Evolving Comparative Advantage and the Impact of Climate Change in Agricultural Markets: Evidence from a 9 Million-Field Partition of the Earth

Transcription

1 Evolvng Comparatve Advantage and the Impact of Clmate Change n Agrcultural Markets: Evdence from a 9 Mllon-Feld Partton of the Earth Arnaud Costnot MIT and NBER Dave Donaldson MIT and NBER September 2012 Cory Smth MIT Abstract A large agronomc lterature has modeled the mplcatons of such clmate change for crop yelds, crop by crop and locaton by locaton. These studes document the harm that clmate change s expected to nflct on a specfc crop at a specfc locaton. The goal of the present paper s to quantfy the macro-level consequences of these mcrolevel shocks. Our analyss bulds on the smple observaton that n a globalzed world, the mpact of mcro-level shocks do not only depend on ther average level, but also on ther dsperson over space,.e. how they affect comparatve advantage. Usng an extremely rch mcro-level dataset that contans nformaton about the productvty both before and after clmate change of each of 39 crops for each of over 9 mllon hgh resoluton grd cells coverng the surface of the Earth, we fnd that nternatonal trade, even wth reasonable levels of trade costs, wll substantally mtgate the ll-effects of clmate change on agrcultural lvng standards n the average country.

2 1 Introducton The warmer clmates predcted by clmatologcal models portend a grm future for many bologcal systems, such as agrcultural plant lfe, on whch human welfare depends. But just how much wll lvng standards suffer as plants wlt n a hotter world? A large agronomc lterature has modeled the mplcatons of such clmate change for crop yelds, crop by crop and locaton by locaton see IPCC, 2007, Chapter 5 for a revew). These studes document the harm that may be nflcted on a specfc crop at a specfc locaton. The goal of our paper s to quantfy the macro-level consequences of these mcro-level shocks. Our analyss bulds on the smple observaton that n a globalzed world whch s the world we nhabt the mpact of mcro-level shocks do not only depend on ther average level, but also on ther dsperson over space. If clmate change makes regons of the world more homogeneous n terms of ther agrcultural productvty, there wll be less trade and welfare wll further decrease. If clmate change nstead rases heterogenety across regons, there wll be more scope for nternatonal trade, whch wll dampen the adverse consequences of clmate change. In short, the macro-consequences of clmate change n a global economy are nherently related to how t affects comparatve advantage across regons of the world. To shed lght on the relatonshp between clmate change and comparatve advantage, we take advantage of an extremely rch mcro-level dataset on agrcultural productvty: the Food and Agrculture Organzaton s FAO) Global Agro-Ecologcal Zones GAEZ) dataset. Ths dataset uses agronomc models and hgh resoluton data on geographc characterstcs such as sol, topography, elevaton and, crucally, clmatc condtons to predct the yeld that would be obtanable at over 9 mllon hgh resoluton grd cells coverng the surface of the Earth. The GAEZ dataset s avalable both under contemporary growng condtons and under a clmate change scenaro smlar to those used by the UN s Intergovernmental Panel on Clmate Change IPCC). By comparng productvty for a gven crop under the two scenaros at each of our 9 mllon grd-cells, we can therefore drectly observe the evoluton of comparatve advantage across space, as predcted by clmatologsts and agronomsts. A sample of the GAEZ predctons can be seen n Fgure 1. Here we plot, for each grd cell on Earth, the predcted percentage change n productvty assocated wth clmate change for two of the world s most mportant crops: wheat panel a)) and rce panel b)). As s clear, there exsts a great deal of heterogenety n the effects of clmate change both across crops and over space many regons see a dfferental productvty change n wheat and rce, and ths relatve productvty change s dfferent from that of other regons. Further, the contours of the effects of clmate change on rce and wheat appear not to reflect country borders. Wthn-country heterogenety s a central feature of these data.. There s a more systematc way to see that an understandng of the mpact of clmate 1

3 change n agrculture requres an understandng of what wll happen to comparatve advantage. A smple regresson demonstrates the fact that, at least accordng to the GAEZ estmates, clmate change wll dstort comparatve advantage consderably around the world. If we regress the log change n each grd-cell s yeld.e. before and after clmate change) on a country and a crop fxed effect, the R-squared from ths regresson s only 50 percent. Put dfferently, half of the effects of clmate change wll preserve the exstng pattern of agrcultural comparatve advantage around the world.e. yelds wll evolve n a manner that s constant wthn countres and/or wthn crops) but half of the effects of clmate change wll alter ths pattern. It s the latter half of these effects of clmate change that are the focus of the present paper. To go beyond the evoluton of comparatve advantage documented n the agronomc GAEZ data and quantfy the economc macro-consequences of clmate change, we need an economc model of agrcultural markets that can predct: ) where crops are produced and consumed despte the presence of trade frctons), and n turn, whch productvty changes are relevant and whch ones are not; ) how shocks to the supply of crops affect prces around the world; and ) how changes n productvty and prces map nto welfare changes. We propose a perfectly compettve model of trade n whch each country conssts of a large number of felds wth heterogeneous productvty across multple crops. These are the theoretcal counterparts of the 9 mllon grd-cells n the GAEZ data. In ths model, comparatve advantage,.e. relatve productvty dfferences across crops and felds, determnes the pattern of specalzaton wthn and between countres. Fnally, nternatonal trade s subject to ceberg trade costs whose magntude pns down the level of ntegraton of local agrcultural markets. Besdes the hghly detaled GAEZ data, our quanttatve model depends only on a small number of parameters: ) the elastcty of substtuton between crops from dfferent countres, whch s the equvalent of the Armngton elastcty n standard Computatonal General Equlbrum CGE) models; ) the extent of wthn-feld heterogenety n productvty, whch s unobserved n the GAEZ data; and ) the elastcty of trade costs wth respect to dstance, whch we assume s the sole determnant of ceberg trade costs. These three parameters can be separately estmated usng trade, output, and prce data n a straghtforward and transparent manner. Armed wth these three parameters and the detaled knowledge of the pattern of comparatve advantage across felds and crops around the world, we smulate our model under the baselne no-clmate change scenaro and explore three counterfactual scenaros. In our frst scenaro, we study the consequences of clmate change.e., a change n the GAEZ productvty from contemporary growng condtons to clmate change condtons under the assumpton that farmers are free to change ther output decsons and countres are free 2

