Understanding the International Elasticity Puzzle

Transcription

1 Understanding te International Elasticity uzzle Hakan Yilmazkuday y November 28, 208 Abstract International trade studies ave iger macro elasticity measures compared to international nance studies, wic as evoked mixed policy implications regarding te e ects of a cange in trade costs versus excange rates on welfare measures. Tis socalled international elasticity puzzle is investigated in tis paper by drawing attention to te alternative strategies tat te two literatures use for te aggregation of foreign products in consumer utility functions. Using te implications of aving a nite number of foreign countries in nested CES frameworks tat are consistent wit te two literatures, te discrepancy between te elasticity measures is explained by sowing teoretically and con rming empirically tat te macro elasticity in international trade is a weigted average of te macro elasticity in international nance and te corresponding elasticity of substitution across products of foreign source countries. JEL Classi cation: F2, F4, F4 Key Words: International Elasticity uzzle; International Trade and Finance. Te autor would like to tank ng Wang, Robert Feenstra, Andres Rodriguez-Clare, Costas Arkolakis, George Alessandria, Virgiliu Midrigan, seminar participants at Florida State University, and conference participants at Midwest Macroeconomics Meetings at University of ttsburg, Nort American Summer Meeting of te Econometric Society at Wasington University in St. Louis, Georgetown Center for Economic Researc Biennial Conference at Georgetown University, and Soutern Economic Association Annual Meetings at Tampa FL for elpful comments and suggestions. Te usual disclaimer applies. y Department of Economics, Steven J. Green Scool of International and ublic A airs, Florida International University, Miami, FL 3399, USA; yilmazk@ u.edu; pone:

2 Understanding te International Elasticity uzzle Abstract International trade studies ave iger macro elasticity measures compared to international nance studies, wic as evoked mixed policy implications regarding te e ects of a cange in trade costs versus excange rates on welfare measures. Tis socalled international elasticity puzzle is investigated in tis paper by drawing attention to te alternative strategies tat te two literatures use for te aggregation of foreign products in consumer utility functions. Using te implications of aving a nite number of foreign countries in nested CES frameworks tat are consistent wit te two literatures, te discrepancy between te elasticity measures is explained by sowing teoretically and con rming empirically tat te macro elasticity in international trade is a weigted average of te macro elasticity in international nance and te corresponding elasticity of substitution across products of foreign source countries. JEL Classi cation: F2, F4, F4 Key Words: International Elasticity uzzle; International Trade and Finance.

3 Introduction International trade studies ave iger macro elasticity measures compared to international nance studies. Since price movements due to policy canges are converted into welfare adjustments troug tese elasticities, tis observation evokes mixed policy implications regarding te e ects of trade costs in international trade versus te e ects of excange rates in international nance (e.g., see Rul (2008)). Due to tese mixed implications on welfare, tis observation is called te international elasticity puzzle. In order to ave a better idea about te magnitude of tis puzzle, consider a sort summary of studies given in Table. Altoug elasticity measures di er across tese studies, international nance studies mostly follow Backus, Keoe, and Kydland (994) wit a macro elasticity value of about.5, wile international trade studies mostly follow Anderson and Van Wincoop (2004) or recently Simonovska and Waug (204a) and Simonovska and Waug (204b) wit a macro elasticity value of about 5. It is implied tat if we directly employ tese numbers in a policy analysis, say, in order to investigate te e ects of a foreign price cange due to tari s or excange rates, international trade studies imply quantity canges tat are at least tree times te international nance studies. Tis paper attempts to understand te international elasticity puzzle by drawing attention to te alternative strategies te two literatures ave for te aggregation of foreign products in consumer utility functions. In particular, wile te majority of international nance models include a unique foreign country (in teir two-country frameworks) in order to ave an understanding of te macroeconomic developments in te ome country, te majority of international trade models include multiple foreign countries in order to investigate te bilateral trade patterns of te ome country. Since aving alternative numbers of foreign countries is re ected as alternative macro elasticity measures between te two literatures in a nested constant elasticity of substitution (CES) framework, as sown in tis paper, te international elasticity puzzle can be understood by paying attention to te alternative ways tat foreign products are aggregated in te two literatures. Since te trade elasticity used in new trade models, suc as Eaton and Kortum (2002), corresponds to te elasticity of substitution across countries (including ome country) minus one in international trade as sown in studies suc as by Anderson and Van Wincoop (2004), te commonly used trade elasticity of about 4 suggested by Simonovska and Waug (204a) and used by new trade models corresponds to te elasticity of substitution across countries of about 5. 2

