How Large are the Gains from Economic Integration? Theory and Evidence from U.S. Agriculture,

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1 How Large are the Gans from Economc Integraton? Theory and Evdence from U.S. Agrculture, Arnaud Costnot MIT and NBER Dave Donaldson MIT, NBER and CIFAR PRELIMINARY AND INCOMPLETE August 15, 2011 Abstract In ths paper we develop a new approach to measurng the gans from economc ntegraton based on a Roy-lke assgnment model n whch heterogeneous factors of producton are allocated to multple sectors n multple local markets. We mplement ths approach usng data on crop markets n 1,500 U.S. countes from 1880 to Central to our emprcal analyss s the use of a novel agronomc data source on predcted output by crop for small spatal unts. Crucally, ths dataset contans nformaton about the productvty of all unts for all crops, not just those that are actually beng grown. Usng ths new approach we estmate: () the spatal dstrbuton of prce wedges across U.S. countes from 1880 to 2002; () the gans assocated wth changes n the level of these wedges over tme; and () the further gans that could obtan f all wedges were removed and gans from market ntegraton were fully realzed.

2 1 Introducton How large are the gans from economc ntegraton? Snce researchers never observe markets that are both closed and open at the same tme, the fundamental challenge n answerng ths queston les n predctng how local markets, ether countres or regons, would behave under counterfactual scenaros n whch they suddenly become more or less ntegrated wth the rest of the world. One promnent response to ths challenge, the reduced form approach, argues that knowledge about such counterfactual scenaros can be obtaned by comparng countres that are more open to countres that are more closed (or analogously, by comparng a country to tself before and after ts level of trade openness changes). 1 Frankel and Romer (1999) s a well-known example. The mplct assumpton about counterfactual scenaros emboded n the reduced form approach s that currently open economes would behave, were they to be less open, n exactly the same manner as countres that are currently less open are currently behavng. An unsettled area of debate n ths lterature concerns the credblty of ths counterfactual assumpton. A potental weakness of ths approach s that t does not estmate polcy nvarant parameters of economc models, thereby lmtng ts relevance for polcy and welfare analyss. Another promnent approach, the structural approach, ams to estmate or calbrate fully specfed models of how countres behave under any tradng regme. Eaton and Kortum (2002) s the most nfluental applcaton of ths approach n the nternatonal trade lterature. A core ngredent of such models s that there exsts a set of technologes that a country would have no choce but to use f trade were restrcted, but whch the country can choose not to use when t s able to trade. Estmates of the gans from economc ntegraton, however defned, thereby requre the researcher to compare factual technologes that are currently beng used to nferor, counterfactual technologes that are delberately not beng used and are therefore unobservable to the researcher. Ths comparson s typcally made through the use of functonal form assumptons that allow an extrapolaton from observed technologes to unobserved ones. The goal of ths paper s to develop a new structural approach wth less need for extrapolaton by functonal form assumptons n order to obtan knowledge of counterfactual scenaros. Our basc dea s to focus on agrculture, a sector of the economy n whch scentfc knowledge of how essental nputs such as water, sol and clmatc condtons map nto outputs s unquely well understood. As a consequence of ths knowledge, agronomsts are able to predct typcally wth great success how productve a gven parcel of land (a feld ) would be were t to be used to grow any one of a set of crops. Our approach combnes 1 We use the terms reduced form and structural n the same sense as, for example, Chetty (2009). 1

3 these agronomc predctons about factual and counterfactual technologes wth a Roy-lke assgnment model n whch heterogeneous felds are allocated to multple crops n multple local markets. We mplement our approach n the context of U.S. agrcultural markets from 1880 to 2002 a settng wth an uncommonly long stretch of hgh-qualty, comparable mcro-data from an mportant agrcultural economy. Our dataset conssts of approxmately 1,500 U.S. countes whch we treat as separate local markets that may be segmented by barrers to trade analogous to countres n a standard trade model. many felds of arable land. 2 Each county s endowed wth At each of these felds, a team of agronomsts, as part of the Food and Agrculture Organzaton s (FAO) Global Agro-Ecologcal Zones (GAEZ) project, have used hgh-resoluton data on sol, topography, elevaton and clmatc condtons, fed nto state-of-the-art models that embody the bology, chemstry and physcs of plant growth, to predct the quantty of yeld that each feld could obtan f t were to grow each of 17 dfferent crops. In our Roy-lke assgnment model, these data are suff cent to construct the producton possblty fronter assocated wth each U.S. county, whch s the essental ngredent requred to perform any counterfactual analyss. Counterfactual analyss n our paper formally proceeds n two steps. Frst we combne the productvty data from the GAEZ project wth data from the decadal Agrcultural Census on the total amount of output of each crop n each county. Under perfect competton, we demonstrate how ths nformaton can be used to nfer local crop prces n each county and tme perod as the soluton of a smple lnear programmng problem. Second, armed wth these estmates of local crop prces, we compute the spatal dstrbuton of prce wedges across U.S. countes from 1880 to 2002 and ask: For any par of perods, t and t, how much hgher (or lower) would the total value of agrcultural output across U.S. countes n perod t have been f wedges were those of perod t rather than perod t? The answer to ths counterfactual queston wll be our measure of the gans (or losses) from changes n the degree of economc ntegraton n U.S. agrcultural markets over tme. A natural concern wth our use of the FAO-GAEZ data centers on ts relablty for our purposes namely, as a reflecton of the state of relatve productvty levels across felds and crops wthn any gven county and year (the absolute level of a county s productvty relatve to that predcted n the FAO-GAEZ data s rrelevant for our exercse). For example, ths data source would be unsutable for our purposes f technologcal change has been based across crops (for example, f rrgaton became more affordable over tmeand some crops beneft more from rrgaton than other crops). As a response to ths concern we develop n Secton 2.5 below an alternatve procedure that s robust to general, unknown crop-specfc 2 Whle we use the term felds to descrbe the fnest spatal regons n our dataset, felds are stll relatvely large spatal unts. For example, the medan U.S. county contans 26 felds. 2

