green Revolution will even-tually become land sparing.

agricultural intensification | land use change | greenhouse gases |technological change

Increasing world food supplies while minimizing the environ-mental footprint of agriculture is increasingly recognized as

a major challenge (1, 2). Global crop output is estimated to in-crease significantly by 2050 as a result of population growth andchanges in diet (3, 4). This output increase can be achievedthrough either clearing new land for agriculture or through in-tensifying production on existing land. Both of these optionshave major environmental implications, and there is a livelydebate on which option offers greater promise (5–7).One side of the debate is best characterized by Norman Borlaug’s

assertion that agricultural innovation is land sparing (8–10). Inother words, Borlaug argued that intensifying agricultural pro-duction is better for the environment overall because the sameamount of food could be produced using less land, thereby sparingland for nature. Waggoner (11), in a report titled “How much landcan 10 billion people spare for nature?,” lent further credence tothis idea. Stevenson et al. (12), using a global simulation model,made the case that the Green Revolution (GR) spared land.However, these assertions assume that the overall impact on theenvironment would be lower because of land sparing withoutconsidering the greater environmental impact per unit area ofhigher-intensity production systems. Green et al. (13), in a land-mark paper, presented an analytical model for evaluating thebiodiversity benefits of land sparing vs. “wildlife-friendly farming”(often termed land-sharing) modes of production. They applied

this model in a recent field study to find support for land sparing(14). Others have, however, argued that the analytical model ofGreen and colleagues is overly simplistic and promoted instead theconcept of an “agro-ecological matrix” as an alternate land-sharing mode of production to promote biodiversity (15, 16).Another recent study investigated the climate impact of the

historical intensification of agriculture compared with alternatescenarios of extensive modes of production. They compared CO2emissions from clearing of land, CH4 emissions from rice paddycultivation, N2O emissions from agricultural soils, and CO2, CH4,and N2O emissions from fertilizer production and use. Inten-sification would increase emissions from soils and from fertilizeruse but decrease emission from clearing. The study found thatdifferences in CO2 emissions from land clearing dominated andthat the historical intensification of agriculture lowered overallgreenhouse gas emissions because of land sparing (17). Given thatgreenhouse gas emissions from our global food systems constitutea third of total greenhouse gas emissions (18), this is an importantcontribution to the debate on how to reduce global emissions.Irrespective of the outcome of the debate surrounding the

putative environmental benefits of intensification, another majorcriticism of the Borlaug hypothesis is that land sparing does not,in fact, occur in practice. The validity of the proposition rests,among other things, on Borlaug’s assumption of a fixed demandfor food. Borlaug’s hypothesis has recently been brought intoquestion by a series of studies on land use change that argue infavor of a competing hypothesis—dubbed by some as Jevons’

Significance

Agriculture is a key driver of tropical deforestation, and thereis heated debate about whether productivity-enhancing cropinnovations can slow such environmental degradation. For fixedfood demand, globally higher yields will reduce cropland andhence deforestation. However, regional innovations often boostagricultural profitability and lower prices, thereby leading tocropland expansion in the innovating region. This paper developsa framework for understanding the impact of regional innova-tions on global land use and the environment. Although thehistorical Green Revolution in Asia, Latin America, and the MiddleEast is shown to have been land sparing, a future Green Revo-lution in Africa could lead to global cropland expansion in thecontext of a more fully integrated global agricultural economy.

Author contributions: T.W.H. and N.R. designed research; T.W.H. and U.L.C.B. performedresearch; T.W.H., N.R., and U.L.C.B. analyzed data; and T.W.H., N.R., and U.L.C.B. wrotethe paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Freely available online through the PNAS open access option.1To whom correspondence should be addressed. Email: hertel@purdue.edu.2Present address: Liu Institute for Global Issues and Institute for Resources, Environment,and Sustainability, University of British Columbia, Vancouver, BC, Canada, V6T 1Z2.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1403543111/-/DCSupplemental.

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paradox—which suggests that increases in agricultural productivitywill, in fact, be accompanied by an expansion in land area (19, 20).Rudel et al. (19) scrutinized United Nations Food and AgricultureOrganization (FAO) data for 961 agricultural sectors in 161countries over a 15-y period and found little evidence of higheryields being accompanied by reduced area. Ewers et al. (21)similarly analyzed FAO data on crop yields and per capita area for23 staple crops and total per capita cropland area over a 21-yperiod and found a weak land-sparing effect in developing coun-tries but no effect in developed countries.The literature evaluating the Borlaug hypothesis suffers from

two major problems. First, the statistical studies suffer from thechallenge of estimating what would have happened in the ab-sence of such agricultural innovation (i.e., they are unable toaccount for the counterfactual world in their analysis). Second,there is a strong tendency in this literature to focus on particularregions of the world (5, 22, 23), thereby ignoring impacts of re-gional innovations on land use and CO2 emissions in the rest ofthe world, where these may fall. Accordingly, this paper intro-duces a general framework for analyzing the impacts of regionaland global innovations on long run agricultural output, prices,land rents, land use, and associated CO2 emissions. In so doing,it facilitates a reconciliation of the apparently conflicting views ofthe impacts of agricultural productivity growth on land use, globalCO2 emissions, and environmental quality.Fig. 1 provides an overview of key elements of the land-sparing

debate. The top left panel presents a supply and demand diagramexplaining the equilibrium output and price in the innovating re-gion (region A) before and after introduction of an improvedagricultural technology (12, 24), which increases yields and shiftsthe region’s supply curve (QSA) to the right (to QS*A). Price isdetermined in the world market by the intersection of the worldsupply (QSW) and world demand (QDW) curves. The world supplycurve represents the horizontal summation of supplies in bothregion A and in the rest of the world (RoW), represented by theright panel. From this diagram, it is clear that the innovation in Awill result in a lower world price (PW falls to P*W) and hencea reduction in RoW output and land use. It is this land-sparing

impact of region A’s innovation in RoW that is often ignored inthe case study-based literature (5). The impact of the innovationon land use in region A is ambiguous, because it is the net out-come of two competing forces. On the one hand, improvedtechnology means fewer inputs are required to produce the samelevel of output. However, improved technology also lowers costsand induces an expansion in equilibrium output, as shown in thetop leftmost portion of Fig. 1. Not only is the impact on land usein region A ambiguous, this regional ambiguity is inherited by theglobal change in land use, as will be shown later in our analyticalsolution of this model.Although the foregoing analysis appears straightforward, it is

hardly this simple in practice, because supply in region A is notthe only thing that is changing. Consider, for example, the his-torical period analyzed by Rudel et al. (19). During this period,global food demand was growing strongly due to the combinationof population and income growth. This growth translated intoan outward shift in global demand (QDW to QD*W in Fig. 1,Lower). There was also technological progress in crop productionin nearly every region of the world (25). These innovations arerepresented by the outward shifts in supply in both region A and inRoW, resulting in the global price reduction shown in Fig. 1,Lower. Given the multiplicity of factors at work here, it is difficultto know what would have happened if technological progress inregion A had not occurred or if it had been slower. For this, weneed a formal model. Accordingly, we use the Simplified In-ternational Model of Prices Landuse and the Environment(SIMPLE) model of global agricultural land use (SI Text andFig. S1) (26) to reexamine the historical record considered byRudel et al. (19) and Ewers et al. (21), as well as to explorefuture Green Revolution scenarios. Importantly, this version ofSIMPLE has been modified to allow for the segmentation ofregional markets (Fig. S1), a point to which we will return below.

ResultsThe Historical Green Revolution Was Indeed Land and CO2 EmissionsSparing Compared with a Counterfactual World Without TheseAgricultural Innovations. There was a remarkable increase (>200%)in global crop production over the 1961–2006 period as a result ofthe Green Revolution (Fig. 2, Upper, blue bars for observed globalvalues). Most of this output expansion was achieved throughhigher yields especially in regions that experienced the GreenRevolution. The expansion in cropland area was just 11%, andreal crop prices fell by 29% over this historical period. The other

Fig. 1. Three-panel diagrams depicting the impacts of an improvement intechnology in region A on world price and output in the RoW. (Upper) Im-pact of an improvement in technology in region A alone. The TFP gain shiftssupply in A to the right, thereby increasing global supply and depressingworld price when taken alone. This outward supply shift depresses pro-duction in RoW, which doesn’t benefit from the new technology. A keyfactor in determining the impact on output and land use in region A is theslope of the excess demand curve (EDA). (Lower) Impact of simultaneousshifts in world demand and regional supplies in A and in RoW. When thesupply shift in A is combined with an outward shift in demand, as well astechnological change in RoW, the impact on RoW cropland area is no longerclear cut.

Fig. 2. Observed and simulated changes in global and regional output,yield, cropland area, and prices over the historical period 1961–2006. Thebaseline simulation (green bar) reflects the presence of the historicalGreen Revolution in Asia, Latin America, and the Middle East. The coun-terfactual simulation (red bar) excludes TFP growth attributed to thisGreen Revolution.