4 Regarding te details, wen a nite number of goods and foreign countries is considered in nested CES frameworks tat are consistent wit bot literatures, tis paper nds alternative expressions for te price elasticity of demand as a function of te macro elasticity measures in te two literatures. In order to investigate te conditions under wic te two literatures ave te very same policy implications (e.g., regarding canges in trade costs versus excange rates), tis paper equalizes te price elasticity measures between te two literatures. Tis strategy results in an expression tat connects te alternative macro elasticity measures in te two literatures, were good-level details are cancelled out during te equalization of te price elasticity measures. In particular, it is teoretically sown tat te macro elasticity in international trade is a weigted average of te macro elasticity in international nance and te elasticity of substitution across products of di erent foreign source countries, were te weigt is sown to depend on te number of foreign countries and ome expenditure sares. Terefore, te alternative strategies in te two literatures for te aggregation of foreign products are re ected as alternative macro elasticity measures between te two literatures. Te implications of equalizing te price elasticity of demand measures between te two literatures are also tested empirically. Since tis investigation requires data on bot domestic and foreign trade, it cannot be acieved by using any international trade data set, were domestic trade are not recorded. As an alternative, tis paper uses te available trade data witin te U.S. by considering interstate trade as foreign trade and intrastate trade as domestic trade. Te results based on te estimation of macro elasticity measures in bot literatures con rm te teoretical solution provided in tis paper tat te macro elasticity in international trade is a weigted average of te macro elasticity in international nance and te elasticity of substitution across products of di erent foreign sources. Terefore, te discrepancy between te macro elasticity measures in te two literatures can in fact be understood by paying attention to te alternative ways tat foreign products are aggregated in te two literatures. Compared to te literature, te nested CES framework in tis paper works in a similar way to te one introduced by Atkeson and Burstein (2008) wo ave sown tat considering nite number of goods (and tus good-speci c market sares implying variable markups) is essential to explain wy export and import prices sow substantial and systematic deviations from relative purcasing power parity () in comparison wit source country producer prices. In comparison, aving a nite number of source countries in tis paper results in aving source- 3

5 country-speci c expenditure sares entering into price elasticity measures. Tis is in contrast to studies suc as by Gali and Monacelli (2005) considering in nite number (a continuum) of source countries, were source-country-speci c expenditure sares are ine ective in te calculation of price elasticity measures. Since good-level details (and tus te corresponding expenditure sares) are sown to cancelled out during te equalization of te price elasticity measures between te two literatures, aving a nite number of source countries (rater tan aving a nite number of goods) is te key to understand te international elasticity puzzle. Suc a teoretical implication (of aving sizable source-country-speci c expenditure sares) is igly supported by te data as well; e.g., witin te U.S., te expenditure sare of Kentucky on te products imported from Oio is about 48% for te second quarter of 202, wile te expenditure sare of Delaware on te products imported from New York is about 43% for te rst quarter of 202 (according to te data used in te empirical investigation, below). Tis paper deviates from te existing literature due to two main reasons. First, wile existing studies in te literature ave attempted to understand te puzzle by using te very same functional forms to aggregate across foreign products, tis paper draws attention to te di erence between te strategies in te aggregation of foreign products between te two literatures. In particular, wile providing several supply-side explanations to te puzzle, studies suc as by Rul (2008), Fitzgerald and Haller (204), Ramanarayanan (207), Crucini and Davis (206) or Feenstra, Luck, Obstfeld, and Russ (208) all consider te very same functional forms between te two literatures in order to aggregate across foreign products. However, a common aggregation strategy is not consistent wit eiter international trade or international nance studies, were te former aggregates across source countries in te upper-tier (e.g., see Anderson and Van Wincoop (2003), Anderson and Van Wincoop (2004), Head and Ries (200), Hillberry and Hummels (203), or Hummels (200), among many oters), and te latter aggregates across ome and foreign countries in te upper-tier (e.g., see Backus, Keoe, and Kydland (994), Blonigen and Wilson (999), Corsetti, Dedola, and Leduc (2008), Enders, Müller, and Scoll (20), or Heatcote and erri (2002), among many oters). Terefore, recognizing te di erence between te functional forms to aggregate foreign products (as in tis paper) is te key to understand te puzzle in te rst place. Second, compared to te existing literature, te overall investigation in tis paper abstracts from te complications due to aving a time dimension so tat we can focus on te 4

6 di erences between te two literatures due to te way tat tey aggregate across foreign products. In contrast, studies suc as by Rul (2008), Fitzgerald and Haller (204) Ramanarayanan (207) or Crucini and Davis (206) all focus on solutions based on te di erence between te two literatures due to te frictions created by te time dimension, suc as uncertainties on productivities, te speed of adjustment of capital, or rm entry/exit decisions over time. However, since tese studies do not recognize tat te two literatures ave distinct functional forms to aggregate across foreign products, teir time-related frictions will only complicate te investigation, leading to improper comparisons between te two literatures. Te rest of te paper is organized as follows. Te next section introduces demand-side models tat are consistent wit te two literatures. Section 3 attempts to understand te international elasticity puzzle by considering te importance of expenditure sares in CES frameworks wit nite number of goods and countries. Section 4 provides empirical support for te teory introduced in tis paper. Section 5 concludes. Te Appendix sows te derivations of certain equations used in te main text. 2 Te Economic Environment Tis section introduces a model of international economics consisting of ome and foreign countries. It is important to empasize tat te model and its implications are independent of te supply side, since suc details are e ectively eliminated during te comparison of international trade and international nance literatures (using teir implications for te price elasticity of demand at te product level, as sown in te Appendix). Terefore, we only focus on te demand side until te empirical investigation below, were at least some structure is necessary on te supply side for estimation purposes. In terms of te notation, te superscripts represent te location of consumption, wile te subscripts represent te location of production and goods. 2. Individuals In most international nance studies, tere are two tiers of aggregation representing te consumer utility: an upper-tier aggregation between ome and foreign goods, and a lower-tier aggregation between foreign goods. In most international trade studies, tere are also two tiers of aggregation: an upper-tier aggregation between countries of origins (including te 5

