Trade Elasticities. 1 Introduction. Jean Imbs Isabelle Mejean

Transcription

1 Trade Elaticitie Jean Imb Iabelle Meean Abtract The welfare gain from trade depend on the degree of openne, the price elaticity of trade, and on their diperion acro ector. Thi paper etimate both parameter at ector-level for 28 developing and developed countrie. It compute the welfare gain from trade in the preence of heterogeneity in both parameter, and evaluate the importance of each. The paper introduce an aggregate trade elaticity, defined a the elaticity which equalize welfare gain in one and multiple ector model. The value for thi aggregate elaticity vary greatly acro countrie, and they do o becaue of their pattern of production. In contrat, tandard etimate of aggregate trade elaticity hardly diplay any difference acro countrie. JEL Claification Number: F32, F02, F15, F41 Keyword: Price Elaticity of Import, Sectoral Etimate, Trade Performance, Heterogeneity. 1 Introduction The welfare gain from trade can be computed on the bai of the price elaticity of trade, and the degree of openne to foreign trade. Thi reult, due to Arkolaki et al. (2012), ha recently been extended to cae allowing for ector-level heterogeneity. Oa (2015) and Cotinot and Thank are due to Brent Neiman and Andrei Levchenko, for their dicuion of an early verion of thi paper, and to audience at the September 2010 San Francico Fed Pacific Bain Reearch Conference and the January 2011 American Economic Aociation Meeting. Pari School of Economic (CNRS) and CEPR. Correponding author: Pari School of Economic, boulevard de l Hopital, Pari, France eanimb@gmail.com, Ecole Polytechnique, CREST and CEPR, iabelle.meean@polytechnique.edu,

2 Rodriguez-Clare (2013) dicu the implication of heterogeneou trade elaticitie. Levchenko and Zhang (2014) allow for ector-pecific degree of openne. Thi paper combine both dimenion, and evaluate their repective importance. We introduce a meaure of a country trade elaticity that depend directly on the ectorlevel pecialization of production and export. The notion that a country trade performance i directly related to the pecialization of it production i ubiquitou in the media, but abent from the conventional etimate of thi important parameter. For intance, Houthakker and Magee (1969) etimate price elaticitie of import for 15 developed economie, and find no two etimate are ignificantly different from each other. Little ha changed ince then: the aggregate price elaticity of import i a mall number, cloe to zero from below, and it tend to be o for mot countrie. The reult in Arkolaki et al. (2012) ought to imply the ame welfare gain whether they are computed uing ector-level or aggregate parameter. We ue thi identity to introduce an aggregate trade elaticity, expreed a a weighted average of ector-level elaticitie, where the weight reflect the pecialization of the economy. The aggregate trade elaticity take the value that equate the welfare gain from trade implied by heterogeneou ector to thoe implied by the one-ector model. Thi exercie enable u to decompoe the ource of crocountry difference in aggregate trade elaticitie into difference in the ize of ector, their openne, and their trade elaticity. We find that aggregate trade elaticitie are cloe to the US in mot developed countrie, with the exception of the UK, Autralia, and Canada, where they are ubtantially larger in abolute value. Mot emerging market have much larger elaticitie (in abolute value) than the US, e.g., China, Turkey, Chile, or Slovakia. In both cae, the difference come from high value of trade elaticitie at ector level. Sector-level heterogeneity in trade elaticitie ha firt-order conequence on the aggregate trade performance of countrie. Arkolaki et al. (2012) how that the welfare gain from trade are given by d ln W MS = β ε ln λ 2

3 where and repectively denote a ector and an importing country, λ i the hare of dometic expenditure in country ectoral conumption, β i the hare of ector in final expenditure, and ε i the trade elaticity. A hown later, the analogou aggregate verion i given by d ln W OS = 1 ε ln λ Since the implied welfare gain mut be identical, it follow that ε = ( β ) 1 ln λ 1 (1) ln λ ε which expree an aggregate trade elaticity a a weighted average of ector-level elaticitie. The paper follow Imb and Meean (2015) to etimate value for ε, and calibrate meaure of openne and expenditure hare for 28 developed and emerging market. The reulting etimate of ε range from 3.4 to 9.9, with lowet value in Cypru, Chile, and China. The cro-country average equal 5.9. Developed economie have etimate around 5, 4.9 in the US, although Canada, the UK, Autralia, and Greece have ubtantially larger value (in abolute value), cloer to 6, or even 9 in Greece. The value of ε are clearly ignificantly different from claic trade elaticity etimate obtained from aggregate data. We decompoe thee international difference into three component: (i) the diperion in etimate of ε acro countrie, (ii) difference in ectoral openne to trade λ, and (iii) difference in the ectoral allocation of expenditure β. Trade in mot economie in Wetern Europe i about a elatic a in the US ( 4.9), and the difference are minimal acro all three component of our decompoition: France, Germany, Hong Kong, Japan have imilar aggregate elaticitie, and alo imilar ector-level pattern. Some exception are Norway, Sweden, the UK, Autralia, Canada, and Greece, that all have ubtantially larger elaticitie in abolute value. In all thee cae, the difference reflect the fact that ectoral trade i more elatic than in the US, epecially in large and open ector. Thi eem to correpond to relatively pecialized developed economie - either in commoditie, or perhap in the financial ector. 3

