Constant versus Variable Markups: Implications for the Law of One Price

Transcription

1 Constant versus Variable Markups: Implications for the Law of One Price Hakan Yilmazkuday y April 12, 2016 Abstract This paper compares the implications of havin constant versus variable markups on the Law of One Price (LOP) by decomposin the ood-cateory level prices into marinal costs of production, markups, and trade costs. Usin a trade model, it is shown that the case of constant markups correspon to lo-linear trade reressions, while the case of variable markups correspon to lin-lo trade reressions. Empirical results show that marinal costs of production contribute most to the deviations from LOP for both cases of constant and variable markups; the decomposition of marinal costs further shows that destination-speci c quality measures play the biest role. JEL Classi cation F12, F13, F14 Key Wor: The Law of One Price; Constant Markups; Variable Markups; Trade Costs. The author would like to thank Hamid Beladi, two anonymous referees, Costas Arkolakis, Scott Baier, Eric Bond, Ariel Burstein, Jonathan Eaton, Rob Feenstra, Yoto Yotov, participants of International Trade Workshop at Florida International University, University of Illinois at Urbana-Champain, Midwest International Economics Meetins at Michian State University, SAET Conference on Current Tren in Economics at MINES ParisTech for their helpful comments and suestions. The usual disclaimer applies. y Department of Economics, Florida International University, Miami, FL 33199, USA; hyilmazk@ u.edu 1

2 1 Introduction The workhorse empirical models of international trade based on constant markups (e.., lo linear ravity studies) have been criticized by the international nance literature that they cannot match the data on international price di erences, especially when exporters price discriminate across importers. 1 Accordinly, one of the most successful strateies in the international nance literature has been to nest constant elasticity of substitution (CES) models to have variable markups (i.e., markups chanin with the quantity sold) such that the so-called "Penn e ect", accordin to which the price level is hiher in richer countries, can be explained. 2 Nevertheless, when it comes to measurin the e ects of constant versus variable markups on international price dispersion, the existin studies have mostly focused on calibratin complicated models (e.., the in uential investiation by Atkeson and Burstein, 2008, followed by many international trade and nance studies 3 ). Therefore, there is a lack of an easy-to-implement estimation stratey in the literature on this subject. This paper introduces such an estimation stratey considerin the trade implications of havin constant versus variable markups by usin constant relative risk aversion (CRRA) versus constant absolute risk aversion (CARA) consumer utility functions, respectively. 4 The functional form of the 1 The followin studies are examples showin that importers with hiher income levels pay hiher prices for imports from a iven source: Hummels and Klenow (2005), Hummels and Luovskyy (2009), Baldwin and Harrian (2011), Alessandria and Kaboski (2011), Johnson (2012), and Manova and Zhan (2012). Studies such as by Crucini and Yilmazkuday (2014) show how the retail sector can contribute to international price di erences. 2 Studies such as Helpman and Kruman (1985), Lapham (1995), Berin and Feenstra (2001), Alessandria (2004), Corsetti and Dedola (2005), Hellerstein (2006), Atkeson and Burstein (2008), Simonovska (2015), amon many others, have all investiated international price di erences usin monopolistically competitive models with non-constant elasticities of demand. 3 Amiti et al. (2014), Berman et al. (2012), and Edmond et al. (2012) are just a few examples. 4 As shown by Behrens and Murata (2007), CRRA correspon to constant markups (throuh CES), while CARA correspon to a speci c case of variable markups (throuh non-ces) when the pricin decision of the producers 1

3 importer-country utility function further determines the price elasticity of demand and the elasticity of substitution (across products imported from di erent countries) throuh utility maximization. When each source country maximizes its pro ts usin a pricin-to-market stratey, it is shown that CRRA preferences correspon to CES and thus constant markups, while CARA preferences correspon to non-ces and thus variable markups. The key innovation is that, when trade implications are estimated to obtain elasticity measures (and thus implied markups), havin cases of constant versus variable markups is reduced to usin quantities in los versus levels on the left hand side of the estimated equations, where the riht hand sides are exactly the same; i.e., constant markups correspond to lo-linear reressions (as in CES-based ravity studies), while variable markups correspond to lin-lo reressions. Compared to the existin literature, this empirical innovation is closely related to a study by Novy (2013) who has shown that translo demand systems also correspond to lin-lo reressions under certain circumstances. However, such reressions implied by translo demand systems cannot distinuish between the elasticity of demand/substitution and the distance elasticity of trade costs, where the former is the key to measure and identity markups as in this paper. 5 Usin the NBER-UN data on quantity traded and unit prices coverin bilateral trade between 171 countries for 749 ood cateories, we estimate trade patterns implied by the model (i.e., lois also considered; the rest of this paper will follow these utility functions in order to distinuish between constant versus variable markups. Several other papers, includin Behrens and Murata (2012a,b), Behrens et al. (2012), Yilmazkuday (2013,2015a), have considered CARA preferences under di erent contexts. See Arkolakis et al. (2015) for other speci cations in the literature under which variable markups can be obtained. 5 Usin lin-lo reressions, Novy (2013) considers the endoeneity of the trade cost elasticity to focus on the heteroeneous impact of trade costs across country pairs, while this paper deviates by considerin the endoeneity of the elasticity of demand to investiate the implications on LOP. Another dimension that this paper deviates from Novy (2012) is that he uses total exports data amonst 28 OECD countries, while we use a ood-cateory level data coverin the lobe. 2