7 ome country), and a lower-tier aggregation between goods of eac origin country. At te upper-tier aggregation (i.e., at te macro level), tere is usually a unique foreign country (or an index of overall foreign/imported products) in international nance studies tat is connected to te trade balance of te destination country, wile tere are multiple foreign countries/regions in international trade studies tat are connected to bilateral trade of te destination country wit eac source country. Accordingly, altoug tese literatures connect foreign products to ome products by using an upper-tier aggregation, te number of foreign countries is di erent at te upper-tier aggregation, and, tus, tere are alternative aggregation strategies of foreign products across te two literatures. Terefore, wile products coming from alternative foreign countries are already connected to eac oter troug te upper-tier aggregation in international trade, suc alternative foreign countries are not distinguised between eac oter in international nance. In order to connect tese two literatures, we consider an additional middle-tier aggregation across foreign countries wile modeling individual utilities in international nance. Te lower-tier aggregation is acieved across alternative goods coming from a particular country, wic is te same between te two literatures, because te products coming from any country does not depend on ow tey are aggregated at te destination country. In sum, in tis paper, international trade individuals ave two tiers of aggregation, representing source countries and goods, wile international nance individuals ave tree tiers of aggregation, representing ome versus foreign countries, foreign countries, and goods. It is assumed tat tere are nite number of goods and countries in bot literatures. Furter details of eac literature are provided in te following subsections, wile te de nition of variables and parameters are given in Tables 2 and Individuals in International Trade International trade studies suc as by Anderson and Van Wincoop (2004), Head and Ries (200), Hillberry and Hummels (203), or Hummels (200), among many oters, ave te following upper-tier CES aggregation, also called te Armington model as in Arkolakis, Costinot, and Rodríguez-Clare (202), representing utility C in ome country : C X i i C i () 6

8 were C i represents products coming from country i (wic represents ome products wen i = ), is te elasticity of substitution across source countries (including bot ome and foreign countries) wic we call as te macro elasticity in international trade, and i a taste parameter (satisfying i i = ). C i is furter given by te following lower-tier aggregation: C i X j C is (2) were C represents good j coming from country i (wic represents good j produced in ome country wen i = ), is te elasticity of substitution across goods, and s represent taste parameters (satisfying j = ). Te optimal allocation of any given expenditure yields te following demand functions, were j, per units of C, C i and C, respectively: and are te corresponding prices C = j C i (3) and C i = i i C (4) wic can be utilized for te estimation of te macro elasticity in its log form using data on bot international trade and intranational/domestic trade, since te latter is captured wen i = (as we acieve in te empirical investigation, below). Te last two expressions can be combined as follows: C = i j i C (5) Finally, price indices are connected to eac oter troug te standard expressions of: X i i and i X j j 7

9 2..2 Individuals in International Finance International nance studies suc as by Backus, Keoe, and Kydland (994), Blonigen and Wilson (999), Corsetti, Dedola, and Leduc (2008), Enders, Müller, and Scoll (20), or Heatcote and erri (2002), among many oters, ave te following upper-tier CES aggregation representing utility G in ome country : G C + G f (6) were C (as in Equation 2 wen i = ) and G f represent ome and foreign products, respectively, is te elasticity of substitution across ome and foreign products wic we call as te macro elasticity in international nance, and is a taste parameter representing te preferences of individuals toward ome products (tat is related to ome bias). Most international nance studies stop teir disaggregation at tis level wic tey use for teir investigations. Neverteless, it is understood tat tere is an additional tier of aggregation among foreign source countries for ome country (represented by i 6= ) in te background, wic we acieve by putting more structure on te index of foreign products G f as follows and call it te middle-tier aggregation: G f X i6= i C i (7) were C i represents products imported from foreign country i as in te international trade literature above (as de ned in Equation 2), because te products coming from foreign country i do not depend on ow tey are furter aggregated at te destination country; is te elasticity of substitution across foreign countries, and i s (satisfying i6= i = ) represent source-speci c taste parameters. Te lower-tier aggregation is assumed to be te same as in te international trade literature. Hence, te optimal allocation of any given expenditure yields te demand function in Equation 3 for tis lower-tier aggregation, wit te de nitions of, j, and being te same as in te international trade literature. Regarding te middle tier, te optimal allocation of any given expenditure yields te following demand function, were Q f is te 8