4 technologcal change (or ndeed crop-specfc errors n the FAO-GAEZ model) as long as ths technologcal change (or model error) affects all felds n a county equally. Dong so requres addtonal nformaton that was also collected n the US agrcultural census, namely the amount of land devoted to each crop (not just the physcal quantty of output). That s, we show that, as long as the pattern of comparatve advantage (across felds and crops) wthn a county-year s preserved by technologcal change, the allocaton of felds to crops can stll be solved for (even wth unknown crop-specfc technologcal change) usng data on land use by crop and the resultng equlbrum allocaton can then be used to correct estmated local crop prces for crop-specfc technologcal change. A second potental concern wth our estmates s that they relate only to the 17 crops covered by the FAO-GAEZ project a set of actvtes that does not span the set of all uses of land n the Unted States. More specfcally, at prces prevalng n a gven county and tme perod, the optmal use of land may not be n one of the 17 crops at all. Wth ths concern n mnd Secton 2.4 below develops an extenson to our baselne model n whch there s an outsde use of land whose prce and productvty level (n each county and year) are unknown We show that, just as n the case of crop-specfc technologcal change descrbed above, wth data on the total amount of land beng used to grow the sum of the 17 crops the estmaton of prces and productvty of each of these 17 crops s not jeopardzed by potental outsde uses of land. Relaton to the Lterature. In the trade lterature, most structural work amed at quantfyng the gans from market ntegraton s based on the semnal work of Eaton and Kortum (2002). A non-exhaustve lst of recent quanttatve papers buldng on Eaton and Kortum s (EK) approach ncludes Dekle, Eaton, and Kortum (2008), Chor (2010), Donaldson (2010), Waugh (2010), Ramondo and Rodrguez-Clare (2010), Calendo and Parro (2010), Costnot, Donaldson, and Komunjer (2011), and Feler (2011). The EK approach can be sketched as follows. Frst, combne data on blateral mports and trade costs to estmate the elastcty of mport demand (most often through a smple gravty equaton). Second, use functonal forms n the model together wth elastcty of mport demand to predct changes n real GDP assocated wth a counterfactual change n trade costs; see Arkolaks, Costnot, and Rodrguez-Clare (2011). Our approach, by contrast, focuses entrely on the supply-sde of the economy. Frst we combne data on output and productvty to estmate producer prces, and n turn, trade costs. Second we use the exact same data to predct the changes n nomnal GDP assocated wth a counterfactual change n trade costs. As emphaszed above, the man beneft of our approach s that t weakens the need for extrapolaton by functonal form assumptons. The man cost of our approach n addton to the fact that t apples only to agrculture s that t only allows us to nfer producton gans from trade. In order to estmate consumpton gans 3

5 from trade, we would also need consumpton data, whch s not avalable at the US county level over our extended tme perod. Our proposal s related more broadly to work on the economc hstory of domestc market ntegraton; see e.g. Shue (2002) and Keller and Shue (2007). Usng market-level prce data ths body of work typcally ams to estmate the magntude of devatons from perfect market ntegraton. Our approach, by contrast, frst estmates market-level prces (and hence can be appled n settngs, lke ours, where prce data s not avalable), and then goes beyond the prevous lterature by estmatng the magntude of the producton eff cency gans that would occur f market ntegraton mproved. A fnal area of research to whch ths paper relates s the recent macro lterature on aggregate productvty losses due to msallocaton of producton, e.g., Restucca and Rogerson (2008) and Hseh and Klenow (2009). In ths lterature msallocaton s defned as an nstance n whch the value of the margnal product of a factor s not equalzed across productve unts (typcally frms) wth devatons from such equalty,.e. wedges, dentfyng the extent of dstortons. Although we wll nterpret prce wedges as physcal trade costs throughout ths proposal whch means that the allocaton s eff cent gven the transportaton technology our approach could easly be extended to nvestgate the mportance of msallocaton of land across countes. Snce our approach bulds on detaled nformaton about technology, t also has the potental to reduce the role of functonal form assumptons both when dentfyng msallocaton and when measurng ts aggregate productvty consequences. The rest of ths paper s organzed as follows. Secton 2 ntroduces our theoretcal framework, descrbes how to measure local prces, and n turn, how to measure the gans from economc ntegraton. Secton 3 descrbes our data. Secton 4 presents our man emprcal results. Secton 6 concludes. All formal proofs can be found n the appendx. 2 Theoretcal Framework 2.1 Endowments, Technology, and Market Structure Our theoretcal framework s a Roy-lke assgnment model, as n Costnot (2009). We consder an economy wth multple local markets ndexed by I {1,..., I}. In our emprcal analyss, a local market wll be a US county. In each market, the only factors of producton are dfferent types of land or felds ndexed by f F {1,..., F }. L (f) 0 denotes the number of acres covered by feld f n market. Felds can be used to produce multple crops ndexed by c C {1,..., C}. Felds are perfect substtutes n the producton of each crop, but vary n ther productvty per acre, A c (f) > 0. Total output Q c of crop c n market s 4

6 gven by Q c = f F Ac (f) L c (f), where L c (f) 0 denotes the number of acres of feld f allocated to crop c n market. Note that A c (f) may vary both wth f and c. Thus although felds are perfect substtutes n the producton of each crop, some felds may have a comparatve as well as absolute advantage n producng partcular crops. All crops are produced by a large number of prce-takng farms n all local markets. The profts of a representatve farm producng crop c n market are gven by Π c = p c f F Ac (f) L c (f) r (f) L c (f), where p c and r (f) denote the prce of crop c and rental rate per acre of feld f n market, respectvely. Proft maxmzaton by farms requres p c A c (f) r (f) 0, for all c C, f F, (1) p c A c (f) r (f) = 0, f L c (f) > 0 (2) Local factor markets are segmented. Thus factor market clearng n market requres c C Lc (f) L (f), for all f F. (3) We leave good market clearng condtons unspecfed, thereby treatng each local market as a small open economy. In the rest of ths paper we denote by p (p c ) c C the vector of crop prces, r [r (f)] f F the vector of feld prces, and L [L c (f)] c C,f F the allocaton of felds to crops n market. 2.2 Measurng Local Crop Prces Our dataset contans measures of total farms sales, Ŝ, total output per crop, ˆQ c, as well as total acres of land covered by feld f, ˆL (f), for all local markets. Throughout our emprcal analyss, we assume that none of these varables s subject to measurement error: Ŝ = c C pc Q c, (4) ˆQ c = Q c, for all c C, (5) ˆL (f) = L (f), for all f F. (6) Our dataset also contans measures of productvty per acre, Â c (f), for each feld n each market f that feld were to be allocated to the producton of crop c. Snce we only have 5

