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Explaining the cross-sectional distribution of law of one price deviations

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Explaining the cross-sectional distribution of law of one price deviations

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Content Explaining the Cross-Sectional Distribution of Law of One Price Deviations by Rahul Giri A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy (ECONOMICS) August 2008 Copyright 2008 Rahul Giri Dedication Dedicated to my parents, without whose sacrifices I could not have accomplished this. ii Acknowledgments My interest in economics goes back to the high school lectures on demand, supply, and the then esoteric concept of the “invisible hand”. Looking back it seems strange that pursuing a Ph.D. was never on the horizon, not even at the time of getting a masters in economics. To me there is only one way to explain it - the “invisible hand” at work! At USC, my research took shape under the guidance of Prof. Caroline Betts. Her work in the field of international economics has greatly influenced my research. Prof. Betts has been a great mentor and advisor, guiding me when I was lost but still allowing me to explore different directions, which is the core of research. I wish to thank her for the constant support and encouragement she has provided throughout this process, especially during the job market period. Iamalsoextremelythankful toProf. VincenzoQuadriniforpatiently spendinghours together to discuss and resolve issues, especially those related to the model. I am also grateful to him for his advise on job market related issues. My discussions with Prof. Doug Joines, Prof. Yong Kim, Prof. Guillaume Vandenbroucke and Prof. Richard Easterlin have been very beneficial. I would also like thank Rubina Verma for critical feedback on my research, as well as for being there for me through the highs and lows of the Ph.D. program. Special thanks to Engin Volkan and Murat Ungor for their comments. I am also grateful to Subha Mani, Utteeyo Dasgupta, Ashish Agarwal, Rajini Parmeswaran and Abhijit Chaudhari for helping me through this journey. Last but not the least, this dissertation would not have been possible without the love and support of my family - my mother, Lata Giri, my father, Girjesh Giri and my brother, Varun Giri. iii Table of Contents Dedication ii Acknowledgments iii List Of Tables vii List Of Figures viii Abstract ix Chapter 1: Introduction 1 Chapter 2: Data on Distribution Sector 9 Chapter 3: A Ricardian Model with International Trade Costs and Local Distribution Costs 13 3.1 Ricardian Trade Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.1.1 Production and Consumption . . . . . . . . . . . . . . . . . . . . . 13 3.1.2 Market Clearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.1.3 Retail Price of Individual Goods . . . . . . . . . . . . . . . . . . . 15 3.1.4 Calibration Methodology . . . . . . . . . . . . . . . . . . . . . . . 16 3.1.5 Variance of LOOP Deviations . . . . . . . . . . . . . . . . . . . . . 18 3.1.6 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Results: Ricardian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3 Ricardian Trade Model with A Local Distribution Sector . . . . . . . . . . 23 3.3.1 Production and Consumption . . . . . . . . . . . . . . . . . . . . . 23 3.3.2 Market Clearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3.3 Retail Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3.4 Calibration Methodology . . . . . . . . . . . . . . . . . . . . . . . 26 3.3.5 Variance of LOOP Deviations and Distribution Margins for Indi- vidual Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.3.6 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4 Results: Ricardian Model with Distribution . . . . . . . . . . . . . . . . . 29 3.4.1 Role of Heterogeneity in Distribution . . . . . . . . . . . . . . . . . 30 3.4.2 Role of Trade Costs . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 iv Chapter 4: A First Step Toward Investigating the Role of Market Struc- ture 37 4.1 Ricardian Model with Bertrand Competition . . . . . . . . . . . . . . . . 37 4.1.1 Production and Consumption . . . . . . . . . . . . . . . . . . . . . 37 4.1.2 Market Clearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.1.3 Trade, Market Structure and Retail Prices in Base Goods Sector . 38 4.1.4 Aggregate Trade Shares, Trade Costs and Share of Costs in Revenues 41 4.1.5 Calibration Methodology . . . . . . . . . . . . . . . . . . . . . . . 43 4.1.6 Simulating Retail Prices and Good-by-Good Price Dispersion . . . 44 4.1.7 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2 Results: Ricardian Model with Bertrand Competition . . . . . . . . . . . 48 4.3 Ricardian Model with Bertrand Competition and Local Distribution Costs 50 4.3.1 Production and Consumption . . . . . . . . . . . . . . . . . . . . . 50 4.3.2 Market Clearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3.3 Retail Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3.4 Calibration Methodology . . . . . . . . . . . . . . . . . . . . . . . 53 4.3.5 Simulating Retail Prices and Good-by-Good Price Dispersion . . . 54 4.3.6 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4 Results: Ricardian Model with Bertrand Competition and Local Distrib- ution Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.4.1 Role of Heterogeneity in Distribution . . . . . . . . . . . . . . . . . 