Trade Elasticities PRELIMINARY. DO NOT CIRCULATE. Abstract

Transcription

1 Trade Elaticitie Jean Imb y Iabelle Méjean z PRELIMINARY. DO NOT CIRCULATE Abtract Arkolaki et al (2011) how the welfare gain from trade can be ummarized by import hare and the price elaticity of import. The claim hold in a multi-ector model, which net a one-ector verion. Both verion mut have identical welfare prediction, provided they are calibrated adequately. For 29 countrie, we compute multi-ector welfare on the bai of ectoral import hare and etimated ector-level trade elaticitie. From the one-ector verion, we ak what value of the trade elaticity at country-level can replicate uch welfare meaure. Thi i the trade elaticity that mut be ued in the one-ector trade model conidered in Arkolaki et al (2011). The elaticitie are alway igni cantly di erent from conventional macroeconomic etimate. Acro 29 countrie, they range from 2:1 to 6:6, with lowet value in China and India. They take value around 4 in developed countrie. We ue the theory to decompoe thee international di erence. We nd the ditribution of ectoral trade elaticitie i key. JEL Clai cation Number: F32, F02, F15, F41 Keyword: Price Elaticity of Import, Sectoral Etimate, Trade Performance, Heterogeneity. Thank are due to Brent Neiman, for hi dicuion of an early verion of thi paper, and to audience at the September 2010 San Francico Fed Paci c Bain Reearch Conference and the January 2011 American Economic Aociation Meeting. Thi paper wa written while Imb wa the Wim Duienberg Fellow at the European Central Bank, whoe hopitality i gratefully acknowledged. y Pari School of Economic and CEPR. Correponding author: Pari School of Economic, boulevard de l Hopital, Pari, France jeanimb@gmail.com, z Ecole Polytechnique, CREST and CEPR, iabelle.mejean@polytechnique.edu,

2 1 Introduction Trade elaticitie meaure the repone of traded quantitie to price hock. They are often ued to gauge a country external performance, but their fundamental economic interpretation i in fact model dependent. In an endowment economy with Armington preference like Krugman (1980), the price elaticity of import map directly with the elaticity of ubtitution between international varietie. In a Ricardian model with perfect competition among heterogeneou rm like Eaton and Kortum (2002), or with monopolitic competition like Mélitz (2003), it relate with the ditribution of rm productivity. In pite of uch di erence, import price elaticitie are u cient to ummarize the fundamental feature of all three clae of model, a recently demontrated by Arkolaki et al (2011) [ACRC henceforth]. In all three model, the welfare conequence of moving from oberved, current trade to autarky can be evaluated with etimate of import price elaticitie ", and the oberved hare of dometic expenditure jj. The reult generalize to a multi-ector etting. In thi paper, we follow Imb and Méjean (2011) and compute the aggregate welfare gain W MS implied by ector-level trade elaticitie ", and ector-level expenditure hare jj. We do o uing the multi-ector model of ACRC, which we how net the one-ector verion. Since they come from the ame model, the two verion mut imply identical welfare, provided they are calibrated adequately. We ak what value of " mut be choen for the one-ector model to imply the value of W MS obtained from ectoral data. Such value repreent the calibration of import price elaticitie that belong in the one-ector trade model in ACRC. The exercie i conducted for 29 countrie at variou level of development. The oneector etimate of " that mimic W MS, denoted by " OS, range from 2:1 to 6:6, with lowet value in China and India. The cro-country average equal 4:33. Developed economie have etimate around 4, 4:5 in the US, and lightly lower value for Canada, Japan, Korea or Singapore, cloe to 5. The highet elaticitie are found for pecialized mall open economie, Kuwait and Sri Lanka. The value of " OS are clearly igni cantly di erent from claic trade 2

3 elaticity etimate obtained from aggregate data. Conequently, the welfare meaure calibrated to aggregate data, W A, i ytematically di erent from W MS, even though in theory both arie from two neted verion of the ame model. If the calibration i adequate, two di erent value cannot both be true imultaneouly. While the hare of dometic expenditure jj and jj are readily available from accounting data, trade elaticitie mut be etimated. Etimate obtained from aggregate data are not necearily the ame a thoe implied by ectoral information. In particular, the trade elaticity implied by aggregate data may in fact di er from an (adequately) weighted average of ectorpeci c trade elaticitie. If it doe, a heterogeneity bia prevail, and the price elaticity of import obtained from aggregate data i e ectively diconnected from ectoral information. 1 In that cae, W A di er from W MS becaue of an econometric iue aociated with an etimation performed on aggregate. Put di erently, in the preence of heterogeneity bia, aggregate data hould not be ued when evaluating the gain from trade. The reult matter beyond the evaluation of the welfare gain from trade. To undertand why, it i ueful to re-viit the intuition behind ACRC reult. Change in country j trade are triggered by hift in production cot w i in the foreign country i, and/or by change in trade cot ij. Neither a ect dometic income. Therefore, trade-induced change in real income, i.e. in welfare, can only tem from the price index. How doe the dometic price index in country j repond to hift in w i and/or ij? That depend on the model. In the Armington model, the price repone i proportional to the change in the quantitie traded, a ubtitution occur between import and dometic good, caled by the (invere of the) import price elaticity. Thu, two parameter only, jj and ", ummarize the welfare gain from trade in country j. The former becaue it re ect traded quantitie in the current tate of economy j, and the latter becaue it map change in quantitie into change in price, which are what matter for 1 Levchenko, Lewi and Tear (2010) etimate trade repone at ectoral level. Their elaticitie are larget in ector ued a intermediate good. Buiere et al (2011) obtain trade elaticite for each component of aggregate demand. Their etimate of overall, aggregate trade elaticity are much larger than conventional one. 3