4 linear and lin-lo trade reressions) to obtain estimates of (constant and variable) markups after controllin for source-speci c quality measures and distance e ects (includin time-to-trade). After estimatin markups by trade equations, we estimate price equations implied by the model to decompose destination prices into marinal costs of production, markups, and trade costs. While marinal costs of production are further decomposed into source-speci c input costs, source-speci c quality and destination-speci c quality measures, trade costs are further decomposed into freiht costs and border costs. The decomposition of destination prices is further used to calculate the source of deviations from the Law of One Price (LOP) across destination countries for the cases of constant and variable markups at the ood-cateory level. The results under the case of constant (variable) markups imply that, on averae across oo, marinal costs of production has the lion s share with a contribution of about 92% (97%) to the mean of deviations from LOP, while trade costs contribute only about 8% (2%). The contribution of markups is almost none on averae across oo in both cases, althouh, in the case of variable markups, they can contribute up to 10% of the deviations from LOP for certain oo. The results are very similar when the variance of deviations from LOP for the averae ood is considered: marinal costs of production contribute about 96% (98%) and trade costs contribute about 5% (2%) when constant (variable) markups are considered. Since marinal costs of production explain the lion s share of the deviations from LOP, their decomposition into source-speci c input costs, source-speci c quality and destination-speci c quality measures is of further interest. Such a decomposition is also directly connected to the existin literature which has mixed evidence on the quality of exports. In particular, while studies such as by Verhooen (2008), Bastos and Silva (2010), Manova and Zhan (2012), Martin (2012), Sheu (2014), and Harrian et al. (2015) provide evidence that is consistent with the destination-speci c quality measures, other studies such as by Iacovone and Javorcik (2010), and Luovskyy and Skiba (2015) 3

5 provide evidence that is consistent with common quality across destination countries (captured by source-speci c quality measures in this paper). The correspondin results support the former set of studies by showin that destination-speci c quality measures contribute most to marinal costs of production, followed by source-speci c quality measures and source-speci c input costs, for both cases of constant and variable markups, and for both the mean and the variance of deviations from LOP. The rest of the paper has been oranized as follows. Section 2 introduces the economic environment to motivate the empirical investiation. Section 3 depicts the methodoloy and data used in the estimation. Section 4 discusses the estimation results and connects them to the correspondin results in the literature. Section 5 investiates the deviations from LOP. Section 6 concludes. 2 Model Trade patterns of countries are modeled at the ood level. Each destination country maximizes its utility obtained from imported oo. Each source country maximizes its pro ts at the ood level by followin a pricin-to-market stratey. Since we do not have/use any production data, we only focus on the trade and price implications of havin CRRA versus CARA utility functions, which correspond to CES versus non-ces functions (to be proved, below), respectively. We model the utility of the destination countries at the ood level to avoid any further assumptions for the areation across oo. Accordinly, a typical destination country d has the followin utility U d maximization out of consumin varieties of ood comin from di erent source countries, each denoted by s : max U d = X s u [q ] (1) 4

6 subject to X p q = E d (2) s where q is the quantity of products imported from country s, p is the price of q at the destination (i.e., country d), E d is the total expenditure of country d on ood, and brackets [:] stand for "is a function of". 2.1 Case of CRRA: Constant Markups The CRRA utility function is de ned as follows: u [q ] = (q ) (3) where > 0 represents a ood--speci c taste parameter, and represents a source-destinationood-speci c demand shifter capturin utility due to quality (as in Hummels and Klenow, 2005) and disutility due to slow delivery of a product (as in Hummels and Schaur, 2013): = s d (D ) u (4) where s represents the quality of ood due its location of production (i.e., the source country s), d represents the quality of ood due its location of consumption (i.e., the destination country d), and (D ) u > 0 represents the distance-related taste of the consumer, with D representin distance and u representin the elasticity of utility with respect to distance. We do not put any restrictions on the sin of u; while the case of u > 0 (utility function decreasin in distance) would represent concerns related to time-to-trade, the case of u < 0 (utility function increasin in distance) would represent preferences toward products comin from distant countries (e.., exotic oo). Hence, the demand shifter captures both quality and taste; the inclusion of taste (due to distance) will be the key in the identi cation of quality versus taste parameters in the estimation, below. 5

7 Besides the direct e ect of distance in the utility function, as will be shown below, there is also an indirect e ect of distance throuh the trade-costs component of prices, which is typical in most trade studies. The reason for includin this direct e ect is to distinuish between the e ects of distance in reressions explainin quantities (e.., ravity-type reressions in international trade studies) and the e ects of distance in reressions explainin prices (e.., price reressions international nance studies), where the coe cient in front of distance is di erent from each other, similar to how Ruhl (2008) has compared the Arminton elasticity across international trade and nance studies. 6 We assume the very same functional form of utility across importers on purpose, because we would like to avoid explainin trade patterns by parameter heteroeneity. By maximizin the utility function with respect to the budet constraint, the demand function can be obtained as follows: q = E d 1 1 X p ) ( s 0 (p ) 0 1! 1 (5) Accordin to Equation 5, after assumin that individual source countries have neliible impact on the destination price areates, the (absolute value of) price elasticity of demand " can be obtained as follows: " = = 1 1 (6) which is ood speci c (i.e., " = " for all d; s) and independent of the quantity purchased. Reardin the elasticity of substitution across varieties of a ood, the substitutability of ood imported from source country s for ood imported from source country s 0 is iven by: (q ; q 0 ) = d ln q q 0 du. d du dq d 0 d ln dq = 1 1 As is evident, due to our assumption of individual source countries havin neliible impact on the destination price areates, the expressions for the elasticity of substitution and the price elasticity 6 For sure, when it comes to the empirical investiation, D may well capture any other distance-related e ects that are embedded in the preferences (e.., distance-related search costs). 6