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important point to note is that both yields and area expanded in theGreen Revolution region, whereas in the RoW, aggregate yieldsexpanded and area remained essentially unchanged (Fig. 2: Lower,blue bars for observed regional values). These results arebroadly consistent with the observation of Rudel et al. (19), whoconcluded that “rising yields and declining cultivated areas, does notgenerally characterize agricultural sectors between 1990 and2005.” They suggested that this is evidence of technologicalchange failing to be land sparing. However, they were not ableto generate a counterfactual against which to consider whatwould have happened had the technological progress not oc-curred. This shortcoming motivates the use of SIMPLE to un-dertake the counterfactual analysis.The SIMPLE model’s historical baseline, in the presence of

the GR scenario, reproduces output, yield, and price changes atthe global level reasonably well (Fig. 2, Upper, green bars). Weaggregate outcomes from the 15 regions in SIMPLE into the GRregion and RoW, in keeping with Fig. 1. SIMPLE’s predictedyield and output growth in the Green Revolution region is lowerthan observed, suggesting that we are not capturing all of thecomplexity of these innovations in historical total factor pro-ductivity (TFP; the ratio of an output index to an index of landand nonland inputs) measure used in this model (27). However,overall, this model with segmented regional markets performsbetter over this historical period than the previous version whichassumed integrated world markets (26).With this historical baseline simulation in hand, we are now

in a position to explore a counterfactual scenario that we dub theno Green Revolution (no-GR) scenario. In this case, techno-logical progress in Asia, Latin America, and the Middle East isslower due to the absence of improved germplasm. Rather thancrop TFP growing at an annual average rate of 1.6% in Asia andLatin America, it grows at just 0.5% in our counterfactual (12,28). By subtracting the results of our counterfactual no-GRscenario (red bar in each group of Fig. 2) from the GR scenario(green bars), we obtain a model-based assessment of the impactof the Green Revolution on cropland use, yields, output, andglobal price over this historical period.Results in Fig. 2 show that the Green Revolution causes land

area in the affected region to be smaller than it would have beenwithout the Green Revolution (26% with GR and 37% withoutGR). The growth in global output is also notably greater in thecase of the Green Revolution. Rather than a reduction in globalcrop prices as observed in the historical GR baseline, the modelsimulates a 30% price increase over the 1961–2006 period underthe no-GR counterfactual. RoW cropland use is much lowerunder the GR scenario (−2% with GR and +9% without); hence,we see from Fig. 2 (Upper) that the Green Revolution was indeedland sparing at the global scale compared with the no-GRcounterfactual (11% global cropland increase with GR and 21%without GR). Furthermore, the error bars reported in Fig. S2show that these land use deviations from baseline in the GRregion, the RoW, and worldwide are all robust to variation in theSIMPLE model parameters (Tables S1 and S2).We can also assess the impact of the GR on CO2 emissions

from land cover change. To do so, we multiply the land coverchange predicted by SIMPLE by carbon emission factors perhectare estimated using yield and carbon loss estimates fromWest et al. (29) (SI Text). [Note that unlike Burney et al. (17), herewe are only considering CO2 emissions from land cover change,neglecting emissions from intensification, e.g., N2O from fertilizeruse. Burney et al. (17) found that differences in CO2 emissionsdominate the overall effect on greenhouse gases.] These resultsare also reported in Fig. S2 and show robust evidence of globalCO2 savings from the GR, with a mean reduction of ∼1,300MMg. Both of these findings are consistent with the recent workof Stevenson et al. (12), who analyzed this question in the contextof their comparative static simulation of a disaggregated globaleconomic model of agriculture.

A Prospective African Green Revolution Would Also be Land and CO2

Emissions Sparing if World Agricultural Markets Remain Segmented.Given the lagging nature of yield growth in Africa, considerablenew investment is flowing into research and development in thisregion, with the goal of launching an African Green Revolution.Such a development could yield significant benefits in terms ofenhanced food security, increased rural incomes, and poverty re-duction. If successful, will such an advance have a similarly ben-eficial impact on global land use and CO2 emissions? To test thishypothesis, we perform two, forward-looking simulations usingSIMPLE. In our baseline, we specify changes in population,income, biofuels, and TFP from 2006 to 2051 (Table S3) asdescribed in Baldos and Hertel (30). Baseline TFP growthrates are slower than over the 1961–2006 period, as isexpected in the face of higher temperatures and more variablerainfall (31). Our counterfactual simulation is one in which,beginning in 2025, African TFP grows at a higher rate com-mensurate with the Asian Green Revolution discussed pre-viously. Differences in cropland area between the African GreenRevolution and the baseline are reported in the upper left panelof Fig. 3. Error bars correspond to 95% CIs with respect toparameter uncertainty (SI Text). Here, we see that the meanchanges in global land use and CO2 emissions are negative (−16Mha and −194 MMg) and once again statistically robust. How-ever, unlike the historical Green Revolution, the reductions inland use and emissions in the innovating region (sub-SaharanAfrica in this case) are no longer robust to parameter variation.Our numerical simulations with SIMPLE provide the missing

counterfactual analyses of the impact of the historical and pro-spective Green Revolutions on regional and global land use.However, they are necessarily limited, because the results de-pend not only on the behavioral parameters, but also on the stateof the world and the characteristics of the affected region as wellas the RoW. To investigate the land-sparing issue at a deeperlevel, we revert to a theoretical model. A key feature of this the-oretical model will be the assumption of fully integrated worldmarkets. This assumption contrasts with evidence that agriculturalcommodity markets were segmented as a result of high and vari-able trade barriers during much of the historical period (32). Thus,it is hardly surprising that the distribution of global productionpredicted by the SIMPLE model under segmented domestic, and

Fig. 3. Sensitivity analysis of the regional and global cropland change andtheir corresponding carbon emissions given a future African Green Revolutionunder both segmented and integrated markets: difference between with vs.without Green Revolution TFP growth. Error bars reflect 95% CIs obtainedfrom Monte Carlo analysis with respect to parameter uncertainty.

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international markets better approximates what was observed overthe 1961–2006 period (26). However, the world economy ischanging rapidly. One of the primary objectives of the UruguayRound Agreement, which resulted in formation of the WorldTrade Organization in 1994, was to bring greater discipline tointernational agricultural trade, and there is evidence that dis-tortions to agricultural trade are being dismantled (33). There-fore, it is of great interest to examine how these findings might bealtered in the context of a more fully integrated global economy.After appropriate condensation of the demand side, adding

the assumption of fully integrated world markets and modestsimplification of the supply side, the SIMPLE model can becondensed and solved analytically (SI Text and Table S4). Inparticular, we aggregate across all of the sources of crop de-mand, including biofuels, as well as direct consumption, inputdemands in livestock, and crop use in processed foods in eachof the 15 model regions. This aggregation has no effect on modelbehavior and simply results in a single, global demand schedule, asshown in Fig. 1 (middle graph). On the supply side, we aggregateacross countries within the GR and no-GR regions. The theo-retical model also assumes that the price of nonland inputs isunaffected by the innovation (This assumption tends to exag-gerate the potential for endogenous intensification.) With thesesimplifications, we can now obtain a general theoretical solution tothe model expressed in terms of percentage changes in equi-librium prices and quantities as a function of the change in cropTFP (SI Text). The analytical model offers the followinginsights into the land-sparing nature of agricultural innovations.

Global TFP Growth in Agriculture Will Increase Land Use and CO2

Emissions if and Only if the World Demand for Crops Responds Stronglyto Changes in Price. If we start by postulating a common rate oftechnological change worldwide (superscript W denotes globalvariables), then the percentage change in worldwide land use(qWL ) given a 1% change in global TFP (tW ) is given by the fol-lowing expression (see Table S4 for a full discussion of the termsin this expression):

qWL�tW =

�«WD − 1

���1+ σW

��1�θWL

�− 1

���νWL

�θWL

�

+ «WD

��νWL

�θWL

��;