10 price per unit of G f : C i = i G Q f (8) f wic can be utilized for te estimation of in its log form using data only on international trade (as we acieve in te empirical investigation, below). Regarding te upper tier, te optimal allocation of any given expenditure yields te following demand function, were Q is te price per unit of G : G f = Q f Q G (9) wic can be combined wit Equations 3 and 8 to ave te following demand function for good j coming from foreign country i: C = i j Q f Q f Q G (0) rice indices are connected to eac oter troug te standard expressions of: Q f X i6= i () and Q + Q f (2) Finally, te demand for good j produced at ome is given by: C j = j j C (3) were C = G (4) Q As is evident, as te (macro) elasticity of substitution across ome and foreign products governs te substitutability between ome and foreign products, it also sows up in te demand function for ome products troug teir relative price wit respect to te overall price index Q (tat includes foreign prices according to Equation 2). We will use tis information during our empirical investigation, below. Te latter two expressions can be 9

11 combined as follows: C j = j j G (5) Q were te price indices of ome products s are also te same across te two literatures, since tey are independent of ow foreign products are aggregated. 2.2 rice Elasticity of Demand In any CES aggregation, te elasticity of substitution corresponds to te price elasticity of demand if te expenditure sare of components in tat aggregation is negligible (i.e., wen tere in nite number of components). However, tis cannot be te case wen tere are nite number of components (as in tis paper), especially wen ome and foreign products are aggregated, were te expenditure sare of foreign products may not be negligible in a global world wit ig levels of trade openness. Accordingly, wile calculating te price elasticity of demand in ome country, on top of te elasticity of substitution, we also consider te e ects of disaggregated prices on aggregated price indices (due to aving a nite number of goods and countries). Te tecnical details of derivations are given in te Appendix. In international trade, te price elasticity of demand for good j coming from country i (representing ome products wen i = ) is implied as C = " ; ; ; i = + i (6) were we ave considered te e ects of j on aggregated price indices of and as well; = C i C i is te expenditure sare of good j imported from country i among all products imported from country i, and i te overall consumption. = i C i C is te expenditure sare of country i products in As is evident, te price elasticity of demand in Equation 6 is a function of te macro elasticity in international trade, te elasticity of substitution across goods, and expenditure weigts. Compared to te existing literature, tis expression is very similar to te one considered by Atkeson and Burstein (2008) in an alternative nested CES framework wen price competition is considered across rms (i.e., Equation 9 in teir paper), were an upper-tier aggregation is acieved in a continuum of sectors (wic implies i = 0 for te upper-tier in tis paper), and a lower-tier aggregation is acieved across a nite number 0

12 of goods. Atkeson and Burstein (2008) ave sown tat considering nite number of goods (and tus good-speci c market sares implying variable markups) is essential to explain wy export and import prices sow substantial and systematic deviations from relative in comparison wit source country producer prices. Di erent from Atkeson and Burstein (2008), te upper-tier aggregation in tis paper is acieved across a nite number of foreign countries, and tus we ave i > 0. Suc an implication (of i > 0) is igly supported by te data used in tis paper as well (see below for data details); e.g., witin te U.S., te expenditure sare of Kentucky on te products imported from Oio is about 48% for te second quarter of 202, wile te expenditure sare of Delaware on te products imported from New York is about 43% for te rst quarter of 202. Similarly, in international nance, te price elasticity of demand for good j coming from foreign country i is implied as C = " ; ; ; ; i ; f = + i + i f (7) were we ave considered te e ects of on aggregated price indices of i, Q f and Q as well; i = i C i Q f G f (were i 6= ) is te expenditure sare of country i products among all foreign products, and f = Q f G f = Q G is te expenditure sare of foreign products (i.e., imports) in te overall consumption, wit = representing te ome expenditure sare. As is evident, te price elasticity of demand is a function of te macro elasticity in international nance, te elasticity of substitution across foreign countries, te elasticity of substitution across goods, and expenditure weigts. As in te case of Equation 6, te implications provided in Equation 7 (of aving sizable expenditure weigts) are also consistent wit te data used in tis paper, were te state of Wasington as a i value of about 97% for te products coming from Oregon in te rst quarter of 202. It is important to empasize tat bot Equations 6 and 7 ave te same de nition (i.e., te price elasticity of demand for good j coming from foreign country i). Since tis micro detail cannot be canged by te arti cially created aggregation strategies in te two literatures, in te next Section, we equalize Equations 6 and 7 in order to ave implications for te discrepancy between te two macro elasticity measures of and.