4 Panel a): Wheat Panel b): Rce Fgure 1: Percent changes n yeld due to clmate change n GAEZ model for wheat and rce. Large green areas are those for whch yelds are zero both before and after clmate change. to trade subject to our estmated trade costs). We then contrast the welfare mplcatons of clmate change under ths scenaro to those n a counterfactual world n whch countres can trade, but farmers cannot reallocate productons, and conversely, a counterfactual world n whch farmers can reallocate producton, but countres are under autarky. Ths allows us to quantfy how much changes n comparatve advantage wthn and between countres, respectvely, may o set or magnfy the e ects of a hotter clmate. Ultmately, whle we nd that the negatve e ects of clmate change wll be substantal for most countres e.g. the e ect s approxmately 13 percent of expendture on agrcultural goods n the world average country), these negatve e ects would be much worse f elds could not change ther what they grow 38 percent loss) or f countres could not trade at all 19 percent loss). The lterature on nternatonal trade and clmate change s large and vared, though 3

5 mostly based on Computatonal General Equlbrum CGE) models. A frst group of papers focuses on the drect mpact of nternatonal trade on the level of carbon emssons caused by nternatonal transportaton; see e.g. Crstea, Hummels, Puzzello, and Avetysyan forthcomng) and Shapro 12). A key nsght s that although nternatonal transportaton negatvely affects the envronment, the assocated welfare consequences are an order of magntude smaller than the gans from nternatonal trade. A second group of papers focuses on the ssue of carbon leakages,.e. the dea that f only a subset of countres tax carbon emssons, the level of emssons of nontaxng countres s lkely to go up; see Felder and Rutherford 1993), Babker 2005), Ellott, Foster, Kortum, Munson, Cervantes, and Wesbach 2010). More closely related to ths paper are studes on nternatonal trade and adaptaton n agrculture; see Relly and Hohmann 1993), Rosenzweg and Parry 1994), Tsgas, Frswold, and Kuhn 1997) and Hertel and Randhr 2000). The man dfference between prevous papers and the present analyss les n the level of dsaggregaton at whch we observe the mcro-consequences of clmate changes whle the exstng lterature works wth country averages, we aggregate up n a theoretcally consstent manner from the full set of nne mllon felds around the world. We document n Secton 4 below how an analyss based on natonal averages performs sgnfcantly worse at matchng the data wthn sample.) By feedng ths rch mcro-data nto a general equlbrum n whch comparatve advantage determnes the pattern of specalzaton, both wthn and across countres, we are then able to study, quantfy and compare the gans from adaptaton to clmate change through local and nternatonal specalzaton. Fnally, our analyss s related to Costnot and Donaldson 2011) who also use the GAEZ data to quantfy the gans from economc ntegraton n U.S. agrcultural markets from 1880 to The rest of ths paper s organzed as follows. Secton 2 ntroduces our theoretcal framework. Secton 3 descrbes the data that feeds nto our analyss. Secton 4 descrbes our emprcal parameter estmaton procedure and presents our parameter estmates as well as measures of goodness of ft of the model). Secton 5 then presents the results of our counterfactual smulatons. Fnally, Secton 6 descrbes some robustness extensons that are n progress and Secton 7 offers some concludng remarks. 2 Theory 2.1 Basc Envronment We consder a world economy comprsng multple countres, ndexed by I {1,..., I}. In each country, the only factors of producton are felds, ndexed by f F {1,..., F }, 4

6 each comprsng a contnuum of heterogeneous parcels of land, ndexed by ω [0, 1]. We thnk of land as equpped land,.e. land plus physcal captal and labor, though we abstract from the allocaton of physcal captal and labor across felds. All felds have the same sze, whch we normalze to one. In our dataset, the sze of a feld s equal to 5 arc-mnute grd-cell and there are 9 mllon such grd-cells on Earth. Felds can be used to produce multple goods ndexed by k K {0,..., K}. Goods 1,..., K are crops, whereas good 0 wll be an outsde good. We thnk of the outsde good as resdental housng, forestry, manufacturng, or any agrcultural actvty such as lvestock producton) that does not correspond to the crops ncluded n our dataset. There s a representatve agent n each country whose preferences can be represented by a two-level utlty functon: U = K ) k=0 C k β k, 1) C k = I j=1 C k j ) σ 1)/σ ) σ/σ 1), for all k = 1,..., K, 2) where β k 0 denotes exogenous expendture shares, wth K k=0 βk = 1; σ > 0 denotes the elastcty of substtuton between crops from dfferent orgns, e.g. French versus U.S. wheat; C k j denotes the consumpton n country of crop k = 1,..., K produced n country j, wth C k the aggregate consumpton of crop k n country ; and C 0 denotes the aggregate consumpton of the outsde good n country. Parcels of land are perfect substtutes n the producton of each good, but vary n ther exogenously-gven productvty per acre, ω) 0. Total output Q k of good k n country s gven by Q k = 1 f F 0 Afk ω) L fk ω) dω, 3) where L fk ω) 0 denotes the endogenous number of acres of parcel ω n feld f allocated to good k n country. For all goods k K, we assume that the productvty of each parcel can be expressed as ln ω) = ln + ε fk ω). 4) The frst term, > 0, s a common productvty shfter of all parcels n feld f. It measures the comparatve and absolute advantage of a feld n producng partcular goods. The GAEZ project data gve us drect nformaton about for all crops k = 1,..., K as a functon of global temperatures, whch wll be the core nputs n our quanttatve exercse. ε fk ω) reflects unobserved wthn-feld heterogenety n productvty across parcels. In lne wth Eaton and Kortum 2002), we assume that ε fk ω) s ndependently drawn for each 5