4 welfare. 2 In other word, W A di er from W MS becaue the bia in the etimated trade elaticity implie a bia in the repone of price and real income to term of trade hock. Within the con ne of the (tatic) model in ACRC, aggregate data hould not be ued to calibrate the repone of aggregate income to a term of trade hock. Doing o imply aume away the ectoral dimenion of the data. The claim generalize to the model with endogenou upply conidered by ACRC. In Ricardian trade model, the dometic price index aggregate the (minimum) price of good acro production location. But the price repone to term of trade hock i not necearily proportional to the change in import v. dometic expenditure anylonger. Entry deciion (triggered by change in production or trade cot) can di er acro location, with hetereogenou conequence on trade ow. ACRC how how Eaton and Kortum (2002) aume away thi heterogeneity o that trade ow are till proportional to price hock. The key aumption i the Frechet ditribution of rm productivity, which in fact alo pin down the ratio of traded quantitie to relative price. So the price elaticity of import continue to determine the repone of real income to term of trade hock, i.e. welfare. With monopolitic competition and rm entry, the dometic price index incorporate not only production cot acro location, but alo the number and ma of (imperfectly ubtitutable) varietie produced in each location. Either one can repond to term of trade hock, which in general break down the proportionality between price and change in import v. dometic expenditure. ACRC how that in Mélitz (2003), the aumption that rm-peci c productivity i ditributed following a Pareto ditribution retore the proportionality between price and traded ow. The proportion i now given by the Pareto coe cient. Once again, the price elaticity of import i key to determining the repone of real income to term of trade hock, and welfare. 2 To be precie, jj i relevant when meauring the welfare loe aociated with going from current trade to autarky. 4

5 We nd that " OS, the one-ector trade elaticity implied by W MS, i igni cantly di erent from an etimate obtained from aggregate data, " A. But what i it imilar to? Uing theory, we compare " OS with an adequately weighted average " W of ectoral etimate ". The weight repreent the ize of each ector in overall expenditure, and their degree of openne to international trade. Thee weighted average are calculated for 29 countrie. They are virtually identical to " OS. We conclude that the calibration of one-ector model hould build from averaged ectoral etimate, if the model i to mimick the repone of real income to term of trade hock that i implied by a multi-ector model. A calibration uing aggregate data doe not correpond to the model decribed in ACRC. We perform our exercie for 29 countrie at variou level of development. There are large international di erence in the etimate of " OS, which are typically abent in etimate from macroeconomic data. Uing the de nition of " W a a weighted average of ", international di erence can come either from the weight or the etimate of ". We decompoe international di erence in " OS into three component: (i) the diperion in etimate of " acro countrie, (ii) di erence in ectoral openne to trade, and (iii) di erence in the ectoral allocation of expenditure. Trade in mot economie in wetern Europe i lightly le elatic ( 4) than in the US ( 4:5). The di erence re ect the fact that ectoral trade i lightly le elatic than in the US, epecially in large and open ector. An exception i Germany, whoe etimated elaticity i low relative to the ret of Europe, equal to 3:54. At the ector level, German trade i in fact more elatic than in the US, epecially in open and large ector. But on the other hand, the large ector in Germany are relatively more open, o that foreign hock have izeable e ect on the dometic price index - i.e the trade elaticity i low. The Chinee trade elaticity i 6:60, the lowet in the ample. Thi happen becaue in China, large and open ector are relatively more elatic than in the US. The ame i true, albeit to a maller extent, of Japan, Korea, and Canada. India, whoe elaticity i 6:13, ha uch low etimate becaue conumption fall on cloed ector, o that foreign hock have 5

6 relatively little e ect on the dometic price index - i.e. the trade elaticity i high. The international di erence uncovered in thi paper point to the importance of ectoral pecialization in explaining the elaticity of trade - meaured by " OS - and ultimately the repone of real income to term-of-trade hock, i.e. welfare. Of particular relevance in our ample i the diperion in ector-peci c elaticitie, and it covariance with ectoral openne and expenditure hare. In contrat, etimate of " A are virtually identical acro countrie. There are no international di erence to explain in the rt intance. And ince they built from aggregate data, etimate of " A are eentially independent on the ectoral compoition of output and trade. The ret of the paper i tructured a follow. Section 2 how the one-ector verion of ACRC i a pecial cae of the multi-ector model, with identical welfare implication. Section 3 decribe our etimation of ector-level elaticitie, and data ource. Section 4 compute the one-ector trade elaticitie " OS implied by the multi-ector model. They are compared with macroeconomic etimate, then with adequately weighted average of ector level etimate. The ection cloe with a decompoition of international di erence in trade elaticitie. Section 5 veri e the robutne of the reult. Section 6 conclude. 2 Welfare in One v. Multi-Sector Trade Model Thi ection etablihe that the one-ector verion of ACRC i neted into the multi-ector model they develop in ection 5.1. We follow Appendix A in ACRC, and conider rt perfect, then monopolitic competition. By de nition, change in aggregate welfare W MS aociated with moving to autarky in the multi-ector world are given ln W MS ln ln P (1) where Y i aggregate income and P i the price index. 6

7 2.1 Perfect competition Labor market clear. Auming balanced ln Y ln w = 0, where the econd equality come from the choice of labor a the numeraire. The change in welfare correponding to a change in trade cot, e.g. a move to autarky, i entirely driven by a change in price. By de nition, the price index i given by P = Y (P ) (2) where denote the (Cobb-Dougla) expenditure hare in ector, and P i the ector-peci c price index. The welfare lo aociated with a move to autarky i given ln W MS = ln P (3) Under perfect competition, the ectoral price index i a weighted average of the marginal cot of production acro all exporting countrie, with weight given by import hare. Appendix A in ACRC how that for mall change in the price index, the de nition impli e ln P = 1 ln jj (4) where jj i the hare of dometic expenditure in ector. Subtituting into equation ln W MS = X ln jj (5) Now conider jj = P P X jj Y, the aggregate hare of dometic expenditure, where X jj and Y denote dometic and total expenditure in ector, repectively. By de ln jj = jj jj = X jj ln jj (6) 7