58 4.4.2 Role of Trade Costs . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Reference List 63 List of Appendices Appendix A Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 A.1 Price of Intermediate Composite . . . . . . . . . . . . . . . . . . . . . . . 67 A.2 Expenditure Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 A.3 Sectoral Allocations of Inputs in the Ricardian Model with Distribution Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Appendix B Data for Parameterization and Parameterization Methodology . . . . . . . . . 70 B.1 Data on Gross Output and Value Added . . . . . . . . . . . . . . . . . . . 70 B.2 Bilateral Trade Data and Expenditure Shares . . . . . . . . . . . . . . . . 70 B.3 Labor Force and Capital-Labor Ratio . . . . . . . . . . . . . . . . . . . . 71 B.4 Basic Price Value of Traded Goods as a ratio of Purchaser Price Value of Traded Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 v Appendix C Appendix to Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 C.1 The Joint Distribution of Lowest and Second-Lowest Cost . . . . . . . . . 72 C.2 The Distribution of Markups . . . . . . . . . . . . . . . . . . . . . . . . . 73 C.3 Price Index in a Destination . . . . . . . . . . . . . . . . . . . . . . . . . . 74 C.4 Probability that Country j is Lowest-Cost Supplier to Country i . . . . . 75 C.5 Distribution of Costs Conditional on Source Country j . . . . . . . . . . . 76 C.6 Share of Production and Delivery Costs in Per Capita Expenditure of Country i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 vi List Of Tables 1.1 Good-by-Good Price Dispersion in Data . . . . . . . . . . . . . . . . . . . 2 2.1 Data on Distribution Margins - by Countries . . . . . . . . . . . . . . . . 11 2.2 Data on Distribution Margins - by Goods . . . . . . . . . . . . . . . . . . 11 3.1 Estimates of Trade Costs: Ricardian Model with Perfect Competition . . 20 3.2 Ricardian Model Versus Data . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3 Country-Specific Distribution Parameter: Ricardian Model with Distribu- tion Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4 Ricardian Model with Distribution Costs Versus Data . . . . . . . . . . . 29 3.5 Ricardian Model with Homogeneous Distribution Costs Versus Data . . . 31 3.6 Ricardian Model with Distribution Costs: Role of Trade Costs . . . . . . 33 4.1 Estimates of Trade Costs: Ricardian Model with Bertrand Competition . 47 4.2 Ricardian Model with Bertrand Competition Versus Data . . . . . . . . . 49 4.3 Country-Specific Distribution Parameter: Ricardian Model with Bertrand Competition and Distribution Costs . . . . . . . . . . . . . . . . . . . . . 56 4.4 Ricardian Model with Bertrand Competition and Distribution Costs Ver- sus Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.5 Ricardian Model with Bertrand Competition and Homogeneous Distribu- tion Costs Versus Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.6 RicardianModel with BertrandCompetition and Distribution Costs: Role of Trade Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 vii List Of Figures 1.1 Empirical Distribution of Var(Q i (x)|x) 1/2 in the Data . . . . . . . . . . . 3 3.1 Distribution of Var(Q mi (x)|x) 1/2 : Ricardian Model . . . . . . . . . . . . . 22 3.2 Distribution of Var(Q mi (x)|x) 1/2 : Ricardian Model with Distribution Costs 30 3.3 Distribution of Var(Q mi (x)|x) 1/2 : Role of Heterogeneity in Distribution Costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4 Effect of Trade Costs on Empirical Distribution of Var(Q mi (x)|x) 1/2 . . . 34 4.1 Distribution of Var(Q mi (x)|x) 1/2 : Ricardian Model with Bertrand Com- petition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 Distribution of Var(Q mi (x)|x) 1/2 : Ricardian Model with Bertrand Com- petition and Distribution Costs . . . . . . . . . . . . . . . . . . . . . . . . 57 4.3 Distribution of Var(Q mi (x)|x) 1/2 : Role of Heterogeneity in Distribution . 59 4.4 Effect of Trade Costs on Empirical Distribution of Var(Q mi (x)|x) 1/2 . . . 61 viii Abstract Observed trade flows provide one metric to gauge the degree of international goods market segmentation. Deviations from the law of one price provide another. New survey dataonretailpricesforabroadcrosssectionofgoodsacross13EUcountries,compiledby Crucini, TelmerandZachariadis(2005), showthat(i)theaveragedispersionoflawofone price(LOOP)deviationsacrossallgoodsis28percentand(ii)therangeofthatdispersion across goods is large, varying from 2 percent to 83 percent. Quantitative multi-country ricardianmodels, a laEatonandKortum, usedataonbilateraltradevolumestoestimate international trade barriers or trade costs. I find that a multi-country ricardian model with perfectly competitive markets, in which heterogeneous and asymmetric trade costs are carefully calibrated to match observed bilateral trade volumes, can account for 85 percent of the average dispersion but only 21 percent of the variation in price dispersion. When the model is augmented to permit heterogeneity in local costs of distribution - across goods and countries - and is calibrated to match data on distribution margins, it can reproduce 96.5 percent of the average dispersion of law of one price deviations and 32 percent of the variation in that dispersion. Changing the market structure in the production of goods, from perfectly competitive to competition in prices, leads to a large