[1]

where «WD > 0 is the absolute value of the global price elasticity ofdemand for crops. We refer to this as the demand margin of priceresponse. This unit-free measure describes the slope of the worlddemand schedule in Fig. 1, reporting the percentage change inglobal demand in response to a 1% change in price (Table S4). Ifit is greater than one, then demand is termed price elastic as thequantity response is larger than the price change (in percentageterms). The global price elasticity of demand depends on theresponsiveness of both consumer demands and livestock andfood processing demands for crops. The term σW ½ð1=θWL Þ− 1�captures the potential for yield increases in response to highercrop prices (the intensive margin of supply response), whereinthe parameter σW describes the potential for substituting non-land for land inputs in crop production (elasticity of substitution)and θWL < 1 is the share of land in global production costs. Theterm ðνWL =θWL Þ reflects the potential for cropland expansion givenincreases in crop prices (the extensive margin of supply response),wherein νWL is the global supply elasticity of cropland. This termrepresents the percentage change in global cropland supply inresponse to a one percent change in cropland returns.Eq. 1 confirms that TFP growth will cause land to expand if

and only if world demand for crops is price elastic ð«WD > 1Þ. Thispoint is well understood in the literature (5); however, our an-alytical expression offers additional insights. In particular, themagnitude of any expansion or contraction will depend on thecropland area response, the importance of land in total costs,and the potential for substitution of nonland inputs for land. We

can say unambiguously that the larger the elasticity of sub-stitution in production ðσW Þ, the more muted will be the globalcropland area response to TFP growth. For large values of theintensification parameter relative to the price elasticity of de-mand (i.e., σW � «WD , so the third term in the denominator isnegligible relative to the second), we have the additional result thatthe land area response to TFP is diminished when the cost share ofland in total crop production rises. Finally, note that the de-nominator in this expression hinges on the relative sizes of theintensive/extensive margins fσW ½ð1=θWL Þ− 1�= ðνWL =θWL Þg and thedemand/extensive margins ½«WD =ðνWL =θWL Þ�. As the extensivemargin of supply response becomes relatively larger, the de-nominator in Eq. 1 shrinks and the entire right side of Eq. 1becomes larger, so that more land will be converted in the wakeof a given improvement in productivity.Of course the focus of the land-sparing debate has been on

asymmetric innovations, such as those shown in Fig. 1, Upper,which take us back to the two-region model, where the analysisbecomes more nuanced. Eq. 2 gives the analytical expressionfor the percentage change in global land use in response to a1% change in TFP in region A alone ðtA > 0Þ:

qWL�tA = δ

�νAL

�θAL��

«AD − 1���

«AD + «AS

�

+ ð1− δÞ�νRL�θRL��

−«AS − 1���

«AD + «AS

�:

[2]

In this expression, δ denotes the share of global cropland areain region A, so ð1− δÞ is the share of global cropland in RoW.Therefore, the percentage change in global land use is a weightedcombination of the change in land use in the two regions. We alsointroduce a key concept, namely the excess demand elasticityfacing region A: «AD = ½«WD + ð1− αÞ«RS �=α. This elasticity governsthe slope of the EDA schedule in Fig. 1, and it is a central parameterin the two-region model. It reflects the fact that the demand facingregion A’s suppliers is really a combination of the price respon-siveness of world demand ð«WD Þ and supply response in the RoWð«RS Þ. In other words, when producers in region A become moreproductive and world prices fall, not only will global demandincrease, but producers in RoW will reduce their production,thereby further accommodating the output expansion in region A.The slope of the excess demand curve depends critically on therelative share of region A in global production, parameterizedhere by α. As α→ 0, as would be the case if region A representeda single farm, the excess demand elasticity approaches infinity,implying that a single farmer cannot influence world markets.Eq. 2 is also where the assumption of integrated markets comes

into play. If instead, markets in A and RoW were segmented, theprice changes in A would not be fully transmitted into RoW,therefore reducing the responsiveness of both demand andsupply in RoW, resulting in a smaller value for «WD . This two-regionanalysis offers the following insight.

Jevon’s Paradox is Most Likely to Arise When Global Food Demand isPrice Responsive and Yields in the GR Region Are Relatively Low. Atthis point, it is important to emphasize that it is not possible tosay whether global land use change will be positive or negativefollowing a productivity improvement in the affected region. Theanswer critically depends on the relative size of this region andits land supply response relative to the RoW. The sign of thesecond term on the right side of Eq. 2 is always negative, in-dicating that, in the face of the inevitable price decline owing totA > 0, land area in the rest of the world will decline (recall Fig. 1,Upper, right graph). The ambiguity in global land use arises due tothe first term. In particular, a necessary condition for Jevon’s par-adox, ðqWL =tAÞ> 0, is that the first term on the right side of Eq. 2must be positive, and for this, we require an elastic excess demandfacing region A, «AD > 1. However, this is not a sufficient conditionfor Jevons’ paradox. The first term must also be large enough todominate the second one. This condition is more likely if, inaddition to the elastic excess demand condition (which is likely to

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come from having a small share of global production: α→ 0), re-gion A simultaneously comprises a relatively large share of globalcropland such that δ→ 1. Of course, these two conditions canonly coexist if yields are very low in the innovating region. Inaddition, if region A’s cropland supply response is relativelylarge, i.e., ðνAL=θALÞ � ðνRL=θRLÞ, Jevon’s paradox also becomesmore likely. Finally, a larger intensive margin in RoW results ina greater contraction of output in that region and therefore morescope for the low-yielding innovating region to expand its area.However, it is not possible to say anything more precise aboutthe conditions for global area expansion or contraction in thisgeneral case (SI Text).Special cases yield more clear-cut predictions (SI Text). One

that is particularly useful to discuss here is the case when bothregions have the same supply response. Now the condition forJevons’ paradox simplifies to

«WD >�YA�YW

��«WS + 1

�− «WS ⇒

�qWL

�tA�> 0; [3]

where ðYA=YW Þ is the ratio of yields in region A to global yields.Therefore, the likelihood of global land area expanding in theface of innovation in region A increases when yields in the af-fected region are low, relative to the world average yields. Thelogic is as follows: (i) agricultural area in region RoW falls in thewake of the productivity improvement in A; (ii) the RoW areadisplaced by increased production in A will be smaller, and thusthe smaller is this yield ratio (smaller right side in Eq. 3); andfinally (iii) the larger the increase in global demand due to theresultant price decline (larger left side in Eq. 3), the greater theoverall increase in global output that needs to be supported.We can use this framework to shed further insight into the land-

sparing nature of the Green Revolution. Table S5 summarizesthe parameters underpinning Eq. 2 in the year 2006, aggregatedfrom the 15 regions in SIMPLE to the level of the historicalGreen Revolution region and RoW. Relative yields in the his-torical GR region were 40% above the world average in 2006.Based on Eq. 3, this mitigates against Jevons’ paradox. Croplandarea response is only about 80% of the world average, increasingthe likelihood of TFP growth being land-sparing, based on Eq. 2.The excess demand elasticity (0.98) is also relatively low, againmitigating against Jevons’ paradox based on Eq. 1. Thus, it isno surprise that when we plug the aggregated parameters inTable S5 into Eq. 2, we find that qWL =tA = −0.26 < 0, and thissingle-equation prediction provides the same land-sparing resultobtained from simulation of the full SIMPLE model albeit inthe context of segmented markets.

In the Context of Integrated World Markets, an African Green RevolutionWill Only Be Land Sparing if It Is Sustained over Several Decades. Thesecond set of parameters reported in Table S5 sheds light onpotential impacts of an African Green Revolution in the contextof fully integrated world markets. In particular, compared withthe historical Green Revolution region, sub-Saharan Africa coversa smaller share of global cropland area (13%) but has a muchstronger cropland area response to price (0.64 vs. 0.44 for theworld) and exhibits yield and emissions efficiencies that arerelatively low (just 69% and 50% of the global average, respec-tively). In light of Eq. 2, these factors suggest that an AfricanGreen Revolution has the potential to exhibit Jevons’ paradox.Indeed, if we plug the parameters from Table S5 into Eq. 2, wefind that qWL =tA = 0.02 > 0, which suggests that the AfricanGreen Revolution would be not land sparing if implemented in2006 in the presence of fully integrated world markets. We canalso see from Eq. 2 why the African GR is land sparing in thepresence of segmented markets. For Africa, the excess de-mand elasticity is <1 (0.74: see parenthetic entries in TableS5), thereby suggesting a land-sparing outcome when evalu-ated using Eq. 2, because both terms on the right side becomenegative in this case.

At this point in the theoretical analysis, we must introduce anadditional complication: the fact that the parameters reported inEq. 2 are in fact variables that will change as a result of economicgrowth, as well as a potential Green Revolution. The most ob-vious instance is that of relative yields. We expect this ratio torise in the wake of an African GR. Indeed, we can use Eq. 2 tocalculate the critical point at which (holding other variablesconstant) further productivity growth in the region would boostthe yield ratio sufficiently to eventually change the sign in thisexpression. We find that the critical value for the yield ratio is0.86, which would be achieved after ∼20 y of GR-inducedproductivity growth.We can also return at this point to the SIMPLE model, only

now assuming fully integrated world markets. As before, we startfrom the 2006 base and project the global economy forward, firstunder the baseline assumptions and subsequently assuming thatthe African GR commences in 2025 and persists through 2050.Results are reported in the right panel of Fig. 3. As anticipatedby our theoretical model, the impact on global land use is am-biguous. However, given the insights offered by Eq. 3 and thepreceding discussion, it is clear that the longer this GR persists,the more likely it is to become cumulatively land sparing.