8 A one-ector verion of the model impoe unique parameter, i.e. " = " and jj = jj. Thi of coure ay nothing about the calibration of either " or jj. The latter doe have a de nition, pelled out in equation (6), and i directly obervable. The former, in contrat, mut be etimated - and there i nothing in the model uggetive that thi hould be baed on aggregate data. Let W MS denote the welfare implied by the multi-ector model, with ectoral heterogeneity aumed away. With uch impli ln W MS = 1 ln jj = 1 ln jj ln W OS (7) " " where W OS i the welfare repone in the one-ector model. Under perfect competition, the one ector model i a pecial cae of the multi-ector verion. 2.2 Monopolitic Competition Under monopolitic competition with free entry, a zero pro t condition hold that equate gro pro t to xed entry cot. Once again income Y = L, o ln Y = 0. With retricted entry, ACRC impoe that pro t be proportional to income to obtain the ame reult. In either cae, therefore, we continue to have equation (3). Now however P i an ideal price index compoed of all the imperfectly ubtitutable varietie produced acro exporting countrie. Appendix A in ACRC how that for mall change in price, we ln P = 1 ln jj + 1 ln N (8) where N denote the meaure of good that can be produced in ector. Subtituting into welfare ln W MS = X ln jj X ln N (9) Conider again a one-ector verion of the model, impoing the additional contraint that " = " and jj = jj. The thu contrained meaure of multi-ector welfare W MS change 8

9 according ln W MS = 1 ln jj 1 " ln N (10) If entry i retricted, then by aumption N = N and we have once ln W MS ln W OS. Under free entry, gro pro t are jut u cient to cover the total xed cot of new varietie, = N F. The ector peci c budget contraint rewrite Y = wl + N F = wl = L (11) Sectoral labor allocation varie with ectoral income. Auming with ACRC that ectoral pro t are proportional to ectoral income, we ln N ln ln L (12) So contrained welfare ln W MS = 1 ln jj 1 " ln L (13) But we have: 0 ln Y ln P Y ln W MS ln W OS. P Y = ln Y = ln L. So once again, Inamuch a they tem from the ame theory, the two verion mut have the ame welfare implication provided " and jj are calibrated adequately, ln W MS ln W OS (14) The natural analogy for one-ector variable i to obtain them from aggregate data. But a fundamental di erence exit between " and jj. By de nition, jj = P jj: the aggregate dometic hare i a weighted average of ectoral hare. The hare of dometic expenditure i directly obervable, from ectoral or indeed aggregate data. In contrat, " mut be etimated. 9

10 There i potentially a di erence between a value for " that i obtained from aggregate data, and a weighted average of ", obtained from ectoral data. Thi di erence can be undertood a a heterogeneity bia. The following experiment i therefore poible: (i) ue ectoral data to etimate ", and to calibrate jj, (ii) compute the welfare ln W MS, (iii) calibrate jj from aggregate data, and (iv) ue equation (14) to back the value of ", denoted by " OS, that mut be ued to obtain identical welfare gain acro the two verion. 3 In particular, equation (14) implie " OS ln ln W MS (15) The quetion i whether " OS can be etimated with aggregate data. 3 Etimation and Data We rt review the Armington demand ytem ued to etimate the price elaticitie of import at ector level. The approach i imilar to Feentra (1994), adapted to ector-level data by Imb and Méjean (2011). Then we review the data needed for the etimation and the welfare computation. 3.1 Etimation Demand in ector of country j i de ned a an Armington aggregator of varietie indexed by i. Sectoral demand at time t i given by C jt = " X i2i ijt C ijt # 1 1 (16) 3 The actual formulae for W MS depend on market tructure. It i given by equation (5) under perfect competition, and equation (13) under monopolitic competition. For lack of reliable employment ectoral data acro the countrie in our ample, we focu on the perfect competition meaure. 10

11 where i 2 I indexe both countrie and varietie, including j, the variety produced dometically. The parameter ijt denote preference hock. Aggregate conumption in country j combine demand in each ector = 1; :::; S according to C jt = Y 2S C jt j j j (17) where j denote the hare of expenditure on ector in country j. The repreentative agent chooe her conumption allocation on the bai of price incluive of tranport cot ijt. Utility maximization implie that nominal demand for variety i in each ector i given by P PijtC ijt = 1 ijt Pjt ijt 1 P jt C jt (18) P where Pijt i the local currency price of variety i of good, and Pjt = i2i P ijt ijt The price elaticity of ectoral import " = 1 can be etimated from equation (18). It cale the (logarithm) repone of ectoral import to an exogenou hock in (logarithm) relative price. A i well known, endogeneity iue notwithtanding, " can be obtained from a gravity etimation derived from equation (18). To ee thi, aume hift in relative price are driven by hock to trade cot. Equation (18) can be rewritten in logarithm: ln P ijtc ijt = A jt + " ijt + ijt (19) where A jt = ln P jtc jt and ijt = ln ijt 1. Equation (19) repreent a claical gravity regreion, that fall in the category decribed in ection 6 of ACRC. Etimate ariing from equation (19) can therefore be interpreted within the three clae of model dicued there. Of coure, equation (19) i not necearily well identi ed. For one thing, trade cot are not the only caue for price hock. For another, the reidual ijt are not necearily orthogonal to ijt. To achieve identi cation, Feentra (1994) or Imb and Méjean (2011) impoe a imple 11