13 3 Implications for te International Elasticity uzzle We are interested in understanding te international elasticity puzzle regarding mixed policy implications. We consider te fact tat te reactions of micro quantities (e.g., actual amount of goods traded in real life) to any canges a ecting micro prices (e.g., good-level productivities, excange rates, or tari rates) cannot be a ected by ow tey are aggregated at upper tiers of consumer utility, and tus tey sould be equalized across te two literatures. In oter words, we would like to know te conditions under wic te two literatures would provide te same policy implications. Accordingly, we equalize te price elasticity of demand measures for individual goods (coming from individual foreign countries) between international trade and international nance in tis section. Te tecnical details of derivations are given in te Appendix. Since te left and sides of Equations 6 and 7 ave te same de nition (i.e., te price elasticity of demand for good j coming from foreign country i), equalizing tem to eac oter results in te following expression: were = (N i ) (N i )+ = + ( ) (8) wit N i representing te number of foreign countries. As is evident, te macro elasticity in international trade is a weigted average of te macro elasticity in international nance and te elasticity of substitution across foreign countries (in international nance), were weigts are determined by te number of foreign countries N i and te ome expenditure sares of s. It is easy to sow tat in a special case in wic tere is a unique foreign country under investigation (i.e., N i = ) as in most studies in international nance, it is implied tat = 0 and tus te two literatures converge to eac oter regarding teir macro elasticity measures as =. However, as te number of foreign countries investigated increases as in most international trade studies, gets iger and tus te two literatures diverge from eac oter as goes away from. Terefore, Equation 8 represents te general relationsip between te macro elasticity measures of te two literatures based on te number of countries used in te investigation. It is important to empasize tat te elasticity of substitution across goods, togeter wit te corresponding expenditure weigts, as been e ectively eliminated in Equation 8 (as sown in te Appendix) due to aving te very same lower-tier aggregation (across goods 2

14 of a foreign source country) in te two literatures. Terefore, te comparison between te macro elasticities of (coming from international trade) and (coming from international nance) does not depend on te value or te determination of tat governs te comparison across individual good caracteristics tat depend on ow tey are produced (and/or priced) in foreign source countries and/or ow tey are transported. It is implied tat aving a nite number of foreign countries (rater tan a nite number of goods) is essential for a comparison of macro elasticities between te two literatures. It is also implied tat independent of te supply side (e.g., aving intermediate inputs or xed production costs), or te aggregation of te varieties of eac good (e.g., aving a good-level or rm-level analysis), te results in tis paper remain te same, since suc micro-level details would e ectively be eliminated during te comparison of te two literatures. 2 In contrast, in te existing literature, Rul (2008) as proposed a solution to te international elasticity puzzle based on rm-level entry costs and uncertainties on future productivities in a Melitz (2003) framework; Fitzgerald and Haller (204) ave bot xed and sunk costs of export participation, were participation in di erent export markets are considered as independent decisions after conditioning on a common marginal cost of production; Crucini and Davis (206) consider te speed of adjustment of capital in te distribution sector; Ramanarayanan (207) considers intermediate inputs in wic eterogeneous producers face a plant-level irreversibility in te structure of inputs used in production; Arkolakis, Eaton, and Kortum (202) consider te di erence between te adjustments in extensive and intensive margins of trade in an Eaton and Kortum (2002) framework. Note tat all of tese details are e ectively eliminated in Equation 8 (as sown in te Appendix), because tey are related to te good-level production stories tat ave noting to do wit ow products of foreign source countries are aggregated troug te macro elasticities of versus. Overall, according to Equation 8, te policy implications are equalized between te two literatures by construction, altoug te arti cially created upper-level elasticities, and are allowed to adjust to be consistent wit tis micro equality. Te next section tests tis implication empirically. 2 As an example, one can easily (i) include an additional tier of CES aggregation across rms tat disaggregates eac foreign good imported from a source country, (ii) play wit te supply side by including intermediate inputs, productivity di erences, xed costs, or (iii) include dynamic cannels in te determination of good-level caracteristics. However, wen te micro-level price elasticities of demand are equalized between te two literatures, suc micro-level details would be e ectively eliminated as sown in te Appendix for te derivation of Equation 8. 3

15 4 Empirical Investigation We ave so far proposed a teoretical background to understand te international elasticity puzzle by sowing tat te macro elasticity in international trade is a weigted average of te macro elasticity in international nance and te elasticity of substitution across foreign countries in international nance (according to Equation 8). Hence, te con icting estimates in te two literatures (as given in Table ) can be understood by carefully considering te alternative de nitions of foreign basket of goods. In tis section, we will test tis implication empirically, wic requires te estimation of, and. Since te objective is to make a comparison between te two literatures, some clari - cation is necessary regarding ow te literature as estimated tese elasticity measures. In particular, some international trade studies suc as by Yotov (202), Simonovska and Waug (204a) or Simonovska and Waug (204b) combine international trade wit ad oc measures of domestic trade obtained from te problematic national income and product accounts in teir elasticity estimations, and tus teir estimates correspond to in tis paper. Obviously, tese papers are di erent from tose oter international trade studies suc as by Hummels (200) or Head and Ries (200) wo use data on international trade only, and tus suc estimates correspond to in tis paper. Terefore, te international trade literature estimates te values of and intercangeably, meaning tat bot estimates of (obtained by te log version of Equation 4) and (obtained by te log version of Equation 8) can be compared wit te existing literature depending on te data used in te estimation. Similarly, te macro elasticity in international nance can eiter be estimated by using te log version of 9 or te log version of Equation 4; due to data availability, we consider te latter option in our empirical investigation below. 4. Data and Estimation Metodology We use Equations 4, 8 and 4 for te estimation of, and, respectively, wic require data on bot domestic and foreign trade. Since international trade data sources do not collect data on domestic trade, rater tan employing te problematic domestic trade values implied by national income and product accounts, we sift our focus to interstate trade data witin te U.S. obtained from te Commodity Flow Survey (CFS) for te year of 202, wic provide quarterly export data on bot interstate (foreign) trade and intrastate (domestic) 4