7 , f, k, ω) from a Gumbel dstrbuton: [ ] F ε) = Pr ε fk ω) ε = exp [ exp θε κ)], 5) where θ > 1 measures [ the ] extent of wthn-feld heterogenety and the constant κ s set such that = E ω) n Equaton 4). 1 Fnally, snce we do not have dsaggregated productvty data n the outsde sector, we assume that n all countres I, all felds f F have the same productvty n the outsde sector, A f0 = A 0, whch we normalze to one n all countres. All markets are perfectly compettve. Internatonal trade n crops k = 1,..., K s subject to ceberg trade costs. In order to sell one unt of a good n country j, frms from country must shp τ k j 1 unts, wth τ k = 1. Non-arbtrage therefore requres the prce of a crop k produced n country and sold n country j to be equal to p k j = τ k jp k, 6) where p k s the producer of farm-gate prce of crop k n country. The outsde good, by contrast, s not traded. In lne wth the prevous notaton, we denote by p 0 the prce of the outsde good n country. 2.2 Compettve Equlbrum In a compettve equlbrum, all consumers maxmze ther utlty, all frms maxmze ther profts, and all markets clear. Gven Equatons 1), 2), and 6), utlty maxmzaton by consumers n any country requres C 0 = β0 Y, for all I 7) p 0 ) τ Cj k j p k σ j = I ) j =1 τ j p k 1 σ β k Y, for all, j I and k = 1,..., K, 8) j where Y k K pk Q k denotes total ncome n country. Proft maxmzaton requres that all parcels of land are allocated to the good that maxmzes the value of ther margnal product. Let π fk denote the share of parcels n a feld f 1 Formally, we set κ θ ln Γ ) θ 1 θ, where Γ ) denotes the Gamma functon,.e. Γt) = + v t 1 exp v)dv for any t >

8 located n country that are allocated to a good k. By Equaton 3)-5), we therefore have π fk = Pr { ω) A fl } ω) > pl f l k = p k l K p k ) θ p l Afl The prevous expresson hghlghts n a smple manner how relatve productvty dfferences,.e. comparatve advantage, determnes factor allocaton n ths economy. Gven factor allocaton, total output for good k n country can be expressed as Q k = f F E [ ω) p k ω) = max l K pl A fl ω) whch, usng agan Equatons 4) and 5), smplfes nto Q k = f F l K p k ) θ p l Afl ) θ ) θ. ] p k θ 1)/θ l K ) θ p l Afl ) θ,. 9) Fnally, good market clearng requres that the supply of each good s equal to ts demand: Q 0 = C 0, for all I, 10) Q k = j I τ jcj, k for all I and k = 1,..., K. 11) Let p ) p k denote the vector of producer prces, Q k K ) Q k denote the vector k K of output levels, and C C 0, ) ) Cj k denote the vector of consumpton levels n j I,k 0 country. In the rest of ths paper we formally defne a compettve equlbrum as follows. Defnton 1 A compettve equlbrum s a set of producer prces, p ) I, output levels, Q ) I, and consumpton levels, C ) I, such that Equatons 7)-11) hold. 3 Descrpton of Data Our analyss draws on four man types of data: ) estmates of agrcultural productvty, at each hgh-resoluton land parcel on Earth and for each of a seres of crops, for a baselne.e. pre-clmate change) scenaro; ) smlar agrcultural productvty estmates, calculated n a smlar manner, but for a clmate change scenaro; ) data on actual output, producer prces and trade flows, by crop, for each country; v) data on total GDP by country; and 7

9 v) data on varous potental determnants of trade costs. constructon of each of these nputs here n turn. We descrbe the sources and 3.1 Agrcultural Productvty Estmates at Baselne The frst data source that draw on provdes estmates of average productvty durng the baselne, or pre-clmate change, perod. We requre a measure of n the model above, namely the productvty for crop k of a small parcel of land whch we refer to as a feld, f) n country. We obtan these measures from the Global Agro-Ecologcal Zones GAEZ) project, whch s organzed under the auspces of the Food and Agrculture Organzaton FAO) and the IIASA. 2 descrpton here. Because ths data source s non-standard we provde a lengthy Crucally the GAEZ productvty estmates are avalable for each feld f regardless of whether feld f s actually growng crop k. The GAEZ project provdes these estmates by drawng on state-of-the-art agronomc models of how each crop k wll fare n the growng condtons avalable at feld f. The prmary goal of the GAEZ project s to nform farmers and government agences about optmal crop choce for gven prces) n any gven locaton on Earth that s, to help farmers to know how productve they would be at crops they are not currently growng. Three nputs enter the GAEZ project s agronomc model. vector of attrbutes descrbng the growng characterstcs at feld f. The frst nput s a long These characterstcs nclude eght dfferent sol types and condtons, elevaton, average land gradent, and clmatc varables based on ranfall, temperature, humdty, wnd speed and sun exposure). The sze of a feld f n the GAEZ data s governed by the lmtatons placed by the spatal resoluton of the clmatc data, whch s the land characterstc whose underlyng data s most coarse. Snce the clmatc data s avalable at the 5 arc-mnute level, ths governs the sze of feld n our analyss. 3 At the 5 arc-mnute level there are 9,000,796 grd cells on Earth; we are left wth 2,114,956 felds wthn the 187 countres n our sample after throwng out grd cells that le over water. The second nput s a set of hundreds of model parameters, each specfc to crop k, that govern how a gven set of land characterstcs map nto the yeld of crop k accordng to the GAEZ project s agronomc model. The parameters used by GAEZ are an aggregaton of such parameters found n the agronomc lterature and each s estmated through the use of feld experments at agrcultural research statons. They are not estmated through the use of any sort of statstcal procedure that compares outputs to nputs across a populaton of farmers wthout the absence of expermental control a procedure that the 2 We accessed these data here: Type&dAS=0&dFS=0&feldman=man_py_sx_qdns&dPS=1e1d6e7d7ec3368cf13a68fc523d1ed4870e8b45. 3 Many other nputs are avalable at the 30 arc-second grd-cell level. 8