overprediction of average price dispersion but helps to account for 44 percent of the variation in price dispersion, still leaving 56 percent of variation unexplained. Heterogeneity in trade costs, and in local distribution costs, and variable markups in the production of goods cannot account for observed heterogeneity in the dispersion of law of one price deviations. ix Chapter 1 Introduction Thelawofoneprice(LOOP)statesthatoncethepriceofatradedgoodisexpressed in a common currency, the good should sell for the same price in different countries. The intuition is that, in perfectly integrated international markets, free trade in goods will arbitrage away price differentials across countries. Traditionally, the size of observed bi- lateraltradeflowshasbeenusedasthemetrictogaugetheactualdegreeofgoods’market integration - or its absence, the degree of market segmentation. The size of deviations from the LOOP provides an alternative measure. The most commonly cited sources of goods market segmentation that give rise to LOOP deviations are: (i) the costs of inter- national transactions or barriers to trade, (ii) the prevalence of non-traded input costs of distributing and retailing traded goods in local markets, and (iii) markups over mar- ginal costs. In my dissertation, using a multi-country ricardian model, I explore whether bilateral trade costs, local costs of distribution and variable markups can quantitatively account for the distribution of observed, good by good LOOP deviations. How large are deviations from the LOOP? Although there is consensus in the liter- ature that deviations from LOOP are large, many empirical studies are limited by the use of price index data, or of prices of a very narrow set of individual goods 1 . Until recently, due to these data limitations, very little has been known about the magnitude of absolute deviations from the LOOP for a broad cross section of goods. Crucini et al. (2005), however, use local-currency retail prices on a broad cross-section of goods across 13 European Union (EU) countries to study good-by-good deviations from LOOP for the years 1975, 1980, 1985, and 1990. Engel and Rogers (2004), and Rogers (2001) also use a broad cross-sectional dataset of absolute retail prices to analyze European price 1 Isaard (1977) and Giovannini (1988) are examples of studies that use price indices data while Knetter (1989,1993),GhoshandWolf(1994),Cumby(1996),HaskelandWolf(2001)andLutz(2004)areexamples of studies that use prices of a narrow set of goods. 1 dispersion. I use the findings of Crucini et al. (2005) as a measure of LOOP deviations. This study provides the largest coverage of goods (1800 goods). Furthermore, the data allow the authors to look at LOOP deviations at four different points in time over a 15 year period. This ensures that the results are not being driven by a specific year of data. Crucinietal.(2005)definetheretailpriceofagoodinagivencountryastheaverageof surveyed prices across different sales points within the capital city of that country. Prices are adjusted for differences in value added taxes across countries, and then expressed in a common currency. Denote retail price of good x in country i by P i (x). The deviation from LOOP for good x in country i is defined as the deviation of the logarithm of the common currency price of good x in country i from the cross-country geometric average price of good x, or Q i (x) = logP i (x)− P N j=1 logP j (x)/N, where N is the number of countries. Then standard deviation of Q i (x) across countries, given by Var(Q i (x)|x) 1/2 , is the “cross-country dispersion of LOOP deviations” in the price of goodx. The authors also call this “good-by-good price dispersion”. I focus on two measures of LOOP deviations: (i) the average good-by-good price dispersion, and (ii) the variation in good-by-good price dispersion. Table 1.1: Good-by-Good Price Dispersion in Data 1975 1980 1985 1990 Avg. Avg. 0.2290 0.2941 0.3024 0.2855 0.2778 Max 0.7496 0.7751 0.8189 0.8319 0.7939 Min 0.0227 0.0784 0.0672 0.0458 0.0535 IQR 0.1297 0.1646 0.1749 0.1689 0.1595 P90 - P10 0.2427 0.2976 0.3281 0.3350 0.3008 ThefirstrowofTable1.1showstheaveragegood-by-goodpricedispersion(averageof Var(Q i (x)|x) 1/2 over goods) for each of the four years, and also in the final column, the average of this measure over the four years. The average good-by-good price dispersion is about 28 percent over the four years. 1975 shows the smallest average price dispersion. However,averagepricedispersionhasremainedquitestablefortheotherthreeyears. The jump in price dispersion between 1975 and 1980 is argued to be due to a smaller sample of countries in the 1975 survey 2 . The same feature emerges in measures of variation in good-by-good price dispersion. The variation in good-by-good price dispersion is large, 2 In total, there are 13 countries in the sample - Austria, Belgium, Denmark, France, Germany, Greece, Ireland,Italy,Luxembourg,Netherlands,Portugal,SpainandUnitedKingdom. However,the1975survey covers nine EU countries. Greece, Portugal, and Spain were added in 1980. Austria was added in 1985. 