12 upply tructure, given by Pijt = ijt exp( ijt) Cijt! (20) where ijt denote a technological hock, and! i the invere elaticity of upply in ector. Shock to relative price can now arie either becaue of trade cot, or technological development. Feentra (1994) famouly howed that combining equation (18) and (20) can achieve identi cation under further aumption on the fundamental hock ijt and ijt. We implement hi procedure, adapted to ector level data, a decribed in Imb and Méjean (2011). For each importing country j and each ector, identi cation i obtained in the cro-ection of exporter i. The data needed are therefore multi-lateral information on traded quantitie and price. To alleviate meaurement error, imported value are replaced with market hare m ijt = P ijt C ijt Pjt C jt where jt = 1 + jt P jt C jt P i6=j P ijt C ijt correct for dometic conumption in ector. Price are meaured a unit value. The etimation i performed for each ector, and for each country. Common correlated e ect are accounted for acro the ector of a ingle country following Imb and Méjean (2011). Many alternative approache exit to etimate trade elaticitie. Mot ret on an identi - cation of the exogenou component of trade cot in equation (19), typically contrained to be time-invariant. Eaton and Kortum (2002) invoke an arbitrage argument to reaon that bilateral trade cot mut be approximated by the maximum di erence in price level oberved acro good for a given country pair. Simonovka and Waugh (2011) how that thi approach create biaed etimate of ij, becaue of the limited number of good for which uch information i available. They propoe intead to implement a imulated method of moment on Eaton and Kortum (2002). Bernard, Eaton, Jenen and Kortum (2003), or Eaton, Kortum and Kramarz (forthcoming) t a multi-country Ricardian model on detailed rm-level data, which deliver - among other - trade elaticity etimate. It hould be clear thi paper doe not rely on the very methodology ued to etimate trade elaticitie. Any alternative econometric approach i acceptable, provided it fall under the 12

13 umbrella of the gravity equation (19). That will guarantee the argument developed in ACRC applie to the reulting etimate. The neceary data mut alo be relatively parimoniou, o that elaticitie can be etimated at ectoral level, for a range of countrie. The only intance of uch etimate that we are aware of i due to Broda, Green eld and Weintein (2006), who alo make ue of the Feentra (1994) approach. Of coure, an open quetion i how di erent the reult would be with alternative ectoral trade elaticity etimate. Although a precie aement of thi concern i impoible for lack of alternative international, ectoral etimate, we provide a dicuion in Section Data Sectoral information i needed on the cro-ection of imported quantitie and unit value for a cro-ection of countrie. In the main text, elaticitie are etimated on the bai of the United Nation ComTrade databae, uing export declaration for maximum coverage. Alternatively, a et of etimate wa obtained uing the BACI dataet, compiled by CEPII, which i meant to harmonize ComTrade and can for meaurement error or duplicate. The alternative reult are reported in Section 5. The data trace multilateral trade at the 6-digit level of the harmonized ytem (HS6), and cover around 5,000 product for a large cro-ection of countrie. The univere of product i partitioned into ector according to the 3-digit ISIC (reviion 2) level, which make for a maximum of 26 ector. The data are yearly between 1995 and Before 1995, the number of reporting countrie i untable. And the unit value reported in ComTrade experience a tructural break in Value of " are etimated on the complete time erie. Identi cation require that the cro-ection of countrie exporting to j be wide enough for all ector, and remain o over time. We retain good for which a minimum of 20 exporting countrie are available throughout the period. Both unit value and market hare are notoriouly plagued by meaurement error. We compute the median growth rate at the ector level 13

14 for each variable, acro all countrie and year. The bilateral trade ow are excluded for all ector with growth rate in exce of ve time that median value, either in unit value or in market hare. The reulting ample cover about 85 percent of world trade. Table 1 preent ome ummary tatitic for the 33 countrie we have data for. The number of ector range from 10 to 26. The Table alo report the total number of exporter into each country j. It i given by the number of ector in country j, multiplied by the number of exporting countrie for each ector. The average number of exporter range from 35 in Sri Lanka to more than 90 in the United State. For each ector, the data imply an average number of exporting countrie equal to 53. The main data contraint i not impoed by trade data. The binding limitation concern the weight that enter W MS, and are ued to decompoe the ource of international di erence in trade elaticitie. Both and jj require information on dometic conumption at ectoral level, that mut be compatible with the trade data in ComTrade. The contraint raie iue of concordance ince information i needed on both production and trade at the ectoral level. Thi i what reduce the coverage from 33 to 29 countrie. We ue a dataet built by Di Giovanni and Levchenko (2009) who merge information on production at the 3-digit ISIC (reviion 2) level from UNIDO and on bilateral trade ow from the World Trade Databae compiled by Feentra et al (2005). Dometic conumption at the ectoral level i computed a production net of export, and overall conumption i production net of export but incluive of import. We poit P k Y j Y j X j + M j X j + M j (21) where X j (M j ) denote country j export (import) in ector. And jj Y j Y j X j X j + M j (22) To focu on meaningful computation, a minimum of 10 ector i impoed for all countrie. The contraint tend to exclude mall or developing economie, uch a Panama or Poland. 14