8 of demand are exactly the same; therefore, the case of CRRA in fact represents models based on constant-elasticity-of-substitution (CES) assumption. Considerin Equation 5, each source country s follows a pricin-to-market stratey by maximizin the pro t out of sales to country d: = q (p c ) (7) where c is the source-and-destination-and-ood-speci c marinal cost of exportin from country s to country d (includin trade costs and other costs reardin the quality of ood produced in country s and consumed in country d) iven by: c = w s ( s) s ( d ) d (8) where ws represents source-speci c input costs, ( s) s and ( d d ) respectively represent the part of the marinal cost due to the source- and destination-speci c quality (with s and d representin the elasticity of marinal cost with respect to quality), and represents the ross trade costs from source s to destination d for ood that is further de ned as: = (D ) b (9) where (D ) represents freiht costs (with D bein the distance and bein ood-speci c elasticity of trade costs with respect to distance), and b represents source-and-destination-andood-speci c (ross) border costs (e.., tari rates or ravity-type variables other than distance). 7 7 We are well aware that our de nition of trade costs is very simple; however, it is ood enouh for the empirical analyis that we will have, below, where our data set distinuishes between FOB exporter prices and CIF importer prices. We will also treat b s as a part of the residuals in our investiation usin the trade implications of our model. One can easily extend this analysis by includin other ravity-type variables into our trade-cost expression, but investiatin such variables/costs is simply not the focus of this paper. 7

9 It is important to emphasize that the e ect of distance throuh trade costs (i.e., parameterized by ) is di erent from the direct e ect of distance in the utility function (i.e., parameterized by u). The pro t maximization problem results in the followin pricin stratey: p = c (10) which implies that the price elasticity of demand (in Equation 6) can be rewritten as: " = p p c = 1 1 (11) and that the ross markup denoted by can be written as: = " " 1 = 1 (12) which is ood-speci c (i.e., = for all d; s) and hence common across (source and destination) countries accordin to Equation 10. Usin Equations 4, 8, and 9, we can rewrite Equation 5 as follows:! q = E d ( s d ) 1 1 X ( ) (13) p (D ) b 1 s 0 (p ) 0 1 which is one of the expressions we will estimate, below, where we have de ned as the distance elasticity of trade accordin to: = u + (14) The importance of this expression will be clearer when we will distinuish between the e ects of distance on quantities versus prices, below. Finally, usin Equations 8, 9, 10, and 12, the destination price in country d can be rewritten as follows: p = w s ( s) s ( d ) d (D ) b (15) which is another equation that we will use durin the estimation process, below. This price expression will also be the key expression for decomposin destination prices into its components and havin implications for LOP. 8

10 2.2 Case of CARA: Variable Markups The CARA utility function is de ned as follows: u [q ] = e q (16) where is aain iven by Equation 4. Maximizin this function with respect to the budet constraint results in the followin demand function: Ed q = X 1 s 0 ln X p s 0 p 0 0 p 0 p 0 Usin the de nition of taste parameters and trade costs iven in Equations 4, 8 and 9 (that are common across CRRA and CARA cases), after some simple manipulation, we can rewrite this demand function as the followin lin-lo expression: 0 X E 1 1 d ln q = 0 p p B s 0 0 X C A + ln ( s) + ln ( d ) s 0 p 0 (17) ln (p ) ln (D ) ln (b ) (18) which is another expression we will estimate, below, where is aain iven by Equation 14. Accordin to Equation 17, after assumin that individual source countries have neliible impact on the destination price areates, the (absolute value of) price elasticity of demand can be obtained as follows: " = = 1 q (19) which chanes with the quantity q traded.8 Reardin the elasticity of substitution across varieties of a ood, the substitutability of ood imported from source country s for ood imported from source country s 0 is iven by: (q ; q 0 ) = d ln q q 0 du. d du dq d 0 d ln dq = 1 q 8 This result is consistent with studies such as by Yilmazkuday (2015b) who empirically show that the elasticity of demand systematically chanes from one importer country to another. 9

11 As is evident, aain due to our assumption of individual source countries havin neliible impact on the destination price areates, the expressions for the elasticity of substitution and the price elasticity of demand are exactly the same; therefore, the case of CARA implies variable elasticities of substitution (i.e., non-ces). Considerin Equation 17, source country s maximizes its pro ts iven (aain) by Equation 7. This time, the rst order condition implies that: q = p p c (20) which can be substituted into Equation 19 to obtain an alternative expression for the price elasticity of demand: " = p p c = 1 q (21) where the rst equality is exactly the same as the rst equality in Equation 11. The ross markup aain denoted by can be written as: = " " 1 = 1 1 q (22) where the rst equality is exactly the same as the rst equality in Equation 12. Usin the approximation of ln (1 + x) x for small values of x, one can also write the followin approximation for lo ross markups: ln = ln (1 q ) = ln (1 q ) q (23) when q correspon to a small value, which is in fact supported by studies such as by Yilmazkuday (2015a). Therefore, both CRRA and CARA imply the very same price elasticity of demand when the elasticity is expressed in terms of source prices and marinal costs, and they imply the very same ross markup when the markup is expressed in terms of the price elasticity of demand. Nevertheless, 10