2 ranging from a minimum of 2 percent to a maximum of 83 percent, across the four years. However,Iusetheinter-quartilerange(IQR)astheprimarymeasureofvariationinorder tominimizetheeffectofextremevaluesonthemeasurementofvariationingood-by-good price dispersion. IQR is the difference between the 25 th and the 75 th percentile of good- by-good price dispersion. The data show that IQR, averaged over the four years, is 0.16. I also report the difference between the 10 th and 90 th percentile of good-by-good price dispersion (P90 - P10), which is 0.30 when averaged over the four years. The fact that the value of P90 - P10 is almost double that of the IQR suggests that the distribution of good-by-good price dispersion is skewed. This is clarified in Figure 1.1, which depicts the kernel density of good-by-good price dispersion (reproduced from Crucini et al. (2005)) for the four years. All four distributions are skewed to the right. One striking feature of the data is that both the average good-by-good price dispersion and the variation in good-by-good price dispersion, as depicted by IQR, P90 - P10 and the kernel density, are very stable over time. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.005 0.01 0.015 0.02 0.025 0.03 Price Dispersion Probability 1975 1980 1985 1990 Figure 1.1: Empirical Distribution of Var(Q i (x)|x) 1/2 in the Data Chapter 3 of the dissertation investigates the ability of a multi-country ricardian model, which incorporates international trade costs and local costs of distribution, to quantitatively account for (i) the average good-by-good price dispersion and (ii) the variation in good-by-good price dispersion measured by Crucini et al. (2005). In this chapter I abstract from variable markups by assuming that all markets are perfectly competitive. Although the role of bilateral trade costs for the time-series behavior of bilateral relativepriceshasbeenstudiedelsewhere(AtkesonandBurstein(2007),BerginandGlick 3 (2006),BettsandKehoe(2001)forexample),theabilityoftradecoststocontributetoan account of cross-sectional price dispersion has not been formally investigated. Eaton and Kortum (2002) quantify the size of trade costs using data on bilateral trade volumes for OECDcountries. Theyfindthattradecostsarelarge,andvarysubstantiallyacrosstrade partners. In chapter 3 of the dissertation, the first question that I attempt to answer is: In a multi-country ricardian model in which trade costs are carefully calibrated to match bilateral trade volumes, to what extent can measured cross-country heterogeneity in trade costs account for the average dispersion of LOOP deviations and the variation in dispersion of LOOP deviations? If international trade costs were the only source of segmentation in goods’ markets, in a world with zero international trade costs one would not observe any deviations from LOOP; all goods would be freely traded. However, Sanyal and Jones (1982) argue that there is no freely traded good. They emphasize the importance of local non-traded inputs that are used to deliver goods to final consumers in local markets. This implies that, even if a good could be traded costlessly across borders, the LOOP would not hold in retail prices as long as there are non-traded local inputs. Therefore, local non-traded inputs provide a second source of deviations from the LOOP. Several recent studies have emphasized distribution costs, in particular, as a potential source of LOOP deviations in the retail prices of goods. The function of the distribution sector in an economic system is to transfer goods and services from producers to consumers in an efficient manner. Costsofdistributionincludetransportationandstorage,wholesaletrade,andretailtrade. Burstein et al. (2003) show that distribution costs represent more than 40 percent of the retailpricefortheaverageconsumergoodintheU.S.,androughly60percentoftheretail price in Argentina. Goldberg and Campa (2006) find that that distribution margins vary widely across countries for a given good and also across goods within a country. The second question that I attempt to answer in chapter 3 is: To what extent can a version of the multi-country ricardian model, modified to include a distribution sector in whichdistributioncostsarecarefullycalibratedtodataonobserveddistributionmargins, quantitatively account for the observed dispersion in LOOP deviations? In order to address these two question, I develop a general equilibrium version of the Eaton and Kortum (2002) trade model. The baseline variant of the model is attribut- able to Alvarez and Lucas (2007), except that I allow trade costs to be asymmetric and heterogeneousacrosstradingpartners. Inthemodel,countriestradegoodswhicharepro- duced using labor, capital and an intermediate input. Labor and capital are non-traded factor inputs, whereas the intermediate input is produced by combining the individual 4 tradedgoods. Toquantifytheroleoflocaldistributioncosts, Iextendthisbaselinemodel by embedding a distribution sector, and explicitly modeling retail goods as products of the individual traded goods, and non-traded distribution services. In this version of the model, any individual traded good, whether imported or produced domestically, must be combined with local distribution services for it to be delivered to the consumer. The number of units of distribution services that are needed to deliver 1 unit of a retail good to the consumer varies across goods. Furthermore, some countries are more efficient in delivering goods to the consumers than other countries. Thus the extended model allows for both good-specific, and country-specific, heterogeneity in distribution costs. I follow the gravity literature to proxy trade costs by distance, language, border and membership of