15 The UNIDO data are in USD, and available at a yearly frequency. The value of and jj are computed over ve-year average in order to limit the conequence of cyclical uctuation in trade. Two et of etimation are reported. In the main text, we ue average weight between 1991 and For robutne, we alo conider average between 1996 and The UNIDO dataet i focued on manufacturing good only, which can bring into quetion the validity of trade elaticity etimate. But the vat majority of traded good are manufacture, o that the truncation remain minimal. We have experimented with the value for and jj implied by the OECD Structural Analyi databae (STAN), which provide information on all ector of the economy. For countrie covered by both dataet, i.e. OECD member, the end elaticitie were in fact virtually identical. At leat for OECD member, thi ugget the ampling caued by the UNIDO dataet i kept to a minimum. The lat column in Table 1 report the fraction of total trade a orded by UNIDO data. The coverage i below 40 percent for mall open economie uch a Hong Kong, Cypru, or Chile, but above 70 percent for large developed economie uch a the US, France or Spain. Coverage i clearly limited for mall open, developing economie. But, contrary to OECD data, it leave the door open to ome analyi for the developing world, not leat China where coverage i above 50%. 4 Trade Elaticitie in the One-Sector Model We report the etimate of " implied by ectoral data for the 29 countrie with the required data, and dicu the correponding value of " OS. One-ector elaticitie are rt compared with conventional macroeconomic etimate, and then with the weighted average of ectoral elaticitie " implied by theory. International di erence in thee weighted average are then acribed to di erent weight acro countrie, v. di erent etimate of ". 15

16 4.1 Sector-Level Etimate, Multi-Sector Welfare Lo and " OS Table 2 preent ome ummary tatitic of the etimate of " implied by ComTrade data between 1995 and There i coniderable heterogeneity in mean ectoral elaticitie acro countrie. Developed countrie diplay average value around 4, Germany at 4:06, France at 4:25, or Spain at 4:30. Specialized oil exporter alo diplay relatively low average ectoral elaticitie. Both Kuwait and Venezuela have etimate below 4 in abolute value. In contrat, developing exporting economie preent etimate at leat twice larger. China ha the larget mean ectoral elaticity, equal to 9:22, cloely followed by India, Korea and Sri Lanka. Sectoral heterogeneity i izeable within countrie a well. The ditribution of etimate tend to be mot diparate and kewed in developing economie. For intance, etimate of " range between 2:56 and 29:01 in China, with a median of 5:85, ubtantially below the mean of 9:22. In India, etimate range from 1:41 to 29:01. Range tend to be narrower for European developed countrie, uch a France, Germany, Italy or Spain. The ditribution there tend to be more ymmetric, with mean and median elaticitie cloer together. Country and ector e ect each explain approximately 10 percent of the cro-country diperion in etimate of ". Cloe to 80 percent of the variance in " mut therefore correpond to international di erence in the trade elaticity for each ector. The reult i apparent from Table 2, where ome ectoral etimate are dratically di erent from one country to the next. For intance, the price elaticity of Textile import i 6:00 in Spain, but 29:01 in Sri Lanka. Import of Rubber Product are inelatic in Kuwait (" = 1:56), but elatic in the Philippine (" = 24:06). Such diparitie may correpond to di erence in the very nature of the good imported. For intance, textile import into Spain are likely to be of higher quality than the (probably intermediate) good imported by Sri Lanka. Such heterogeneity in ectoral etimate i relevant to thi paper inamuch a it a ect the welfare gain from trade implied by the multi-ector verion of ACRC. We now compute the welfare ln W MS aociated with a move from current trade to autarky, acro all the 16

17 countrie with relevant data. The welfare lo i given by equation ln W MS = X ln jj whoe etimation require calibrated value for and jj. Welfare loe get cloe to zero for low value ln jj, i.e. in cloed economie where jj i cloe to 1. They decreae in trade elaticitie, becaue low " mean large price repone to hift in the quantitie traded, i.e. large welfare lo. And they increae in, i.e. in the hare of ector in expenditure. Armed with the welfare gain implied by the multi-ector verion, and oberved value for jj, the one-ector value of " OS i given by " OS ln ln W MS Thi i the trade elaticity that equate welfare in the one-ector model of ACRC to what i implied by it multi-ector verion. A ACRC, we conider the welfare lo aociated with a move to autarky, ln jj = ln jj. The rt three column in Table 3 report etimate ln W MS, the calibrated value of jj, and the correponding etimate of " OS for the 29 countrie with data. Standard error are obtained uing the Delta method, a detailed in the Appendix. The welfare loe from autarky are highet in mall open economie, like Hong Kong (40:3% of real income), Singapore (22:5%) or Kuwait (45:7%). They are lowet in large, cloed economie, uch a Japan (1:34%), India (1:97%), China (3:08%) or the US (3:97%). Finally the loe are etimated around 10% of real income for developed, Wet European economie. The ranking correlate with meaure of overall openne, a re ected in the aggregate hare of dometic expenditure jj Y j X j Y j X j +M j. It take lowet value in mall open economie, like Hong Kong or Singapore, and highet in large or cloed countrie, uch a Japan, the US or India. But openne i not the ole determinant of ln W MS alo decreae with trade 17

18 elaticitie, and depend on their ditribution acro ector. The cae of Kuwait i illutrative, where the welfare lo i 45:7%, the highet in our ample. Kuwait i very open to trade, with jj = 0:38. But it i not nearly a open a Hong Kong, ln W MS i nonethele alo cloe to 40%. The large welfare lo in Kuwait come from relatively low average ectoral elaticitie, a illutrated in Table 1. It alo come from the cro-ector correlation between jj and ". For given average openne and average trade elaticity, the welfare ln W MS take higher (abolute) value if open ector tend to diplay low elaticitie. Thi tend to happen in Kuwait, an open economy on average, whoe import are pecialized in ector with low trade elaticitie. The pecialization of trade matter for welfare. The third column in Table 3 report the value of " OS implied by oberved jj and etimated W MS. There are once again coniderable cro-country di erence. Etimate of the one-ector trade elaticity range from around 2 in Indoneia, Kuwait and Sri Lanka, down to 6 in China or India. Intermediate value between 4 and 5 are found for developed economie, with 4:48 for the US or 3:95 for the UK. No obviou correlate of " OS i apparent from Table 3, a developing economie can be found at either extreme of the range of etimate. Are uch etimate di erent from the literature? The average of " OS acro countrie equal 4:33. Thi i cloe to half of the value found in Eaton and Kortum (2002), but not any di erent from the corrected etimate preented in Simonovka and Waugh (2011). It i within the range of etimate in Bernard, Jenen, Eaton and Kortum (2003) or in Eaton, Kortum and Kramarz (2011). Thee paper do not eek to etimate trade elaticitie per e, and o no ectoral value are reported. Nor are trade elaticitie obtained for more than one country in each paper. 4 It i however reauring that the average of " OS i no di erent from reult in the literature that pertain to developed countrie. In our ample, trade elaticitie in wetern Europe and the US are cloe to 4, a they are in the literature. Thi ugget the etimate of " OS in Table 3 do not crucially depend on the etimation approach adopted here. Neither do the comparion and the decompoition of international di erence preented in the next 4 Broda and Weintein (2006) do preent international, ectoral etimate. They are cloe to thoe in thi paper - unurpriingly given the imilarity in the etimation method. 18

