Is the Armington Elasticity Really Constant across Importers?

Transcription

1 MPRA Munich Personl RePEc Archive Is the Armington Elsticity Relly Constnt cross Importers? Hn Yilmzudy June 2009 Online t MPRA Pper No , posted 30. June :53 UTC

2 Is the Armington Elsticity Relly Constnt cross Importers? Hn Yilmzudy y June 2009 Astrct This pper shows tht the Armington elsticity, which refers to oth the elsticity of sustitution cross goods nd the price elsticity of demnd under the ssumption of lrge numer of vrieties, systemticlly chnges from one importer country to nother in n interntionl trde context. Then nturl question to s is "Wht determines the Armington elsticity?" The nswer comes from the distinction etween the elsticity of demnd with respect to the destintion price (i.e., the Armington elsticity) nd the elsticity of demnd with respect to the source price. Under dditive trde costs, it is shown tht the elsticity of demnd with respect to the destintion price is equl to the sum of the elsticity of demnd with respect to the source price nd the elsticity of demnd with respect to the trde costs. The empiricl results using the United Sttes export dt t the stte level support this reltion; hence, it is more liely to hve constnt elsticity of demnd with respect to the source price rther thn constnt Armington elsticity under dditive trde costs. In terms of policy implictions, the constnt Armington elsticity undervlues the e ects of policy chnge round 3 or 4 times compred to the importer-speci c Armington elsticities. JEL Clssi ction: F12, F13, F14 Key Words: Armington Elsticity; Interntionl Trde; Trde Rtios; Stte Exports; the United Sttes 1. Introduction Mny trde models hve in common feture tht countries (or regions) produce nd trde di erentited goods tht re to some extent sustitutle for ech other. In these models, the constnt elsticity of sustitution (CES) mong the products of di erent countries (i.e., the Armington, 1969, elsticity) is criticl prmeter for determining the ehvior of trde ows nd interntionl prices. As Ruhl (2008) points out, the importnce of this prmeter hs mnifested in two of the leding rnches of interntionl economics: the interntionl usiness cycle literture tht sees to understnd the high frequency uctutions in mcroeconomic ggregtes, nd the sttic pplied generl equilirium literture tht focuses on explining the ptterns of trde nd the e ects of trde policy. Especilly in the context of the sttic pplied generl equilirium trde literture, McDniel nd Blistreri (2002) provide ey insight: the Armington elsticity is ey prmeter tht is used y policymers to derive quntittive results, ecuse the e ects of n interntionl trde policy chnge re evluted y the conversion of policy chnges into price e ects. These price e ects (i.e., price chnges) re the ey in determining the e ects of trde policies on the rel mcroeconomic vriles such s output, employment, trde ows, nd economic welfre, s well s other importnt vriles of interest. In terms of modeling, the connection etween the price chnges The uthor would lie to thn Eric Bond, Mrio Crucini, Jonthn Eton, Dvid Hummels, Yoto Yotov, nd Midwest Interntionl Economics Fll 2008 Meeting prticipnts in Ohio Stte University for their helpful comments nd suggestions. The usul disclimer pplies. y Deprtment of Economics, Temple University, Phildelphi, PA 19122, USA; Tel: ; Fx: ; e-mil: sudy@gmil.com

3 nd the rel mcroeconomic vriles is usully chieved y employing the Armington elsticity (e.g., the e ects of chnges in tri s nd txes on the rel vriles re evluted through this elsticity). Therefore, there is no question tht the mesurement of the Armington elsticity is of fundmentl importnce in determining the response of trde models to policy experiments. But, is this criticl prmeter relly constnt? This pper investigtes whether the Armington elsticity systemticlly chnges from one importer country to nother in the context of interntionl trde. For instnce, when exports of the U.S. sttes to the rest of the world re considered, the Armington elsticity corresponds to the CES mong the products of di erent sttes. While some U.S. prtner countries my hve higher Armington elsticities, some others my hve lower elsticities. Then nturl question to s is "Wht determines the di erence etween these elsticities?" In the context of Armington ggregtors, under the ssumption of lrge numer of vrieties (i.e., the usul ssumption of monopolistic competition tht the individul vriety prices hve zero e ects on the ggregted price index of ll vrieties), the constnt elsticity of sustitution is equl to the price elsticity of demnd. Hence, nything tht ects the price elsticity of demnd should lso ect the elsticity of sustitution cross goods. Under dditive trde costs, this pper shows tht the price elsticity of demnd with respect to the destintion price (EDD) cn e decomposed into two prts for ny type of demnd function: the elsticity of demnd with respect to the source price (EDS) nd the elsticity of demnd with respect to the trde costs (EDT). It is lso shown tht EDD is the sum of EDS nd EDT. Furthermore, this pper depicts tht EDD is incresing in EDS nd trde costs, while it is decresing in source prices. In order to test the reltion mong EDD, EDS, trde costs, nd source prices, the U.S. export dt tht cover the exports from ech stte of the United Sttes to 230 countries round the gloe etween re used. The empiricl nlyses support the view tht EDD increses with trde costs nd decreses with source prices. This result suggests tht while it is more liely to hve constnt EDS cross countries, EDD is not constnt, nd it chnges from one importer country to nother, mostly due to trde costs through EDT. Since EDD is equl to the elsticity of sustitution in the context of Armington ggregtors, this result lso implies tht the elsticity of sustitution is not constnt; this is opposed to the CES ssumption tht is commonly used in the trde literture. The intuition for this result is s follows: It is nown tht n importer s demnd for n exporter s good depends on oth the source price nd the trde costs. However, the formtion of elsticity is the ey here. For instnce, given tht n importer is going to import from prticulr source, s in the sptil pricing theory, the importer my form her elsticity s she is t the source, lthough her demnd still depends on trde costs. 1 In other words, given tht n importer is going to shop t prticulr source, preferences should e de ned over the source prices, which cptures the extent to which individuls re willing to sustitute etween di erent vrieties. In such cse, di erent importers shopping t the sme source my shre the sme EDS. This is the cse when importers shop in n exporter country y considering the prices t the source; i.e., y forming their demnds ccording to the source prices. The trde costs re only dditionl costs tht importers hve to py, nd the importers re wre of this issue through their demnd functions. The mirror imge of this exmple in the context of individul ehvior cn e relted to the story tht individuls form their elsticities ccording to the source prices tht they fce in the mret (e.g., the shopping centers). Given tht n individul is going to shop t prticulr store, the dditionl trde costs relted to going to the store (e.g., deprecition of crs, gs prices, uto insurnce costs, driving riss) re only dditionl costs tht hve to e pid y the individul. In this context, given tht n individul is going to shop t prticulr store, she only compres the source prices; thus, the elsticity mesure should e formed with respect to the source prices t the store. When this story is generlized to the context of U.S. exports t the stte level where there is n elsticity of sustitution etween the products of di erent sttes, given tht country is going to import good from the U.S., tht country compres only the source prices in di erent sttes; thus the elsticity should e formed with respect to the source prices in di erent sttes. In terms of modeling, prtil equilirium trde model is introduced where ech country hs distinct import demnd for di erent countries goods (represented y su-utility). For instnce, the United Kingdom (U.K.) hs 1 See Greenhut et l. (1987) for n excellent nlysis of imperfect competition in the context of sptil pricing. 2