free trade regions. Trade costs are obtained by estimating a structural gravity equation implied by the model, using data on proxies and trade volume for each bilateraltradingpair. Thegravityequationimpliesthattheshareofcountryj incountry i’s total expenditure on traded goods relative to the share of countryi in its own expen- diture on traded goods is a function of ‘country-specific’ differences in costs of producing tradable goods and cost of transporting goods from country j to country i. In order to measure the potential heterogeneity in distribution costs across goods and countries, I construct data on distribution margins for 29 categories of goods across 19 OECD countries. I use the average distribution margin of each country, computed from thedata,tocalibratethecountry-specificdifferencesinefficiencyofdeliveringgoodstothe consumers. The heterogeneity across goods, in a country, in units of distribution services used is controlled by matching the cross-country average of dispersion in distribution margins across goods computed from the data. I find that the standard multi-country ricardian trade model with perfectly compet- itive markets, featuring heterogeneous and asymmetric trade costs, does a good job of matching the average good-by-good price dispersion, but it fails to generate the variation in good-by-good price dispersion observed in the data. It can explain 85 percent of aver- age price dispersion, but only 21 percent of the variation in price dispersion. Accounting for differences in costs of distribution across goods and across countries significantly im- proves the model’s performance in matching the data. The model does a very good job of matching the average price dispersion - explaining 96.5 percent of the average disper- sion. It can also explain 32 percent of the variation in price dispersion. Heterogeneity in distribution costs plays an important role in matching the variation in good-by-good price dispersion. In the case of trade costs, the level of trade costs is more important than the asymmetries in trade costs. As the level of trade costs declines, the distribution 5 of good-by-good price dispersion shifts to the left, implying a decline in average good- by-good price dispersion, without any significant change in the variation of good-by-good price dispersion. The degree of market segmentation implied by international trade barriers and dif- ferences in the costs of distribution can explain the dispersion in LOOP deviation for an “average” retail product very well. However, these two sources of market segmentation can explain only one-third of the variation in price dispersion across a broad spectrum of retail products. Heterogeneity in distribution costs is important in explaining the variation in good-by-good price dispersion, but it is not enough. Inchapter4ofthedissertation, Ifocusonmarkupsovermarginalcostsinordertoac- countforthe‘two-thirdunexplained’variationinpricedispersion. Irelaxtheassumption of perfectly competitive markets in the production of traded goods. This is motivated by recent developments in trade theory, which have focused on the firm or the plant as the unit of analysis. This ‘new’ approach is the result of emerging empirical evidence that shows that the differences among firms are crucial to understanding international trade. Recentwork of Bernardand Jensen(1995) andBernardand Jensen(1999)(for the U.S.), Clerides et al. (1998) (for Colombia, Mexico and Morocco) and Aw et al. (2000) (for Taiwan and South Korea) highlights the following stylized facts about firm level differ- ences and performance of exporters relative to non-exporters: (i) significant productivity dispersion among firms, (ii) only a small fraction of firms export, (iii) higher productivity among exporters, (iv) employment, shipment, wages and capital intensity are all higher for exporters, and (v) exports are a small fraction of total shipments among export- ing plants. These facts hold up even for firms within specific industries. Furthermore, Bernard and Jensen (1999) and Clerides et al. (1998) find that it is the more productive firms that become exporters and not the other way around. Thetheoreticalworkwhichtriestoexplainthesestylizedfactscanbedividedintotwo broad strands. The first strand extends the two country ricardian model, with iceberg costs, of Dornbusch et al. (1977) by allowing for more than two countries and incor- porating imperfect competition. Bernard et al. (2003) take this route. In their model specialization emerges endogenously through the exploitation of comparative advantage, and a firm (or a plant) exports only when its cost advantage over it competitors around the world is high enough to overcome the trade costs. The other strand of literature empahsizes fixed costs of exporting, for example, Roberts and Tybout (1997) and Melitz (2003). Theideaisthatonlythemostproductivefirmscanpaythefixedcostsofaccessing foreign markets. 