10 model outlned above suggests would be napproprate wthout controllng for endogenous sortng of felds nto crops based on prevalng prces). The thrd and fnal nput nto the GAEZ model s a set of assumptons about the extent to whch complementary nputs such as rrgaton, fertlzers, machnery and labor) are appled to the growng of crop k at feld f. Naturally, farmers decsons about how to grow ther crops and what complementary nputs to apply affect crop yelds n addton to the land characterstcs such as sunlght) over whch farmers have relatvely lttle control. For ths reason the GAEZ project constructs dfferent sets of productvty predctons for dfferent scenaros regardng the applcaton of complementary nputs. In the results presented here we use the scenaro referred to as hgh nputs n whch modern machnery, etc., are assumed to be avalable n the GAEZ agronomc model f that s deemed useful) wth ran-fed water supply. The GAEZ data are made avalable as grdded machne-readable fles. We map each grd cell to the country n whch t s located by usng a country-to-grd cell mappng avalable as part of the Global Poverty Dataset produced by CIESIN at Columba Unversty. 4 GAEZ data are avalable for all countres n the world apart from those that are extremely small roughly speakng, smaller than a feld). 5 The GAEZ data are produced for each of 43 crops. The Of these, two crops gram and jatropha) are not avalable n the FAO data on output, prces and trade flows) descrbed below, so we drop these. And two pars of crops dryland rce and wetland rce, as well as pearl mllet and foxtal mllet) are only avalable n the FAO data as aggregates.e. rce and mllet, respectvely) so we take the maxmum yeld over each par, wthn each feld, as our measure of the productvty of these aggregates for example, our measure of =rce = max{=drylandrce, =wetlandrce }); ths mplctly assumes that farmers are usng the type of rce or mllet at whch they are most productve and the prces of each type of rce or mllet s the same). We are then left wth 39 crops that concord precsely wth those crops n the FAO data. 6 Fnally, we obtan these GAEZ productvty estmates for what the GAEZ project refers to as the baselne perod, an average of runs of the GAEZ models for the weather observed n each year from 1961 to Ths has the attracton of averagng, n a coherent manner, over the dosyncrases of any gven year s weather. An alternatve would be to pck the 4 We accessed the CIESIN country mappng fle here: The CIESIN fle s at a fner 2.5 arc-mnute) level than the GAEZ data 5 arc-mnute level). We therefore assgn a feld f e a grd cell n the GAEZ data) to the country that has the largest number of CIESIN grd cells wthn a GAEZ grd cell, breakng the small number of tes randomly. 5 For computatonal ease we work, for now, wth the ffty largest n terms of total world crop revenue) countres n the world. These account for roughly 92 percent of world agrcultural output. 6 Whle n prncple the analyss here could be based on all 39 crops, for computatonal ease we work wth the ten most mportant n terms of total world revenue) crops. These comprse over 90 percent of world agrcultural revenue. 9

11 GAEZ data output from one partcular year but the most recent avalable year s 2000 and the FAO data we use below s from 2009.) 3.2 Agrcultural Productvty Estmates After Clmate Change Our analyss of the mpact of clmate change on global agrcultural markets draws naturally on scentsts predctons about the mpact that clmate change wll have on crop yelds around the world. In Secton 5 below we refer) n our model to productvty ) changng for any country, crop k and feld f from at baselne to after clmate change. We obtan these predctons about crop yelds under an alternatve clmate from the GAEZ project so that our baselne and clmate change productvty estmates are computed under exactly the same mantaned agronomc assumptons. The only change that the ) GAEZ project mplements when computng post-clmate change ) productvty estmates rather than baselne productvty estmates concerns the weather that prevals at feld f n country n each scenaro. As descrbed above, when computng baselne productvty estmates the GAEZ project obtans a separate t for each year t from 1961 to 1990 when the weather from each year s used as the nput to ther model; they then average over these 30 values of. A smlar procedure s used when the GAEZ project computes post-clmate change productvty estmates the average over a separate t for each year t from 2071 to 2100 s reported only nstead of realzed past weather n year t the GAEZ project uses the predcted future weather from year t. Estmates of future weather n year t for t =2071 to 2100) are obtaned from an average of runs of a global crculaton model GCM) of the sort used by clmatologsts to predct the nature of clmate change. Whle the GAEZ estmates are avalable for a range of dfferent GCMs, we use that of the Hadley CM3 A1FI model because of ts promnence n the UN s IPCC programme. 7 Fnally we note that we use the GAEZ clmate change scenaro n whch plant carbon doxde fertlzaton s assumed to be actve. 3.3 Agrcultural Output, Prce, and Trade Flow Data An essental aspect of our analyss s the ablty to estmate all of the unknown parameters n our model, at baselne, n a manner that s consstent wth our model. Ths estmaton procedure descrbed below requres data on actual output, producer prces and trade flows at baselne. We obtan these data from the FAOSTAT program at the FAO. 8 The FAOSTAT program ams to provde data on worldwde producton and trade, by crop and country, that 7 In ongong work we am to compare the output of our model of global agrcultural markets across dfferent clmate change models and predcton horzons. 8 We accessed these data from 10