4 certin demnd (nd corresponding elsticity of demnd) for the United Sttes (U.S.) goods, while Germny hs di erent demnd (nd corresponding elsticity of demnd) for the very sme U.S. goods. The demnd of ech importer country is represented y n Armington ggregtor, which is comintion of di erent goods (ech produced in di erent stte) imported from the U.S. For the Armington ggregtor, it is veri ed tht EDD is the sum of EDS nd EDT, nd tht EDD is incresing in EDS nd trde costs. The empiricl nlysis supports this reltion y hving very high explntory powers. Overll, this pper chllenges mostly the CES type ggregtors tht re commonly used in the interntionl trde nd mcroeconomics literture y showing tht the Armington elsticity is not constnt (i.e., uncommon) cross importer countries. The results of this pper lso correspond to importnt policy implictions: individul responses, rther thn n imposed verge response, of the importers should e ten into ccount, ecuse ech importer hs its own demnd chrcteristics. In prticulr, t the U.S. level, it is empiriclly shown tht the constnt Armington elsticity undervlues the e ects of policy chnge round 3 or 4 times compred to the importer-speci c Armington elsticities. Relted Literture This susection rie y descries how this pper reltes to its closest ntecedents. Since the constnt elsticity of sustitution is equl to the price elsticity of demnd in the context of Armington ggregtors under the ssumption of lrge numer of vrieties, the studies tht hve focused on oth types of elsticities re depicted here. The Dixit-Stiglitz (1977) model is pioneering one tht hs een widely used or extended in mny litertures such s interntionl trde, mcroeconomics, nd growth nd development. 2 However, most of the time, the Dixit-Stiglitz model hs een used with complementry ssumption of CES. But is the Armington elsticity relly constnt cross importers? Becuse, if it is, the elsticity of demnd, the elsticity of sustitution, mrups nd prices re ll invrint from one importer country to nother. But is it relly the cse tht there re constnt mrups nd prices cross ll importers? Older empiricl studies hve focused on how the elsticity chnges y the country of origin of the exports. In prticulr, since Tinergen s (1946) pioneering rticle on the mesurement of elsticities in interntionl trde more thn hlf of century go, there hve een mny studies designed to mesure the reltionship etween chnges in reltive prices nd chnges in reltive exports. 3 Most of these empiricl studies hve estimted the reltion etween the volume of trde nd the reltive price levels cross countries. These studies were referring to the elsticity of the demnd for imported units only of given commodity, or of the elsticity of the demnd supplied y one speci c country. More recent empiricl studies lso show evidence for di erent elsticities of sustitution vlues for di erent goods. 4 Besides tht empiricl literture, theoreticl studies sed on optiml tri rtes show tht the elsticities of sustitution ply n importnt role in determining the optiml tri rtes set y n importer country. 5 Although these theoreticl ppers show tht there cn e positive reltion etween the tri rtes nd elsticity of sustitution under certin prmeters, they don t sy nything relted to reltion etween overll trde costs nd the elsticity of sustitution. Moreover, the reltion tht they re considering is mostly due to unique custion: chnge in the elsticity of sustitution cuses chnge in the optiml tri rtes. They don t tell us nything out how the elsticity of sustitution is determined. They te the elsticities s given nd nd the optiml tri rtes ccordingly. However, none of these studies hs focused on how the Armington elsticity chnges y the importer country. This pper considers the Armington elsticity cross exports of the U.S. sttes in 230 di erent countries round the gloe. It is not only shown tht the Armington elsticity is vrile cross these 230 countries, ut lso shown 2 See Gordon (1990) nd Mtsuym (1995) for literture surveys. 3 See Chng (1948), Pol (1950), Kreinin (1967), Krvis nd Lipsey (1972, 1975), Richrdson (1972, 1973), Hicmn nd Lu (1973), Chou nd Buongiorno (1983), mong mny others. 4 See Hummels (2001), Hed nd Ries (2001), Hrrign (1996), Feenstr (1994), Romlis (2007), Brod nd Weinstein (2006), Gllwy et l. (2003), mong mny others, for di erent elsticity mesures for di erent goods. 5 See Johnson( ), Gormn (1958), more recently Syropoulos (2002), Zissimos (2008), mong others, 3