In the Context of a Fully Integrated Agricultural Economy, the AfricanGreen Revolution Is Likely to Increase CO2 Emissions from CroplandCover Expansion. Within the analytical framework laid out above,it is also possible to derive conditions analogous to Eqs. 1–3 thatbear on the question of global CO2 emissions from land con-version (SI Text). Indeed, the only difference is that, rather thanrelative yields driving the result (Eq. 3), the key metric is theemissions efficiency of region A, relative to the global value.Emissions efficiency refers to the yield per hectare of increasedcropland, relative to the one-time carbon emissions associatedwith bringing that land into crop production. If this ratio is largein absolute value, then we say that the region has a high emissionsefficiency. West et al. (29) calculated these emissions efficiencies(actually, they computed the inverse of our emissions efficiencymeasure) for a global grid and found that they are three timeslower in the tropics compared with the temperate regions andare particularly low in sub-Saharan Africa. Indeed, the emissionsefficiency in the sub-Saharan African region is just half of theworld average (Table S5). This finding naturally raises a con-cern about whether an African Green Revolution would in-crease global CO2 emissions. Because the remaining terms inEqs. 1–3 are identical for the change in global emissions, we areleft with a strong suspicion that this may indeed be the case.The lower right panel in Fig. 3 reports the SIMPLE model

simulated change in global CO2 emissions owing to the AfricanGreen Revolution, in the presence of fully integrated world mar-kets. From these results, the prospective African Green Revolutionboosts CO2 emissions in that region by enough to dominate thedecline in RoW emissions from land use change. The error barsshow this result to be robust to parameter uncertainty.

DiscussionThe literature on the land use implications of technological changein agriculture has suffered from the absence of a unifying ana-lytical framework and the associated absence of counterfactualscenarios in many studies. As with earlier studies (19), we verifythat, indeed, over the 1961–2006 period, increasing yields wereaccompanied by increased cropland area in Green Revolution-affected regions. At first glance, this appears to be a refutation ofthe Borlaug hypothesis and an affirmation of Jevon’s paradox.However, once we consider the counterfactual scenario in whichagricultural productivity in developing countries grew more slowly,due to the absence of the Green Revolution, we find more globalland conversion relative to the real world case and not less. Inother words, the historical Green Revolution did indeed spareland over this period compared with the counterfactual. None-theless, even in the counterfactual scenario, with slower productivitygrowth in the region no longer benefitting from the Green

Hertel et al. PNAS Early Edition | 5 of 6

SUST

AINABILITY

SCIENCE

Revolution, cropland area and yields still both rise over the his-torical period. These results clearly demonstrate the fallacy insimply examining correlations between historical yield and areachanges in the absence of a proper counterfactual.When our framework is used to analyze the impacts of a pro-

spective African Green Revolution, we find that, provided globalcrop markets remain segmented as they have been historically,this would also be land and emissions sparing. However, in thecontext of integrated global markets, we show that innovations willmost likely fail to be land or emissions sparing when they occur inregions with relatively low yields, low emissions efficiencies, andhigh land supply elasticities. These conditions are precisely thosethat apply presently in sub-Saharan Africa. However, we do nottake these results to imply that the world should refrain frominvesting in improved agricultural technology for Africa or thatpolicies should limit the extent of market integration. To thecontrary, any measures that boost relative yields in the region willeventually ensure that cropland area expansion in sub-SaharanAfrica is also land sparing. In addition, measures to discourageconversion of carbon-rich ecosystems to low-yielding crop pro-duction will help to boost environmental efficiencies in the re-gion, thereby ensuring that future land use change does notincrease global CO2 emissions.

Materials and MethodsIn this paper, we use the SIMPLE model (26) (SI Text) to simulate croplandchange over the historical period from 1961 to 2006. The 15 regions (Table S3)are aggregated into two regions for reporting: Green Revolution and Rest ofthe World (RoW). Each of the 15 regions consumes crops, livestock products,and other processed foods, with the demand characteristics varying byproduct and also by per capita income in the region. Crop production is

based on the combination of land and nonland inputs in variable pro-portions. By increasing the intensity of nonland inputs per hectare, yieldscan be increased, given sufficient economic incentive. Production can alsobe expanded at the extensive margin by converting more cropland. Themodel is simulated over the 1961–2006 historical period by specifyingexogenous changes in population and per capita income by demand region,as well as changes in TFP in crops, livestock, and processed foods production.As in Fig. 1, long run equilibrium is achieved when global crop supply equalsdemand, subject to the segmentation of regional markets that limits thetransmission of global market prices into the domestic economy andtherefore reduces the excess demand elasticity facing the innovating region.

There are several important limitations of our methodology (SI Text). Firstis the assumption that the impact of technological change is limited to theinnovating region. What if all crop innovations were perfectly transferable?In this circumstance, innovation in any region A is automatically transferredto RoW, which takes us back to Eq. 1 in which the impact of the innovation isfelt globally and the condition for Jevon’s paradox is price elastic globaldemand—an unlikely condition, given the evidence on consumer demand(34). A second limitation is that the counterfactual we have constructed hasbeen limited to modifying TFP growth. In reality, agricultural innovationsmay also have influenced population and income growth, which we have keptfixed in our model experiments. Nevertheless we believe that the qualitativeresults and insights gained from this study are likely robust to alternateconstructions of counterfactuals.

ACKNOWLEDGMENTS. We acknowledge David Lobell, Eric Lambin, andRobert Heilmayr, as well as seminar participants at Stanford, the Universityof Minnesota, and the Global Land Project for valuable discussions. T.W.H.acknowledges support from the US Department of Energy Office of ScienceIntegrated Assessment Modeling Program Grant DE-SC005171. N.R. ac-knowledges support from the Natural Science and Engineering ResearchCouncil of Canada and the Gordon and Betty Moore Foundation.

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Supporting InformationHertel et al. 10.1073/pnas.1403543111SI TextSimplified International Model of Prices Land Use and theEnvironment Model. In the model (Fig. S1), per capita con-sumer demands for three food types, crops, livestock, and pro-cessed foods, are log-linear functions of price and income, withrespective food demand elasticities varying as a function of percapita income in each region. Based on international cross-sec-tional estimates by Muhammad et al. (1), the absolute values ofthe income and price elasticities for all food types fall as in-comes grow. Regional food demand is obtained by multiplyingper capita demand by regional population. Because livestockand processed foods are valued-added products, these areproduced within the consuming region using crop and noncropinputs and therefore have region-specific prices. A substantialshare of crop demands in the model is derived demands, ob-tained from the consumer demands for value-added food prod-ucts. This distinction is important, because technological changeand factor substitution in the livestock and processed food in-dustries can lead to varying intensities of crop use in these foodproducts. The global demand for crops is the summation of finaldemands and derived demands summed over all regions. Worlddemand for crop feedstocks in biofuels is exogenously specifiedand serves as an addition to global crop demand.Global crop production in the model is specified for each of

the 15 geographic regions as a constant elasticity of substitutionfunction of land and nonland inputs, each with different yieldsand potentially differing rates of technological progress. Croplandsupply elasticities, which vary by region, are based on the adjustedestimates of Gurgel et al. (2) and Ahmed et al. (3). Nonland factorsupplies to agriculture are also less than perfectly elastic supply,but are more price responsive than land supply, based on the es-timates offered by The Organization for Economic Cooperationand Development (4). In the standard version of the SimplifiedInternational Model of Prices Land use and the Environment(SIMPLE) model, equilibrium is attained in the crop marketswhen supply equals demand, where the equilibrating variable isthe global price of crops. In this paper, we implement marketsegmentation in the SIMPLE model via a finite elasticity ofsubstitution between crop commodities in the domestic and in-ternational markets.The extent of market segmentation in the model is based on

historical evidence regarding the substitutability of goods in in-ternational trade (5), and the error bars reflect the underlyinguncertainty in these historical estimates. However, given the im-portance of this assumption, it is useful to consider the implicationsof changing it. In the most extreme case, namely that in which re-gional markets are entirely independent, supply must equal demandat the regional level. The land-sparing condition is then simplygiven by Eq. 1 in which the price elasticity of demand for crops inthe innovating region must be less than one. This price elasticitycondition strikes us as quite likely for staple crops. As crop pricetransmission across borders increases, the excess demand elasticityfacing the innovating region will be increased as the responsivenessof producers in RoW is rises. This increased excess demand elas-ticity raises the likelihood that land use in the innovating regionwill increase, thereby leading to Jevons’ paradox (Eq. 1). Al-though global markets have not been integrated historically, thefuture is likely to see increasing market integration.

Calculation of Emissions Factors. The carbon loss per hectare ofcropland (including emission efficiency factors) is calculated usinggrid-cell crop dry yield and carbon loss data fromWest et al. (6). To

aggregate grid cell data across 15 regions in SIMPLE, we weightboth pixel-based measures by the actual amount of available landfor clearing. This availability has two components: (i) within eachcurrently cropped pixel, the available land is computed as pixel arealess current extent of cropland; and (ii) within each noncroppedpixel within each region, the available land equals the total pixelarea. However, some of these noncropped pixels could be con-sidered inaccessible, so we only consider pixels adjacent to cur-rently cropped pixels when calculating the emissions efficiencies.