19 ection. 4.2 Comparion Table 3 doe ugget an important reult: the etimate of trade elaticitie are unuual for one-ector model. We now compare our etimate of " OS with alternative candidate. Trade elaticity etimate that arie from aggregate data are rt conidered. Aggregate data are the mot natural ource when it come to etimating parameter that enter one-ector model. It i elf-evident from Table 3 that our etimate of " OS are igni cantly di erent from the conventional value for import price elaticitie obtained in macroeconomic. 5 For intance, Figure 1 reproduce the etimate obtained in Houtakker and Magee (1969) for 15 developed economie. No point etimate are below 2, ome are poitive, and 10 out of 15 are not igni cantly di erent from zero. In fact, virtually no two etimate are igni cantly di erent from each other. For intance, the US price elaticity of import i 0:5, Japan i 0:78, and Canada i 1:5. A imilar exercie wa conducted uing ComTrade data, which we aggregated to country level in order to etimate a gravity equation. Uing the notation from ection 3, we etimate ln P ijt C ijt = A ij + (" A j + 1) ln P ijt + ~ ijt (23) where X t = X t X t 1, P ijt C ijt = P P P ijtc ijt and ln P ijt = 1 P ijt Cijt 2 P ijt C ijt + P ijt 1 C ijt 1 P ijt 1 C ijt 1 ln Pijt i a Tornqvit price index. Identi cation i obtained through time variation. Column 4 in Table 3 report the etimate of " A j. In tark contrat with " OS, the etimate of " A j are all between 0 and 1. Of coure, equation (23) i acutely problematic econometrically, a change in price are endogenou. It i however extremely unlikely a correction for uch endogeneity (which remain largely eluive in aggregate data) would imply etimate of " A j in line with the implication 5 See for intance the etimate reported in Franci et al (1976). The book contain ummarie of available, pertinent, aggregate elaticitie from the literature. Thee were ued to calibrate the Deardor -Stern Michigan CGE Model of World Production and Trade. 19

20 of ACRC, i.e. " OS. At the very leat, no exiting etimate uing aggregate data come even cloe. Etimate of " OS can therefore not be reproduced from aggregate data. But can they be obtained from ectoral data? We make ue of the theory developed by ACRC to derive an analytical expreion of " OS, a a weighted average of ectoral etimate. 6 Conider welfare in the multi-ector model, given by equation (5). After ome ln W MS ln jj X " where ln ln jj > 0 denote the openne of ector relative to the country average. Note that increae in relative ectoral openne a both jj and jj are maller than 1. Welfare loe increae till with the overall openne of the economy, i.e for low value of jj. They alo increae in relative ectoral openne, holding country average contant. By analogy with the expreion for W OS, we have " OS = X! 1 " W (24) " The one-ector elaticity i a weighted average of ector level etimate ", with weight given by. The weight re ect relative openne to trade,, and each ector importance in overall conumption,. The pecialization of production and conumption matter therefore in two way for one-ector elaticitie. Firt, ector that compoe a large fraction of total expenditure receive a mall weight. For a given hock and a given ectoral elaticity, a large value of implie a large repone of the overall price index, i.e. low aggregate trade elaticity. For the ame reaon, relatively open ector enter with a mall weight. For a given hock to traded quantitie, a large value of mean a large repone of the ectoral price index. The repone of the aggregate price index i accordingly large, which mean low aggregate trade elaticity. 6 For implicity and tractability, we focu on the perfect competition cae. 20

21 The lat column in Table 3 report etimate of " W computed uing equation (24). Perhap unurpriingly, the value obtained for " W are identical to " OS, albeit ometime etimated with le preciion. 4.3 International Diperion International di erence in trade elaticitie are abent in etimate obtained from aggregate data. Thu in macroeconomic, trade elaticitie are cutomarily aumed to be identical acro countrie. By de nition, they are invariant to di erence in the pecialization of trade acro countrie. Thi i an undeirable property in light of anecdotal and journalitic argument that the pecialization of production or trade ha direct implication on countrie external performance. The trade elaticity thi paper ugget ought to be ued in one-ector model doe not hare thi property. Cro-country etimate of " OS diplay coniderable heterogeneity. Theory can be ued to identify the ource of uch heterogeneity, and acribe them to the pecialization of trade. Uing the de nition of " W, it i eay to how how the one-ector elaticity in country j will repond to di erent determinant. In particular, a Taylor expanion of equation (24) around a reference country implie (" W " W ) = X " ( ) + X " ( ) + X (" ) 2 (" " ) (25) where = P " 2, and tarred variable denote the reference country parameter. Equation (25) implie that the international diperion in trade elaticitie depend on the ectoral compoition of expenditure, openne, and trade elaticitie, rather that on their average level. International di erence are determined by three covariance term. The rt re ect international di erence in the ectoral compoition of expenditure. The econd one re ect di erence in ectoral openne, and the third quanti e the importance of di erent ectoral 21