5 tht the di erence in terms of elsticities cn e explined y the source prices nd trde costs. For instnce, the elsticity of sustitution in the U.K. for exports of di erent U.S. sttes is di erent from the one in Cnd, nd this di erence, on verge, cn e explined y the di erence in the source prices (due to price discrimintion of the U.S. exporters) nd trde costs (which is di erent cross the U.K. nd Cnd). Nevertheless, this pper is not the rst one nlyzing vrile elsticities cross importers. There re studies in which mret entry ects the elsticity of demnd. Most of the trde theory literture with this feture hs emphsized oligopoly nd homogeneous goods s in Brnder nd Krugmn (1982). 6 The literture on pricing-tomret is nother one tht shows evidence for vrying elsticities. This literture hs shown tht the sme goods re priced with di erent mrups nd thus hve di erent price elsticities of demnd cross importing mrets. 7 For instnce, Feenstr (1989) nd Knetter (1993) elonging to this literture focus on the movements long the sme, non-ces, demnd curves so tht vrition in quntities cused y tri or exchnge rte shocs yields vrition in the elsticity of demnd. However, this literture doesn t provide ny systemtic explntion for the di erence in elsticities cross importers. More recently, Hummels nd Lugovsyy (2009; HL henceforth) ttempt to ridge this gp y showing tht the Armington elsticity increses in importer GDP nd decreses in importer GDP per cpit. However, their log-liner empiricl pproch is open to improvement ecuse of the following possile resons. First, there cn e multicollinerity etween importer GDP nd importer GDP per cpit in such regression. In prticulr, ccording to the dt of this pper covering the period etween (i.e., 230 countries round the gloe), the correltion coe cient etween (log) GDP nd (log) GDP per cpit is round 0.48 (on verge) in typicl yer. Although this correltion coe cient is elow 0.70, which is the threshold vlue s rule of thum to e wrned of potentil prolems with multicollinerity (see Anderson et l., 2006), the overll qulity of the results my e ected. Second, estimting log-liner expressions y using ordinry lest squres (OLS) hs een criticized y Sntos Silv nd Tenreyro (2006), nd Henderson nd Millimet (2008) who suggest tht, under heterosedsticity, the prmeters of log-linerized models estimted y OLS my led to ised estimtes; thus, n lterntive estimtion method, Poisson Pseudo-Mximum Lielihood (PPML), should e preferred. This pper follows this suggestion s roustness nlysis esides using OLS. Besides these possile prolems, the explntory power of HL is very low (i.e., R 2 vlue is round 0.17), which mens tht much of the vrition in Armington elsticities cnnot e explined with only importer GDP nd importer GDP per cpit. When the empiricl nlysis of HL is replicted y using the dt of this pper (i.e., y running regression including importer GDP nd importer GDP per cpit), it is found tht the R 2 vlue is round 0.18, which is very close to wht HL hve. Fortuntely, the pproch used in this pper llows to hve richer list of vriles in such regression including trde costs, import volumes, income levels, exchnge rtes, nd purchsing power prity. For sure, in order to control for possile multicollinerity prolem, correlted vriles (e.g., import volumes nd income levels) re not included into the regression t the sme time. The regression nlyses of this pper hve R-r sqd. vlues up to 0.74 y using OLS nd 0.96 y using PPML, which re much higher compred to the ones in HL. Pln of the Pper The rest of the pper is orgnized s follows. Section 2 introduces simple trde model. Section 3 descries the dt. Section 4 provides insights nd depicts the estimtion methodology. Section 5 gives the empiricl results. Section 6 discusses the policy implictions. Section 7 concludes. The Appendix depicts the connection mong EDD, EDS, nd EDT for generl type demnd function. 2. The Model The economy consists of nite numer of countries. Ech country my import goods from ll ny numer of other countries. In the model, generlly speing, H; c stnds for the vrile H, where is the importer country (i.e., 6 Brod nd Weinstein (2006) empiriclly show how elsticities chnge cross importers. In connection with this literture, more recently, Dele et l. (2008) hve shown tht there is di erence etween short-run nd long-run elsticities due to trde sticiness. 7 See Golderg nd Knetter (1997) for n excellent literture review. 4

6 the destintion), is the good, nd c is the exporter country (i.e., the source) Individuls of the Importer Country The representtive gent in country mximizes utility U C; 1 C; 2 :::C N where C 1 is composite index of goods imported from country 1, C 2 is composite index of goods imported from country 2, nd so on. In country, the composite index of goods imported from country is given y the following CES function: C X i ' 1 C 1 1 (2.1) where C is good i imported from country (e.g., C is good i is produced in region i of country ); > 1 is the Armington elsticity in country for the goods imported from country ; ' is destintion, source, nd good speci c tste prmeter which cn e decomposed s ' i where is destintion (i.e., importer) speci c tste prmeter; is source (i.e., exporter) speci c tste prmeter; nd nlly, i is good speci c tste prmeter. 8 In prticulr,, nd i cn e used s xed e ects in regression nlysis; i.e., their multipliction represents unique tste prmeter etween regions nd in terms of good i. The optiml condition for expenditure on good i, imported y country, from country, is: C ' P P C (2.2) where P P ;i + is the price of good i imported y country, from the source country,, P ;i is the price of good i in country (i.e., the source), > 0 is good speci c net dditive trnsporttion cost from country to 1 P country, nd P i ' P 1 1 is the price index of the goods in country exported from country. It is implied tht P C P i P C. Elsticity of Sustitution Under the ssumption of lrge numer of vrieties (i.e., the usul ssumption tht the udget shre of good i is zero, which implies tht the individul vriety prices hve zero e ects on the ggregted price index of ll vrieties), the elsticity of demnd for the imported good with respect to the destintion price (i.e., EDD) is given y. However, the elsticity of demnd for the imported good with respect to the source price (i.e., EDS) is not constnt, it depends on the source price, the EDD, nd the trde cost, s follows: " P ;i P ;i + (2.3) where " is n importer speci c EDS. Note tht, in specil cse in which trde costs re equl to zero, ". Similrly, the elsticity of demnd for the imported good with respect to the trde costs (i.e., EDT) is cn e clculted s: where is n importer speci c EDT. Comintion of Equtions 2.3 nd 2.4 imply tht: P;i + (2.4) " + which mens tht the elsticity of demnd with respect to the destintion price is equl to the sum of the elsticity of demnd with respect to the source price nd the elsticity of demnd with respect to the trde costs (i.e., EDS 8 Distinguishing etween destintion, source, nd good speci c tste prmeters hs useful properties in terms of the estimtion. 5