4 An exception i Autria, whoe etimated elaticity i cloe to the US ( 4.8). On average, ector-level elaticitie in Autria are ubtantially higher than in other developed countrie. But thi i offet by the fact that thoe ector with relatively low elaticitie are in fact the big ector of Autria, both in term of dometic expenditure and of trade - i.e the aggregate trade elaticity i low. Mot developing economie have aggregate elaticitie that are larger than in the OECD. In mot cae, thi happen becaue ector-level elaticitie are larger in abolute value. For intance, the Chinee trade elaticity i 6.9, and thi happen becaue in China, large and open ector are relatively more elatic than in the US. The ame i true of Chile, Turkey, or Slovakia. An intereting exception i Malayia, whoe elaticity i 3.4. Thi happen not becaue trade i inelatic at ector level, but rather becaue the bulk of final expenditure fall on cloed ector. A a reult, the dometic price index i relatively inulated from foreign hock - i.e. the trade elaticity i high. The international difference uncovered in thi paper point to the importance of ectoral pecialization in explaining the elaticity of trade, and ultimately the repone of real income to term-of-trade hock, i.e. welfare. We how that the diperion in ector-pecific elaticitie ha firt-order effect on the aggregate trade elaticity. Thi tand in tark contrat with etimate of a country trade elaticity ariing from macroeconomic data, that are virtually identical acro countrie. The ret of the paper i tructured a follow. Section 2 dicue our meaure of aggregate trade elaticity, which relie on the equivalence of welfare formula ariing from the one-ector and the multi-ector verion of Arkolaki et al. (2012). Section 3 decribe our etimation of ector-level elaticitie, and data ource. Section 4 compute the one-ector trade elaticitie ε implied by the multi-ector model, and compare them with macroeconomic etimate. The ection cloe with a decompoition of international difference in trade elaticitie. Section 5 conclude. 4

5 2 Welfare in One and Multi-Sector Model Thi ection etablihe that the one-ector verion of Arkolaki et al. (2012) i neted into the multi-ector model they develop in their ection 5.1. Thi hold true under perfect competition a well a, under ome mild retriction, under monopolitic competition. By definition, change in aggregate welfare W MS by aociated with moving to autarky in the multi-ector world are given d ln W MS = d ln Y d ln P (2) where Y i aggregate income in country and P i the price index. Labor market clear. Auming balanced trade, d ln Y = d 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. Auming Cobb-Dougla preference acro ector, the price index i given by P = ( P ) β (3) where β denote the expenditure hare in ector, and P i the ector-pecific price index. The welfare lo aociated with a move to autarky i thu given by d ln W MS = β d ln P (4) Equation (4) ay that the magnitude of the gain from trade in a multi-ector context depend on the extent of ectoral price adutment, the gain being all the tronger (in abolute value) a the price in large ector (in term of expenditure) adut more. One would expect the magnitude of uch ectoral price adutment to be highly enitive to the market tructure and the aumption on the cot tructure. A hown in Cotinot and Rodriguez-Clare (2013), ectoral price adutment can however be ummarized uing a ingle, imple, formula if i) preference are CES within each ector, ii) trade i balanced, iii) the demand for import i conitent with the gravity equation and iv) factor of production are ued in the ame way 5

6 acro all activitie in all ector. Under thee aumption, Cotinot and Rodriguez-Clare (2013) how that ectoral price adutment can be written a follow: d ln P = 1 ε [ d ln λ δ d ln r ] (5) where δ i a dummy variable that characterize the market tructure in ector of country : It i equal to one under monopolitic competition with free entry and zero under perfect or Bertrand competition, or when there i monopolitic competition but retricted entry. r denote the hare of total revenue in country generated from ector. By definition, it i equal to the hare of ector in expenditure, β, in the pecial cae of autarky but not in an open-economy context. Under monopolitic competition with free entry, r impact ectoral price ince entry into one ector entail gain from new varietie. The main inight of Arkolaki et al. (2012) i that the repone of ectoral price to a foreign hock ultimately depend on the magnitude of term-of-trade adutment, whether thoe termof-trade adutment take place at the intenive or the extenive margin. To meaure thoe term-of-trade adutment ex-pot, it i ufficient to quantify the impact that the hock ha had on the dometic hare in conumption λ and multiply it by the invere of the price elaticity of trade to convert the quantity adutment into a welfare equivalent. A underlined in Cotinot and Rodriguez-Clare (2013), market tructure i hown to matter for price adutment in the multi-ector cae, contrary to the one-ector model. Thi i becaue the cro-ectional mobility of factor (d ln r) can partially compenate for any reduction of trade induced by a poitive foreign hock. Combining equation (4) and (5) give a meaure of welfare gain from trade, in a multiector context: d ln W MS = β ε [ d ln λ δ d ln r ] (6) In the pecial cae of moving to autarky: d ln W MS = β ε [ ] ln λ + δ ln r β 6