16 trade. 3 Since we use "202 CFS ublic Use Microdata File" obtained from te web page of te U.S. Census Bureau, following Hillberry and Hummels (2003), we are able to eliminate te problematic observations of wolesale and retail sipments and focus only on mining and manufacturing sipments across states. 4 As in studies suc as by Anderson and Van Wincoop (2003) and Anderson and Van Wincoop (2004), we identify, and troug te coe cients in front of log distance, subject to te determination of te distance elasticity of trade costs. Accordingly, we only consider transportation troug private trucks across states so tat aving alternative transportation modes tat are used less (e.g., water, rail or air) does not a ect te estimated coe cients. Our CFS data set also provides information on te actual distance of sipment between (or witin) states tat canges (due to alternative sipment routes tat consider te exact source and destination locations witin eac state) across quarters of Te estimation requires information on prices wic can be acieved by te details of te supply side. In order to keep te supply side as simple as possible, we only assume te following relationsip between source and destination prices for good j: t = it t (9) were te subscript t represents quarterly nature of te trade data, it > represents (gross) iceberg trade costs, and t represents source prices given by: t = w i z exp (t) (20) were w i represents a source-speci c cost of production tat is steady over te quarters of 202 (e.g., sticky wages), z represents te level of productivity, and exp (t) captures canges in productivity over time tat are common across goods and states. Since trade data are from witin te U.S., we furter approximate time-varying trade costs wit it = d it, were d it represents quarter-speci c distance between states i and (because it represents te actual 3 Tis is well-known data source tat as also been used in earlier studies suc as by Wolf (2000), Hillberry and Hummels (2003) and.yilmazkuday (202) for alternative years. 4 Te nal trade data used in te estimation include observations on Nort American Industry Classi cation System (NAICS) industry codes of 22, 3, 32, 33, 34, 35, 36, 32, 322, 323, 324, 325, 326, 327, 33, 332, 333, 334, 335, 336, 337, See Yilmazkuday (204) for te importance of considering te exact location of sipments in te estimation of distance coe cients. 5

17 sipment distance tat may cange eac quarter), and is te distance elasticity of trade costs. For te estimation of, we use te log version of Equation 4 wit te addition of te time dimension (due to using quarterly data) as follows: log tc it = ( ) log it + log t C t + log it (2) were t j t jt dit it = d it wi exp (t) & it, t j t (z ) can be rewritten according to Equation 9 as it represents it measured at te source, and & it =. Wen quarterly exports data are used (i.e., wen trade is measured it, it is implied tat: at te source as in tis paper), according to it d it log t Cit {z } Quarterly Trade Data = log d it + ( ) log w {z } {z } i Quarterly Distance Source Fixed E ects + log C {z } Destination Fixed E ects (22) + t {z} + ( ) log & it it {z } Quarter Fixed E ects Residuals were te only time-varying variables are te quarterly exports data on te left and side togeter wit time-varying distance measures (due to alternative actual distance measures of sipment across quarters) and preferences (captured by residuals) on te rigt and side. Since we ave bilateral panel data, te identi cation of is acieved troug bot time and dyadic cross-sectional dimensions of te data as in te international trade literature. It is important to note tat te trade data in tis estimation include bot interstate and intrastate trade according to Equation. Similarly, for te estimation of wit quarterly exports data (measured at te source), we use te log version of Equation 8 combined wit Equations 9 and 20 as follows: log t Cit = log d it + ( ) log w {z } {z } i + log Q f G {z } {z f } Quarterly Interstate Trade Data Quarterly Distance Source Fixed E ects Destination Fixed E ects (23) + t {z} + ( ) log & it it {z } Quarter Fixed E ects Residuals 6