7 + EDT EDD). The Appendix shows tht this reltion holds for ny type of demnd function, not just the CES formultion. According to Eqution 2.3, " P;i + (i.e., EDD) increses in " (i.e., EDS) nd trde costs, nd it decreses in the source prices, ceteris prius. There couple of possiilities. One of them is tht is constnt (i.e., common) nd " is vrile (i.e., uncommon) cross importer countries; this would imply tht the Armington elsticities re constnt (i.e., common) cross importer countries. However, s will e shown elow, the dt don t support this possiility. Another possiility is tht " is constnt (i.e., common) nd is vrile (i.e., uncommon) cross importer countries; this would imply tht the Armington elsticities increse in the trde costs nd decreses in source prices. As will e shown elow, the dt support this second possiility. 9 Hence, it is more liely to hve constnt (i.e., common) " nd vrile (i.e., uncommon) cross importer countries. Eqution 2.5 is the ey expression in this pper. The vlidity of the reltion etween, source prices (i.e., P;i ), nd trde costs (i.e., ) cn e tested, nd if signi cnt result cn e found, this would support the clim tht is not constnt cross importers. Insted, n lterntive elsticity of demnd, which is with respect to the source price (i.e., " ), my e constnt cross countries. Hence, such signi cnt reltion would chllenge the usul de nition of the Armington elsticity in the literture through the equlity etween the elsticity of demnd nd the elsticity of sustitution in Armington type ggregtors, under the ssumption of lrge numer of vrieties. P ;i (2.5) 3. Dt The min source of trde dt is the United Sttes Stte Export Dt otined from the TrdeStts Express. 10 The dt cover the yers 1999 through 2007 for the exports of the US sttes to 230 countries round the gloe. All gures re on Free Alongside Ship vlue sis. 11 The series credits export merchndise to the stte where the goods egn their nl journey to the port (or other point) of exit from the United Sttes, s speci ed on o cil U.S. export declrtions led y shippers. Although this dt set is regrded s the est ville source for stte export dt, in the dt, the origin of movement cn e either the loction of the fctory where the export item ws produced or, in mny cses, the loction of distriutor or wrehouse. In ny cse, these re exporter rms; thus, they hve pricing strtegies nd most proly they re more experienced in the exporting process compred to the non-exporter rms. Moreover, ech exporter rm, whether it is fctory or wrehouse, hs distinct pcging, trnsporttion, mreting nd pricing strtegies, which me their products di erent from ech other, even though they my e exporting the very sme product. 12 The totl vlues of exports from ech stte to the destintion countries re used. To me the connection etween the model nd the empiricl nlysis, the exports of ech stte re considered s di erent good produced in the U.S., which re connected to ech other through the Armington elsticity. For instnce, the exports of New Yor Stte represent prticulr U.S. good, nd the exports of Cliforni represent nother U.S. good for the importer (i.e., the destintion) country. When testing the vlidity of Eqution 2.5, in order to control for trde greement di erences, dummies for di erent economic regions tht export goods from the U.S. re used. Tle 1 shows the list of economic regions tht re included into the estimtion process. When testing the vlidity of Eqution 2.5, Gross Domestic Product (GDP), 9 Nevertheless, there is n ovious third possiility in which oth nd " re vrile cross importers. This prticulr possiility is lso considered in the estimtion procedure, elow. 10 TrdeStts Express drws ll stte export sttistics from the Origin of Movement (OM) series compiled y the Foreign Trde Division of the U.S. Census Bureu. 11 For further informtion on U.S. trde dt, visit 12 See Cssey (2006), Coughlin nd Wll (2002), Cronovich nd Gzel (1999), Hywrd nd Ericson (1995), nd Coughlin nd Mndelum (1991) for further discussions on the stte exports dt. 6

8 GDP per cpit, popultion, exchnge rte, nd purchsing power prity dt otined from World Development Indictors for the yers re lso used. Finlly, for distnce mesures, gret circle distnces etween ech country nd ech stte of the U.S. re clculted y using ltitudes nd longitudes of cpitl cities of the countries nd sttes. Tle 1 - Economic Regions Africn Growth nd Opportunities Act (AGOA) Anden Community (CAN) Asi-Pci c Econ. Coopertion (APEC) Assn. of Southest Asin Ntions (ASEAN) Cri. Community & Common Mt. (CARICOM) Centrl Americn Common Mret (CACM) Centrl Am.-Dominicin Rep. FTA (CAFTA-DR) Commonwelth of Independent Sttes (CIS) Europen Free Trde Assn. (EFTA) Europen Union Free Trde Aggreement of the Americs (FTAA) Gulf Coopertion Council (GCC) North Americn FTA (NAFTA) Org. of Petroleum Exporting Countries (OPEC) South Americn Customs Union (SACU) South Asin Assn. for Regionl Coop. (SAARC) Southern Cone Common Mt. (Mercosur) 4. Estimtion Methodology The rst step is to estimte (i.e., EDD) for ech destintion (i.e., importer) country. Then, the vlidity of hving positive reltion etween nd trde costs given in Eqution 2.5 is tested. For roustness, two di erent estimtion methods re employed, ordinry lest squres (OLS) nd Poisson Pseudo-Mximum Lielihood (PPML). In this section, the conditions under which OLS nd PPML cn e used re considered Estimtion of In order to hve n ccurte estimte of, di erence-in-di erence version of Eqution 2.2 is estimted. As will e shown in more detils elow, employing di erence-in-di erence pproch e ectively elimintes the distriution mrgin nd the tri s (or the quots) from the theoreticl trde eqution, which mes the estimtion results roust to these issues. First, the rtio of two di erent goods (e.g., goods i nd r) in country imported from country 7

9 (i.e., the U.S.) is ten s follows: C C ;r ' ' ;r i r P P P ;r P P P ;r C C Second, the rtio of two di erent goods (e.g., goods i nd r) in country imported from country (i.e., the U.S). is ten s follows: C ;i C ;r ' ;i ' ;r P ;i P P ;r C C i r P P ;i P ;r Finlly, the rtio of the rst two rtios is ten to otin:, 0 C C ;r C ;i C i r P P ;r 1, 0 i r P ;i P ;r 1 A P P ;r P ;i + P ;r + ;r, P ;i P ;r, P ;i + ;i P ;r + ;r where the lst equlity is otined y using the de nition of trde costs, P P ;i +. Note tht ll the prices on the right hnd side of the lst line re relted to the source prices in the U.S. In prticulr, they correspond to the source prices t di erent sttes of the U.S. in the empiricl nlysis. Since the totl exports dt re considered, nd since ll the source prices elong to only one country (i.e., the U.S.), it is resonle to set these source prices equl to one to otin the following simple expression to e estimted: C C ;r, C ;i C ;r ;r, 1 + ;i 1 + ;r For ech country, is estimted y using this expression. Setting source prices equl to one implies tht the export vlues in dollr terms now lso represent the quntity of exports. Although setting source prices equl to one my seem s strong ssumption from conservtive resercher s point of view, this is one of the est fesile pproches considering its empiricl convenience tht will e clerer elow. The est pproch should clculte source prices t ech stte; however, ecuse the dt represent the totl exports rther thn disggregted level exports (e.g., good level exports), it is not fesile to clculte or estimte source prices which re comprle cross sttes from the ville dt. Nevertheless, this strong ssumption will e relxed, nd its implictions will e discussed further elow. For roustness, possile mesurement errors in ech of the vriles in Eqution 4.1 re considered. Two di erent types of mesurement errors re ten into ccount: proportionl nd dditive. (4.1) 8