7 Cotinot and Rodriguez-Clare (2013) ue thi framework to quantify the gain from trade in a ample of 32 countrie. They notably compare the number obtained under different aumption about market tructure, and δ = 0 or δ = 1. The difference are negligible: welfare gain are roughly imilar, averaging 14% under monopolitic competition and 15.3% under the alternative aumption. Baed on thi reult, the ret of our analyi focue on the cae δ = 0 for all,, auming the reallocation of revenue acro ector ha negligible conequence. Baed on equation (6), we will compute the welfare lo that would be induced by countrie moving to autarky and analyze the origin of the heterogeneity acro countrie in our ample. There are three potential driver of uch heterogeneity, which potentially interact with each other: i) cro-country difference in the tructure of conumption (in the {β }), ii) crocountry difference in the enitivity of ectoral trade to price adutment (in the {ε }), and iii) cro-country difference in the opene of different ector (in the {λ }). Y Conider now λ X Y, the aggregate hare of dometic expenditure, where X and denote dometic and total expenditure in ector. By definition d ln λ = β dλ λ = λ λ β d ln λ (7) A one-ector verion of the model impoe unique parameter, i.e. ε = ε and λ = λ. Contraining ector-level heterogeneity away, the expreion for the welfare gain of trade in a multi-ector environment become 1 β d ln λ = 1 d ln λ = d ln W OS (8) ε ε where the firt equality make ue of equation (6). W OS i welfare in the one-ector model. The one ector model i a pecial cae of the multi-ector verion, with heterogeneity aumed away. Inamuch a they tem from the ame theory, the two verion mut have the ame welfare implication provided ε and λ are calibrated adequately. The natural analogy for one-ector 7

8 variable i to obtain them from aggregate data. But a fundamental difference exit between ε and λ. By definition, λ = β λ : the aggregate dometic hare i a weighted average of ectoral hare. The hare of dometic expenditure i directly obervable, from ectoral or aggregate data. In contrat, ε mut be etimated. There i potentially a difference between a value for ε that i obtained from aggregate data, and a weighted average of ε, obtained from ectoral data. The paper conduct the following experiment: (i) ue ector-level data to etimate ε, and calibrate λ, (ii) compute welfare W MS, (iii) calibrate λ from aggregate data, and (iv) ue thee number to back the value of ε that mut be ued to obtain identical welfare gain acro the two verion, following: ε = d ln λ d ln W MS = ( β ) 1 ln λ 1 (9) ln λ ε Having recovered the (aggregate) elaticity which i conitent with empirical evidence gathered from ectoral data, it i poible to analyze the cro-country heterogeneity in aggregate elaticitie (thu in aggregate welfare) that i attributable to variou dimenion of heterogeneity. 3 Etimation and Data In equation (9), the only parameter which are not directly oberved from the data are the ectoral elaticitie. We now ummarize the approach ued to etimate them uing import data oberved at ector level. The empirical trategy i inpired by Feentra (1994) and detailed in Imb and Meean (2015). That paper alo implement alternative approache, notably a gravity-type regreion conitent to Caliendo and Parro (2015). Reult preented for the US were conitent acro empirical trategie, o that we focu in thi paper on the tructural trategy decribed below. The ection cloe with a review of the data needed for etimation and welfare computation. 8

9 3.1 Etimation The trategy conit in etimating tructurally an equilibrium model of bilateral trade flow. The demand-ide of the model feature Contant Elaticity of Subtitution between varietie of (diaggregated) product exported by variou countrie. The import demand equation write a follow: d ln it = ε d ln P it + Φ t + ξ it (10) where i denote a variety, i.e. an origin country and t i a time indicator. it i the market hare of country i in expenditure on good of country, at time t. The intercept Φ t i timevarying and common acro countrie. For intance it capture variation in the multilateral reitance index introduced by Anderon and van Wincoop (2003). Finally, ξ it i an error term combining preference hock and trade cot. The hock are aumed to be independent and identically ditributed acro ector and countrie. To account for the endogeneity of price, Feentra (1994) impoe a imple upply tructure: Pit = exp(υit) ( ) ω Cit 1 ω where C it i real conumption of good k imported from country i, and ω map into the price elaticity of upply in ector. The technology hock υ it i independent and identically ditributed acro ector and countrie. After rearranging, thi implie d ln P it = ω d ln it + Ψ t + δ it (11) where Ψ t i a time-varying intercept common acro origin countrie, and δ it = ( 1 ω ) dυ it i an error term that depend on upply hock. Solve equation (10) for ξ it, and equation (11) for δ it, expre both in deviation from a reference country r, and multiply term for term to obtain: Y it = ψ 1 X 1it + ψ 2 X 2it + e it (12) 9