7 access to these measures at one pont n tme, 2002, we assume that measured productvty s equal to the true productvty, A c (f), tmes some market specfc error term: Â c (f) = α A c (f), for all c C, f F. (7) [ We refer to X ˆQc, ˆL ] (f), Ŝ, Âc (f) as an observaton for market. Unless c C,f F otherwse specfed, we assume from now on that all observatons satsfy Equatons (4)-(7). Before statng our man theoretcal result, t s useful to ntroduce two defntons. Defnton 1 A vector of crop prces, p, s compettve condtonal on an observaton X f and only f there exst a vector of feld prces, r, and an allocaton of felds to crops, L, such that Equatons (1)-(7) hold. Broadly speakng, Defnton 1 states that a vector of crop prces, p, s compettve condtonal on observaton X f there exsts a compettve equlbrum n market such that: () the allocaton of felds to crops s consstent wth X ; and () crop prces are equal to p. Defnton 2 An allocaton L s eff cent condtonal on an observaton X f and only f t s a soluton of the followng plannng problem max L mn c C { f F Âc (f) L c (f) / ˆQ c } (P) c C (f) ˆL (f), for all f F, (8) L c (f) 0, for all c C, f F, (9) where C {c C ˆQ c > 0} denotes the set of crops wth postve output n market. Formally, Defnton 2 states that an allocaton L s eff cent condtonal on an observaton X f and only f () t s consstent wth X ; and () t maxmzes the utlty of a representatve agent wth Leonteff preference whose consumpton concde wth output levels observed n the data. One can show that f L was not eff cent n the sense of Defnton 2, then there would be no error term α such that L s consstent wth X and les on the PPF of market, hence our choce of termnology. Ths observaton s at the core of the followng theorem. Theorem 1 A vector of crop prces, p, s compettve condtonal on X f and only f there exsts an eff cent allocaton L condtonal on X such that for any par of crops c, c C, the relatve prce of the two crops satsfes p c /p c = Âc (f) /Âc (f), f L c (f) > 0 and L c (f) > 0, (10) p c /p c Âc (f) /Âc (f), f L c (f) > 0 and L c (f) = 0, (11) 6

8 Fgure 1: Measurng Local Crop Prces wth nomnal prces such that c C p c ˆQ c = Ŝ. Theorem 1 characterzes the set of compettve prces assocated wth any observaton. The logc behnd Theorem 1 can be sketched as follows. By the zero proft condton, for any par of crops that are produced n equlbrum, relatve prces are equal to the nverse of the relatve productvty of the margnal feld,.e. the feld nvolved n the producton of both crops n equlbrum. By the Frst and Second Welfare Theorems, the dentty of the margnal feld n a compettve equlbrum can be recovered from a plannng problem. Our procedure s llustrated n Fgure 1 for a market producng two crops, corn and wheat, usng four types of felds. From data on endowments and productvty, one can construct the Producton Possblty Fronter (PPF). Knowng the shape of the PPF, nformaton about relatve output levels of the two crops can then be used to nfer the slope of the PPF at the observed vector of output, and n turn, the relatve prce of the two crops produced n ths market. Accordng to Theorem 1, one can nfer the set of compettve crop prces by solvng a smple lnear programmng problem. Snce our dataset ncludes approxmately 1,500 countes over 17 decades, ths s very appealng from a computatonal standpont. In spte of the hgh-dmensonalty of the problem we are nterested n the medan U.S. county n our dataset features 17 crops and 26 felds and hence or almost possble perfectly specalzed allocatons of crops to felds (and the equlbrum allocaton wll not be perfectly specalzed) t s therefore possble to characterze the set of compettve crop prces n each county n a very lmted amount of tme usng standard software packages. 7

9 Fnally, note that for any par of goods produced n a gven local market, the relatve prce s genercally unque. Non-unqueness may only occur f the observed vector of output s colnear wth a vertex of the producton possblty fronter assocated wth observed productvty levels and endowments. Not surprsngly, ths stuaton wll never occur n our emprcal analyss. 2.3 Measurng the Gans from Economc Integraton Before measurng the gans from economc ntegraton, one frst needs to take a stand on how to measure economc ntegraton across markets. Intutvely, the extent of economc ntegraton should be related to dfferences n local crop prces. For one thng, we know that f crop markets were perfectly ntegrated, then crop prces should be the same across markets. To operatonalze that dea, we ntroduce the followng defnton. Defnton 3 For any par of crops c, c C n any perod t, we defne the extent of economc ntegraton between market and some reference market as the percentage dfference or wedge, τ c t p c t/p c t 1, between the prce of crop c n the two markets. Armed wth Defnton 3, one can then estmate the gans (or losses) from changes n the degree of economc ntegraton across markets between two perods t and t > t by answerng the followng counterfactual queston: How much hgher (or lower) would the total value of output across local markets n perod t have been f wedges were those of perod t rather than perod t? Formally, let (Q c t) denote the counterfactual output level of crop c n market n perod t f farms n ths market were maxmzng profts facng the counterfactual prces (p c t) = p c t/ (1 + τ c t ) rather than the true prces pc t = p c t/ (1 + τ c t). Usng ths notaton, we express the gans (or losses) from changes n the degree of economc ntegraton between two perods t and t > t as: tt c C (pc t) (Q c t) c C pc ˆQ 1. (12) t c t I I By constructon, tt measures how much larger (or smaller) GDP n agrculture would have been n perod t f wedges were those of perod t rather than those of perod t. In Equaton (12) we use local prces both n the orgnal and the counterfactual equlbrum. The mplct assumpton underlyng tt s that dfferences n local crop prces reflect true technologcal consderatons. Under ths nterpretaton of wedges, farmers face the rght prces, but producer prces are lower n local markets than n the reference market because of the cost of shppng crops. Ths metrc s n the same sprt as the measurement 8