10 Proportionl Mesurement Errors The version of Eqution 4.1 with the proportionl mesurement errors is given y: C + C ;r + ;r, C ;i + ;i C ;r + ;r 1 + +, 1 + ;r + ;r 1 + ;i + ;i 1 + ;r + ;r If there re relized export oservtions (i.e., nonzero trde oservtions), the mesurement errors re proportionl to the export vlue. On the other hnd, in the cse of zero trde oservtions, the mesurement error is dditive. 13 The intuition ehind this is s follows: if there is relized (nonzero) trde oservtion, the mesurement error should e proportionl to the oservtion. For instnce, hving the very sme mesurement error for oth trde of $1 million nd trde of $1000 is less liely thn hving proportionl mesurement errors. On the other hnd, if there is no trde oservtion (i.e., trde oservtion is equl to zero), it is more liely to hve n dditive mesurement error insted of proportionl mesurement error, which would me no di erence to the vlue of zero. Under these ssumptions, if there re no zero trde oservtions, Eqution 4.2 cn e rewritten s follows: C + C C ;r + C ;r ;r, C;i + C ;i ;i C;r ;i ;i C ;r ;r 1 + ;r ;r ;r 1 + ;r ;r where C nd so on. If ting the log of oth sides results in: C C;i log C;r log C;r 1 + log ;i log ;r 1 + ;r where ;;i;r (1+ ;r)(1+ ;i) (1+ )(1+ ;r) ;r squres (OLS) when (1+ ;r)(1+ ;i) (1+ )(1+ ;r) 1+ ;r 1+ ;i ;r 1+ ;r 1+ ;i + log ;;i;r ;i ;r 1 A (4.2) (4.3) (4.4). This expression cn e estimted y ordinry lest ;;i;r, where ;;i;r is rndom vrile sttisticlly independent of the regressors. In such cse, ;;i;r ;;i;r nd therefore is sttisticlly independent of the regressors. If there is zero trde oservtion, sy C 0, Eqution 4.2 cn e rewritten s follows: C ;r + C ;r ;r, C;i + C ;i ;i C;r ;i ;i C ;r ;r 1 + ;r ;r ;r 1 + ;r ;r If the log of oth sides re ten, the following is otined: log C;r log where 0 ;;i;r (1+ ;r)(1+ ;i) (1+ ;r) squres (OLS) when (1+ ;r)(1+ ;i) (1+ ;r) C ;i C ;r ;r log 1+ ;r ;r ;r 1+ ;i 1+ ;r + log 1 + ;i 1 + ;r + log 0 ;;i;r ;i ;r 1 A (4.5) (4.6). This expression cn e estimted y ordinry lest 1+ ;i ;;i;r, where ;;i;r is rndom vrile sttisticlly independent of the regressors. In such cse, ;;i;r ;;i;r nd therefore is sttisticlly independent of the regressors. 13 Helpmn et l. (2008) show tht lmost 50% of the oservtions re zero trde oservtions in interntionl trde. Thus, considering those oservtions is essentil in empiricl wor. 9

11 Additive Mesurement Errors Although OLS is consistent under the ssumptions mde (i.e., ssuming tht error terms re dditive for zero trde oservtions nd multiplictive for nonzero trde oservtions), for roustness, unique dditive error term is lso considered. In such cse: where E r;;;j ;r C C ;r ; 1+ ;i 1+ ;r C C ;r, C ;i C ;r ;r 0. This cn e rewritten s:, C ;i C ;r ;r, 1 + ;i 1 + ;r, 1 + ;i 1 + ;r + ;;i;r (4.7) ;;i;r (4.8) where ;;i;r ;;i;r 1+ (4.9) ;i nd E expression: ;;i;r ;r log ; 1+ ;i 1+ ;r C C ;r 1+ ;r 1+ ;r 1. Ting the log of oth sides in Eqution 4.8 results in the following log-liner log C ;i C ;r log ;r ;i 1 + ;r To otin consistent estimtor of the slope prmeters y OLS, it is ssumed tht E + log ;;i;r log ;;i;r ;r (4.10) ; 1+ ;i 1+ ;r does not depend on the regressors. 14 Becuse of Eqution 4.9, this condition is met only if ;;i;r cn e written s follows: 0 1 +, ;i A 1 + ;r 1 + ;;i;r ;r where ;;i;r is rndom vrile sttisticlly independent of the regressors. In such cse, ;;i;r 1+ ;;i;r nd therefore is sttisticlly independent of the regressors, implying tht E log 1+ ;;i;r is constnt ;r ; 1+ ;i 1+ ;r Until now, the conditions under which OLS cn e used s n estimtion method hve een introduced. Nevertheless, for roustness, following Sntos Silv nd Tenreyro (2006), the ssumption of E log 1+ ;;i;r 1+ ;r ; 1+ ;i 1+ ;r not depending on the regressors is lso relxed y considering the Poisson Pseudo-Mximum Lielihood (PPML) estimtor. As Sntos Silv nd Tenreyro (2006), nd Henderson nd Millimet (2008) suggest, under heterosedsticity, the prmeters of log-linerized models estimted y OLS my led to ised estimtes; thus, PPML should e used. To show this, Eqution 4.8 cn e written s follows:, C C;i C;r C;r exp 1 + log ;i log ;r 1 + ;;i;r (4.11) ;r Assuming E ;;i;r ;r ; 1+ ;i 1+ ;r 1, then Eqution 4.11 my e estimted consistently using the PPML estimtor. In sum, two di erent estimtion methods re considered in the estimtion of Eqution 4.1: OLS nd PPML. 14 It is well nown tht modeling zero interregionl ows using norml error process leds to prolems. If the dependent vrile cnnot te vlue elow zero, then norml error process is poor pproximtion. Nevertheless, it is not concern here, ecuse the log-linerized eqution does hve vlues elow zero, y considering the (log) rtio of export vlues. 15 Under the ssumption of unique dditive mesurement error, the issue of zero trde oservtions cn e hndled y setting zero trde oservtions equl to one. This ssumption is necessry mostly ecuse the log of zero nd division y zero re oth unidenti ed. 10