Monte Carlo Analysis with Respect to Model Parameters. Sensitivityanalysis on the model outcomes is conducted via Monte Carlosimulations (Tables S1 and S2). Inputs to each simulation aredrawn from independent triangular distributions of eight globalparameters (Table S1). Parameters that guide consumption andproduction behavior in SIMPLE are taken from several sources.Demand elasticities in the model consist of income and priceelasticities (EIY and EIP, respectively) for each food commodity(i.e., crops, livestock and processed foods). These elasticities arebased on the country-level estimates by Muhammad et al. (1).Production parameters in SIMPLE include the following: theprice elasticity of nonland input supply (ENLAND), derived fromKeeney and Hertel (7), and the 15-y price elasticity of US landsupply (ELAND), which was taken from Ahmed et al. (3). We donot have robust estimates of the unobserved intensification pa-rameters (i.e., elasticities of substitution) in crop and livestockproduction; hence, we rely on model calibration to derive theseparameters. The elasticity of substitution between land andnonland inputs in crop production (ECROP) is calibrated sep-arately for the historical and future simulations. In the former,this parameter is calibrated by targeting observed global crop-land expansion from 1961 to 2006, whereas in the latter, this isdone by ensuring that the economic yield response to crop pricesin the model matches the estimate from Keeney and Hertel (8),i.e., a 1% increase in global crop price translates to a 0.25%increase in global crop yields. For the elasticity of substitution inthe livestock sector (ECRPFEED), we rely on the methods out-lined in Baldos and Hertel (9), albeit using updated data. TheArmington elasticity (ESUB) that governs the substitution be-tween domestic and global crop commodities for both consumersand producers is based on the average for all crops taken from theGTAP parameter file (10). Carbon loss per hectare (C_EMIS_HA)is derived from West et al. (6) as previously outlined.Some parameters are converted to regional values using re-

gional scalars (Table S2), which are used to scale up or down aglobal parameter. This scaling reflects the notion that if the trueincome elasticity of demand for livestock in one region is higherthan in the base case, then all of them are too high, because theseare derived from the same global study. Scalars of the land supplyelasticity are constructed using on the variations in the regionalelasticities of land supply fromGurgel et al. (2) as a guide. Regionalscalars for the carbon loss per hectare of cropland are computedusing the methods and data mentioned above.Our sample size is 1,000 experiments. Except for the Armington

elasticities, the maximum and minimum of all parameter distri-butions are constructed using the assumption that these are ±30%away from the mode due to limited empirical evidence. The rangeof the Armington elasticities is based on maximum and mini-mum values found in the GTAP parameter file for differentindividual crop sectors (10).

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Robustness Results for the Historical Green Revolution. Fig. 2 reportspercent changes under the historical baseline: 1961–2006*[inclusive of the Green Revolution (GR)], as well as for the no-GRcounterfactual scenario. On the other hand, Fig. S2 reports theactual differences (i.e., GR – no-GR) in global and regional landuse and CO2 emissions, along with the error bars denoting the 95%CIs. From these results, it is clear that the historical GR was bothland and emissions sparing given the uncertainty in model pa-rameters, with mean reductions of 144 Mha and 1,306 MMg CO2,respectively.

Derivation of Eqs. 1–3 in the Text. In the theoretical model, there area number of key parameters that will be important. These param-eters are summarized in Table S4 for the sake of convenience.

Key Behavioral Relationships in the Theoretical Model. Long run demand.Economic behavior in this farm sector model follows the approachdeveloped in Hertel (11) and is extended to deal with technologicalprogress (12). It is expressed in terms of cumulative percentagechanges in key sector-level variables, as summarized in Box S1.The first equation describes the long run changes in the demandfor crops output as a function of endogenous responses to therelative scarcity of agricultural output, as measured by the changein output price, po, translated through the farm-level price elas-ticity of demand, −«D < 0. The latter represents a sales share-weighted summation of the individual elasticities associated withthe different sources of demand for crops (direct consumption,livestock use and processed foods, in the case of SIMPLE).

Demand for farm inputs. The second equation in Box S1 governs thelong run supply of output from the farm sector (see ref. 18 for thederivation of Eqs. 2 and 3). In periods of depressed prices, weexpect producers (and land) to exit agriculture, thereby reducingthe overall supply of farm products and raising prices until theyare sufficient to cover costs. In the long run no farm operator canafford to make continued losses. Similarly, in boom times, whenagricultural prices are rising, we expect farmers to expand theiroperations, thereby bidding up the price of land until any excessprofits are eliminated. With these forces in play, we expect that,over time, zero economic profits will prevail in the farm sector.This condition means that, once all factors of production are

paid the value of their marginal product, total revenue will beexhausted. Assuming cost minimization we can express thechange in unit costs in terms of the cost-share-weighted sum ofinput prices:

Pjθjpj.

The third equation in Box S1 describes the change in deriveddemands for agricultural inputs. Once again, this is based on theassumption that producers in the sector seek to minimize theircosts in the long run. In the absence of technical change, there aretwo factors driving the demand for an input such as nitrogenfertilizer in the long run. First is the so-called expansion effect.This effect is captured by qo. If aggregate agricultural outputexpands by 10%, then, with all else equal, one would expectthe demand for fertilizer, and indeed all other inputs, to rise by10%.† However, there is a second factor at work, the substitutioneffect: σðpj − poÞ. This effect modifies the equi-proportional ex-pansion based on changes in the relative scarcity of inputs.(Recall from Eq. 2 that the percentage change in long runoutput price is equal to the percentage change in unit costs, oralternatively, the average input price rise.) Thus, if land becomesmore scarce, we expect an intensification of fertilizer use:qfert − qo= σðpfert − poÞ< 0, where the left side of this expressionis the change in fertilizer intensity of agricultural output.In the long run, what we typically observe in agriculture is that

the prices of nonland inputs are dictated by the nonfarm econ-omy, which is why these are treated as exogenous in this model asin the fourth equation in Box S1. The returns to agricultural land,however, are endogenous, and depend on both land demand(third equation of Box S1) and land supply (fifth equation of BoxS1). As with commodity demand, the land supply response toscarcity in the farm sector is governed by an endogenous re-sponse to prices, as governed by the price elasticity of land supplywith respect to land rents, νL.The focus of this analysis is on the impacts of technological

change, which is a key driver of long run agricultural output andprices (14). In the theoretical model laid out in Box S1, there isjust one type of technological progress: output-augmenting, t, orHicks-neutral technical change, which is the predominant typeexplored in the literature.

Analysis of Single Region Impacts. Substituting equation 4 in Box S1into equation 2 in Box S1, and solving for land rents, we obtain

pL = θ−1L ðpo+ tÞ: [S1]

This result is the well-known magnification effect in economicswhereby any change in output price is magnified as it is transmit-ted back to the returns to the sector-specific factor, land. The de-gree of magnification depends on the share of these farm-ownerinputs in total costs. For example, if farm-owned inputs accountfor half of total costs and the prices of purchased (variable) inputsare exogenous to agriculture in the long run equation 4 in Box S1,then, in the face of perfectly elastic farm-level demand (i.e.,po= 0), a 1% decline in agricultural productivity will result ina 2% decline in farm income. This magnification effect arisesbecause farmers cannot share the burden of the adverse produc-tivity change with purchasers of their product, nor can theseburdens be passed to the suppliers of nonfarm inputs, the priceof which is set by the nonfarm economy. Of course, if the non-farm inputs are not in perfectly elastic supply, then some of thelosses will be shared with suppliers of inputs (e.g., fertilizer

Box S1. Analytical model of long run demand and supplyfor agricultural land

(1) qo=−«Dpo Demand for agricultural output(2) po+ t =

P

jθjpj Agricultural entry/exit; zero profits

(3) qj =qo− t − σðpj −po− tÞ,∀j=1−N

Demand for agricultural inputs

(4) pj =0, ∀j≠ L Supply of nonland inputs(5) qL = νLpL Supply of land to agriculture

Notation: All price and quantity variables represent percentagechanges in the underlying indexes. qo, % change in long run agricul-tural output; qj , % change in long run use of agricultural input j; t,cumulative output-augmenting technical change in agriculture; po, %change in the price of agricultural output; pj , % change in the price ofagricultural input j; σ≥ 0, nonnegative elasticity of substitution be-tween land and nonland inputs; «D ≥ 0, nonnegative price elasticityof demand for aggregate farm output; νL ≥ 0, nonnegative elasticityof land supply to agriculture; θj ≥0, nonnegative cost share of input j.

*For the historical analysis, we start with the 2006 database then create the 1961 data-base via hindcasting. However, the results are reported as changes from 1961-2006 forease of interpretation.

†Eq. 3 reflects the phenomenon of constant returns to scale (CRTS), which suggests thata doubling of all inputs will result in a doubling of output. There is ample evidence thatthis does not apply at the level of individual farms. Very small farms often suffer frominsufficient scale to fully exploit machinery and other modern technology. However, atthe sector level, in the presence of relatively free entry/exit of firms, it can be shown thatthe industry technology will exhibit constant returns to scale (13).