10 where Y it = (d ln P it d ln P rt) 2, X 1it = (d ln it d ln rt) 2, X 2it = (d ln it d ln rt)(d ln P it d ln P rt), and e it = ( ξ it ξ rt) ( δ it δ rt) 1 ε. Feentra (1994) oberve that the time average of e it i zero, provided the hock ξit and δit are orthogonal to each other. The time average of X1it and X2it contitute therefore appropriate intrument in equation (12), ince cov it ( X 1i, e it) = cov it ( X 2i, e it) = 0. They olve the iue of endogeneity preent in the import demand equation. 1 Since they are average over time, identification i effectively obtained acro countrie. The procedure in Feentra (1994) conit in etimating equation (12) and recovering the tructural parameter ˆε and ˆω from the etimated coefficient, ˆψ 1 and ˆψ 2. For ome combination of the etimated coefficient, however, the recovered value are not theoretically conitent. In uch circumtance, we follow Broda and Weintein (2006). We apply a grid earch algorithm over all the theoretically-conitent value for (ε, ω) and elect the combination of parameter which minimize the root mean quare error. Becaue we do not want thi procedure to create a bia, we retrict the grid earch to value of ε higher than Data Sectoral information i needed on bilateral import and unit value (i.e., price) at ector-level for a cro-ection of countrie. We ue the United Nation ComTrade databae, uing export declaration for maximum coverage. The data report 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. Price elaticitie are etimated for each ISIC ector of each importing country, but the data are collected at the mot diaggregated (HS6) level. 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 1 In practice, an intercept i included in equation (12) to account for the meaurement error ariing from the unit value ued to approximate price. Given the origin of potential meaurement error, the intercept i allowed to vary at the mot diaggregated level, i.e. for each HS6 category. 10

11 in Identification require that the cro-ection of countrie 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 for each variable, acro all countrie and year. We drop all ector with growth rate in exce of five 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 28 countrie with available data. The number of ector (and the number of etimated elaticitie ε ) range from 10 to 26. The Table alo report the total number of exporter into each country, i.e., the number of ector in each country multiplied by the number of exporting countrie for each ector. For each ector, the data imply an average number of exporting countrie of 53. The main data contraint concern the weight that enter W MS. Both β and λ 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 to 28 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 flow 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 define β k Y ( Y X + M X + M ) (21) where X production. And (M ) denote country export (import) in ector and Y λ Y Y X X + M the value of it (22) 11

12 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. The UNIDO data are in USD, and available at a yearly frequency. The value of β and λ are computed over five-year average in order to limit the conequence of cyclical fluctuation in trade. Two et of etimation have been conidered. In the main text, we ue average weight between 1991 and For robutne, we have alo conidered average between 1996 and Reult are very imilar and are available upon requet. The UNIDO dataet i focued on manufacturing good only, which can bring into quetion the validity of trade elaticity etimate. But the vat maority of traded good are manufacture, o that the truncation remain minimal. We have experimented with the value for β and λ 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 iue caued by the UNIDO dataet i kept to a minimum. The lat column in Table 1 report the fraction of total trade covered 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 ε implied by ectoral data for the 28 countrie with the required data, and dicu the correponding value of ε. One-ector elaticitie are compared with conventional macroeconomic etimate, and then with a weighted average of ectoral elaticitie ε. The Section cloe with a decompoition of the international difference in etimate of ε. 12

13 4.1 Sector-Level Etimate, Multi-Sector Welfare and ε Table 2 preent ome ummary tatitic of the etimate of ε implied by ComTrade data between 1995 and There i coniderable heterogeneity in mean ectoral elaticitie acro countrie. Developed countrie diplay average value around 5: Germany at 4.6, France at 4.8, or the US at 5.9. In contrat, developing exporting economie preent etimate at leat twice larger. Cypru ha the larget mean ectoral elaticity, equal to 14.4, cloely followed by Chile, Indoneia and Guatemala. 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 ε range between 1.8 and 29.0 in Chile, with a median of 8.2, ubtantially below the mean of In Indoneia, etimate range from 2.3 to Range tend to be narrower for European developed countrie, uch a France, Germany, Italy or the UK. The ditribution tend to be more ymmetric alo, with mean and median elaticitie cloer together. Country and ector effect each explain approximately 10 percent of the cro-country diperion in etimate of ε. Cloe to 80 percent of the variance in ε mut therefore correpond to international difference in the trade elaticity for each ector. The reult i apparent from Table 3, where ome ectoral etimate are dratically different from one country to the next. For intance, the elaticity for Fabricated Metal product i 3.5 in France, but 26.6 in Indoneia. Import of Potterie are inelatic in Autralia (ˆε = 1.9), but elatic in Sweden (ˆε = 29.0). Such diparitie may correpond to difference in the very nature of the good imported. For intance, Metal product imported by France are likely to be of higher quality than thoe imported by Indoneia. Thi heterogeneity in ectoral etimate i relevant inamuch a it affect the welfare gain from trade implied by the multi-ector verion of Arkolaki et al. (2012). We now compute the 2 Note that thee interval are omewhat mileading becaue of the lower bound impoed on etimated elaticitie obtained uing a grid earch procedure. For intance, the range of etimated elaticitie i quite large in Table 2 for the US, [ 29.0, 3.0] but i trongly reduced once the ingle elaticity equal to -29 i neglected, to [ 5.1, 3.0]. Thi i typically not the cae for developing countrie. For intance, once the ingle value of 29 i dropped, the interval are equal to [ 24.6, 1.8] in Chile, and [ 24.3, 2.3] in Indoneia. 13