12 4.2. Estimtion of the Reltion etween nd Trde Costs As ove, it is resonle to set these source prices equl to one to otin the following simple expression to e estimted y using Eqution 2.3: " 1 + (4.12) Eqution 4.12 is estimted y using the very sme methodology tht is used to estimte Eqution 4.1. For roustness, gin, two di erent types of mesurement errors re considered: proportionl nd dditive Proportionl Mesurement Errors In prticulr, if the mesurement errors (of trde costs) re multiplictive, Eqution 4.12 cn e rewritten s follows: 1 + " Ting the log of oth sides results in: log log " log where (1+ ) (1+ ) is ssumed to e independent nd to hve men of zero to e estimted y OLS Additive Mesurement Errors Alterntively, if there is unique dditive error term, Eqution 4.12 cn e rewritten s follows: " This cn e rewritten s: " 1 + (4.13) where 1 + " 1 + (4.14) nd E Ting the log of oth sides in Eqution 4.13 results in the following log-liner expression: log log " log (4.15) To otin consistent estimtor of the slope prmeters y OLS, it is ssumed tht E log 1 + does not depend on the regressors. Becuse of Eqution 4.14, this condition is met only if cn e written s follows: " 1 + where is rndom vrile sttisticlly independent of the regressors. In such cse, 1 + nd therefore is sttisticlly independent of the regressors, implying tht E log 1 + is constnt. The ssumption of E log 1 + not depending on the regressors is lso relxed y considering the PPML estimtor. To show this, Eqution 4.13 cn e written s follows: exp log " 1 + (4.16) Assuming E log 1 + 1, then Eqution 4.11 my e estimted consistently using the PPML estimtor. In sum, gin, two di erent estimtion methods re considered in order to test the vlidity of Eqution 4.12: OLS nd PPML. 16 Becuse of the empiricl strtegy used for zero trde oservtions in the estimtion of s, there is no zero oservtion issue in this second estimtion. 11

13 4.3. Trde Costs The connection etween the model nd the empiricl nlysis in terms of trde costs hs to e clri ed. Anderson nd vn Wincoop (2004) ctegorize the trde costs under two nmes, costs imposed y policy (tri s, quots, etc.) nd costs imposed y the environment (trnsporttion, wholesle nd retil distriution, insurnce ginst vrious hzrds, etc.). In this context, trde costs re de ned s follows: 1 + D 1 + t (1 + w ) {z } {z } {z } freight other distriution where D is the distnce etween country nd stte i of country (i.e., the U.S.) to cpture the freight costs; t is representing the (net) costs relted to tri s (nd quots) from country (i.e., the U.S). to country ; nd w is the (net) costs relted to the locl wholesle nd retil distriutions, nd insurnce in country Estimted Equtions By using the de nition of trde costs, the nl version of Eqution 4.1 to e estimted cn e introduced s follows: C C ;r, C ;i C ;r D 1 + t (1 + w ) D ;r (1 + t ) (1 + w D ;i D;r t (1 + w ) A 1 + t (1 + w ) D D ;r, D ;i D ;r (4.17) where vlues for ech country cn e estimted. Note tht employing di erence-in-di erence pproch e ectively elimintes the distriution mrgin nd the tri s (or the quots) from the theoreticl trde eqution, which mes the estimtion results roust to these issues. In terms of the estimtion strtegy, fter ting verge of trde (i.e., export) rtios over time (etween 1999 nd 2007), since ll the vriles nd prmeters depend on either or, the eqution cn e estimted for ech (; ) country pir seprtely. Hence, seprte regression is run for ech possile (; ) pir nd the estimtes coming out of regressions with the highest explntory powers re selected. For instnce, in order to hve n estimte of for country, ll possile trde rtios tht include country re considered. Then, mong those estimted regressions, the one with the highest explntory power (in terms of R-r sqd.) is selected. The corresponding is the one otined from tht regression with the highest explntory power. After hving mesures of s, the reltion etween nd trde costs is tested. In prticulr, the nl version of Eqution 4.12 to e estimted cn e written s follows: " D 1 + t (1 + w ) (4.18) where economic region speci c dummies re used for " 1 + t (1 + w ) s. Using these dummies cn lso e thought s prt of the roustness nlysis to let " s e region speci c vriles. In such cse, the trde costs other thn the freight costs re mostly controlled in the estimtion, however neither " nor 1 + t (1 + w ) s cn e identi ed due to the dummy vrile trp. Although hving very similr (mostly the sme) tri rtes, 1 + t s, re resonle within the sme economic region, one my thin tht the countries in the sme economic region my not shre the sme " s nd/or the sme distriution costs, (1 + w ) s. In such cse, " (1 + w ) cn e thought s prt of the error term (i.e., the unoserved term) in the estimtion process where " is the country speci c EDS. As n lterntive, the locl distriution costs cn lso e relted to the wge rtes of the importer countries, where wge rtes cn e proxied y income, income per cpit, or purchsing power prity. 17 Since imports of 17 See Alessndri nd Kosi (2004) who lins lrger mrups in high income importer s to consumer s opportunity cost of serch. Also see Crucini nd Yilmzudy (2009) who show the locl distriution costs re directly relted to the wge rtes in the distriution sector. 12