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producers) in the form of lower prices. Because small scale, lowincome farm households are likely to be less commercialized,this magnification effect will typically be less pronounced forthem than for commercialized farms which are well-integratedinto the nonfarm economy.The notion that farmers might face a perfectly elastic demand

for their products depends on the geographical scope of theproductivity shock. As the span of the technological innovationexpands to a global scale, the assumption that farm prices willremain unchanged becomes increasingly unrealistic. Widespreadimprovements in agricultural productivity (relative to their baselinerealization) will result in increased global output and thereforelower prices (again, relative to baseline). The extent of the en-suing price decline will depend on the relative price elasticities ofcommodity supply and farm level demand, and the latter willdepend on the scope of the technology shock. If the innovation isadopted on only one plot of land, then the farm level demandelasticity is likely to be very high indeed, approaching the case offixed commodity price as discussed in the previous paragraph. Onthe other hand, if the technological improvement affects theentire region, then the farm level demand elasticity will approachthe consumer demand elasticity for food, which may be quite smallin absolute value.We can solve for the equilibrium outcome when commodity

prices are allowed to vary as a function of the Hicks-neutralchange in productivity. The easiest way to do this is to use thefirst equation in Box S1 to eliminate qo from the third equation,and then use the second equation to eliminate po. Equating thethird and fifth equations in Box S1 to reflect equilibrium in theland market leaves us with one equation in one unknown,namely land rents, which depend on all of the economic pa-rameters in the model as well as the productivity shock:

pL = tf½«D − 1�=½νL + σð1− θLÞ+ θL«D�g= βLt: [S2]

Plugging Eq. S2 into the equation 5 in Box S1, because landsupply varies directly with land returns, we obtain

qL = tfνLβLg: [S3]

Substituting in the expression for βL and rearranging, as well asadding superscripts to denote the fact that we are considering aworldwide change in technology, we obtain Eq. 1. We can seethat the impact of technological progress in agriculture on landsupply is ambiguous. In particular, because all of the parametersin the denominator of βL are nonnegative, t> 0⇒ pL < 0 if, andonly if «D < 1. That is, land supply and associated greenhousegas (GHG) emissions will fall following a favorable techno-logical innovation if and only if farm level demand is inelastic.This condition is a more general statement of Borlaug’s land-sparing hypothesis and confirms the findings of Angelsen andKaimowitz (15).The farm level demand elasticity which is pertinent to Eq. 1 is

directly related to the geographic scope of the productivity shocks.In those cases where the technological innovation is global inscope, such that producers worldwide are affected, then the rel-evant demand elasticity is the global price elasticity of demand forfood, translated back to the farm level. Because the demand forfood tends to be price inelastic, we may conjecture that a positiveinnovation will reduce land area and emissions.In addition to explaining the circumstances under which crop-

land and GHG emissions might fall under technological innovation,Eq. S2 offers insights into the likely magnitude of such pricechanges. In particular, the change in land rents, for a given farmlevel demand elasticity and a given factor-neutral productivityshock, will be greater and the smaller the elasticity of land supply(νL) and the smaller the elasticity of substitution between land and

nonland inputs (σ) will be. Eq. S2 can be rewritten in termsof the implied commodity supply elasticity in this model,«S = θ−1L νL + σðθ−1L − 1Þ, where the first term represents arearesponse to the commodity price change and the second re-flects yield response to higher commodity prices. This sub-stitution results in Eq. S4

pL = f½«D − 1�=θL½«S + «D�gt= βLt: [S4]

Increasing the land supply elasticity or the elasticity of substitu-tion boosts the aggregate supply responsiveness of output, therebydampening the resulting price changes.Plugging Eq. S4 into Eq. S1 and solving for the equilibrium

output price change gives

po=−f½«S + 1�=½«S + «D�gt= βOt; [S5]

from which we see that favorable innovations will depress com-modity price. The resulting equilibrium change in output can sim-ply be read off the demand schedule

qo= «DβOt: [S6]

Assessing the Impacts of Agricultural Technology on Global Land Useand Emissions. In the preceding section, all of the analysis focusedon a single region, be it an individual farm, a province, a nation, acontinent, or the world. However, when the relevant scale is lessthan global, this single region analysis misses the response of therest of the world to these developments. To understand theimpacts of a continental scale technology shock on global landuse, we need to factor in not only the changes that arise in theinnovating region but also the response of producers in theunaffected region.Global price effects in a two-region model. We begin with a reducedform representation of the preceding model, as portrayed in Fig. 1,in which supply in each region is a simple function of price. Withintegrated world markets, an outward shift in region A’s supplycurve ensures an output rise in A, a fall in the rest of the world(RoW), and a decline in world price.Mathematically, we have

qoA = «AS po+ΔAS ; qoR = «RS po; and qoW = «WD po: [S7]

Global market clearing requires that demand equals aggregatedregional supplies

qoW = αqoA + ð1− αÞqoR; [S8]

where α=QOA=QOW denotes that share of global production inthe affected region. Solving for the equilibrium change in globalprice in response to the shift in region A’s supply curve

po=−αΔAS

��«WS + «WD

�= βWO tA: [S9]

Where the global supply elasticity is just the weighted combina-tion of the regional supply elasticities: «WS = α«AS + ð1− αÞ«RS .We can now relate the two-region problem back to the single

region problem dealt with previously by rewriting Eq. S9 asfollows:

po=−ΔAS

����«WD + ð1− αÞ«RS

��α�+ «AS

�=−ΔA

S

��«AD + «AS

�;

[S10]

where «AD = ½«WD + ð1− αÞ«RS �=α is the elasticity of excess demandfacing producers in region A. This elasticity reflects the residualdemand for region A’s product, once the supply response in therest of the world is accounted for. As such, it is larger than the

Hertel et al. www.pnas.org/cgi/content/short/1403543111 3 of 9

ordinary demand elasticity. Indeed, even if global demand is whollyinelastic, the excess demand response can be elastic if producers inthe rest of the world are sufficiently responsive to a price changeinduced by developments in region A. Because this combinedprice response is weighted by the inverse of the share of regionA’s production in the world market, as α→ 0, the excess demandelasticity facing these producers becomes infinite. This result issimply a formal representation of the one region result in whichimpacts of a localized innovation in the case where the regionaleconomy is fully integrated into the world economy results in thefull benefit of the productivity improvement flowing through toproducers in the innovating region.Global land use impacts.Having established the impact of a shock tosupplies in region A on world prices, we can work our way back tothe regional demands for land and ascertain the aggregated impacton global land use and GHG emissions. However, before we at-tempt to do so, we must first be more explicit about the nature ofthe productivity shock in region A, because the type of technologychange matters for the impact on land use. Throughout thissection, we focus on the Hicks-neutral productivity shock, as thequalitative insights from the two region model will be similar re-gardless of the type of shock applied in region A.Referring to the model structure laid out in Box S1, the supply

shift may be written as follows: ΔAS = ð«AS + 1ÞtA. Substituting this

expression into Eq. S10 gives the following price impact owing tothe technology shock:

po=−�«AS + 1

�tA��

«AD + «AS

�= βOt

A; [S11]

which is identical to Eq. S5, excepting for the A superscripts onthe supply and demand elasticities. These superscripts makeexplicit the key assumption imbedded in the earlier analysisthat these shocks apply to a particular region, not to globalagriculture.With Eq. S11 in hand, the percentage change in global land

use may be written as

qWL = δqAL + ð1− δÞqRL = δ�νAL

�θAL�ðβO + 1ÞtA + ð1− δÞ

�νRL�θRL�βOt

A;

[S12]

where δ=QAL=Q

WL is the share of the affected region’s agricul-

tural land cover in the global total, and the changes in regionalland use are obtained from the regional land supply schedules.As noted in the main text, it is not possible to say, in the general

case, whether global land use change will be positive or negativefollowing a productivity improvement in the affected region: ao> 0.The answer depends critically on the relative size of this region andits land supply response relative to the rest of the world. To seethis, rewrite Eq. S12 as follows:

qWL�tA =

�δ�νAL

�θAL��

«AD − 1���

«AD + «AS

�

+ ð1− δÞ�νRL�θRL��

−«AS − 1���

«AD + «AS

��; [S13]

which is Eq. 2. The sign of the second term within the brackets []is always negative, indicating that, in the face of the inevitableprice decline, owing to tA > 0, land area in the rest of the worldwill decline. The ambiguity in global land use arises due to thefirst term. In particular, a necessary condition for Jevon’s para-dox: ðqWL =tAÞ> 0, is that the first term on the right side of Eq. S13be positive, and for this, we require an elastic excess demandfacing region A, «AD > 1. However, this is not a sufficient condi-tion. The first term must also be large enough to dominate thesecond one for global land use to rise in the face of technologicalchange in region A. This condition is more likely if, in addition tothe elastic excess demand (which is likely to come from havinga small share of global production: α→ 0), A comprises a rela-

tively large land area such that δ→ 1. Of course, these two con-ditions can only coexist if yields are very low in the innovatingregion. In addition, if region A’s land supply is relatively moreresponsive, i.e., ðνAL=θALÞ � ðνRL=θRLÞ, Jevon’s paradox becomesmore likely. However, because these extensive margin supply elas-ticities also enter into the supply and excess demand elasticities inβO, it is difficult to say anything more precise about the conditionsfor global area expansion or contraction in the most general case.Therefore, we turn to the analysis of some special cases to gainadditional insight into the competing forces at work here.Equal extensive margins. In the first special case, we assume that theextensive margin of supply response is equal in the two regions,i.e., νAL=θ