12 the pricin stratey (i.e., markups) of the source country determined throuh di erent demand structures is the key factor determinin the price elasticity of demand and the ross markups for the cases of CRRA versus CARA. Althouh the price elasticity of demand and the ross markup expressions are ood speci c (i.e., they are common across source and destination countries) in the case of CRRA (accordin to Equations 10 and 12), they chane with respect to oo, toether with source and destination countries, in the case of CARA (accordin to Equations 20 and 22). Therefore, for each ood, we have constant elasticities and markups in the case of CRRA, while we have variable elasticities and markups in the case of CARA. Finally, usin Equations 8, 9, 20, and 22, the destination price in country d is iven (aain) by Equation 15, where the only di erence is the de nition of markups. 3 Estimation Methodoloy and Data This section depicts the details of estimatin the equations of quantity traded and price implied by the cases of constant and variable markups. The main objective is to estimate markups and trade costs to further use them in decomposin the price data into marinal costs, markups, and trade costs. Since the estimation methodoloy depen on the data employed, we start with depictin the details of the data set rst. 3.1 Data Trade data are from NBER-UN world trade data set as documented by Feenstra et al. (2005) which we refer for further/technical details. The data set includes value (price times quantity) of bilateral trade between 171 countries for 749 ood cateories classi ed accordin to 4-diit Standard International Trade Classi cation Revision 2 (SITC4-R2) between The data also include 11

13 quantity of trade, which allows to calculate the unit prices for each ood cateory. However, since there may be possible problems in terms of comparin unit prices at di erent points in time, as in Jaimovich and Merella (2012), we focus on the data (with both value and quantity observations) only for the year of 2000 (which is the latest year in the data featurin the most-recent data collection techniques) for which the number of source countries is 171 and the number of destination countries is 169. Since we need both unit prices and quantities in our analysis, we restricted ourselves to the part of the data that have both measures; accordinly, we ended up with havin 527,371 bilateral trade observations (correspondin to 62% of the oriinal data set) at the ood level for the year of We accept that the selection of the NBER-UN world trade data set cateorized accordin to SITC4-R2, especially because it is at the 4-diit level, may be restrictive. Nevertheless, this data set has been used widely in the literature; hence, it lea to easier comparison with earlier studies. Moreover, the main objective of this paper is to focus on an easy-to-implement empirical innovation to distinuish between constant versus variable markups; therefore, the widely-used SITC4-R2 data for the year of 2000 are ood enouh to make a point, especially throuh a static trade model like ours. The data set ives primacy to trade ows reported by the importin country, whenever they are available, assumin that these are more accurate than reports by the exporters. If the importer report is not available for a country-pair, however, then the correspondin exporter report is used instead. The value of bilateral trade reported by the importer is CIF (cost, insurance, freiht), whereas the data reported by the exporter is FOB (free on board). Therefore, in order to employ as many observations as possible, we need to distinuish between CIF and FOB based unit prices in our estimation; the correspondin details will be provided below. The other data we use in the estimation are for reat circle distances between countries (where 12

14 latitudes and lonitudes have been obtained from The Goole Geocodin API). 3.2 Estimation of Trade Equations We start with the implications for trade patterns in the case of constant markups iven by Equation 13, which can rewritten in a lo-linear format as follows after controllin for the di erence between CIF and FOB based unit prices by an indicator function: ln (q ) = 0! 1 ln ( ) A d + ln ( d ) s 0 (p ) Destination-and-Good Fixed E ects + ln ( s) 1 Source-and-Good Fixed E ects (24) ln (p ) 1 Source-Price E ects I {z} ln (D ) 1 Indicator Function Distance E ects ln (b ) 1 Residuals where the indicator function I, which is also available in our data set under the title of "Direction of Trade", takes a value of 1 (or 0) when prices p are calculated accordin to the data reported by the exporter (or importer). The trade patterns in the case of variable markups iven by Equation 18 is already iven in lin-lo format as follows: 0 X E 1 1 d ln 0 p p q = B s 0 0 X C A + ln ( d ) + s 0 p 0 Destination-and-Good Fixed E ects ln ( s) Source-and-Good Fixed E ects (25) ln (p ) Source-Price E ects I {z} ln (D ) Indicator Function Distance E ects ln (b ) Residuals As is evident, both expressions can be estimated usin trade data in quantities, destinationand-ood- xed e ects, source-and-ood- xed e ects, price data, and distance data (to measure the combination of freiht costs and time-to-trade) if the unobserved border costs are assined the role of residuals (of which details/restrictions we discuss, below). Therefore, they turn out to be very 13

15 similar to each other in terms of their estimated expressions; the only di erence is to have quantities in los for the former and quantities in levels for the latter on the left hand side of the expressions. Accordinly, Equation 24 is attemptin to explain the quantities in los, while Equation 25 is attemptin to explain the quantities in levels. Since we employ residuals as border costs, when we take the implications literally, both models have explanatory power of 100% reardless. 9 Since we have data for both quantities and prices, in order to avoid any simultaneity bias, we estimate Equations 24 and 25 at the ood level usin two-stae least squares (TSLS), for which we estimate the implications of the model reardin prices in the rst stae and use their tted values in the second stae; the details are iven in the next subsection. 3.3 Estimation of the Price Equation Since the unit-price data we have are either CIF or FOB, they do not include any border costs b s. Hence, in order match the data with the model, usin the same indicator function I, we can write the lo version of Equation 15 after droppin b s as follows: ln p = ln w s + s ln s + d ln d + (1 I ) ln D + ln + v (26) where we have included the stochastic term of v to capture any measurement errors due to usin unit values as the measure of prices. In Equation 26, the only di erence between the cases of constant versus variable markups is due to the de nition of ln. In particular, for the case of constant markups, Equation 26 can be rewritten (usin Equation 12) and estimated as the rst 9 We consider border-related costs as residuals that are not shocks but rather part of the trade model; within this context, one cannot select one of the two models just because it implies lower border-related costs. 14