12 s both consstent and complete. We use four varables from FAOSTAT n our analyss. The frst varable we use s the output, n physcal unts.e. tonness), of crop k n country, denoted by Q k n the model above. The second varable, whch we denote by p k, s the producer prce.e. the prce pad to producers, after taxes and subsdes) of crop k n country. The thrd varable s the total value of exports of crop k from country to country j, denoted by Xj k below n the notaton ntroduced above, Xj k = ) τ j p k C k j ). We obtan ths varable from the mports of reportng countres the country that collected the data underlyng the trade flow n queston, n contrast to the partner country n any trade flow) n the FAOSTAT data. Fnally, the fourth varable that we use s the landed or CIF) prce of crop k sent from country to country j, whch we obtan from the unt value.e. the total reported value of a trade flow dvded by the total reported quantty traded) assocated wth mports as reported by reportng countres who report mports n CIF terms. For example, f j s a reportng country then the value of ts mports of crop k from country, denoted Xj, k s n CIF terms.) As descrbed above, we work wth the 39 crops that concord between the FAO and GAEZ data whch cover over 98% of world crop output, accordng to the FAO). Concordng crops n the output and prce data to crops n the GAEZ data s straghtforward snce both treat crop products only n ther pre-processed forms. Concordng crops n the trade data to crops n the GAEZ data, however, s more nvolved because for some crops the traded product s prmarly a processed verson of the pre-processed or raw ) output of the crop. In the majorty of cases countres trade some quantty of both the processed and the raw product of a gven crop; n these cases we work only wth the trade n the raw product. 9 In the case of two crops ol palm and cotton) there s very lttle trade n the raw verson of the crop but the FAO provdes converson factors to convert the processed verson of a crop nto ts raw crop equvalent quantty. And n one case cassava) there s trade only n the processed verson and no converson factor s avalable. We therefore drop ths crop from our analyss when t nvolves trade flows. Fnally, we work wth the 187 countres that are reported n both the GAEZ data and the FAO data. Ths spans the vast majorty of world agrcultural output snce only very mnor countres are omtted from the GAEZ or FAO data). 9 We do ths n order to estmate model parameters the strength of determnants of trade flows and the elastcty of substtuton across varetes of a crop, e σ usng data that s as relevant as possble to the crops n ther raw form. These model parameters are never estmated usng moments that requre us to match the overall level of a crop s exports e the exports of both ts raw and processed forms). 11

13 3.4 Non-Agrcultural GDP Data In order to estmate the value margnal product of the outsde sector n each country.e. p 0 A 0 ) we requre data on the total value of GDP n the entre economy n 2009, the same year as the FAO data from above). We obtan ths from the World Bank wth the excepton of Myanmar, whose GDP data we obtaned from the CIA World Factbook) Data on Determnants of Trade Costs A central component of the model ntroduced above concerns trade costs that s, the frctons that mpede trade between countres. We follow the extensve gravty lterature and model trade costs as a functon of observed potental) determnants of trade costs such as dstance. 11 We obtan dstance measures from the Gravty dataset produced by CEPII Model Parameter Estmaton To smulate the model descrbed n Secton 2, we need estmates of: ) preference parameters, ) ) β k and σ n Equatons 2) and 1); ) technology parameters, and θ n Equatons 4) and 5); and ) trade costs, τ j) k n Equaton 6). Secton 4.1 descrbes how we estmate each of these parameters. Secton 4.2 reports our results. Secton 4.3 explores the model s ft gven estmated parameters. 4.1 Estmaton Procedure We proceed n three steps. Step 1: Trade Costs. We use prce data to estmate trade costs, τ k j. In our dataset, f a country exports a crop k to another country j, we observe both the producer prce n country, p, as well as the unt values of crop k shpped from country nto j, whch we use as a proxy for the consumer prce of that crop n country j, p k j. Usng Equaton 6), we then compute the log of trade costs as ln τ k j = ln p k j ln p k. 12) 10 We accessed the World Bank GDP data here: and Myanmar s GDP here: 11 Whle t s straghtforward to extend the set of determnants of trade costs for example, to nclude an ndcator for whether tradng partners share a common language as n Eaton and Kortum 2002) for smplcty we focus for now on dstance as the sole determant of trade costs. In future work we am to relax ths constrant. 12 We access ths data from 12

14 Many country-pars and crops n our dataset, however, have zero trade flows. In ths case, trade costs are not drectly observable. To get around ths ssue, we assume that trade costs are a log-lnear functon of dstance between countres plus some nose: ln τ k j = α ln d j + δ k j. 13) We then use observed trade costs for country-pars and crops wth postve trade flows, from Equaton 13), to estmate α n Equaton 13) by Ordnary Least Squares OLS). In all subsequent sectons, we use α ln d j as our preferred measure of trade costs between country and country j for all crops whether trade flows are zero or not). Step 2: Technology. We use output, prce, and land data to estmate the extent [ of wthnfeld heterogenety θ. Snce the productvty of felds across crops, = E ω), s ] drectly observable n the GAEZ data, ths s the key technologcal parameter that needs to be estmated. The basc dea s to fnd θ such that the output levels predcted by the model, Equaton 9), best fts the output levels observed n the data. The only ssue s that n order to compute output levels predcted by the model, we need estmates of p k. For crops, productvty and prces are drectly observable, but for the outsde good they are not. To nfer p 0 A f0 = p 0 A 0, we use the fact that accordng to our model, the value of output n the outsde sector s equal to where L 0 p 0 A 0 ) θ f F l Kp l Afl ) θ p 0 Q 0 = p 0 A 0 L 0, ) θ 1)/θ s equal to the amount of land allocated to the outsde sector. In our model, p 0 Q 0 s also equal to total ncome n country mnus the total value of crops produced n that country, k 0 pk Q k. So we can measure p 0 A 0 as GDP n country mnus the total crop value dvded by total acres of land allocated to the outsde sector, whch are all observable n the data. Gven p 0 A 0, as well as data on output, Q k, crop prces, p k, and felds productvty,, we use Non-Lnear Least Squares to estmate θ as the soluton of mn,k 0 ln Q ) 2 k θ) ln Q k, 14) θ where Q k θ) s the output level predcted by our model for a gven value of θ,.e., Q k θ) = f F l K p k ) θ p l Afl ) θ θ 1)/θ. Step 3: Preferences. We start by usng trade data and our estmates of trade costs 13