18 were te only di erence wit respect to Equation 22 is tat te trade data only include interstate trade (and exclude intrastate trade) according to Equation 7. Since we ave bilateral panel data, te identi cation of is again acieved troug bot time and dyadic cross-sectional dimensions of te data as in te international trade literature. Finally, for te estimation of wit quarterly exports data (measured at te source), we use te log version of Equation 4 combined wit Equations 9 and 20 as follows: log tc t = log d t {z } {z } Quarterly Intrastate Trade Data Quarterly Distance + log (w ) Q G {z } State Fixed E ects (24) + t {z} + ( ) log & t t {z } Quarter Fixed E ects Residuals were only intrastate trade data are used. Since te panel data are at te state level for tis estimation, te identi cation of dimensions of te data as in te international nance literature. is acieved troug te time and cross-sectional Overall, te estimations of, and are simply acieved by canging te way tat te observations are pooled across states, wile te rigt and side variables are tecnically te same. In particular, can be estimated wen data on bot interstate and intrastate trade are pooled, can be estimated wen data on only interstate trade are used, and can be estimated wen data on only intrastate trade are used. After te estimations are acieved, elasticity measures of, and can furter be identi ed for any given measure tat can be borrowed from te literature, as also acieved by studies suc as by Anderson and Van Wincoop (2003) or Anderson and Van Wincoop (2004). It is important to empasize tat te comparison between te relative values of, and (and tus te comparison of te two literatures regarding teir macro implications) do not depend on te value of, since it is teir multiplication wit te same (i.e.,, and ) tat is estimated as te coe cient in front of log distance in Equations 22, 23 and Empirical Results Te estimation results are given in Table 4, were all estimates of, and are statistically signi cant and ave teir expected signs. As is evident, for any given value of, 7

19 te estimated macro elasticity measures in international trade (represented by or ) are iger tan tose in international nance (represented by ). Terefore, te existence of te international elasticity puzzle is con rmed by te empirical results of tis paper, independent of. Regarding te main objective of our empirical investigation, te estimation results in Table 4 also con rm Equation 8 in te sense tat is a weigted average and, were represents te weigt based on te number of foreign countries and te ome expenditure sare. In particular, according to Equation 8, tis weigt can be rewritten as follows: = = (25) were te second equality as been obtained by multiplying bot te numerator and te denominator by, in order to sow tat our results are independent of te value of. According to te estimates of, and in Table 4, an estimate of = 0:88 is implied wit a 95% con dence interval (calculated by te Delta metod) between 0:763 and 0:996. Wen we directly use te teory-implied de nition of in Equation 8, we obtain a value of 0:937 by using ome expenditure sares s and te number of foreign countries N i (tat correspond to te number of interstate trade partners in our empirical investigation) for eac state. 6 Terefore, te teory-implied measure of = 0:937 lies witin te 95% con dence interval of te estimated measure of (obtained by te estimated values of, and in Table 4). It is implied tat independent of te value of, is in fact a weigted average and, and te weigts are determined by te number of foreign countries and ome expenditure sares as indicated by Equation 8. Terefore, te equalization of price elasticity measures is enoug to understand te discrepancy between te macro elasticity measures in te two literatures, bot teoretically and empirically. In order to sow te contribution of tis paper in a clear way, consider te opposite case in wic te implications of a nite number of foreign countries are not considered (and tus expenditure weigts are negligible in te calculation of price elasticity measures). In suc a case, we would ave = 0 for all, wic would imply tat = and tus = according to Equation 8, suggesting tat tere is no connection between te two literatures regarding teir macro elasticity measures of and. Apparently, suc a restrictive assumption is 6 In tis calculation, we use te measures of (N i ) = 938 and = 30:345 tat are obtained from te very same data used in te estimation. 8

20 inconsistent wit not only solving te international elasticity puzzle teoretically but also te estimated value of = 0:88 (wit a 95% con dence interval between 0:763 and 0:996) empirically. Terefore, in tecnical terms, it is essential to consider a nite number of countries (and tus positive expenditure weigts entering price elasticity calculations) to understand te international elasticity puzzle. To furter ceck te consistency of tese empirical results wit tose in te literature, we would also like to work on te actual estimates of, and. Accordingly, we need a measure of in our investigation. We borrow te value of = 0:45 from Yilmazkuday (202), wit a wide range between 0:8 and 0:84 (for robustness purposes) tat also covers te estimate of = 0:38 by Limao and Venables (200) obtained by using actual sipping company quotes as well as using international trade costs data. 7 Based on = 0:45, te implied elasticity estimates of, and are also given in Table 4. 8 Wile te elasticity estimate of = 4:875 (wit a 95% con dence interval between 2:508 and 2:672) is igly consistent wit te international trade literature (as detailed in Table ), te elasticity estimate of = 0:65 (wit a 95% con dence interval between 0:020 and 2:984) is igly consistent wit te international nance literature (also as detailed in Table ). Terefore, our empirical investigation not only elps us understand te international elasticity puzzle but also results in elasticity estimates tat are igly consistent wit te existing literature on bot international trade and international nance. 5 Conclusion International trade studies ave iger macro elasticity measures compared to international nance studies. Tis observation as been puzzling for many researcers due to te fact tat price canges (tat are caused by canges in international nance measures suc as excange rates or by canges in international trade measures suc as trade costs) are transferred into quantity and tus welfare canges troug tese elasticities, and aving alternative elasticity measures corresponds to alternative policy implications (as in Rul (2008)). 7 Yilmazkuday (202) nds te value of = 0:45 (wit a range between 0:8 and 0:84 across industries) as te average estimate across NAICS industries obtained by using interstate trade data (coming from Commodity Flow Survey) witin te U.S. for te year of An alternative estimate of = 0:38 as been found by Limao and Venables (200) using actual sipping company quotes, but tis value would not cange any of our empirical results, below, since it is witin te range of 2 [0:8; 0:84] tat we consider in our calculations. 9