10 of the mpact of trade costs n quanttatve trade models; see e.g. Eaton and Kortum (2002) and Waugh (2010). 3 A few comments are n order. Frst, t should be clear that our strategy only allows us to dentfy wedges relatve to some reference prces. Ths mples that measurement error n reference prces may affect our estmates of the gans from economc ntegraton. We come back to ths mportant ssue n the next sectons. Second, our strategy only allows us to dentfy the producton gans from economc ntegraton. Snce we do not have consumpton data, our analyss wll reman slent about any consumpton gans from economc ntegraton. 2.4 Extenson I: Non-Agrcultural Land Use The frst of our two extensons allows for non-agrcultural land uses, e.g. forests, servces, or manufacturng. For expostonal purposes, we smply refer to such actvtes n short as manufacturng. Crop producton s as descrbed n Secton 2.1. But unlke n our baselne model, land can also be used to produce a composte manufacturng good accordng to Q m = f F Am L m (f), where L m (f) 0 denotes the number of acres of feld f allocated to manufacturng. The key dfference between agrculture and manufacturng s that land productvty s assumed to be constant across felds n manufacturng: A m s ndependent of f. Zero-proft condtons and factor market clearng condtons (1)-(3) contnue to hold as descrbed n Secton 2.1, but now for all sectors j C {m}. In terms of measurement, the key dfference between agrculture and manufacturng s that nstead of havng access to a quantty ndex for our composte manufacturng good as well as a measure of productvty, we only observe the total acres of land devoted to manufacturng actvtes: ˆL m = f F Lm (f). (13) [ Equatons (4)-(7) are unchanged. We now refer to Y ˆQc, ˆL (f), Âc (f), ˆL ] m as an c C,f F observaton for market and assume that all observatons now satsfy Equatons (4)-(7) and (13). In ths envronment our defnton of compettve prces and eff cent allocatons can be generalzed as follows. 3 An alternatve metrc mght use the reference prces both n the orgnal and the counterfactual equlbrum. In ths case the mplct assumpton underlyng tt would be that dfferences n local crop prces reflect true dstortons. In order to maxmze welfare whatever the underlyng preferences of the U.S. representatve agent may be farmers should be maxmzng profts takng the reference prces p c t as gven, but because of varous polcy reasons, they do not. Such an alternatve welfare metrc would be n the sprt of the measurement of the mpact of msallocatons on TFP n Hseh and Klenow (2009). 9

11 Defnton 1(M) A vector of crop prces, p, s compettve condtonal on an observaton Y f and only f there exst a vector of feld prces, r, and an allocaton of felds to crops, L, such that Equatons (1)-(7) and (13) hold. Defnton 2(M) An allocaton L s eff cent condtonal on an observaton Y f and only f t s a soluton of the followng plannng problem max L mn c C { f F Âc (f) L c (f) / ˆQ c } (P-M) j C {m} L j (f) ˆL (f), for all f F, (14) L j (f) 0, for all j C {m}, f F, (15) f F L m (f) ˆL m. (16) where C {c C ˆQ c > 0} denotes the set of crops wth postve output n market. Compared to Defntons 1 and 2, the prevous defntons requre compettve prces and eff cent allocatons to be consstent wth the observed allocaton of land to non-agrcultural actvtes. Note also that snce Defnton 1 (M) only apples to the vector of crop prces, t only requres condtons (1) and (2) to hold for all c C rather than all sectors j C {m}. Modulo ths change of defntons, Theorem 1 remans unchanged. 2.5 Extenson II: Crop-and-County Specfc Productvty Shocks Our second extensons allows for a weakenng of the assumpton that the FAO s predctons are rght and rght n all years t up to a scalar. More specfcally, we now relax Equaton (7) and allow for crop-and-market specfc productvty shocks: Â c (f) = α c A c (f). (17) In order to nfer what s now a vector of error terms α (α c ) c C for each local market, we use an extra pece of nformaton contaned n our dataset: the total acres of land allocated to crop c n county, L c. Snce we have access to ths measure n all perods, we agan assume that t s not subject to measurement error: L c = f F m L c (f). (18) [ We now refer to Z ˆQc, ˆL (f), Ŝ, Âc (f), L ] c as an observaton for market and c C,f F assume that all observatons now satsfy equatons (4)-(6) and (17)-(18). In ths envronment, we ntroduce the followng extensons of Defntons 1 and 2. 10