14 country re positively relted to its income, the volume of imports my lso e n indictor for high locl mrups (i.e., high locl distriution costs). Hence, vriles such s income, income per cpit, purchsing power prity, nd imports cn lso e included into the regression nlysis for roustness. It is worth noting tht the trde costs cn lso e de ned s 1+ D 1 + t (1 + w ) where represents the elsticity of distnce. In such cse, the estimted eqution would e " D 1 + t (1 + w ), where would e the estimte otined from Eqution This chnge would only ect the mgnitude of region speci c dummies nd the de nition of the coe cient in front of the distnce mesures, ut it would hve no e ect on the min purpose of the empiricl nlysis in terms of nding systemtic reltions cross importers. Nevertheless, for roustness, restriction in which 1 will e tested, elow Source Prices Up to now, the source prices hve een set equl to 1 for empiricl convenience. This simplicity would hve lmost no e ect on the estimtion of Eqution 4.1, since the rtio of two source prices is considered there. 18 However, some importnt informtion my get lost y doing so when " (P ;i + ) P ;i is estimted where the numertor includes the destintion prices while the denomintor includes the source prices. In sic terms, it cn e shown esily tht decreses in P ;i. Thus, nything tht ects the source prices lso ects. In specil cse under which there is price discrimintion, if the exporter rms t the source hve incresing returns to scle, or if they wnt to hve mret ccess to n importer country (to increse future pro ts) through lower prices, the following re implied: Source prices my decrese (i.e., my increse) with incresing imports of the importer countries. Since incresing exports cn e chieved y incresing incomes of the importer countries, source prices my lso decrese (i.e., my increse) with incresing sizes of the importer countries (which cn e proxied y income or popultion levels). If the level of prices or the stndrd of living is low in n importer country, the exporter rm my wnt to reduce its prices further in order to hve mret ccess to this country. In such cse, the lower the prices (which cn e proxied y the exchnge rte) or the lower the stndrd of living (which cn e proxied y the purchsing power prity), the lower re the source prices (i.e., the higher is ). Although economic region speci c dummies re used while testing the reltion in Eqution 4.18, they my not cpture ll the country speci c vrition in due to the pricing strtegies mentioned ove. Hence, consistent with wht is suggested relted to controlling for the locl distriution costs in the importer country (i.e., including income, income per cpit, purchsing power prity, nd imports into the regression nlysis ), dditionl vriles such s exports, income, popultion, exchnge rte, nd purchsing power prity cn e included in the estimtion of Eqution 4.18 for roustness. 5. Empiricl Results The results for the estimtion of re given in Tle According to Eqution 4.1, ctully, the rtio of the destintion prices re considered. However, fter controlling for the rtio of trde costs, the rtio of the destintion prices pproximtely reduce to the rtio of source prices. 13

15 Tle 2 - Estimtion of First Qurtile Medin Third Qurtile (OLS) 3:11 7:04 20:57 R-r sqd. (OLS) 0:36 0:46 0:57 (PPML) 10:71 27:34 41:12 R-r sqd. (PPML) 0:98 0:98 0:99 As is evident, while the medin OLS estimte of is 7.04, the medin PPML estimte of is The medin R-r sqd. vlue for OLS is 0:47 while the medin R-r sqd. vlue for PPML is 1: Although the medin OLS estimte of (i.e., 7.04) is close to the estimtes in the literture, the medin PPML estimte of (i.e., 27.34) is higher thn the ones in the literture. In prticulr, Hummel s (2001) estimtes rnge etween 4.79 nd 8.26; the estimtes of Hed nd Ries (2001) rnge etween 7.9 nd 11.4; the estimte of Bier nd Bergstrnd (2001) is out 6.4; Hrrign s (1996) estimtes rnge from 5 to 10; Feenstr s (1994) estimtes rnge from 3 to 8.4; the estimte y Eton nd Kortum (2002) is out 9.28; the estimtes y Romlis (2007) rnge etween 6.2 nd 10.9; the (men) estimtes of Brod nd Weinstein (2006) rnge etween 4 nd The min source of this di erence my e using di erent dt sets. In prticulr, while these studies in the literture mostly mesure the elsticity of sustitution for di erent goods, this pper mesures the elsticity of sustitution for di erent U.S. sttes. Nevertheless, this doesn t ect the min result of this pper. By using the estimted mesures, the reltion etween, trde costs, nd source prices is estimted. The OLS estimtion results otined y using the OLS estimtes of re given in Tle 3, nd the PPML estimtion results otined y using the PPML estimtes of re given in Tle 4. In ll regressions, only uncorrelted vriles re included to void ny multicollinerity prolem. For instnce, GDP, GDP per cpit, nd imports, or the exchnge rtes nd purchsing power prities cn lso e correlted with ech other. As is evident, ll the estimtes re highly signi cnt in ll of the estimtions which supports tht EDD,, is not constnt cross countries. In prticulr, EDD increses in trde costs nd decreses in the source prices. Hence, the empiricl results in fct chllenge the de nition of constnt elsticity of sustitution in the literture. It is more plusile tht EDS my e constnt cross countries. The highest explntory power (i.e., R-r sqd. of 0.74) in OLS regressions is chieved when (log) distnce, (log) imports, nd (log) purchsing power prity re included into the regression. In such cse, one percent increse in distnce leds to round 1.1 percent increse in the elsticity, one percent increse in imports leds to round 3.7 percent increse, nd one percent increse in purchsing power prity leds to round 0.2 percent increse. The highest explntory power (i.e., R-r sqd. of 0.96) in PPML regressions is chieved when (log) distnce, (log) GDP per cpit, nd (log) purchsing power prity re included into the regression. In such cse, one percent increse in distnce leds to round 1 percent increse in the elsticity, one percent increse in GDP per cpit leds to round 0.3 percent increse, nd one percent increse in purchsing power prity leds to round 0.1 percent increse. 19 Note tht the R-r sqd. vlues for OLS nd PPML don t correspond to the R-r sqd. vlues of the prticulr estimtes given in the tle. They re the rst qurtile, medin, nd the third qurtile of the R-r sqd. distriution. 14