16 stae of TSLS as follows: ln p = ln ws + s ln s + (1 I ) ln D Source-and-Good Fixed E ects Distance-Related E ects (27) + d ln d Destination-and-Good Fixed E ects {z} ln + v {z} Constant Residuals while, for the case of variable markups, it can be approximated by usin Equations 23 and 25 to be estimated as the rst stae of TSLS as follows: 2 ln p Two Times Source Price Data ln ws + (1 + s) ln s + (1 I ) ln D I ln D Source-and-Good Fixed E ects Distance-Related E ects 0 E d + X ln s 0 X s 0 p p p 0 0 C A + (1 + d ) ln d Destination-and-Good Fixed E ects + v ln b Residuals (28) where the di erence between measurement errors and lo border costs (indirectly comin from the demand function due to variable markups) is assined the role of residuals. 10 Once the price expressions are estimated, the tted values for lo prices ln d p are used in the estimation of Equations 24 and 25 at the ood level as the second stae of TSLS. Reardin the identi cation of in the case of variable markups, since it shows up in both price and quantity reressions, we take the estimates of it comin from the rst-stae of TSLS (i.e., the price reression of Equation 28) as iven and estimate the second-stae of TSLS (i.e., the quantity reression of 25) 10 It is important to emphasize that, since the unit-price data we have are either CIF or FOB, the estimated residuals may also be capturin export-related costs that exporters pass on importers at the port. 15

17 as follows: q = 0 E d X 1 s 0 X ln s 0 p p p 0 0 C A + ln ( d ) + Destination-and-Good Fixed E ects lnd p +! I d ln (D ) Price E ects ln (b ) Residuals ln ( s) Source-and-Good Fixed E ects (29) where the tted values of ln d p and I d ln (D ) obtained in the rst stae of TSLS are used. 3.4 Identi cation of Estimated Parameters and Variables Usin trade data in quantities q s, (1 ) s and s can be obtained as the coe cients in front of price expressions in Equations 24 and 29. Usin estimated (1 ) s, s are identi ed for the case of constant markups by usin the coe cients in front of ln (D ) s in Equation 24, while s are identi ed in the estimation of Equation 28 for the case of variable markups. Similarly, s are identi ed as the coe cients in front of (1 I ) ln (D ) s in Equations 27 and 28, which can further be used to identify u s accordin to Equation 14, since s are already identi ed. Estimated (1 ) s and s can be used to identify markups ( s) where data on quantities are also used in the case of variable markups (accordin to Equation 22). Estimated (1 ) s and s can be used to identify source-speci c quality measures s s in Equations 24 and 29 by usin the source-and-ood xed e ects. By reressin the tted source-and-ood xed e ects in Equations 27 and 28 on the identi ed s s, one can also identify source waes ws s and s s; hence, the component of marinal costs of production capturin source-speci c quality ( s) s is identi ed. While the component of marinal costs of production capturin destination-speci c quality ( d d ) is identi ed as the tted values of destination-and-ood xed e ects in Equation 27 for the case of constant 16

18 markups, they are identi ed by takin the di erence between the tted values of destination-andood xed e ects in Equations 28 and 29 for the case of variable markups, where estimated s are also used. Border costs (b s) are identi ed by combinin tted residuals in Equations 24 and 29 with the estimated (1 ) s and s. Such a stratey brins two restrictions (both of which are consistent, at least, do not contradict) with the model: (i) the sum of residuals is zero; (ii) residuals are orthoonal to destination-and-ood- xed e ects, source-and-ood- xed e ects, price data, and distance data (i.e., the border costs will capture the pattern of trade that cannot be explained by any of these variables). 11 This completes the identi cation of the price components in Equation 15. It is important to emphasize that, due to usin tted xed e ects, the identi cation of ws, ( s) s, ( d ) d and b are all achieved in relative terms rather than in levels; however, such identi cations are ood enouh for the main objective of this paper, which is to investiate the deviations from LOP where lo relative prices (and thus lo relative values of price components) are considered. 4 Estimation Results for Trade Patterns This section depicts the estimation results and connects them to the existin literature. 4.1 Estimation Results The identi cation of > 0 and > 0 estimates are the key for the determination of markups, which is the main focus in this paper. The summary statistics of the ood-level estimates are iven in Table 1, where we have taken a conservative approach (for comparison purposes) by inorin the 11 Yilmazkuday (2012) has estimated taste parameters as model residuals in a closed-economy framework. Since we already estimate taste parameters throuh source-and-ood- xed e ects, and since we have an open-economy framework, employin the border costs as residuals is new to this paper. 17

19 oo that have neative estimates for either s or s; this has resulted in havin the summary statistics for 681 (out of 749) ood cateories. These 681 ood cateories are also oin to be the ones that we will use while investiatin the deviations from LOP, below. As is evident in Table 1, accordin to the estimation of Equation 24 for the case of constant markups, the distribution of s has an averae (across oo) of about 0.78, which correspon to an averae ross markup of about 1.32 (accordin to Equation 10). Interestinly, accordin to the estimation of Equation 29 for the case of variable markups, the averae (across oo and countries) ross markup is also about Nevertheless, there are sini cant di erences across oo; when the top and bottom one percentiles are inored, constant markups rane between 1.03 and 2.10, while variable markups rane between 1.00 and Compared to the existin literature, the averae (across oo) markups (of about 1.32) are in line with rm-level studies also featurin variable markups, such as De Loecker et al. (2015) that suest a median markup of about 1.10 for Indian rms or De Loecker and Warzynski (2012) who provide estimates of markups for Slovenian manufacturin plants ranin between 1.03 and 1.28 (obtained by di erent estimation methodoloies). When distance elasticity of trade costs s are considered, the averae is about 0.25 and 0.52 for the cases of constant versus variable markups, which are relatively close to the distance elasticity estimates in the international trade literature that are about 0.3 (see Hummels, 2001; Limao and Venables, 2001; Anderson and van Wincoop, 2004). The elasticity of utility with respect to timeto-trade u has a median value of 0:03 for the case of constant markups and a median value of 0:74 for the case of variable markups; therefore, more than half of the oo in our sample are traded due to their exotic nature rather than concerns due to time-to-trade. This di erence between estimated s and u s clearly shows the contribution of includin distance in the utility function that helps distinuishin between the e ect of distance on prices (e.., freiht-related costs) versus 18