14 welfare lo d ln W MS aociated with a move to autarky, acro all the countrie with relevant data. The welfare lo i given by equation (5): d ln W MS = β ε ln λ whoe etimation require calibrated value for β and λ. Welfare loe get cloe to zero for low value of ln λ, i.e. in cloed economie where λ i cloe to 1. They decreae in trade elaticitie, becaue that mean large price repone to hift in the quantitie traded. And they increae in expenditure hare. Armed with the welfare gain implied by the multi-ector verion and oberved value for λ, the one-ector value of ε i given by ε = ln λ d ln W MS Thi i the trade elaticity that equate welfare in the two verion of the model. The firt three column in Table 4 report etimate of d ln W MS, the calibrated value of λ, and the correponding etimate of ε for the 28 countrie with data. Standard error are obtained uing the Delta method detailed in the Appendix. The welfare loe from autarky are highet in mall open economie, like Hong Kong (36.3% of real income) or Malayia (28.2%). They are lowet in large, cloed economie, uch a Japan (1.2%), India (2.3%), China (3.0%) or the US (3.6%). On average, the loe are etimated around 7.5% of real income for developed, Wet European economie. The ranking correlate with meaure of overall openne, a reflected in the aggregate hare of dometic expenditure λ Y X Y X +M. It take lowet value in mall open economie, like Hong Kong or Malayia, and highet in large or cloed countrie, uch a Japan, the US or India. But openne i not the ole determinant of welfare: d ln W MS alo decreae with trade elaticitie, and depend on their ditribution acro ector. The comparion of Greece and 14

15 Autria i illutrative of two countrie which are roughly a open to trade, pending around half of their conumption on imported good, but with different ectoral pecialization and elaticitie, leading to different level of welfare loe. The welfare lo from moving to autarky i twice a large in Autria than in Greece (repectively 13.5 and 7.8%). The difference i in part attributable to lower average ectoral elaticitie in Autria, a illutrated in Table 2. It alo come from the cro-ector correlation between λ and ε. For given average openne and average trade elaticity, the welfare lo d ln W MS take higher (abolute) value if open ector tend to diplay low elaticitie. Thi tend to happen in Autria, 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 4 report the value of ε implied by oberved λ and etimated W MS. There are once again coniderable cro-country difference. Etimate of the one-ector trade elaticity range from around 3.4 in Malayia, down to 10.0 in Cypru. Intermediate value between 4 and 5 are found for developed economie, with 4.9 for the US or 5.4 for the UK. No obviou correlate of ε i apparent from Table 4, a developing economie can be found at either extreme of the range of etimate. 4.2 Comparion Table 4 doe ugget an important reult: the etimate of ε are unuual for one-ector model. We now compare our etimate of ε with alternative candidate. Trade elaticity etimate that arie from aggregate data are firt 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 4 that our etimate of ε are ignificantly different from the conventional value for import price elaticitie obtained in macroeconomic. 3 For intance, Figure 1 reproduce the etimate obtained in Houthakker and Magee (1969) for 15 developed economie. No point 3 See for intance the etimate reported in Franci et al. (1976). The book contain ummarie of available aggregate elaticitie from the literature. 15

16 etimate are below 2, ome are poitive, and 10 out of 15 are not ignificantly different from zero. In fact, virtually no two etimate are ignificantly different 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 it C it = A i + (ε A + 1) ln P it + ν it (23) where X t = X t X t 1, P it C it = P ( itc it and ln P it = 1 P ) it Cit 2 P it C it + P it 1 C it 1 P it 1 C it 1 ln Pit i a Tornqvit price index. Identification i obtained through time variation. Column 4 in Table 4 report the etimate of ε A. In comparion with ε, the etimate of ε A are much cloer to zero. Of coure, equation (23) i acutely problematic, a change in price are endogenou. But it i unlikely a correction for endogeneity would imply etimate of ε A cloe to ε. At the very leat, no exiting etimate uing aggregate data come even cloe. Etimate of ε can therefore not be reproduced from aggregate data. Rather, they are given by a weighted average of ector level etimate ε, with weight given by β ln λ ln λ : ε = ( ) 1 ln λ 1 β ln λ ε The weight reflect the relative openne to trade and each ector importance in overall conumption. The pecialization of the economy matter in two way: 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 β 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 ln λ ln λ 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. 16