22 trade elaticitie. In abolute value, the elaticity in country j i relatively high if (i) conumer pend le (relative to the reference country) in open and inelatic ector, (ii) large and inelatic ector are alo cloed (relative to the reference), and (iii) ector that are elatic (relative to the reference) alo tend to be large and open. Performing the decompoition decribed in equation (25) i traightforward, given the data requirement involved in computing W MS. For reference, Figure 2 reproduce the cro-country etimate of " W reported in Table 3. The elaticitie are repreented relative to the US, which i the reference country ued in implementing the decompoition in equation (25). Figure 3 report the correponding three element for 29 countrie, with H = P = P " ( ), and E = P " ( ), (" ) 2 (" " ). Since all three can take either ign, international di erence in each component of equation (25) tend to be magni ed. It i intereting to note that high average etimate of ", which tend to happen in the developing world a hown in Table 2, do not tranlate into large negative value for E. For intance, Sri Lanka and Venezuela have large poitive value of E, wherea they are negative in China. In Indoneia, Egypt or the Philippine, E i actually cloe to zero. A i obviou from equation (25), there i no correlation between ectoral average of " and the value of E. International di erence in " W arie becaue the ectoral ditribution of ", and change from one country to the next. Figure 3 ugget thee international di erence are mallet a regard, a tend to be the leat important element of " W " W acro the 29 countrie. In other word, the ditribution of ectoral openne diplay relatively mall cro-country diperion, a compared with conumption expenditure or ectoral elaticitie ". Several reult are of particular interet. Both China and India diplay ubtantially larger elaticitie of trade than the US, with value around 6:25. Figure 3 reveal thi happen for di erent reaon. Chinee trade tend to be elatic becaue E < 0, wherea H < 0 in India. Chinee trade would be a elatic a the US if it had imilar ectoral elaticitie. But they are in fact larger in abolute value: Chinee import are elatic and pecialized in large and open ector. The ame i true of Korea, Japan and Canada, albeit with maller magnitude. In 22

23 contrat, India trade i elatic becaue India pend le than the US on open ector. Indian trade would actually become le elatic than the US if it hared the ame. Mot European elaticitie are lightly cloer to zero than the US. Thi typically happen becaue E take mall, poitive value. In the United Kingdom for intance, E = 0:50 explain mot of the di erence with the US. The ame i true in France, Italy, Spain or Sweden, where poitive value of E are the main reaon for the (mall) dicrepancy with the US. Thee are countrie where relatively inelatic ector compoe a large fraction of expenditure, in open ector. An major exception in Europe i Germany, where " W i etimated to be 3:54. That i till cloe to the US or the ret of Europe. But Figure 3 illutrate the apparent imilarity mak in fact large dicrepancie. Firt, H = 1:73: German conumer pend more in open, inelatic ector than their US counterpart. If thi were the ole di erence with the US, the German trade elaticity would jump up to 2:75. But in addition, E < 0 in Germany, around 1:5. Thi mean open, large ector in German expenditure tend to be more elatic than in the US. In the end, the German trade elaticity i cloe to the US becaue the ectoral allocation of conumption and the ditribution of ectoral trade elaticitie work in oppoite direction. The two countrie with lowet etimate of " W are Kuwait and Sri Lanka. Figure 3 ugget both countrie have large, poitive value for E and. The two countrie preent value of that are ytematically larger than in the US, acro all ector. The actual value of jj cover broad range in both countrie, with only a few cloed ector, o that the ditribution in both countrie are heavily kewed. Thi tranlate in high - a few very high - value of a mot ector are more open than the average. Thu take poitive value. The ame i at play in a third country, Egypt. In addition, in both countrie, the ector with highet value for happen to be relatively le elatic than the US, which implie E > 0. What make both countrie pecial i the concordance of both coincidence: a kewed ditribution of, with high value preciely in relatively inelatic ector. The decompoition of " W i relevant to undertanding the international diperion in trade 23

24 elaticitie. It i of coure alo important for welfare. The welfare gain from trade decreae in the trade elaticity, o that large etimate of " OS mean lower welfare than what i implied by aggregate data. For intance, Figure 3 ugget the welfare gain from trade in China would be ubtantially higher if the ditribution of ectoral elaticitie were cloer to the US. They would be higher in India if India pent more on open ector. They would be lower in Kuwait if openne were more evenly ditributed acro ector. To our knowledge, there i no alternative methodology that implie uch a cloe mapping between the ectoral pecialization of conumption and production, the elaticity of trade, and ultimately the welfare gain from trade. 5 Robutne 5.1 Trade data from BACI TBC 5.2 Calibration of and jj baed on data TBC 5.3 Alternative Etimation of Sectoral Elaticitie TBC 6 Concluion The welfare gain from trade are computed for 29 countrie, on the bai of the multi-ector model developed by Arkolaki et al (2011) [ACRC]. Welfare i given by the tatic repone of real income to a term-of-trade hock, and it i ummarized by import hare and trade elaticitie. The multi-ector welfare meaure i computed from oberved ectoral import hare 24