6 Given this strong empirical evidence, in chapter 4, I follow the first strand of theoret- ical literature to relax the assumption of perfectly competitive market structure in the production of traded goods; I allow the producers of traded goods to compete in prices, ala bertrand. The literature that emphasizes fixed costs suffers from the problem that a producer would either export nothing or else export to different countries in proportion to the market sizes. This result is not in line with the fact that exports form a very small fraction of revenues of exporters. Each country has many potential producers of each good; each producer characterized by a level of efficiency with which it can produce a unit of the good. Given the trade costs, the lowest-cost (most efficienct) supplier of a good captures the market. However, due to competition in prices the most efficient pro- ducer charges a price higher than its marginal cost but less than equal to the marginal cost of the second-lowest cost supplier of the good. Thus, competition in prices results in good-specific markups. The objective of this chapter is to examine the implications of the change in the market structure, from perfect competition to bertrand competition, on good-by-good price dispersion. Can the variable markups help to explain a greater proportion of the variation in good-by-good price dispersion? I find that the ricardian model with bertrand competition, but no distribution costs, overpredictstheaveragegood-by-goodpricedispersionby76percent. Thus, ascompared to the two variants of the ricardian trade model with perfectly competitive markets the model with bertrand competition performs worse. Incorporating distribution costs into the model with bertrand competition leads to a marginal decline in the extent of overpre- diction of average price dispersion. However, with respect the variation in good-by-good price dispersion, incorporating competition in prices improves model performance signif- icantly. The variant without distribution costs can account for 42 percent the variation in price dispersion, which is a 100 percent improvement over the model with perfect competition and no distribution costs and a 32 percent improvement over the model with perfectcompetitionanddistributioncosts. Inthepresenceofdistributioncoststhemodel with bertrand competition can account for 43.5 percent of variation. As compared to the two variants of the ricardian trade model with perfect competition, this model results in a 107 percent improvement over the variant without distribution costs and 36 percent improvement over the variant with distribution costs. Heterogeneity in distribution costs is important in matching the data. But, it is more important in explaining the variation in good-by-good price dispersion than the average price dispersion. On the other hand, trade costs play a more important role in driving average good-by-good price dispersion. 7 Both, heterogeneity in trade costs and level of trade costs, play an important role in de- terminingtheaveragepricedispersion,buttheleveloftradecostsismoreimportantthan heterogeneity in trade costs. The importance of heterogeneity in trade costs in driving average price dispersion stands in sharp contrast with the importance of heterogeneity in trade costs in the model with perfect competition. In case of the ricardian model with perfect competition it is the level of trade costs, and not the heterogeneity in trade costs, that is important in determining the average good-by-good price dispersion. At the end of the day, even with variable markups, about 56 percent of the variation in good-by-good price dispersion remains unexplained. The dissertation is organized in the following manner: the next section discusses the data on distribution costs. This is followed by chapter 3, which starts with the ricardian trade model with perfectly competitive markets and its calibration, which is followed by the discussion of the results. This leads to the section where I modify the ricardian trade model to incorporate a distribution sector and discuss the calibration of this augmented model, which is followed by the discussion of results for the augmented model. The last section concludes chapter 3. This is followed by chapter 4, which starts by discussing the ricardian trade model with bertrand competition. This is followed by the calibration of the model and the results of the model. Then, I extend this model by incorporating the distribution sector, and move on to discuss the calibration and results of the extended model. The last section concludes chapter 4. 8 Chapter 2 Data on Distribution Sector In this section, I explore the potential for distribution costs to account for the vari- ation in good-by-good price dispersion. In terms of national accounts, the distribution sectorincludesretailtrade, wholesaletradeandtransport, storageandwarehousing. The distribution sector is large, both in terms of employment and value added. According to Burstein et al. (2003), retail and wholesale trade account for 23.3 percent of total employment and 17.1 percent of total value added in the U.S. economy in 1997. The cor- responding numbers for Argentina stand at 21.4 percent and 16.1 percent. Interestingly, the employment share of wholesale and retail trade is larger than that of manufacturing (15.2 percent for the U.S. and 15.1 percent for Argentina) and the share in value added of wholesale and retail trade is almost as large as that of manufacturing (18.8 percent for the U.S. and 18.2 percent for Argentina). Burstein et al. (2003) show that distribution costs represent more than 40 percent of the retail price for the average consumer good in the U.S., and roughly 60 percent of the retail price in Argentina. Goldberg and Campa (2006) present evidence on distribution margins (distribution costs as a ratio of retail value of products) in 29 product categories across 