15 to estmate the elastcty of substtuton σ between crops from dfferent countres. Let Xj k = ) τ j p k C k j denote the value of exports of crop k from country to country j. We assume that trade flows are observed wth measurement error so that Equaton 8) mples ln Xj k = E k + Mj k + 1 σ) ln τ k j + η k j, 15) where E k 1 σ) ln p k can be treated as an exporter fxed effect; Mj k = ln ) β k j Y j I ) ) ln n=1 τ nj p k 1 σ n can be treated as an mporter fxed effect; and η k j s the measurement error n trade flows referred to above. We obtan our estmate of σ by estmatng Equaton 15) usng OLS. In prncple we can estmate a separate elastcty of substtuton across varetes wthn each crop k that s a separate σ k for all k) but for smplcty we frst focus on one pooled estmate of σ that s the same across all crops. To conclude, we use trade and output data to measure the share of expendtures β k across goods n dfferent countres. For each crop k = 1,..., K, we compute total expendture S k on crop k n country as j I Xk j, where total mports, j Xk j, are drectly observable n the data and the value of domestc consumpton, X, k s computed as the value of output mnus exports, p k Q k j Xk j. Gven total expendtures for all crops k = 1,..., K and countres, we can compute β k as the rato of S k over GDP n country. Expendture shares on the outsde good are then gven by one mnus k 0 βk. 4.2 Estmaton Results We now dscuss a prelmnary set of parameter estmates obtaned usng the procedure outlned above. To reduce computatonal complexty n the counterfactual smulatons below we focus on a lmted set of the 50 largest countres and 10 largest crops, n terms of value of output. Because of the skewness of economc actvty n agrculture, across countres and crops, ths dataset stll spans over nnety percent of world agrcultural GDP and trade. We also scale down the number of felds by a factor of 4 that s, each grd cell s now 2 tmes larger n wdth and heght). Based on ths augmented set of data, we obtan for the model s three parameters, presented n Table 1. The frst parameter estmate s α, whch governs the elastcty of trade costs wth respect to dstance. Ths s approxmately α = 0.11 SE = 0.003), whch s n lne wth standard estmates n the emprcal trade lterature but estmated usng dfferent methodologes and based on a manufacturng sample. The second parameter estmate s θ, whch governs the wthn-feld, wthn-crop productvty heterogenety n agrculture through ts nverse effect on the dsperson of the productvty dstrbuton). Wthn any gven feld t s the elastcty of relatve supply across any two crops) to relatve prces. We fnd that, approxmately, θ = 2.39, whch suggests that wthn-feld heterogenety s sub- 14

16 Table 1: Parameter estmates Parameter Descrpton Parameter estmate Parameter standard error α Elastcty of trade costs wth respect to dstance ) θ Wthn feld heterogenety dsperson and wthn feld elastcty of substtuton n supply) N/A σ Elastcty of substtuton n demand across varetes of a crop) ) Notes: Parameter estmates usng method descrbed n Secton 4. Standard errors for θ to be computed n future w ork usng a bootstrap procedure. stantal. 13 Fnally, the thrd parameter we estmate s σ, the elastcty of substtuton across varetes of a crop wthn any gven crop). We fnd that σ = SE = 0.77), whch s a very hgh elastcty of substtuton, perhaps to be expected for the case of relatvely homogenous agrcultural goods. In short we fnd t reassurng that these parameter estmates are of plausble magntudes and that, where standard errors are avalable, they are very precsely estmated. 4.3 Model Ft It s natural to ask, before we go on to consderng how our model behaves under the counterfactual scenaro of new agrcultural productvtes brought about by clmate change, how well the model fts the data wthn sample. Fgure 2 a) plots the ft of the moment that we use to estmate θ, namely a comparson between log output n the model and n the data at our preferred estmate of θ = There s a postve and statstcally sgnfcant correlaton between the model and the data a regresson of the former on the latter, wth a constant, yelds a coeff cent estmate of SE = ). For comparson Fgure 2 b) plots the analogous fgure but for a nave case where we allow all felds wthn each country to be dentcal and to have yelds, n each crop, equal to the country-specfc average yeld and where we re-estmate θ based on ths new productvty data). As the comparson 13 We do not yet know the standard devaton of our estmate of θ. Whle there s no closed form for ths standard error n future work we wll use a bootstrap procedure to estmate t. 14 Ths and all other standard errors referred to n ths secton are clustered at the country level. 15