16 Tle 3 - Trde Costs, Source Prices, nd y OLS Dependent Vrile: log Dist (0.01) (0.13) (0.12) (0.12) (0.11) (0.14) (0.13) Impo (0.01) (0.73) (0.69) GDP (0.01) (0.07) (0.07) GDPP (0.01) (0.06) (0.05) XR (0.05) (0.04) (0.04) (0.05) PPP (0.05) (0.03) (0.03) (0.02) Dum No No No No No No Yes Yes Yes Yes Yes Yes Yes R-r Notes: The estimtion is y OLS. Since we hve two-stge estimtion procedure, the ised OLS stndrd errors re corrected ccording to Dumont et l. (2005) nd they re given in prenthesis. The smple size for ll estimtions is 266 fter repeting the oservtions of the countries elonging to more thn one economic regions ecuse of the economic region speci c dummies. Dist stnds for log distnce, Impo for log imports, GDP for log GDP, GDPP for log GDP per cpit, XR for log exchnge rte, PPP for log purchsing power prity, Dum for economic region speci c dummies, nd R-r for R-r sqd. The results in Tle 3 nd Tle 4 re lso roust to the selection of di erent mesures used. For instnce, using log GDP, log GDP per cpit, or log imports, ll result in very similr explntory powers, lthough their mgnitudes re, of course, di erent in numericl terms. Similrly, using exchnge rte or purchsing power prity lso result in very similr explntory powers, this time with very similr numericl mgnitudes. Overll, s summry of oth tles, on verge, one percent increse in distnce leds to round 1 percent increse in the elsticity, one percent increse in income leds to round 0.2 percent increse, one percent increse in imports leds to round 4 percent increse, one percent increse in exchnge rte leds to round 0.1 percent increse, nd one percent increse in purchsing power prity leds to round 0.1 percent increse. These results re ll supported y high explntory powers. Finlly, in oth estimtion methods, the restriction of hving coe cient of one for log distnce mesures re tested, nd the null hypotheses of vlid restrictions re ccepted. In other words, the (log) distnce mesure my in fct enter the regression nlyses with coe cient of one. 15

17 Tle 4 - Trde Costs, Source Prices, nd y PPML Dependent Vrile: log Dist (0.01) (0.18) (0.19) (0.16) (0.16) (0.15) (0.16) Impo (0.01) (0.97) (0.91) GDP (0.01) (0.05) (0.05) GDPP (0.01) (0.06) (0.06) XR (0.05) (0.03) (0.02) (0.03) PPP (0.05) (0.03) (0.02) (0.03) Dum No No No No No No Yes Yes Yes Yes Yes Yes Yes R-r Notes: The estimtion is y PPML. The stndrd errors re in prenthesis. The smple size for ll estimtions is 266 fter repeting the oservtions of the countries elonging to more thn one economic regions ecuse of the economic region speci c dummies. Dist stnds for log distnce, Impo for log imports, GDP for log GDP, GDPP for log GDP per cpit, XR for log exchnge rte, PPP for log purchsing power prity, Dum for economic region speci c dummies, nd R-r for R-r sqd. Comprison with Hummels nd Lugovsyy (2009) The empiricl results re compred with the results of Hummels nd Lugovsyy (2009; HL henceforth) in terms of vrying Armington elsticities from one importer country to nother. HL theoreticlly show tht the Armington elsticity increses in popultion density nd decreses in GDP per cpit. Besides testing this reltion coming from their model in log-liner form, they lso test n implied reltion tht the elsticity is higher in lrge mrets (proxied y log GDP), nd lower in rich mrets (proxied y log GDP per cpit), conditionl on mret size. In sum, they hve two ey reltions in order to show how elsticities di er etween importer countries. In terms of this pper s nottion, HL hve the following reltions: f (log (GDP ) ; log (GDP P )) nd log f (log (P OP ) ; log (GDP P )) 16

18 where GDP P denotes GDP per cpit, nd P OP denotes popultion. Notice tht the rst regression is semi-log reltionship, nd the second one is log-liner. The possile issues relted to their log-liner estimtion pproch hve lredy een discussed in the introduction, they won t e repeted here. Insted, the explntory power of this pper will e compred with theirs y using the dt of this pper. If the regression nlysis of HL is replicted y using the dt of this pper, the results in Tle 5 re otined. While the rst two columns of Tle 5 show the results of HL for comprison, the other columns show the results of this pper. As is evident in the rst column, HL show tht elsticities increse with GDP nd decrese with GDP per cpit, where R 2 is Alterntively, ccording to the second column, HL show tht elsticities decrese with GDP per cpit nd increse with popultion, where R 2 is not depicted. Although HL estimtes re signi cnt nd hve their expected signs, the explntory power of their OLS estimtion is too low compred to the results of this pper in Tle 3. When their method is replicted y using the dt of this pper (i.e., y including oth GDP nd GDP per cpit into the regression), the results in column 3 re otined, where the signs of the estimtes re s expected from the theory of HL, ut they re not signi cnt when estimted y OLS; the R-r sqd. is lso low in column 3. Column 4 shows tht no estimtion cn e mde y PPML when oth GDP nd GDP per cpit re included into the regression, most proly due to multicollinerity prolem. When the lterntive regression of HL is replicted y using the dt of this pper (i.e., y including GDP per cpit nd popultion into the regression), the results in columns 5 nd 6 re otined. In column 5, where OLS is used, the results of this pper re consistent with HL in terms of hving signi cnt e ects nd the expected signs of the estimtes. However, the R-r sqd. vlue is still too low compred to the OLS results of this pper in Tle 3. When the PPML estimtion is employed in column 6, high R-r sqd. vlue is otined, ut this time the signs of the estimtes re not s expected from the theory of HL. And, compred to the explntory powers in Tle 4, this regression hs lower power. Tle 5 - Comprison with HL Dependent Vrile log( ) log( ) log( ) log( ) log( ) HL (OLS) HL (OLS) OLS PPML OLS PPML OLS PPML GDP ? (0.001) (1.202)? (0.112) (0.030) GDPP ? (0.003) (0.003) (0.817)? (0.056) (0.016) (0.090) (0.023) POP (0.001) (0.031) (0.009) R-r 0.17? 0.18? Notes: The stndrd errors re in prenthesis. Since we hve two-stge estimtion procedure, the ised OLS stndrd errors re corrected ccording to Dumont et l. (2005). The smple size for ll estimtions is 266 fter repeting the oservtions of the countries elonging to more thn one economic regions ecuse of the economic region speci c dummies. GDP stnds for log GDP, GDPP for log GDP per cpit, POP for log popultion, nd R-r for R-r sqd. 17