21 OECD countries. Distribution margins vary widely across product categories within the same country and also across countries within the same product category. In light of these facts, recent literature has focused on the role of distribution costs in understanding the behavior of prices. Burstein et al. (2003) study the role of distribution services in understanding the movements of real exchange rate (RER) during exchange rate based stabilizations in Argentina’s 1991 convertibility plan. Corsetti and Dedola (2005) and Goldberg and Campa (2006) study incomplete exchange rate pass-through in the presence of a distribution sector. However, these studies have focused on the time series properties of international relative prices. Instead, I examine the role of differences in costs of distribution across 9 goods and across countries in explaining cross-country dispersion in prices of individual goods. How large are distribution costs as a ratio of the retail price of goods? Does this ratio vary substantially across goods and across countries? To answer these questions, I compute this ratio for 29 product categories across 19 of the 22 OECD countries I include in my analysis. The countries are listed in Table 2.1. The data come from input- output tables, specifically the use tables, which provide information on the value of the supply of goods in “basic price” and the value of the same goods in “purchaser price”. The difference between basic prices and purchaser prices is that purchaser prices include distribution margins and value added taxes (or subsidies), whereas basic prices do not. The use tables also report net taxes for each good. The distribution margin for a good is calculated as: Distribution Margin= Supply in Purchaser Prices−Supply in Basic Prices Supply in Purchaser Prices Careistakentoexcludenettaxesfromthepurchaserpricevalueofeachgood. ForJapan and the United States, data on net taxes are not available. Therefore, for these countries purchaser price value could not be adjusted for net taxes. For the EU countries, goods areclassifiedaccordingtotheClassificationofProductsbyActivities(CPA)classification of goods. Australia, New Zealand, the United States and Japan do not use the CPA classification of goods. Since the EU countries form the majority of countries in my sample the commodity classifications of the non-EU countries were mapped into the CPA classification. Only those product categories were chosen for which the distribution margins were non-negative. The data show that distribution margins are zero or negative for almost all services across countries. In addition, the CPA product category ‘Uranium andthoriumores’wasexcludedbecauseofmissingdata. Formostcountriesinthesample the data are available for the year 1995. For Australia the data are available for 2001-02, for Norway they are available for 2001, for Ireland they are available for 1998 and for the United States they are available for 1997. Data are not available for Canada, Mexico and Switzerland. Table 2.1 provides information on distribution margins by country across all goods. It gives three statistics on distribution margins across goods - the average, the maximum and the minimum value. The second column shows that Japan has the highest average distribution margin whereas Ireland has the lowest. The last two columns show that within each country there is a large variation in distribution margins across goods. 10 Table 2.1: Distribution Margins by Countries Country Average Maximum Minimum Australia 0.2329 0.5698 0.0794 Austria 0.1833 0.4408 0.0000 Belgium 0.1540 0.3800 0.0569 Denmark 0.1952 0.3993 0.0000 Finland 0.1683 0.6302 0.0233 France 0.1567 0.3832 0.0107 Germany 0.2012 0.4658 0.0677 Greece 0.2063 0.4734 0.0001 Ireland 0.1022 0.2728 0.0000 Italy 0.2041 0.4768 0.0040 Japan 0.3361 0.9275 0.1015 Netherlands 0.1752 0.4382 0.0004 New Zealand 0.1338 0.2825 0.0000 Norway 0.2352 0.7141 0.0000 Portugal 0.1489 0.3974 0.0000 Spain 0.1644 0.4301 0.0003 Sweden 0.1612 0.4851 0.0000 United Kingdom 0.1810 0.4921 0.0010 United States 0.2753 0.7215 0.0537 Table2.2liststheaverage,themaximumandtheminimumdistributionmarginacross countries for each CPA product category. ‘Wearing apparel; furs’ has the highest average distribution margin across countries. On the other hand ‘Other transport equipment’ has the lowest average margin. Looking at the last two columns, it is clear that even for the same good there is significant variation in distribution margins across countries. It is clear from the data that distribution margins vary widely across goods and across countries. Using this data, I incorporate heterogeneity in distribution margins in the models to follow, and evaluate its importance in driving the dispersion in LOOP deviations. Table 2.2: Distribution Margins by Goods CPA Product Average Maximum Minimum Products of agriculture, hunting and related services 0.1662 0.3015 0.0141 Products of forestry, logging and related services 0.1449 0.4301 0.0000 Fish and other fishing products; services incidental of fishing 0.2424 0.4768 0.0000 Coal and lignite; peat 0.1530 0.6833 0.0000 Crude petroleum and natural gas; services incidental to oil 0.1022 0.8925 0.0000 11 Table 2.2: (continued) CPA Product Average Maximum Minimum and gas extraction excluding surveying Metal ores 0.1262 0.9275 0.0000 Other mining and quarrying products 0.2015 0.4109 0.0000 Food products and beverages 0.2187 0.3901 