17 Log output) n full model full wthn country heterogenety) Log output) n smple model no wthn country heterogenety) Log output) n data Fgure 2a) Log output) n data Fgure 2b) Fgure 2:Comparson between log output computed n the model y axs) and FAO data x axs), across all crops and countres. Panel a) reports log output calculated usng the full model outlned n Secton 2 and the full GAEZ data hence there s sgnfcant wthn country heterogenety). Panel b) reports log output calculated usng the full model outlned n Secton 2 but based on smplfed GAEZ data wth each feld's productvty replaced wth ts country's average n the GAEZ data, removng all wthn country heterogenety). Best ft lne and 95% confdence nterval are also ndcated. Revenue share n full model full wthn country heterogenety) Revenue share n smple model no wthn country heterogenety) Revenue share n data Fgure 3a) Revenue share n data Fgure 3b) Fgure 3:Comparson between revenue shares computed n the model y axs) and FAO data x axs), across all crops and countres. Panel a) reports revenue shares calculated usng the full model outlned n Secton 2 and the full GAEZ data hence there s sgnfcant wthn country heterogenety). Panel b) reports revenue shares calculated usng the full model outlned n Secton 2 but based on smplfed GAEZ data wth each feld's productvty replaced wth ts country's average n the GAEZ data, removng all wthn country heterogenety). Best ft lne and 95% confdence nterval are also ndcated. between Fgures 2 a) and 2 b) makes clear, the ft of our model mproves substantally when ntra-natonal productvty heterogenety s allowed for; that s, a representatve feld analyss based on the GAEZ data would be an abject falure. A regresson of log model output on log actual output usng a nave, no wthn-country heterogenety model based on averagng GAEZ data delvers a coeff cent of SE = 0.058). Whle the ft of the model n terms of log output, llustrated n Fgure 2 a), ndcates that ths model s capable of capturng, wth some accuracy, the pattern of nternatonal specalzaton, t s also clear that the absolute level of output n the model does not ft that n the data partcularly well. For example, the estmated constant n the regresson llustrated n Fgure 2 a) s equal to 11.2, mplyng that predcted output s consderably hgher than actual output.) Ths s presumably not a frst-order concern gven that our 16

18 analyss focuses on changes n output due to clmate change, rather than any absolute level of output, t s lkely that ths nablty to match output levels stems from our assumpton that agrcultural technologes do not dffer around the world. See Secton 6 below for a lengther dscusson of ths and a proposed soluton that s n progress.) Fgure 3a), however, llustrates how the ft of the model s consderably more successful n terms of matchng relatve crop producton,.e. the pattern of specalzaton that s at the heart of comparatve advantage and therefore at the heart of our analyss here. In Fgure 3 a) we plot the predcted revenue share, for each crop and country, as predcted by the model, aganst the equvalent revenue share n the FAO data. That s, n the case of the model revenue shares on the y-axs we use the model s equlbrum prce and quantty for a crop and dvde by the model s total revenue amongst all crops. The data revenue shares on the x-axs are computed analogously but usng only the FAO prce and quantty data.) Here the ft s consderably better than when evaluatng log output n Fgure 2 a). The lne of best ft has a slope coeff cent of SE = 0.042) and an estmated constant of SE = 0.004).; the R-squared for ths regresson s Agan by way of comparson we plot n Fgure 3 b)) the equvalent ft for a smpler model n whch we gnore all wthn-country heterogenety n the GAEZ data. Here the slope coeff cent s just SE = 0.044) and the R-squared s We see once agan that allowng the wthn-country data to speak to the model s vtal n mprovng ts ft to the real world. Fnally, Table 2 reports the coeff cent estmates from regressons such as those llustrated n Fgures 2 a) and 3 a), for these and other varables n the FAO data. We look at, respectvely, revenue shares as n Fgure 3 a)), log revenues, log output as n Fgure 2 a)), land shares, and log producer prces. A pattern emerges that s smlar to that dscussed above. Varables n levels correlate well between the data and the model that s, the estmated slope coeff cent s postve and very precsely estmated) but the absolute level s off that s, the estmated constant s far from zero.) But what s encouragng here, gven our focus on changes due to clmate change not the absolute level of output before or after clmate change), and gven our focus on comparatve advantage, s how the two varables based on shares revenue shares n column 1) and land shares n column 4) agree between the model and the data. 5 Counterfactual Smulatons 5.1 Consequences of Clmate Change ) We model clmate change as a change n crop productvty from, as measured n the ), GAEZ data baselne scenaro, to as measured n the GAEZ data under the clmate 17

19 Table 2: Model ft depdendent varable: varable 'X' n model, where varable 'X' s revenue share log revenue) log output) land share log producer prce) 1) 2) 3) 4) 5) Varable 'X' n FAO data *** *** *** *** *** ) ) ) ) ) Constant *** *** *** *** ) ) ) ) ) Number of observatons R squared Notes: Each column s a regresson of varable 'X', as computed n the full model outlned n Secton 2) usng the full GAEZ data w th full w thn country heterogenety), on varable 'X' n the FAO data. Varable 'X' vares from column to column. In column 1) varable 'X' s the revenue share for each crop n total crop GDP for each country. In column 2) varable 'X' s logrevenue) for each non zero crop n each country. In column 3) varable 'X' s logoutput) for each nonzero crop n each country. In column 4) varable 'X' s the share of land devoted to each crop n each country. And n column 5) varable 'X' s the log producer prce). Standard errors are clustered at the country level. change scenaro. All other structural parameters are held fxed at the values estmated n Secton 4. Equlbrum condtons are stll gven by Equatons 7)-11). We focus on changes n real ncome, W Y /P, where Y k K pk Q k denotes total ncome n country and P denotes the consumer prce ndex. Gven our preference structure, Equatons 1) and 2), the consumer prce ndex can be computed as P = K ) k=0 P k β k, wth the component of the prce ndex assocated wth crop k gven by P k = I j=1 τ j p k j ) 1 σ ) 1/1 σ). The second column of Table 3 reports the percentage changes n real ncome for the unweghted) world average. Appendx Table A reports the results from all 50 countres used n our prelmnary analyss.) The average world country n our sample of the 50 largest agrcultural countres) wll be hurt by clmate change n a real ncome sense) though naturally there are exceptons. The world average estmated real ncome loss s approxmately 13 percent of agrcultural expendture whch, as reported n column 1), s 7.75 percent of all expendture, for the world average). 5.2 Gans from Local Specalzaton To quantfy the mportance local specalzaton.e., how changes n comparatve advantage at the feld level affect the consequences of clmate change we recompute the equlbrum wth clmate change under the assumpton that the allocaton of all felds to all goods n all 18