12 Defnton 1(C) A vector of crop prces, p, s compettve condtonal on an observaton Z f and only f there exst a vector of feld prces, r, and an allocaton of felds to crops, L, such that Equatons (1)-(6) and (18)-(17) hold. Defnton 2(C) An allocaton L s eff cent condtonal on an observaton Z f and only f t s a soluton of L = arg max mn c C L { f F f F Âc (f) L } c (f) (P-C) Âc (f) Lc (f) L c c C (f) ˆL (f), for all f F, (19) L c (f) 0, for all c C, f F, (20) L c f F (f) = ˆL c, for all c C. (21) where C {c C ˆQ c > 0} denotes the set of crops wth postve output n market. Compared to Defntons 1 and 2, three dfferences are worth notng. Frst, lke n Secton 2.4, compettve prces and eff cent allocatons need to be consstent wth an addtonal observaton, here the allocaton of felds to crops. Second, observed output levels no longer enter explctly the defnton of eff cent allocatons. The reason s that gven any allocaton L, one can always choose crop-and-market specfc α c productvty shocks such that the allocaton s consstent wth observed output levels. Namely, one would smply set α c = f F Âc (f) L c (f) / Q c. Thrd, eff cent allocatons are no longer gven by the soluton of a smple lnear programmng problem. Instead they correspond to the soluton of a fxed pont problem (that stll nvolves lnear programmng). For smplcty, suppose that all crops are beng produced n a gven county. 4 Then modulo ths change of defntons, Theorem 1 generalzes as follows. Theorem 1(C) A vector of crop prces, p, s compettve condtonal on Z f and only f there exsts an eff cent allocaton L condtonal on Z such that for any par of crops c, c C, the relatve prce of the two crops satsfes wth α c = f F p c /p c = Âc (f) α c /Âc (f) α c, f L c (f) > 0 and L c (f) > 0, (22) p c /p c Âc (f) α c /Âc (f) α c, f L c (f) > 0 and L c (f) = 0, (23) / Âc (f) L c (f) Qc and nomnal prces such that c C p c ˆQ c = Ŝ. As hnted above, Theorem 1(C) s less useful than Theorem 1 snce t s harder to solve the fxed pont problem n Defnton 2(C) than the lnear programmng problem n Defnton 4 The other cases smply requre makng addtonal assumptons on prces and/or productvty changes for crops that are not produced n a gven county. 11

13 2. 3 Data Our analyss draws on three man sources of data: predcted productvty by feld and crop (from the FAO-GAEZ project); aggregate county-level data (from the US Agrcultural Census) on output by crop, cultvated area by crop, and total sales of all crops; and data on reference prces. We descrbe these here n turn. 3.1 Productvty Data The frst and most novel data source that we make use provdes measures of productvty (e Âc (f) n the model above) by crop c, county, and feld f. These measures comes from the Global Agro-Ecologcal Zones (GAEZ) project run by the Food and Agrculture Organzaton (FAO). 5 The GAEZ ams to provde a resource that farmers and government agences can use (along wth knowledge of prces) to make decsons about the optmal crop choce n a gven locaton that draw on the best avalable agronomc knowledge of how crops grow under dfferent condtons. The core ngredent of the GAEZ predctons s a set of nputs that are known wth extremely hgh spatal resoluton. Ths resoluton governs the resoluton of the fnal GAEZ database and, equally, that of our analyss what we call a feld (of whch there are 26 n the medan U.S. county) s the spatal resoluton of GAEZ s most spatally coarse nput varable. The nputs to the GAEZ database are data on an eght-dmensonal vector of sol types and condtons, the elevaton, the average land gradent, and clmatc varables (based on ranfall, temperature, humdty, sun exposure), n each feld. These nputs are then fed nto an agronomc model one for each crop that predcts how these nputs affect the mcrofoundatons of the plant growth process and thereby map nto crop yelds. Naturally, farmers decsons about how to grow ther crops and what complementary nputs (such as rrgaton, fertlzers, machnery and labor) to use affect crop yelds n addton to those nputs (such as sun exposure and sol types) over whch farmers have very lttle control. For ths reason the GAEZ project constructs dfferent sets of productvty predctons for dfferent scenaros of farmer nputs. For now we use ther scenaro that relates to mxed nputs, wth possble rrgaton but n future work we wll explore how our results change across such scenaros. 5 Ths database has been used by Nunn and Qan (2011) to obtan predctons about the potental productvty of European regons n producng potatoes, n order to estmate the effect of the dscovery of the potato on populaton growth n Europe. 12

14 Fnally we wsh to emphasze that whle the GAEZ has devoted a great deal of attenton to testng ther predctons on knowledge of actual growng condtons (e.g. under controlled experments at agrcultural research statons) the GAEZ does not form ts predctons by estmatng any sort of statstcal relatonshp between observed nputs around the world and observed outputs around the world. Indeed, the model outled above llustrates how nference from such relatonshps could be msleadng. 3.2 Output, Area and Sales Data The second set of data on whch we draw comprses county-level data from the US Agrcultural Census n every decade from (Hanes, 2010). 6 Of nterest to us are records of actual output of each crop ( ˆQ c ) the amount of land cultvated n each crop ( L c ) and the total value of sales (n contemporary currency unts) obtaned from all crops (Ŝ). We use only the approxmately 1,500 countes that reported agrcultural output data n Although the total output of each crop n each decade n each county s known, such measures are not avalable for spatal unts smaller than the county (such as the feld, f). 3.3 Prce Data A fnal source of data that we use s actual data on observed producer (e farm gate ) prces. Whle prce data s not necessary for our analyss, below we perform some smple tests of our exercse by comparng producer prce data to the predcted prces that emerge from our exercse. Unfortunately, the best avalable prce data s at the state-, rather than the county-, level. Indeed, f county-level producer prce data were avalable the frst step of our emprcal analyss below, that n whch we estmate local prces, would be unnecessary. The state-level prce data we use comes from two sources. Frst, we use the Agrcultural Tme Seres-Cross Secton Dataset (ATICS) from Cooley, DeCano and Matthews (1977), whch covers the perod from 1866 (at the earlest) to 1970 (at the latest). 8 Second, we have extracted all of the post-1970 prce data avalable on the USDA (NASS) webste so as to create a prce seres that extends from 1880 to Whle the Agrcultural Census began n 1840 t was not untl 1880 that the queston on value of total sales was added. For ths reason we begn our analyss n Ths fgure s approxmate because the exact set of countes s changng from decade to decade due to redefntons of county borders. None of our analyss requres the ablty to track specfc countes across tme so we work wth ths unbalanced panel of countes (although the exact number vares only from 1,447 to 1,562). 8 We are extremely grateful to Paul Rhode for makng a copy of ths data avalable to us. 13