17 4.3 International Difference International difference in trade elaticitie are abent from etimate obtained from aggregate data. Thu in macroeconomic, trade elaticitie are cutomarily aumed to be identical acro countrie, and thu invariant to difference in the pecialization of trade acro countrie. Thi i an undeirable property in light of anecdotal and ournalitic argument that the pecialization of production or trade ha direct implication on countrie external performance. The trade elaticity introduced in thi paper doe not hare thi property. Cro-country etimate of ε diplay coniderable heterogeneity, and theory can be ued to identify it ource. Uing it definition, it i eay to how how ε decompoe. In particular, a Taylor expanion of equation (1) around a reference country r implie ε ε r = ε r β Sh βr r βr } {{ } B where Sh r β ln λ rr r 1 ln λ rr ε r β ln λ rr 1 r ln λ rr ε r λ Sh λ r r λ r }{{} L and λ ln λ ln λ + ε Sh ε r r ε r }{{} E (13) Equation (13) implie that the international diperion in trade elaticitie i determined by three term. The firt term (B ) reflect international difference in the ectoral compoition of expenditure. The econd one (L ) reflect difference in ectoral openne, and the third (E ) reflect difference in ectoral trade elaticitie. In abolute value, ε i relatively high if (i) conumer pend le (relative to the reference country) in open and inelatic ector, (ii) large and inelatic ector are 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 (13) i traightforward, given the data requirement involved in computing W MS. For reference, Figure 2 reproduce the cro-country etimate of ε reported in Table 4, along with the decompoition in equation (13) uing the US a reference country. 17

18 It i intereting to note that high average etimate of ε, which tend to happen in the developing world a hown in Table 2, do not necearily tranlate into large value for E. For intance, Chile or Greece have large poitive value of E, wherea they are negative in Indoneia. A i obviou from equation (13), there i no correlation between ectoral average of ε and the value of E. International difference in ε arie becaue the ectoral ditribution of ε, β and λ change from one country to the next. Figure 3 ugget thee international difference are mallet a regard β, a the B term tend to be the leat important element of ε ε r ε r, except perhap in Malayia. The main reaon why etimate of ε vary acro countrie appear to be ummarized in E, i.e., in cro country difference in the ector-etimate of trade elaticitie. Some difference in L do exit a well, but they are much maller, except perhap in Autria. Several reult are of interet. In mot cae, the etimate of ε are larger (in abolute value) or imilar to the US. Amongt developed countrie, only Germany ha an etimate cloer to zero than in the US, at 4.3; France etimate i 4.6. Among developing countrie, elaticity etimate are obervably larger in abolute value, except in Guatemala ( 4.5), Indoneia ( 4.4), and Malayia ( 3.4). The difference are much larger for countrie whoe aggregate elaticitie are etimated above that in the US. For intance, Greece and Chile both diplay value of ε around 9; Canada etimate i 8, Slovakia 7.8, while China i 6.9, Hungary, Portugal, and Turkey are 6.4. A i apparent from thi lit, there i no ytematic correlation beween income level and elaticity etimate: even though mot developed countrie have etimate of ε in the US ballpark (Germany, France, Autria, South Korea, Italy, or Japan all have etimate around 5), there are exception. Figure 3 doe however reveal a ytematic pattern acro countrie: high etimate of ε typically arie becaue of a high value for E. Countrie with elatic trade are one that tend to import more of (relatively) high-elaticity good. In the conventional view of trade elaticitie, thi correpond to heterogeneou price elaticitie of demand for a given ector acro countrie. In the model of Eaton and Kortum (2002), international difference in etimate of ε correpond 18

19 to difference in the diperion of firm technologie at ector level. Deciding which of thee two interpretation dominate in the data i beyond the cope of thi paper. But the fact that high value of ε arie in both developed (Canada, Autralia) and developing (China, Turkey) countrie i uggetive that technology-baed explanation can play a role. The fact that few countrie have etimate of ε lower than the US ugget diperion in firm technology i in fact highet in the US in our ample, i.e., that the US contitute a legitimate benchmark. Among the countrie with larget etimate, China, Slovakia, and Canada tand out: in all three cae, the aggregate elaticity would be the ame a in the US if ector-level etimate of trade elaticitie were thoe of the US, i.e. if E were zero. Thu, large aggregate difference come from international difference in etimate of the elaticity of a given ector, conitent with Table 3. Autralia, Chile, Greece, and to a leer extent Turkey all hare the ame property, but the end effect on ε i mitigated by negative value of L : In thee mall open economie, inelatic ector tend to be much more open to international trade than in the US, which ha mitigating conequence on the etimate of ε. Autralia, in particular, would have a trade elaticity a high a Canada ( 8) if the relative openne of it ector wa the ame a in the US. Mot European elaticitie are imilar to the US, but thi mak ome important difference. The United Kingdom, for intance, would have a much higher elaticity if large ector were more open, cloer to that of Turkey ( 6, 5). Thi i becaue it importing ector do tend to diplay high value of ε. Thi i alo true of Norway and Sweden, where the effect of E and L on ε work in oppoite direction. Autria i an extreme cae of the ame pattern: baed on the etimate of ε there, the value of E in Autria would imply an aggregate elaticity cloe to 10, intead of the 4.8 we etimate. Thi illutrate the importance of letting both trade elaticitie and the extent of openne vary by ector. Interetingly, Germany tend to diplay imilar etimate of ε than the US: but it aggregate elaticity i cloer to zero ( 4.3) becaue both L and B take negative value. Thu, the relatively low elaticity of German trade come not from epecially low trade elaticitie at 19