AL = ðνRL=θRLÞ= ðνL=θLÞ. Therefore, the terms involving

δðνL=θLÞβOtA in Eq. S12 cancel and we are left with the followingexpression:

qWL = ðδ+ βOÞðνL=θLÞtA: [S14]

Now the critical condition for Jevons’ paradox is δ> − βO =f½«AS + 1�=½«AS + «AD�g. This condition is most likely to arise whenthe affected region is large, δ→ 1, and when excess demand isvery elastic: «AD � 0, which, as noted above, can arise whenyields in the affected regions are low. Clearly having elastic globaldemand also makes this condition more likely, as does having amore elastic supply response in the unaffected region (RoW). Inlight of our assumption that the extensive margins of supply re-sponse are equal, this latter condition could arise if the intensivemargin of supply response in the rest of the world is large.Equal intensive and extensive margins.To gain further insight into theconditions for global land area to decline, we can additionallyassume that the intensive margin of supply response is identical inthe two regions, so we may drop the regional subscripts inσðθ−1L − 1Þ as well, so that «AS = «RoWS = «WS . Now the expressionfor the incidence parameter, βO, with the full excess demand ex-pression substituted in, becomes

βO =−�«AS + 1

������«WD + ð1− αÞ

�«RoWS

��α�+ «AS

�

=−α�«WS + 1

���«WD + «WS

�:

[S15]

The condition for Jevons’ paradox may therefore be written asδ> ὫWS + 1�=ð«WD + «WS Þ or alternatively the following condition:

«WD > ðα=δÞ�«WS + 1

�− «WS ⇒

�qWL

�tA�> 0: [S16]

The ratio of the production share to the land share in Eq. S16,ðα=δÞ, reduces to the ratio of yields (output per hectare) inregion A to global yields, which gives us Eq. 3. From this, we seemore clearly that the likelihood of global land area expanding inthe face of innovation in region A increases when yields in theaffected region are low, relative to the world average yields. Thiscondition makes sense, because we know that agricultural area inregion RoW will fall in the wake of the productivity improve-ment in A, and the area displaced by increased production in Awill be smaller, the smaller is this yield ratio (smaller right side inEq. 2) and the larger the increase in global demand due to theresultant price decline (larger left side in Eq. 2).Global emissions impacts. In the literature on climate change miti-gation, the reason for interest in land cover change at global scaleis due to the potential for significant land-based carbon fluxes.Once we have an estimate of land cover change for each region ofthe world, we can attach an emissions factor to these changes,thereby obtaining an estimate of the change in global GHG emis-sions due to land cover change. We expect these emissions factors todepend on where the conversion occurs, previous land coverin that area, as well as the direction of conversion (i.e., intoagriculture or out of agriculture). Such nuances have now been

Hertel et al. www.pnas.org/cgi/content/short/1403543111 4 of 9

incorporated into simulation models seeking to estimate globalcarbon fluxes due to land cover change (16, 17). For purposes ofthis long run analysis, it will suffice to assume that there is justone (average) emissions factor in each region and that it is re-versible; i.e., conversion of one hectare of land to agriculturereleases the same amount of carbon that would be sequestered ifthe parcel of land were to leave agriculture. In this case, we canwrite the change in global emissions (EW ) as follows:

dEW = efAdQAL + ef RdQR

L; [S17]

where ef A is the agricultural land conversion emissions factor inregion A, measured in tons of CO2 per hectare converted. Mul-tiplying each of the terms on the right side of Eq. S17 by Qj

L=QjL,

and dividing through by historical emissions, defined as EW =efAQA

L + ef RQRL, we obtain the following expression for the change

in emissions, as a percentage of historical land-based emissions:

eW = γqAL + ð1− γÞqRL; [S18]

where γ = ef AQAL=ef

WQWL is the share of region A in global his-

torical land-based emissions.The percentage change in emissions may now be expressed in

terms of the model parameters and the technology shock as follows:

eW =�γ�νAL

�θAL��

«AD − 1���

«AD + «AS

�

+ ð1− γÞ�νRL�θRL��

−«AS − 1���

«AD + «AS

��tA;

[S19]

which is the same as Eq. S13, excepting that the two land usechange terms are now weighted by the relative importance ofeach region in total potential emissions. We can then use thesame techniques for evaluating the sign of the right side ofEq. S19 as for global land use change.Extension of the Borlaug hypothesis to the question of emis-

sions suggests that global land-based emissions should fall with animprovement in technology affected region. However, as withglobal land use, it is possible that emissions could rise. The basicconditions are the same as for global land use except for the issueof relative yields. In the case of emissions, the relevant com-parison is between output/unit emissions in region A vs. output/unit emissions in the world as a whole. The lower this index of

relative environmental efficiency in A, the more likely it is thatglobal emissions could rise as a result of technological innovationin that region.This condition can be readily seen if we assume that the two

elements of supply response are the same in both regions, givingrise to an expression similar to Eq. 3. Now a productivity im-provement in region A results in a rise in global emissions if

«WD > ðα=γÞ�«WS + 1

�− «WS ⇒ eW

�tA > 0; [S20]

where α=γ is the relative emissions efficiency of region A. Com-bining insights from the foregoing analysis, we find that the changein global emissions associated with agricultural land use in the faceof technological improvement in a given region of the world isuncertain. However, such emissions are most likely to rise when(i) global food demand is relatively elastic, (ii) the innovatingregion represents a large share of historical emissions from landuse change, (iii) the innovating region has a low relative emis-sions efficiency, (iv) the extensive margin of supply response inthe innovating region is large relative to the rest of the world,and (v) the intensive margin of supply response in the rest of theworld is relatively large.

Numerical Values Associated with the Two-Region Theoretical Model.In the text we discuss the numerical values for key parametersin the theoretical model, which we use to evaluate Eq. 2. Thesenumerical values are obtained by aggregating the 2006 benchmarkSIMPLE model to two regions. This aggregation groups togetherthe historical Green Revolution regions: Asia, Latin America,and the Middle East, leaving all other regions in the RoW, andthe Green Revolution region corresponds to sub-Saharan Africa(Table S5). Because the latter is a much smaller region, as shownby its 9% crop production share and 13% cropland share, weobserve a much larger excess demand elasticity. Also notable isthe relatively high cropland supply elasticity in Africa. All ofthese entries are computed under the assumption of fully in-tegrated crop markets. However, as we have seen above, marketshave historically been segmented. To shed light on the seg-mented markets case, we also compute the excess demandelasticity facing each region in the case of segmented markets.These values are reported in the parenthetic entries of Table S5.

1. Muhammad A, Seale JL, Jr, Meade B, Regmi A (2011) International Evidence on Food

Consumption Patterns: An Update Using 2005 International Comparison Program

Data (Economic Research Service, US Department of Agriculture, Washington, DC).2. Gurgel A, Reilly JM, Paltsev S (2007) Potential land use implications of a global

biofuels industry. J Agric Food Ind Organ 5(2):1–34.3. Ahmed SA, Hertel T, Lubowski R (2008) Calibration of a Land Cover Supply Function

Using Transition Probabilities (Center for Global Trade Analysis, Department of

Agricultural Economics, Purdue Univ, West Lafayette, IN).4. OECD (2001) Market Effects of Crop Support Measures (OECD, Paris).5. Hertel T, Hummels D, Ivanic M, Keeney R (2003) How Confident Can We Be in CGE-

Based Assessments of Free Trade Agreements? Available at: http://www.gtap.

agecon.purdue.edu/resources/res_display.asp?RecordID=1283. Accessed March 30,

2010.6. West PC, et al. (2010) Trading carbon for food: Global comparison of carbon stocks vs.

crop yields on agricultural land. Proc Natl Acad Sci USA 107(46):19645–19648.7. Keeney R, Hertel TW (2005) GTAP-AGR: A Framework for Assessing the Implications of

Multilateral Changes in Agricultural Policies (Center for Global Trade Analysis,

Department of Agricultural Economics, Purdue Univ, West Lafayette, IN).8. Keeney R, Hertel TW (2009) Indirect land use impacts of US biofuels policies: The

importance of acreage, yield and bilateral trade responses. Am J Agric Econ 91(4):

895–909.

9. Baldos ULC, Hertel TW (2013) Looking back to move forward on model validation:insights from a global model of agricultural land use. Environ Res Lett 8(3):034024.

10. Hertel T, McDougall R, Narayanan B, Aguiar A (2014) Behavioral Parameters. Availableat: www.gtap.agecon.purdue.edu/resources/res_display.asp?RecordID=4551. Accessed May19, 2014.

11. Hertel TW (1989) Negotiating reductions in agricultural support: Implications oftechnology and factor mobility. Am J Agric Econ 71(3):559–573.

12. Gohin A, Hertel T (2003) A note on the CES functional form and its use in the GTAPmodel. GTAP Res Memo No 02. Available at: www.gtap.agecon.purdue.edu/resources/res_display.asp?RecordID=1370. Accessed September 8, 2010.