15 4 Emprcal Results Ths secton presents prelmnary emprcal results, based for now only on output data from 1880, 1900, 1920, 1950, 1974 and We present only baselne estmates that s, estmates that do not pursue ether of the extensons (to allow for a non-agrcultural good, and to allow for crop-specfc technologcal change) outlned n Sectons 2.4 and 2.5 above. 4.1 Local Crop Prce Estmates The frst step of our analyss uses Theorem 1 to estmate the local prce for each of our 17 crops (or upper bound on each crop that s not grown) n each of our approxmatley 1,500 countes, n each of our sample years (e 1880, 1900, 1920, 1950, 1974 and 2002). Havng done ths, we frst ask how well these estmated prces correspond to actual prce data. The procedure we follow here s not ntended to be a formal test of our model (and the underlyng agronomc model used by GAEZ). As mentoned before, the best producer prce data avalable s at the state-level, whereas our prce estmates are free to vary at the county-level. Our goal here s more modest. We smply am to assess whether the prce estmates emergng from our model bear any resemblance to those n the data. In order to compare our prce estmates to the state-level prce data we therefore smply compute averages across all countes wthn each state, for each crop and year. (We do not use the prce estmates that are only upper bounds on prces n calculatng these averages.) We then smply regress our prce estmates on the equvalent prces n the data (wthout a constant), year by year (on all years n our sample after the start of the Cooley et al (1977) prce data, 1866), poolng across crops and states. Table 1 contans the results of these smple regressons. In all cases we see a postve and statstcally sgnfcant correlaton between the two prce seres, wth a coeff cent that vares between 0.38 and Whle all coeff cents are less than one (as one would expect f prce estmates agreed well wth prce data) ths s unsurprsng gven that the rergressor, actual prce data, s msmeasured from our perspectve because t consttutes a state-level average of underlyng prce observatons whose samplng procedure s unknown. Gven ths, we consder the results n Table 1 to be encouragng. Our procedure for estmatng local prces had nothng to do wth prce data at all ts key nputs were data on quanttes and technology. But reassurngly there s a robust correlaton between our prce estmates and prce estmates n real data. Havng examned the relatonshp between our local crop prce estmates and outsde data 9 We have also looked at the correlaton between relatve (e across crops, wthn state-years) prce estmates and prce data by runnng regressons across all (unque and non-trval) such crop pars for whch data are avalable. The coeff cents are agan postve, statstcally sgnfcant, and range from 0.30 to

16 Table 1: Correlaton between estmated prces and prce data Dependent varable: estmated prce (from model) (1) (2) (3) (4) (5) (6) observed producer prce (0.351)** (0.247)** (0.311)** (0.158)** (0.338)** (0.110)** observatons Notes: Results from a regresson of estmated local crop prces, averaged wthn states, on state level producer prce data from Cooley et al (1977) and NASS. Robust standard errors n parentheses. ** ndcates statstcally sgnfcant at the 1% level. on producer crop prces, we now explore the extent to whch our estmated prces appear to have anythng systematc to do wth space. That s, do countes that are close to one another have more smlar prces? Do prces declne for countes that are further and further away from major agrcultural wholesale destnaton markets such as Chcago? Whle one would expect transportaton costs to dstort prces over space such that the answer to these questons s n the aff rmatve, t s entrely possble that other types of dstortons (such as producer subsdes) would generate prce dsperson that has no systematc correlaton wth dstance. Table 2 explores the extent to whch proxmate countes tend to have more smlar prces. In all years the correlaton between prce gaps (here, the absolute value of the gap n log prces) and log dstance s postve and statstcally sgnfcant. Whle ths s ndcatve of a spatal relatonshp n our prce estmates, the coeff cent estmates presented n Table 2 should not be nterepreted as estmates of the structural relatonshp between trade costs and dstance. By a free arbtrage argument, the gap n prces for a good between two markets, our dependent varable here, s only equal to the trade cost (for that good) between these two markets when the two markets are actually tradng some of that good between them. For the bulk of our county pars ths wll not be the case and n such settngs the prce gap only puts a lower bound on the trade cost (e f trade costs were lower than the prce gap then arbtrage opportuntes would exst). Hence lttle can be sad about the magntude of the coeff cents n Table 2 (for example, t s not clear how we should expect them to change over tme). That sad, to the extent that there exst transportaton and related costs that separate markets spatally, and more so at a greater dstance, we fnd t encouragng that our prce estmates are uncoverng such spatal relatonshps even though the spatal locaton of any county was not used n the constructon of our prce estmates. The fnal analyss of our local crop prce estmates that we conduct here s to evaluate whether there s a prce gradent across countes wth respect to ther proxmty to major 15

17 Table 2: Proxmty of countes and local crop prce estmates Dependent varable: absolute value of [log(prce n county ) log(prce n county j)] (1) (2) (3) (4) (5) (6) log (dstance from county to (0.0003)** (0.0006)** (0.0005)** (0.0002)**(0.0006)** (0.0008)** county j) observatons 7,631,840 7,446,840 7,105,686 6,543,440 6,018,522 5,296,872 Notes: Results from a regresson of the absolute value of the gap n log prces, between any (unque, non trval) par of countes, and the log dstance between those countes. Robust standard errors n parentheses. ** ndcates statstcally sgnfcant at 1% level. agrcultural wholesale markets. Ths s what one would expect f each county s tradng at least some quantty of a crop to ts nearest wholesale market, and f such tradng occurs at a cost that depends on dstance. For now we smply take three major wholesale markets n our sample area, Chcago, New Orleans and New York, and assgn each county to the nearest of these three locatons. 10 We then estmate the followng regresson: ln p c t = α c,m t + β t ln d + ε t, (24) where d denotes the dstance from county to ts nearest major wholesale market, and α c,m t s a separate fxed effect for each crop tmes each of the three major wholesale markets. These fxed effects are necessary (and mportant for what we do below) because they correspond to the crop-specfc prce at each wholesale market and year. The results from these regressons (estmates of the coeff cent β t for each year t) are presented n Table 3. As n Table 2 we fnd a statstcally sgnfcant correlaton between prces and dstance, but here the coeff cent has a dfferent nterpretaton, and captures more economc meanng. As long as some amount of the produce of a crop n a county s traded wth ts nearest major wholesale market then the coeff cent here dentfes both the drecton of trade (here a negatve sgn ndcates that goods are beng sent to these wholesale markets, as would be expected), and, under a standard free arbtrage assumpton, the extent to whch ncreased dstance ncreases the cost of tradng (e the parameter β t above). In lght of ths, our results are encouragng snce the coeff cents are all negatve, as would be expected, and precsely estmated. They are also revealng: the coeff cents are fallng n absolute value over tme, from n 1880 to n Ths suggests a large 75 percent declne n the cost of tradng goods, per unt dstance, over ths 122 year perod. 10 Ths lst of major wholesale markets can of course be enrched n future work. We am to use a lst that s crop- and year-specfc, and that allows for far more wholesale markets than only the largest three. 16