20 on quantities (e.., preferences). Since the residuals in Equations 24 and 29 are assined the role of border costs, both models have 100% of an explanatory power by construction. Nevertheless, if we would take an econometric approach and accept them as residuals, the explanatory power of the reressions are iven in Table 1. It is important to emphasize that the R-squared measures comin from Equations 24 and 29 cannot be directly compared, since the former has lo quantities and the latter has level of quantities as left hand side variables. Accordinly, in order to make the R-squared values comparable to each other, in Table 1, we take a textbook approach by depictin the R-squared values calculated as the correlation between the level of quantities and the correspondin tted values on the riht hand side. This correspon to the reular R-squared value for the case of variable markups, while it correspon to the correlation between the exponential value of the left hand side and the exponential value of the tted values for the case of constant markups. Therefore, the R-squared values in Table 1 correspond to comparable R-squared values in terms of the explanatory power of reressions based on the level of quantities. As is evident, both constant and variable markups have hih explanatory powers with averae values (across oo) of about 0.60 and 0.54, respectively. 5 Implications for the Deviations from the Law of One Price We would like to compare the contribution of each price component to destination prices across the cases of constant and variable markups by considerin the deviations from LOP. 19

21 5.1 Methodoloy In our data set, since prices reported by importers are CIF and by exporters are FOB, the rst step is to convert all prices into destination prices (i.e., to construct destination prices) usin the followin deviations-from-lop expression (for both cases of constant and variable markups) at the ood level: p ln p d 0 s {z 0 } Relative Destination Prices!! w = ln s ( w + ln s) s ( d + ln ) d (30) s {z 0 } ( s ) 0 s 0 ( d ) 0 d 0 Relative Source Input Costs Relative Source-Speci c Quality Relative Destination-Speci c Quality + ln d 0 s 0 Relative Markups + D ln D d 0 s 0 Relative Freiht Costs b + ln b d 0 s 0 Relative Border Costs where all variables were estimated/identi ed, above. We will consider both the mean and the variance of the deviations from LOP (as in Crucini et al., 2005); while the mean is important to understand the manitude of the deviations, the variance is the common measure of price dispersion in the literature. One di erence is that we will consider the absolute value of relative-price expressions by multiplyin all neative relative-price values (and the correspondin riht-hand-side variables) with 1; such a stratey is important in measurin the actual (absolute value of) deviations from LOP. Since LOP is a concept at the ood level, we will consider the mean and the variance of the variables in Equation 30 across destination countries at the ood level. Therefore, when the mean deviations from LOP will be considered, we will investiate the portions explained by mean (lo) relative source-speci c input costs, source-speci c quality measures, destination-speci c quality measures, markups, freiht costs, and border costs. When the variance of deviations from LOP will be considered, we will consider the followin variance decomposition analysis to compare the contributions 20

22 of marinal costs, markups, freiht costs, and border costs: var p ln p d 0 s {z 0 } Relative Destination Prices w = cov ln s w s 0 p ; ln p d 0 s 0 Relative Source Input Costs + cov ln! ( d +cov ln ) d p! ; ln ( d ) 0 d 0 p d 0 s {z 0 } Relative Destination-Speci c Quality +cov ln D D d 0 s 0 p ; ln p d 0 s 0 ( s) s! p ; ln p d 0 s 0! ( s ) 0 s 0 {z } Relative Source-Speci c Quality Relative Freiht Costs + cov p ; ln ln d 0 s p 0 d 0 s {z 0 } Relative Markups + cov b p ; ln ln b d 0 s p 0 d 0 s {z 0 } Relative Border Costs which hol with exact equality, where var is the variance operator, and cov is the covariance operator. 5.2 Results The results are iven in Table 2, where the mean deviations from LOP are about 1.46 and 3.25 for the cases of constant and variable markups, respectively. As is evident, the di erences in marinal costs of production explain pretty much the whole deviations from LOP in both cases of constant and variable markups. Althouh the contribution of markups in the case of variable markups can o up to 10% for certain oo, on averae across oo, their e ect is none. Similarly, althouh freiht (border) costs contribute up to 21% (23%), their averae e ect across oo is very small, about 3% (5%) for the case of constant markups and about 3% ( 1%) for the case of variable markups. The results are very similar in Table 3 where the variance of deviations from LOP are considered. Compared to the existin literature, the hih contribution of marinal costs and low contribution of trade costs are consistent with studies such as by Yilmazkuday (2014) who investiates the deviations from LOP usin actual data on trade costs. In order to support the summary statistics iven in Table 2 and Table 3, we also consider a 21