21 Tis paper as been an attempt to understand te discrepancy between te macro elasticity measures in te two literatures by carefully taking into account teir alternative strategies used in te aggregation of foreign products. Accordingly, te conditions under wic te two literatures imply te very same policy implications ave been investigated. In nested CES frameworks wit a nite number of foreign countries (tat are consistent wit te existing studies), tis as been acieved by equalizing te price elasticity of demand measures between te two literatures. Suc an approac as resulted in an expression tat explains te discrepancy in te macro elasticity measures. In particular, it as been teoretically sown tat te macro elasticity in international trade is a weigted average of te macro elasticity in international nance and te elasticity of substitution across products of di erent foreign source countries. An empirical investigation as furter supported tis teoretical result in a clear way. Regarding policy implications (e.g., e ects of an excange-rate cange in international nance versus a trade-cost cange in international trade, bot troug destination prices), tey are equalized in tis paper between te two literatures by construction due to equalizing te price elasticity of demand measures, altoug te arti cially created upper-level elasticities are allowed to adjust to be consistent wit tis equality. It is implied tat any policy analysis sould be acieved at te disaggregated (bilateral-country) level and ten aggregated up to obtain macro implications for te destination country; oterwise, te upper-tier macro elasticity measures can be misleading (and tus result in te international elasticity puzzle) due to te way tat foreign products are aggregated at te destination country. Finally, since te supply-side details are cancelled out during te comparison of te price elasticity of demand measures between te two literatures, te teoretical results in tis paper are independent of te supply-side (e.g., aving intermediate inputs or xed production costs) or te aggregation of te varieties of eac good (e.g., aving a good-level or rm-level analysis). References Anderson, J. E., and E. Van Wincoop (2003): Gravity wit gravitas: a solution to te border puzzle, Te American Economic Review, 93(), (2004): Trade costs, Journal of Economic literature, 42(3),

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23 Enders, Z., G. J. Müller, and A. Scoll (20): How do scal and tecnology socks a ect real excange rates?: New evidence for te United States, Journal of International Economics, 83(), Feenstra, R. C.,. Luck, M. Obstfeld, and K. N. Russ (208): In searc of te Armington elasticity, Review of Economics and Statistics, 00(), Fitzgerald, D., and S. Haller (204): Exporters and socks: Dissecting te international elasticity puzzle, Discussion paper, National Bureau of Economic Researc. Gali, J., and T. Monacelli (2005): Monetary policy and excange rate volatility in a small open economy, Te Review of Economic Studies, 72(3), Head, K., and J. Ries (200): Increasing returns versus national product di erentiation as an explanation for te pattern of US-Canada trade, American Economic Review, pp Heatcote, J., and F. erri (2002): Financial autarky and international business cycles, Journal of Monetary Economics, 49(3), Hillberry, R., and D. Hummels (2003): Intranational ome bias: Some explanations, Review of Economics and Statistics, 85(4), (203): Trade elasticity parameters for a computable general equilibrium model, Handbook of Computable General Equilibrium Modeling,, Hummels, D. (200): Toward a Geograpy of Trade Costs, mimeo. Limao, N., and A. J. Venables (200): Infrastructure, geograpical disadvantage, transport costs, and trade, Te World Bank Economic Review, 5(3), Melitz, M. J. (2003): Te impact of trade on intra-industry reallocations and aggregate industry productivity, Econometrica, 7(6), Ramanarayanan, A. (207): Imported inputs, irreversibility, and international trade dynamics, Journal of International Economics, 04, 8. Rul, K. J. (2008): Te international elasticity puzzle, unpublised paper, NYU. 22

24 Simonovska, I., and M. E. Waug (204a): Te elasticity of trade: Estimates and evidence, Journal of International Economics, 92(), (204b): Trade models, trade elasticities, and te gains from trade, Discussion paper, National Bureau of Economic Researc. Stockman, A. C., and L. L. Tesar (995): Tastes and Tecnology in a Two-Country Model of te Business Cycle: Explaining International Comovements, Te American Economic Review, pp Wolf, H. C. (2000): Intranational ome bias in trade, Review of economics and statistics, 82(4), Yilmazkuday, H. (202): Understanding interstate trade patterns, Journal of International Economics, 86(), (204): Mismeasurement of distance e ects: Te role of internal location of production, Review of International Economics, 22(5), Yotov, Y. V. (202): A simple solution to te distance puzzle in international trade, Economics Letters, 7(3), Appendix 6. Derivation of te rice Elasticity of Demand Measures Tis Appendix depicts te derivations of Equations 6 and 7 in te main text. 6.. rice Elasticity of Demand in International Trade Te demand for C representing good j coming from country i in international trade is given by Equation 5 as follows: C = i j i C (26) 23