20 ector level, but rather from the tructure of final conumption, and of openne. A few developing countrie diplay elaticity etimate in the US ballpark, ometime even cloer to zero. It i epecially the cae of Malayia and Indoneia, Guatemala to a leer extent. Thee contitute intereting exception. Malayia etimate of ε = 3.4 i the cloet to zero in our ample. Figure 3 reveal thi happen trictly for tructural reaon: while E > 0 in Malayia, ut like it i in mot other developing countrie, B and L are both negative, quite izeably o. B < 0 in particular reflect the tructure of final expenditure in Malayia, that tend to fall on relatively cloed ector, o that the repone of aggregate quantitie to international price i muted. Malayia provide an illuminating illutration of the decompoition introduced in thi paper, emphaizing that, in principle, the tructure of the economy matter a much a ector-level elaticitie. Guatemala contitute a imilar example, with E > 0 but L < 0. Finally, Indoneia i an outlier, a it i the only developing country that diplay negative value for E, i.e. ector elaticity etimate that are cloer to zero than in the US. The decompoition of ε i relevant to undertanding the international diperion in trade elaticitie. It i of coure alo important for welfare. The welfare gain from trade decreae in the trade elaticity, o that large etimate of ε 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 imilarly be higher in Canada. 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 Concluion The welfare gain from trade are computed for 28 countrie, on the bai of the multi-ector model developed by Cotinot and Rodriguez-Clare (2013). Welfare i given by the tatic re- 20

21 pone 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 and etimated ectoral trade elaticitie. 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 the model, but contrained to imply the ame level of welfare a in the multi-ector model with homogeneou ector. We label thi an aggregate trade elaticity. Etimate of aggregate trade elaticitie are ignificantly different from conventional, macroeconomic trade elaticitie. They are larger in abolute value, and heterogeneou acro countrie, with value ranging between 3.4 and 9.9. China ha low etimate, 6.9. Wetern Europe and the US diplay etimate around 5, but Canada, Chile and Greece are cloer to 9. The lowet value are found for mall-open pecialized economie. Uing the theory, a decompoition of thi international diperion i introduced. Trade elaticitie can differ becaue of the pecialization of conumption, of production, or becaue of international difference in ector-level trade elaticitie. Mot countrie have elaticity etimate larger (in abolute value) than the US becaue ector-level elaticitie are themelve larger in abolute value. Inamuch a welfare depend on the trade elaticity, thee decompoition carry through to welfare. 21

22 Reference Arkolaki, Cota, Arnaud Cotinot, and Andre Rodriguez-Clare, New Trade Model, Same Old Gain?, American Economic Review, February 2012, 102 (1), Broda, Chritian and David E. Weintein, Globalization and the Gain From Variety, The Quarterly Journal of Economic, 2006, 121 (2), Caliendo, Lorenzo and Fernando Parro, Etimate of the Trade and Welfare Effect of NAFTA, Review of Economic Studie, 2015, 82 (1), Cotinot, Arnaud and André Rodriguez-Clare, Trade Theory with Number: Quantifying the Conequence of Globalization, in Gita Gopinath and Elhanan Helpman and Kenneth Rogoff, ed., Handbook of International Economic, Vol. 4, 2013, chapter 4. di Giovanni, Julian and Andrei A. Levchenko, Trade Openne and Volatility, The Review of Economic and Statitic, Augut 2009, 91 (3), Feentra, Robert C, New Product Varietie and the Meaurement of International Price, American Economic Review, March 1994, 84 (1), Feentra, Robert C., Robert E. Lipey, Haiyan Deng, Alyon C. Ma, and Hengyong Mo, World Trade Flow: , NBER Working Paper 11040, National Bureau of Economic Reearch, Inc January Franci, J., B. Schumacher, and R. Stern, Price Elaticitie in International Trade, Macmillan Pre, Houthakker, H. and S. Magee, Income and Price Elaticitie in World Trade, The Review of Economic and Statitic, 1969, 51 (2), Imb, Jean and Iabelle Meean, Elaticity Optimim, American Economic Journal: Macroeconomic, July 2015, 7 (3),

23 Levchenko, Andrei A. and Jing Zhang, Ricardian productivity difference and the gain from trade, European Economic Review, 2014, 65 (C), Oa, Ralph, Why Trade Matter After All, Journal of International Economic, November 2015, 97 (2), A Appendix: Variance A.1 The variance of d ln W MS Conider a Taylor expanion of d ln W MS We have: = β ε ln λ around it etimated value d ln Ŵ MS. d ln W MS = d ln Ŵ MS + = dln Wˆ MS + d ln W MS dε ε =ˆε β (ˆε ) 2 (ε ˆε ) ln λ (ε ˆε ) The variance i therefore given by V ar(d ln W MS ) = ( ) 2 β ) 2 ln λ (ˆε V ar(ˆε ) A.2 The variance of ε A Taylor expanion of ε = ln λ d ln W MS around it etimated value ˆε implie ε = ˆε The variance i therefore given by V ar(ε ) = ln λ ( ) d ln W MS 2 (d ln W MS d ln Ŵ MS ) ( ) 2 ln λ ( ) d ln W MS 2 V ar(d ln W MS ) 23