23 visual representation of results in Fiure 1 and Fiure 2, where ood-level results are provided. In these ures, oo have been ranked in the horizontal axis with respect to their variance of lo relative prices obtained in the case of variable markups; we depict the averae across 80 oo for presentational purposes. As is evident, the results are very similar across individual ood roups in terms of the percentae contribution of price components to the deviations from LOP. Since marinal costs contribute the most to the deviations from LOP, their decomposition is of further interest. As is evident for both cases of constant and variable markups in Table 2, destination-speci c quality measures contribute most to the deviations from LOP, followed by source-speci c quality measures and source-speci c input costs. Since we calculate the deviations from LOP across destination countries after poolin across source countries, this result literally means that destination-speci c quality measures explain most of the price dispersion across destination countries on averae across source countries. In other wor, for a typical source country, export quality measures di er across destination countries in a sini cant way. This result is also supported across oo in Fiure 1; the results are very similar in Table 3 and Fiure 2 as well, where the variance of deviations from LOP are considered. Overall, the results based on the decomposition of marinal costs of production support the evidence in the literature reardin destination-speci c quality measures as shown in studies such as by Verhooen (2008), Bastos and Silva (2010), Manova and Zhan (2012), Martin (2012), Sheu (2014), and Harrian et al. (2015). The results have important implications for our understandin of international price di erences. Althouh the existin literature mostly advocates for the role trade costs in explainin the deviations from LOP, the results in this paper suest that the role of trade costs are relatively minor. Accordinly, if the deviations from LOP are considered as the deree of lobal interation, the main role is played by the quality of exports across destination countries, leavin a small room for welfare improvement throuh the reduction of trade costs. Apparently, in explainin the low derees of 22

24 lobal interation, the preferences of destination countries revealed throuh their demand for hiher quality products are even more important than source-country speci c factors such as their comparative advantae throuh input costs or source-speci c quality measures. Therefore, the future of lobal interation miht be achieved mostly throuh chanes in preferences of consumers toward similar quality products, rather than reduction in other barriers to trade. 6 Conclusion This paper has introduced an easy-to-implement empirical stratey that can distinuish between constant and variable markups. In particular, by considerin the utility maximization of destination countries and the pro t maximization of source countries by a pricin-to-market stratey, we have shown that the case of constant markups (obtained by CRRA utility function) correspon to lolinear reressions estimatin trade patterns (as in CES-based ravity studies), while a special case of variable markups (obtained by CARA utility function) correspon to lin-lo reressions. Combinin the information comin from the estimation of trade patterns and implied prices, markups and trade costs are identi ed, which are further used to decompose destination prices into marinal costs, markups, and trade costs. The decomposition of destination prices is used to investiate the source of deviations from the Law of One Price (LOP). The results show that marinal costs of production contribute most in both cases of constant and variable markups. The decomposition of marinal costs of production further suests that destination-speci c quality measures contribute most to the deviations from LOP, followed by source-speci c quality measures and source-speci c input costs. Hence, preferences of destination countries toward alternative quality of products show up as additional barriers to lobal interation. We are well aware of a caveat that explainin everythin due to the speci cation of the utility 23

25 function is a restrictive approach; however, many existin trade studies employin utilities in a functional form are subject to the very same criticism. Nevertheless, such a modelin stratey in this paper makes the overall analysis very simple and tractable compared to much more complicated models in the literature which practically have very similar implications for international trade and nance. Another caveat is that we do not have any relevant data on either marinal costs or markups to compare the performance of the cases of constant versus variable markups; aain, the existin literature is subject to the very same criticism, since any estimated variable (of markups or marinal costs) depen on the modelin stratey employed. References [1] Alessandria, Geore (2004). International Deviations From The Law Of One Price: The Role of Search Frictions and Market Share. International Economic Review, 45(4), [2] Alessandria, Geore and Joseph Kaboski. (2011). Pricin-to-Market and the Failure of Absolute PPP. American Economic Journal: Macroeconomics, 3(1): [3] Amiti, M., Itskhoki, O., and Konins, J. (2013), "Importers, Exporters, and Exchane Rate Disconnect", American Economic Review, 104(7), [4] Anderson, J.E., Wincoop, E.V., (2004). Trade costs. Journal of Economic Literature 42, [5] Arkolakis, C., Costinot, A.,Donalon, D., and Rodriuez-Clare, A. (2015) "The Elusive Pro- Competitive E ects of Trade, NBER Workin Paper No [6] Atkeson, Andrew and Ariel Burstein, (2008). Pricin-to-Market, Trade Costs, and International Relative Prices," American Economic Review, 98 (5),

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27 [17] De Loecker, Jan and Frederic Warzynski (2011), "Markups and Firm-Level Export Status," American Economic Review, 102(6), [18] De Loecker, J., Goldber, P.K., Khandelwal, A.K., and Pavcnik, N. (2015). "Prices, Markups and Trade Reform," Econometrica, forthcomin. [19] Edmond, C. Midrian, V., and Daniel Yi Xux (2012). "Competition, Markups, and the Gains from International Trade" mimeo. [20] Feenstra, R.C., Robert E. Lipsey, Haiyan Den, Alyson C. Ma, Henyon Mo (2005), "World Trade Flows: ". NBER Workin Paper [21] Harrian, J, Ma, X. and Shlychkov, V. (2015) "Export prices of U.S. rms" Journal of International Economics 97, [22] Hellerstein, R. (2006). A Decomposition of the Sources of Incomplete Cross-Border Transmission. Federal Reserve Bank of New York, Sta Report 250. [23] Helpman, E. and P.R. Kruman, (1985) Market Structure and Forein Trade, MIT Press, Cambride, MA, [24] Hummels, D., (2001), Toward a eoraphy of trade costs, mimeo. [25] Hummels, David and Peter J. Klenow. (2005) "The Variety And Quality Of A Nation s Exports," American Economic Review, 95(2): [26] Hummels, D., and Luovskyy, V., (2009), "International Pricin in a Generalized Model of Ideal Variety", Journal of Money, Credit and Bankin, 42(s1): [27] Hummels, D., and Schaur, G., (2013), "Time as a Trade Barrier", American Economic Review, 103(7),