25 and etimated ectoral trade elaticitie, obtained uing the methodology developed by Feentra (1994) and adapted in Imb and Méjean (2011). The one-ector verion i a pecial cae, and hould have identical welfare prediction to the multi-ector model, provided it i calibrated adequately. On the bai of oberved import hare at country level, we etimate the trade elaticity implied by the one-ector verion of ACRC, contrained to predict multi-ector welfare. Thi i the trade elaticity that belong in the one-ector model conidered by ACRC. The etimate are igni cantly di erent from conventional, macroeconomic trade elaticitie. They are larger in abolute value, and heterogeneou acro countrie, with value ranging between 2:1 and 6:6. China and India have low etimate, below 6. Wetern Europe and the US diplay etimate around 4, wherea Canada, Japan, Korea, and Singapore are cloer to 5. The lowet value are found for pecialized economie, like Kuwait or Sri Lanka. Uing the theory, a decompoition of thi international diperion i introduced. Trade elaticitie can di er becaue of the pecialization of conumption, of production, or becaue of international di erence in ector-level trade elaticitie. European elaticitie are cloe to zero becaue, relative to the US, inelatic ector are open, and compoe a large fraction of expenditure. Germany i a European exception: pending fall on relatively elatic ector. But pending alo fall relatively more on open ector, which mean low elaticity ince the price level i then reponive to foreign hock. The latter e ect dominate, o that German trade i lightly le elatic than the European average. China, and to a maller extent Canada, Japan, and Korea have high elaticitie becaue expenditure fall on ector that are elatic relative to the US. India i an exception amongt exporting countrie. It trade i elatic becaue relatively le pending fall on open ector, o that it price level i le reponive to foreign hock. Inamuch a welfare decreae in the trade elaticity, thee decompoition carry through to welfare. 25

26 Reference Arkolaki, C., A. Cotinot & A. Rodriguez-Clare, 2011, New Trade Model, Same Old Gain American Economic Review. Bernard, A., J. Eaton, J.B. Jenen, & S. Kortum, 2003, Plant and Productivity in International Trade American Economic Review, 93(4): Broda, C. & D. Weintein, 2006, Globalization and the Gain from Variety, The Quarterly Journal of Economic, 121(2): Broda, C., J. Greenfield & D. Weintein, 2006, From Groundnut to Globalization: A Structural Etimate of Trade and Growth NBER Working Paper No Buiere, M., G. Callegari, F. Ghironi, G. Setieri & N. Yamano, 2011, Etimating Trade Elaticitie: Demand Compoition and the Trade Collape of , mimeo Boton College. DiGiovanni, J., & A. Levchenko, 2009, Trade Openne and Volatility, Review of Economic and Statitic, 91:3 (Augut), Eaton, J., & S. Kortum Technology, Geography, and Trade. Econometrica, 70(5): Eaton, J., S. Kortum & F. Kramarz, forthcoming, An Anatomy of International Trade: Evidence from French Firm Econometrica. Feentra, R., 1994, New Product Varietie and the Meaurement of International Price, American Economic Review, 84(1): Feentra, R., 2005, Franci, J., Schumacher, B. & R. Stern, 1976, Price Elaticitie in International Trade, Macmillan Pre, Houthakker, H. & S. Magee, 1969, Income and Price Elaticitie in World Trade, The Review of Economic and Statitic, 51(2): Imb, J. & Mejean, I., 2011, Elaticity Optimim, CEPR Dicuion Paper,

27 Krugman, P., 1980, Scale Economie, Product Di erentiation, and the Pattern of Trade, American Economic Review, 70(5): Levchenko, A., L. Lewi & L. Tear, 2010, The Collape of International Trade During the Crii: In Search of the Smoking Gun, IMF Economic Review, 58:2 (December), Melitz, M., 2003, The Impact of Trade on Intra-Indutry Reallocation and Aggregate Indutry Productivity, Econometrica, 71(6): Simonovka, I. & M. Waugh, 2011, The Elaticity of Trade: Etimate and Evidence, UC Davi Working Paper No

28 Appendix: Variance The variance ln W MS Conider a Taylor expanion ln W MS = P We ln W MS ln ^W MS + X ^ ln(w MS ) + X " ln jj around it etimated ln ^W ln W (" ^" ) " =^" (^" ) 2 (" ^" ) ln jj The variance i therefore given by 2 V ar(^" ) V ar(@ ln W MS ) = X (^" ) 2 ln jj The variance of " OS A Taylor expanion of " OS = ln ln W MS around it etimated value ^" OS implie " OS = ^" OS ln jj (@ ln W MS ) 2 (@ ln W ln ^W MS ) The variance i therefore given by 2 ln jj V ar(" OS ) = (@ ln W MS ) 2 V ar(@ ln W MS ) The variance of " W A Taylor expanion of " W = P " 1 around it etimated value ^"W implie " W = ^" W + P P (^" ) 2 ^" 2 (" ^" ) 28

29 So that the variance i given by V ar(" W ) = X ^"! 4 X (^" ) 2! 2 V ar(^" ) 29

30 Table 1: Summary Statitic # ect # ect exp % Trade Autralia Autria Canada Chile China Cypru Finland France Germany Greece Guatemala Hong Kong Hungary Indoneia Italy Japan Korea Malayia Taiwan Norway Portugal India Slovakia Spain Sweden Turkey United Kingdom United State

31 Table 2: Cro country Etimate of ε Summary Statitic Autralia Autria Canada China Egypt Finland France Nb Sect 16 Mean 8.20 Median 6.30 Minimum 3.51 Other non metallic mineral product Maximum Pottery, China and Earthenware Nb Sect 24 Mean 6.02 Median 5.32 Minimum 2.67 Other non metallic mineral product Maximum Pottery, China and Earthenware Nb Sect 24 Mean 5.68 Median 5.34 Minimum 2.73 Footwear, except vulcanized or moulded rubber or platic footwear Maximum Machinery, except electrical Nb Sect 18 Mean 9.22 Median 5.85 Minimum 2.56 Printing, publihing and allied indutrie Maximum Tranport equipment Nb Sect 19 Mean 5.70 Median 4.76 Minimum 2.61 Other manufacturing indutrie Maximum Tranport equipment Nb Sect 25 Mean 6.56 Median 4.95 Minimum 2.61 Gla and gla product Maximum Wearing apparel, except footwear Nb Sect 25 Mean 4.25 Median 3.89 Minimum 2.48 Wood and cork product, except furniture Maximum 6.63 Wearing apparel, except footwear