24 Figure 1: Houtakker and Magee (1969) elaticity etimate 4 Import elaticitie Note: The grey circle are the point etimate found in Houtakker and Magee (1969). Line around the circle correpond to the confidence interval, at the 5% level. Figure 2: Etimated elaticity etimate in the one-ector model Import elaticitie Note: The grey circle are the point etimate reported in Table 4. Line around the circle correpond to the confidence interval, at the 5% level. 24

25 Table 1: Summary Statitic # ect # ect exp % Trade Autralia Autria Canada Chile China Cypru Finland France Germany Greece Guatemala Hong Kong Hungary India Indoneia Italy Japan Korea Malayia Norway Portugal Slovakia Spain Sweden Taiwan Turkey United Kingdom United State Note: The firt column report the number of ector under tudy, the econd column report the number of ditinct ector origin countrie, which i the dimenionality ued to reach identification. The third column i the percentage of the country aggregate import which the dataet cover. 25

26 Table 2: Summary tatitic on etimated ectoral elaticitie Country Count Mean Median Min Max Autralia Autria Canada Chile China Cypru Finland France Germany Greece Guatemala Hong Kong Hungary India Indoneia Italy Japan Korea Malayia Norway Portugal Slovakia Spain Sweden Turkey Taiwan United Kingdom United State Note: The table report ummary tatitic on the etimated elaticitie, ˆε, by importing country. 26

27 Table 3: Summary tatitic on etimated elaticitie, by ector Sector Count Mean Median Min (Country) Max (Country) Food (Greece) -3.8 (Finland) Beverage (Malayia) -2.3 (Hungary) Tobacco (USA) -2.0 (Germany) Textile (Autralia, Chile, -3.5 (Taiwan) Guatla, Cypru) Wearing Apparel (Autralia, Cypru, -4.6 (Korea) Sweden, Taiwan) Leather product (Greece) -3.8 (Malayia) Footwear (Cypru) -3.0 (Korea) Wood product (Autralia) -2.4 (Italy) Furniture (USA) -1.5 (Hungary) Paper product (Portugal) -1.8 (Chile) Printing & Publihing (Malayia) -2.2 (Chile) Indutrial chemical (Guatemala) -4.1 (USA) Other chemical (Chile) -2.7 (Finland) Petroleum (Spain) -2.5 (UK) Rubber product (Indoneia) -3.5 (France) Platic product (Indoneia) -2.9 (Italy) Potterie (Sweden) -1.9 (Autralia) Gla product (Indoneia) -2.4 (Chile) Other mineral product (Taiwan) -2.1 (Chile) Iron and teel (Chile) -3.3 (France) Non-ferrou metal (UK) -3.0 (Portugal) Fabricated metal pdct (Indoneia) -3.5 (France) Machinerie (Cypru) -4.9 (USA) Electrical apparatu (Cypru, -4.7 (Germany) Hungary, Chile) Tranport equipment (China, -4.1 (Spain) Turkey, Canada) Meauring equipment (Sweden, Guatla) -3.4 (Finland) Other manufacturing (Portugal) -3.1 (Norway) Note: The table report ummary tatitic on the etimated elaticitie, ˆε, by ISIC-rev2 indutry. The countrie diplaying the minimum and maximum elaticitie in each ector are diplayed under parenthee. 27

28 Table 4: Aggregate welfare gain, dometic expenditure hare, and trade elaticitie Country Welfare Dometic Elaticity Aggregate (d ln W MS ) hare (λ ) (ε ) Elat. (ε A ) Autralia (.007) (.810) (.220) Autria (.007) (.238) (.192) Canada (.005) (.630) (.106) Chile (.003) (.609) (.855) China (.002) (.433) (.247) Cypru (.004) (.648) (.419) Germany (.002) (.095) (.170) Spain (.003) (.214) (.233) Finland (.003) (.187) (.307) France (.002) (.118) (.158) United Kingdom (.003) (.188) (.369) Greece (.013) (1.509) (.898) Guatemala (.011) (.428) (1.046) Hong-Kong (.019) (.262) (.193) Hungary (.004) (.319) (.618) Indoneia (.012) (.456) (.238) India (.001) (.198) (.344) Italy (.002) (.156) (.278) Japan (.000) (.164) (.138) Korea (.002) (.239) (.805) Malayia (.031) (.375) (.239) Norway (.005) (.317) (.417) Portugal (.007) (.610) (.345) Slovakia (.005) (.938) (.711) Sweden (.004) (.260) (.240) Turkey (.002) (.315) (.216) Taiwan (.004) (.315) (.209) United State (.001) (.160) (.072) Note: The table report the welfare impact of moving to autarky, computed uing the formula in equation (5) (firt column), the calibrated aggregate hare of dometic good in conumption (econd column) and the aggregate elaticity of import inferred from the previou two column, and defined a the aggregate elaticity which equalize the welfare implication of the one- and multi-ector model. Standard error in parenthee, obtained uing the Delta method decribed in appendix. All etimate are ignificant at the one percent level. 28

29 Figure 3: Source of heterogeneity in one-ector elaticitie Sectoral elaticitie Sectoral opene Sectoral expenditure Note: The figure report the decompoition in equation (13), uing the US a reference. Medium gray correpond to the firt term B, black correpond to the econd term L, and light grey correpond to the third term E. 29