18 Table 3: Local crop prce estmates and proxmty to major markets Dependent varable: log (prce level) (1) (2) (3) (4) (5) (6) log (dstance to closest major (0.012)** (0.015)** (0.024)** (0.008)** (0.010)** (0.011)** market) observatons 4,836 4,431 4,250 3,846 3,758 3,711 Notes: Results from a regresson of the log prce of each crop n each county on the log dstance of that county to ts nearest major wholesale market (taken to be Chcago, New Orleans or New York). Fxed effects are ncluded for each crop tmes each major wholesale market. Standard errors clustered by county are n parentheses. ** ndcates statstcally sgnfcant at 1% level. In the next secton we estmate the gans from ths large reducton n trade costs. We take serously the dstance-trade cost coeff cents n each year from Table 3 and use these estmates of the structural cost of tradng goods over space as the metrc for how much economc ntegraton has taken place over tme (the key ngredent for estmatng the gans of ths heghtened ntegraton). 4.2 Gans from Economc Integraton We now turn to our prelmnary estmates of the gans from economc ntegraton. dscussed n Secton 2.3 above, we formulate these gans as the answer to the followng counterfactual queston: How much hgher (or lower) would the total value of output across local markets n perod t have been f wedges were those of perod t rather than perod t? Gven our ablty to construct the PPF for each county usng the GAEZ productvty data, answerng ths queston s straghtforward once we know the prces that would preval n each county under ths counterfactual scenaro. In order to formulate those prces, however, we are requred to take a stand on the reference prce to use n perod t. To construct reference prces we take an emprcal approach nspred by the regressons that underpnned Table 3 above. Under the assumpton that each county s tradng each crop to ts nearest major wholesale market, the regresson n Equaton (24) above dentfes three separate reference prces for each tme perod and crop,.e. the prce prevalng at each of the three major wholesale markets. Specfcally, each market s prce s dentfed as e αc,m t, and we use the coeff cent estmates α c,m t to calculate our reference prces n ths manner. Our fnal requrement n answerng the above counterfactual queston s a measure of the wedge for each county, crop and year. The method descrbed n Secton 2.3 above proposed that each county s wedge be smply the gap between ts prce level and the reference prce. Whle ths has the attracton of smplcty, t s vulnerable to nosy prce estmates. We As 17

19 therefore use the ftted values from Equaton (24) above (now run separately for each crop so as to estmate a separate dstance coeff cent β c t by crop and year) nstead, both to construct factual prce levels (that are hence smoothed over space) and to construct the counterfacutal prces requred to evaluate counterfactual scenaros. For example, we use the estmate β c t to construct the ftted values for the counterfactual prces n year t ths amounts to askng how the economy n year t would respond f t faced the counterfactual coeff cent on dstance from year t (.e. β c t ) rather than the factual coeff cent on dstance from year t (.e. βc t). Followng ths procedure we fnd that the gans, accordng to the formula n Equaton (12), from movng n 1880 to 2002 dstance costs are large: a 94 percent ncrease n the total value of agrcultural output. Ths s consderably hgher than standard estmates of the statc gans from trade (for example, those n Bernhofen and Brown (2005) s study of Japanese ext of autarky, n whch the estmated gans are no more than nne percent). But ths dfference should not be surprsng: the formula n Equaton (12) mplctly captures productvty gans n the transportaton sector, whereas standard estmates of the gans from trade do not. Our prelmnary estmates of gans n other years are smaller, as s to be expected from the lower estmates of β t that we obtaned n Table 3 for those years. For example, the gan from movng 1974 to 2002 dstance costs s nne percent. There remans much to be done n explorng these estmates further breakng them down by regon, explorng ther robustness to alternatve methods for obtanng reference prces and estmatng wedges, and mplementng the potentally mportant extensons n Sectons 2.4 and 2.5 above. Nevertheless these prelmnary results strke us as both encouragng and plausble. 5 Concludng Remarks In ths paper we have developed a new approach to measurng the gans from economc ntegraton based on a Roy-lke assgnment model n whch heterogeneous factors of producton are allocated to multple sectors n multple local markets. We have mplemented ths approach usng data on crop markets n approxmately 1,500 U.S. countes from 1880 to Central to our emprcal analyss s the use of a novel agronomc data source on predcted output by crop for small spatal unts. Crucally, ths dataset contans nformaton about the productvty of all spatal unts for all crops, not just the endogenously selected crop that farmers at each spatal have chosen to grow n some equlbrum. Usng ths new approach we have estmated () the spatal dstrbuton of prce wedges across U.S. countes n 1880 and 2002 and () the gans assocated wth changes n the level of these wedges over tme. 18