13. Diewert WE (1981) The comparative statics of industry long-run equilibrium. Can JEcon Rev Can Econ 14(1):78–92.

14. Alston JM, Babcock BA, Pardey PG, eds (2010) The Shifting Patterns of AgriculturalProductivity Worldwide (CARD-MATRIC Electronic Book, Center for Agricultural andRural Development, Ames, IA).

15. Angelsen A (2001) Agricultural Technologies and Tropical Deforestation, ed Kaimowitz D(CAB International, Cambridge, MA).

16. Hertel TW, et al. (2010) Global land use and greenhouse gas emissions impacts of USmaize ethanol: Estimating market-mediated responses. Bioscience 60(3):223–231.

17. Plevin RJ, Gibbs HK, Duffy J, Yui S, Yeh S (2011) Agro-ecological zone emission factormodel. Available at: http://plevin.berkeley.edu/docs/Plevin-AEZ-EF-Model-Preliminary-Sep-2001.pdf. Accessed September 27, 2013.

Hertel et al. www.pnas.org/cgi/content/short/1403543111 5 of 9

Fig. S1. Diagram of the SIMPLE model. (Lower; green) Regional crop production for the aggregate crop commodity. (Upper; red) Regional crop demand. Thedisposition of crops includes direct consumption, feedstuff use and food processing, and biofuels. Under market segmentation, consumers and producersinteract in the domestic and international crop markets.

Fig. S2. Sensitivity analysis of the regional and global cropland and CO2 emissions change under the historical simulation: difference between with vs. withouthistorical Green Revolution TFP growth under market segmentation. Error bars reflect 95% CIs obtained from Monte Carlo analysis with respect to parameteruncertainty.

Hertel et al. www.pnas.org/cgi/content/short/1403543111 6 of 9

Table S1. Triangular distributions of selected parameters

Global parameters Parameter Mode Maximum Minimum

Demand elasticitiesIncome elasticities: regression intercept EIY

Crops 0.88 1.15 0.62Livestock 1.05 1.36 0.73Processed foods 1.20 1.56 0.84

Price elasticities: regression intercept EIPCrops −0.74 −0.52 −0.96Livestock −0.83 −0.58 −1.07Processed foods −1.17 −0.82 −1.52

Nonland supply response ENLAND 1.34 1.74 0.94Land supply response ELAND 0.28 0.36 0.20Elasticity of substitution: crop ECROPHistorical simulation 1.13 1.47 0.79Future projection 3.00 3.90 2.10

Elasticity of substitution: livestock ECRPFEED 1.16 1.51 0.81Armington elasticities ESUB 2.50 5.00 1.25Carbon loss per area of cropland (in CO2 Mg/1,000 ha) C_EMIS_HA −6,310 −4,418 −8,202

Table S2. Regional scalars for selected parameters

RegionsLand supplyresponse

Carbon loss per hectareof cropland

Eastern Europe 2.00 0.69North Africa 0.39 0.16Sub Saharan Africa 2.00 2.81South America 2.00 3.22Australia/New Zealand 2.00 0.54European Union+ 0.39 0.79South Asia 1.00 0.52Central America 1.00 2.65Southern Africa 1.00 1.43Southeast Asia 1.00 4.27Canada/US 1.00 1.00China/Mongolia 1.00 1.49Middle East 0.39 0.45Japan/Korea 0.39 2.35Central Asia 2.00 0.92

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Table S3. Key growth rates for the historical and future simulations

Regions Population Per capita income Biofuels

Total factor productivityYield growth fromGreen RevolutionCrops Livestock Processed food

Eastern Europe −0.36 [0.60] 4.75 [0.57] [0.83] 1.04North Africa 1.02 [2.14] 3.49 [2.38] [1.94] −0.30 [0.69]Sub Saharan Africa 2.44 [2.75] 3.80 [0.46] [0.78] 0.42 0.88South America 0.67 [2.05] 2.61 [1.62] [1.74] 2.64 [0.66]Australia/New Zealand 1.04 [1.54] 1.62 [2.11] [1.44] 0.42European Union+ 0.11 [0.48] 1.34 [2.56] [2.10] 0.50South Asia 0.83 [2.14] 4.97 [2.62] [1.16] 1.71 [0.88]Central America 0.84 [2.27] 2.40 [1.97] [1.17] 2.64 [0.66]Southern Africa 0.64 [2.27] 2.62 [1.07] [1.69] 0.42 0.88Southeast Asia 0.79 [2.18] 3.67 [3.34] [1.62] 2.38 [0.88]Canada/US 0.66 [1.06] 1.01 [2.31] [1.65] 0.42China/Mongolia 0.10 [1.56] 5.90 [7.03] [2.01] 2.38 [0.88]Middle East 1.21 [2.24] 1.01 [2.61] [1.42] −0.25 [0.69]Japan/Korea −0.20 [0.85] 1.96 [3.59] [2.18] 0.42 [0.88]Central Asia 0.96 [0.60] 4.90 [0.57] [0.83] 1.04World 5.75 0.94 [1.30] 0.89 [0.89]

Rates within brackets are for the historical period (1961–2006), whereas the rest are for the future period (2006–2051). Data sources from left to right: UNWorld Population Prospects (1), future and historical income growth rates from Fouré et al. (2) and WDI (3), respectively, biofuels from IEA (4, 5), future andhistorical growth rates of crop TFP from Ludena et al. (6) and Fuglie (7), respectively, and future TFP growth rates for crops, livestock, and processed foods fromLudena et al. (6), Griffith et al. (8), and Evenson (9).

1. UN Population Division (2013) World Population Prospects: The 2012 Revision (Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat,New York).

2. Fouré J, Bénassy-Quéré A, Fontagné L (2013) Modelling the world economy at the 2050 horizon. Econ Transit 21(4):617–654.3. World Bank (2013) World Development Indicators (World Bank, Washington, DC).4. IEA (2008) World Energy Outlook (OECD Publishing, Paris).5. IEA (2012) World Energy Outlook (OECD Publishing, Paris).6. Ludena CE, Hertel TW, Preckel PV, Foster K, Nin A (2007) Productivity growth and convergence in crop, ruminant, and nonruminant production: measurement and forecasts. Agric Econ

37(1):1–17.7. Fuglie KO (2012) Productivity Growth in Agriculture: An International Perspective, eds Fuglie KO, Wang SL, Ball VE (CAB International, Cambridge, MA), pp 335–368.8. Griffith R, Redding S, Reenen JV (2004) Mapping the two faces of R&D: Productivity growth in a panel of OECD industries. Rev Econ Stat 86(4):883–895.9. Evenson RE (2003) Crop Variety Improvement and Its Effect on Productivity: The Impact of International Agricultural Research, eds Evenson RE, Gollin D (CAB International, Oxon, UK),

pp 447–472.

Table S4. Summary of terms used in the theoretical analysis

Parameters Description

t : Total factor productivity Ratio of output to inputs used in crop production, accounting for both land andnonland inputs

«D : Price elasticity of crop demand(Demand margin)

Percent change in crop consumption given a one percent change in crop price

«S : Supply elasticity of crops Percent change in crop production given a one percent change in crop priceνL : Supply elasticity of cropland Percent change in cropland area supplied to the crop sector given a one percent

change in cropland returnsνL=θL : Extensive margin of supply The potential for cropland expansion in response to higher crop pricesσ : Elasticity of substitution Scope for input substitution between land and nonland inputs used in crop productionσ½ð1=θLÞ− 1� : Intensive margin of supply The potential for crop yield increases in response to higher crop prices½«D + ð1− αÞ«S�=α : Excess demand elasticity Price responsiveness of demand for regional crop output, once RoW supply response is factored in

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Table S5. Key parameters corresponding to the analytical model based on two alternative two region aggregations

RegionProduction

shareCroplandshare

Croplandsupply

elasticityTotalsupply

Excessdemandelasticity

Relativeyield

Relativeemissionsefficiency

Historical Green RevolutionRoW region 0.34 0.53 0.49 1.08 2.82 (0.78) 0.64 1.05Asia-Latin America-Middle East

Green Revolution region0.66 0.47 0.38 1.03 0.98 (0.50) 1.40 0.96

World 1.00 1.00 0.44 1.05 0.28 (0.29) 1.00 1.00African Green RevolutionRoW region 0.91 0.87 0.41 1.03 0.43 (0.31) 1.05 1.15African Green Revolution

region0.09 0.13 0.64 1.25 13.53 (0.74) 0.69 0.50

World 1.00 1.00 0.44 1.05 0.28 (0.29) 1.00 1.00

Parameters correspond to the definitions in the theoretical model underpinning in Eqs. 1–3. The parameters have been computed based on the 2006database for SIMPLE and associated model parameters, aggregated from 15 regions to the two different groupings of two regions shown here. The historicalGreen Revolution comprises Asia, Latin America, and the Middle East, whereas the African Green Revolution refers to sub-Sahara Africa. In both cases, RoWrefers to the grouping of all remaining regions in the model. The parenthetic entries in this table refer to the values of the excess demand elasticities facingeach region in the presence of segmented markets.

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