20 Table 3: Counterfactual smulaton results Share of Expendture on Crops n Sample Change n real ncome as share of crop expendture) due to clmate change under Trade costs at baselne, full output adjustment Trade costs at baselne, no land share adjustment Autarky, full land share adjustment Gans as share of crop expendture) due to Local Specalzaton = 2) 3) Internatonal Specalzaton = 2) 4) 1) 2) 3) 4) 5) 6) World Average 7.8% 13.0% 37.6% 18.7% 24.6% 5.7% Notes: Column 1) reports the share of total expendture) n each country spent on the crops n our sample. Column 2) reports the change n real ncome expressed as a share of expendture on crops n our sample), betw een the model under baselne and the model under clmate change, w hen trade costs are at the level estmated n the baselne sample as dscussed n Secton 4). Column 3) reports the analogous result to column 2) only for the case n w hch felds cannot change the share of land allocated to each good. Column 4) reports the analogous result to column 2) only for the case w here trade costs are set to nfnty n both baselne and under clmate change). Columns 5) and 6) report dfferences betw een columns 2) and 3), and 2) and 4), respectvely. countres s the same as n the n ntal equlbrum wthout clmate change. Ths mples that total output of good k n country n the counterfactual equlbrum s gven by where p k Afk ) θ ) ) Q k θ 1 = Γ exp eθ θ ) f F ) π fk, 16) ) stll denotes productvty under the clmate change scenaro, but π fk = corresponds to the share of parcels n a feld f located n country that are allocated to a good k n the ntal equlbrum wthout clmate change. The other l Kp l Afl ) θ equlbrum condtons 7), 8), 10), and 11) are unchanged. Column 3) of Table 3 reports the change n real ncome agan relatve to total agrcultural expendture) for the average country from clmate change under ths scenaro. Here the ll-effects of clmate change are, as to be expected, consderably worse than n the fulladjustment scenaro reported n column 3). Column 5) reports what we refer to as the gans from local specalzaton,.e., the dfference between the full local adjustment scenaro column 2)) and the no-local adjustment scenaro column 3)). These are postve and substantal. 5.3 Gans from Internatonal Specalzaton To quantfy the mportance of nternatonal specalzaton.e., how the possblty to explot changes n comparatve advantage across countres through nternatonal trade affects the consequences of clmate change we recompute the equlbrum wth and wthout clmate change under autarky. The equlbrum condtons are the same as n Secton 2.2, except for 19

21 the good market clearng condtons, whch are now gven by Q k = C k, for all I and k K. The fourth column of Table 3 reports changes n real ncome caused by clmate change n the absence of nternatonal. We see that the reductons to real ncome due to clmate change, under autarky, can be substantal. The dfference between column 2 and column 4 reported n column 6) captures what we refer to as the gans from nternatonal specalzaton. At the unweghted) world average level, we estmate that the ll-effects of clmate change are equal to approxmately 19 percent of total agrcultural expendture n autarky, but only to approxmately 13 percent under restrcted trade. That s, the world average country s affected by clmate change to an extent that s about one-thrd less severe when t s able to trade even wth sgnfcant nternatonal trade costs) than when t s under autarky. But t s mportant to note that, due to adverse terms-of-trade effects, not all countres beneft from restrcted trade, as shown n Appendx Table A. 6 Senstvty Analyss n progress) We now descrbe a number of extensons to the analyss presented above that are under preparaton. 6.1 Productvty Measures In our baselne analyss, we assume that GAEZ data perfectly predct productvty across crops and felds. In practce, they do not. In order to take the mperfect ft of the GAEZ data nto account, we now assume that = Âfk T k, where Âfk s the measure n the GAEZ data of the productvty feld f n country f t were to produce crop k and T k s some technologcal shock unpredcted by agronomsts that affects the productvty of all felds n country for crop k. In order to estmate T k, the basc dea s to use data on land shares. If a crop receves a relatvely hgher land share than what our model predcts gven observed prces and productvty n the GAEZ data, then ts true productvty, and hence ts T k, must be relatvely hgher than the true productvty of other crops. 20

22 6.2 Outsde Good In our baselne analyss, we assume that the outsde good s non-tradable. Whle ths assumpton seems reasonable f one nterprets the outsde as resdental housng or servces, t s less so f one nterprets t as forestry or manufacturng. In ths subsecton, we explore the polar case n whch the outsde sector s assumed to be freely traded around the world at a common prce, p 0, though dfferences n productvty across countres, A 0, may now affect the value of the margnal product of land around the world. 6.3 Substtuton Between Crops In our baselne analyss, we assume that crops enter the upper-level utlty functon n a Cobb-Douglas manner. We now consder the case nested of CES utlty functons: U = C 0 ) β 0 K k=1 C k = I β k 1 β 0 ) C k ) ) 1 β 0 ) γ 1 γ γ 1)/γ, 17) j=1 C k j ) σ 1)/σ ) σ/σ 1), for all k = 1,..., K, 18) where γ > 1 s the elastcty of substtuton between crops. We plan to estmate γ through non-lnear least squares n the same way as we have estmated θ on the supply-sde of our model n Secton Concludng Remarks A large agronomc lterature has modeled the mplcatons of such clmate change for crop yelds, crop by crop and locaton by locaton. These studes document the harm that may be nflcted on a specfc crop at a specfc locaton. The goal of ths paper has been to move beyond these mcro-level studes and aggregate them together nto a coherent, macro-level understandng of how clmate change wll affect agrcultural markets. Aggregatng mcro-level mpacts n a globalzed world means that mpacts depend on the smple economcs of comparatve advantage that s, the mpact of mcro-level shocks do not only depend on ther average level, but also on ther dsperson over space. To measure the mpact of clmate change at the mcro-level we draw on an extremely rch dataset that contans agronomst s estmates about the productvty both before and after clmate change of each crop for each of over 9 mllon hgh resoluton grd cells coverng the surface of the Earth. Crucally, the same agronomc model s used to generate both the preclmate change and post-clmate estmates; all that changes n the agronomst s calculatons 21