28 [28] Iacovone, L., and B. S. Javorcik (2010): Multi-product exporters: diversi cation and microlevel dynamics, The Economic Journal, 120, [29] Jaimovich, E. and Merella, V., (2012). "Quality Ladders in a Ricardian Model of Trade with Nonhomothetic Preferences," Journal of the European Economic Association, Volume 10, Issue 4, paes , Auust [30] Johnson, R. C. (2012) Trade and Prices with Heteroeneous Firms, Journal of International Economics, 86(1): [31] Lapham, B. (1995) A Dynamic General Equilibrium Analysis of Deviations from the Laws of One Price. Journal of Economic Dynamics and Control, 19(8), pp [32] Limao, N., Venables, A.J., Infrastructure, eoraphical disadvantae, transport costs and trade. World Bank Economic Review 15 (3), [33] Luovskyy, V. and Skiba A. (2015) "How Georaphy A ects Quality?" Journal of Development Economics, 115: [34] Martin, J., (2012). Markups, quality, and transport costs. European Economic Review 56, [35] Manova, K. B. and Z. Zhan (2012): Export Prices across Firms and Destinations, Quarterly Journal of Economics, 127: [36] Novy, D. (2013) "International trade without CES: Estimatin translo ravity". Journal of International Economics 89: [37] Ruhl, KJ (2008), "The International Elasticity Puzzle", mimeo. 27

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30 Table 1 - Summary of Good-Level Estimation Results Constant Markups (CRRA) Variable Markups (CARA) θ µ δ δ τ 3 δ R-Squared. α 10 u µ δ δ τ δ u R- Squared. Averae st Percentile th Percentile th Percentile Median th Percentile th Percentile th Percentile Notes: These are the summary statistics for the distribution of estimated parameters and the explanatory power of reressions that have been run at the ood level. α 's in the table have been multiplied by 1,000 for presentational purposes. For the case of CARA, the summary statistics of the median across source and destination countries. µ have been obtained as

31 Constant Markups Table 2 - Summary of Mean of Deviations from LOP % Contribution of Deviations Marinal Costs Markups Trade Costs Averae across Country Pairs Source Input Costs Source Quality Destination Quality Constant Markups Freiht Costs Border Costs Averae % 26% 55% 0% 3% 5% 1st Percentile % 5% 17% 0% -7% 0% 10th Percentile % 12% 33% 0% -2% 1% 25th Percentile % 17% 44% 0% 0% 2% Median % 25% 57% 0% 2% 4% 75th Percentile % 33% 67% 0% 6% 7% 90th Percentile % 40% 75% 0% 9% 10% 99th Percentile % 60% 92% 0% 18% 17% Variable Markups % Contribution of Deviations Marinal Costs Markups Trade Costs Averae across Country Pairs Source Input Costs Source Quality Destination Quality Variable Markups Freiht Costs Border Costs Averae % 23% 56% 0% 3% -1% 1st Percentile % 6% 13% -4% -7% -10% 10th Percentile % 12% 30% -2% -2% -5% 25th Percentile % 16% 43% -1% 0% -3% Median % 21% 59% -1% 3% -1% 75th Percentile % 29% 70% 0% 6% 0% 90th Percentile % 37% 80% 2% 10% 4% 99th Percentile % 50% 92% 10% 21% 23% Notes: We consider the mean of the deviations from LOP across destination countries at the ood level by poolin observations across country pairs.

32 Constant Markups Table 3 - Summary of Variance of Deviations from LOP % Contribution of Deviations Marinal Costs Markups Trade Costs Variance across Country Pairs Source Input Costs Source Quality Destination Quality Constant Markups Freiht Costs Border Costs Averae % 24% 63% 0% 2% 3% 1st Percentile % -1% 0% 0% -4% -3% 10th Percentile % 5% 32% 0% -2% 0% 25th Percentile % 12% 49% 0% 0% 0% Median % 21% 64% 0% 2% 2% 75th Percentile % 30% 78% 0% 4% 4% 90th Percentile % 42% 92% 0% 7% 6% 99th Percentile % 99% 104% 0% 11% 13% Variable Markups % Contribution of Deviations Marinal Costs Markups Trade Costs Variance across Country Pairs Source Input Costs Source Quality Destination Quality Variable Markups Freiht Costs Averae % 20% 64% 0% 2% 0% 1st Percentile % -1% 7% -4% -6% -18% 10th Percentile % 6% 31% -2% -2% -5% 25th Percentile % 10% 47% -1% 0% -2% Median % 18% 66% -1% 2% -1% 75th Percentile % 29% 82% 0% 4% 0% 90th Percentile % 41% 94% 2% 6% 5% 99th Percentile % 54% 111% 13% 11% 37% Border Costs Notes: We consider the variance of the deviations from LOP across destination countries at the ood level by poolin observations across country pairs.

33 Fiure 1 - Mean of Deviations from LOP Constant versus Variable Markups (a) Level of Price Dispersion - Constant Markups (b) Level of Price Dispersion - Variable Markups (c) % of Price Dispersion - Constant Markups (d) % of Price Dispersion - Variable Markups Notes: The oo have been ranked accordin to variance of lo relative prices based on CARA preferences. The averae across 80 oo is shown.

34 Fiure 2 - Variance of Deviations from LOP Constant versus Variable Markups (a) Level of Price Dispersion - Constant Markups (b) Level of Price Dispersion - Variable Markups (c) % of Price Dispersion - Constant Markups (d) % of Price Dispersion - Variable Markups Notes: The oo have been ranked accordin to variance of lo relative prices based on CARA preferences. The averae across 80 oo is shown.