20 A Proofs Proof of Theorem 1. The proof of Theorem 1 proceeds n two steps. Step 1: If p s compettve condtonal on X, then there exsts an eff cent allocaton L condtonal on X such that Equatons (10) and (11) hold and prce levels are such that p c ˆQ c = Ŝ. c C By Defnton 1, f p s compettve condtonal on X, then there exst r and L such that condtons (1)-(7) hold. Equatons (4) and (5) mmedately mply c C p c ˆQ c = Ŝ. Condtons (1) and (2) further mply p c /p c = Âc (f) /Âc (f), f L c (f) > 0 and L c (f) > 0, p c /p c Âc (f) /Âc (f), f L c (f) > 0, L c (f) = 0. Thus condtons (10) and (11) hold. Let us now check that f r and L are such that condtons (1)-(7) hold, then L necessarly s eff cent condtonal on X n the sense of Defnton 2. By condtons (1)-(3), L s a feasble allocaton that maxmzes total profts. Thus the Frst Welfare Theorem (Mas-Colell et al. Proposton 5.F.1) mples that L must be a soluton of f F max L f F [Âc (f) /α ] Lc (f) [Âc (f) /α ] Lc (f) Q c, for all c c, c C L c (f) L (f), for all f F, L c (f) 0, for all c C, f F, { where we have arbtrarly chosen c such that c mn c C Q } c > 0. Snce Equaton (5) holds for c = c, we must have Q c [ ] α = Âc (f) L c (f) f F = [ ] Â c (f) /α L c (f), whch can be rearranged as / Q c. Accordngly, L s a soluton of max L Âc (f) L ( c (f) Qc f F Âc / Q c ) f F Âc (f) L c (f) (P ) (f) L c (f), for all c C, (25) c C (f) L (f), for all f F, (26) L c (f) 0, for all c C, f F, (27) Ths establshes that L satsfes all the constrants of (P ). In order to demonstrate that L s a soluton of (P ), we now proceed by contradcton. Suppose that there exsts L satsfyng all the constrants n (P ) such that mn c C [ ]/ [ f F Âc (f) L c ]/ (f) Qc m > mn c C f F Âc (f) L c (f) Qc. (28) 19

21 Snce Inequalty (25) s necessarly bndng at a soluton of (P ), we therefore have [ ]/ f F Âc (f) L c (f) Qc = [ f F Âc (f) L c ]/ (f) Qc, for all c C. (29) Combnng Inequalty (28) and Equaton (29), we obtan [ ]/ f F Âc (f) L c (f) Qc > [ f F Âc (f) L c ]/ (f) Qc, for all c C. (30) Snce L c (f) 0 for all c C, f F, we also trvally have ( Âc (f) L c (f) Qc / Q c ) Âc (f) L c (f), for all c / C. (31) By Inequaltes (30) and (31), L satsfes all the constrants n (P ). By Inequalty (30) evaluated at c = c, we also have [ f F Âc (f) L c ]/ (f) Qc > [ f F Âc (f) L c ]/ (f) Qc. Ths contradcts the fact that L s a soluton of (P ). Thus L s eff cent condtonal on X n the sense of Defnton 2. Ths completes the proof of Step 1. Step 2: If there exsts an eff cent allocaton L condtonal on X such that Equatons (10) and (11) hold and prce levels are such that c C p c ˆQ c = Ŝ, then p s compettve condtonal on X. By assumpton, the observaton X s such that Equatons (4)-(7) hold. Thus by Defnton 1, we only need to show that one can construct a vector of feld prces, r, and an allocaton of felds, L, such that condtons (1)-(3) hold as well. A natural canddate for the allocaton s L soluton of (P ) such that condtons (10) and (11) hold. By Defnton 2, such a soluton exsts snce there exsts an eff cent allocaton L condtonal on X such that condtons (10) and (11) hold. The fact that Inequalty (3) holds for allocaton L s mmedate from Equaton (6) and Inequalty (8). Let us now construct the vector of feld prces, r, such that for wth c α = [ f F r (f) = max c C p c Âc (f) Q c /[ f F Âc (f) L c (f)], (32) { mn c C Q } c > 0. Snce Equaton (5) holds for c = c, Equaton (7) mples Âc (f) L c (f)]/ Q c. Thus we can rearrange Equaton (32) as r (f) = max c C p c A c (f). Ths mmedately mples Inequalty (1). To conclude, all we need to show s that p c A c (f) = r (f) f L c (f) > 0. We proceed by contradcton. Suppose that there exst c C and f F such that L c (f) > 0 and p c A c (f) < max c C p c A c (f). By Equaton (7), ths can 20

22 be rearranged as p c Âc (f) < max c C p c  c (f). Now consder c 0 = arg max c C p c  c (f). By constructon, we have p c 0 /pc > Âc (f) /Âc 0 (f), whch contradcts ether condton (10), f L c 0 (f) > 0, or condton (11), f L c 0 (f) = 0. Ths completes the proof of Step 2. Theorem 1 drectly derves from Steps 1 and 2. QED. Proof of Theorem 1(M). The proof of Theorem 1(M) s smlar to the prevous proof. Step 1: If p s compettve condtonal on Y, then there exsts an eff cent allocaton L condtonal on Y such that Equatons (10) and (11) hold and prce levels are such that p c ˆQ c = Ŝ. c C By Defnton 1 (M), f p s feasble condtonal on Z, then there exst r and L such that (1)-(7) and (13) hold. Equatons (4) and (5) mmedately mply c C p c ˆQ c = Ŝ. Condtons (1) and (2) further mply p c /p c = Âc (f) /Âc (f), f L c (f) > 0 and L c (f) > 0, p c /p c Âc (f) /Âc (f), f L c (f) > 0, L c (f) = 0. Thus condtons (10) and (11) hold. Let us now check that f r and L are such that condtons (1)-(7) hold, then L necessarly s eff cent condtonal on X n the sense of Defnton 2 (M). By condtons (1)-(3), L s a feasble allocaton that maxmzes total profts. Thus the Frst Welfare Theorem (Mas-Colell et al. Proposton 5.F.1) mples that L must be a soluton of f F max L f F [Âc (f) /α ] Lc (f) [Âc (f) /α ] Lc (f) Q c, for all c c, f F Am L m (f) Q m, L j j C {m} (f) L (f), for all f F, L j (f) 0, for all j C {m}, f F, { where we have arbtrarly chosen c such that c mn c C Q } c > 0. Snce Equaton (5) holds for c = c, we must have Q c [ ] α = Âc (f) L c (f) = [ ]  c (f) /α L c (f), whch can be rearranged / Q c. By Equaton (13) we must also have Qm = A m ˆL m. Thus we 21

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