0.0954 Tobacco products 0.3650 0.7141 0.1102 Textiles 0.2250 0.4327 0.0978 Wearing apparel; furs 0.3979 0.6000 0.2112 Leather and leather products 0.3582 0.7215 0.1237 Wood and products of wood and cork (except furniture); 0.1452 0.3085 0.0306 articles of straw and plaiting materials Pulp, paper and paper products 0.1383 0.2282 0.0472 Printed matter and recorded media 0.1657 0.2752 0.0570 Coke, refined petroleum products and nuclear fuels 0.2118 0.4323 0.0000 Chemicals, chemical products and man-made fibres 0.1827 0.2767 0.0348 Rubber and plastic products 0.1468 0.2647 0.0523 Other non-metallic mineral products 0.1730 0.2906 0.0574 Basic metals 0.1013 0.1633 0.0371 Fabricated metal products, except machinery and equipment 0.1400 0.2728 0.0718 Machinery and equipment n.e.c. 0.1499 0.2632 0.0410 Office machinery and computers 0.2073 0.3993 0.0448 Electrical machinery and apparatus n.e.c. 0.1537 0.3557 0.0581 Radio, television and communication equipment and apparatus 0.1513 0.2384 0.0729 Medical, precision and optical instruments, watches and clocks 0.2099 0.3975 0.0667 Motor vehicles, trailers and semi-trailers 0.1815 0.3376 0.0744 Other transport equipment 0.0819 0.2825 0.0213 Furniture; other manufactured goods n.e.c. 0.2904 0.4821 0.1300 12 Chapter 3 A Ricardian Model with International Trade Costs and Local Distribution Costs 3.1 Ricardian Trade Model I start by discussing the the general equilibrium version of the Eaton and Kortum model, due to Alvarez and Lucas (2007). Unlike Alvarez and Lucas (2007), trade costs in the model are country-pair specific and asymmetric, rather than homogeneous. In addition, the model in this chapter, incorporates capital explicitly as an input, which was implicitly present in Alvarez and Lucas (2007) 1 , largely because the calibration strategy I follow differs from that of Alvarez and Lucas (2007), as I will discuss below. Consider a world with N countries. Country i (i = 1,...,N) has L i consumers and each consumer has 1 unit of labor, which is supplied inelastically (all variables are expressed in per capita terms) and k i units of capital. 3.1.1 Production and Consumption Each country produces a continuum of base goods, indexed on the unit interval, which are traded. Base goodx,x∈[0,1], in countryi is produced using a Cobb-Douglas technology. m i (x)=z i (x) −θ k i (x) α l i (x) 1−α β c i (x) 1−β . wherek i (x),l i (x)andc i (x)aretheamountsofcapital, laborandintermediatecomposite, respectively, used to produce base good x in country i, and z i (x) is the inverse of the efficiencyofcountryiinproducinggoodx. Inotherwordsz i (x)isanidiosyncratic“cost”. I assume that idiosyncratic cost of producing goodx in countryi is a random draw from 1 AlthoughlaboristheonlyinputinAlvarezandLucas(2007),forcalibratingthemodelitisinterpreted as ‘equipped labor’, i.e. labor equipped with capital. 13 a country-specific density f i = exp(λ i ). The random cost draws are independent across goods, and the distributions are independent across countries. The random draws are amplified in percentage terms by the parameterθ. The parameterλ i governs the average efficiency level of country i. A country with a relatively large λ i is, on average, more efficient. Alargerθrepresentsalargervarianceinproductivitiesof(producing)individual goods. Therefore,λ i determines countryi’s absolute advantage in producing any goodx whereas θ controls the degree of comparative advantage. Countries trade base goods. In each country there is a representative importing firm that buys each base goodx, at the lowest price. Letm i (x) be the amount of base goodx that the importing firm in countryi buys. Base goods are then combined in countryi to produce an intermediate composite, c i . This composite is a Spence-Dixit-Stiglitz (SDS) aggregator, with an elasticity of substitution, η, between goods: c i = Z ∞ 0 m i (z) 1− 1 η f(z)dz η η−1 . Here each good, x, is identified by its cost draw, z, and f(z) is the joint distribution of cost draws ((z 1 (x),...,z N (x))), over countries. Consumers in every country consume a non-traded final good, y i . The final good is produced using Cobb-Douglas technology with labor, l yi , capital, k yi , and intermediate composite, c yi , as the inputs. y i = h k α yi l 1−α yi i ρ c 1−ρ yi . 3.1.2 Market Clearing The intermediate composite is used as an input in the production of base goods and the final good, so that the market clearing for intermediate composite yields Z 1 0 c i (x)dx | {z } c mi +c yi ≤c i , where c mi is the number of units of the intermediate composite used in the production of all base goods. The labor market, as well as the market for services of capital, must clear; Z 1 0 l i (x)dx | {z } l mi +l yi ≤1 , 14 Z 1 0 k i (x)dx | {z } k mi +k yi ≤k i , where l mi is the share of base goods sector in the labor force, k mi is the share of base goods sector in the capital stock, and k i is the capital-labor ratio of country i. 3.1.3 Retail Price of Individual Goods The object of interest in this baseline model is the price of an individual base good. Profit maximization in the two sectors - base goods and final good - implies that that the return to capital in country i is r i = (α/(1−α))w i k −1 i , where w i is the wage. Then, the domestic cost of producing base good x in country i is Bz i (x) θ w β i p 1−β ci k −αβ i , where B =β −β (1−β) (β−1) α −αβ (1−α) β(α−1) α 1−α αβ andp ci isthepriceofintermediatecompositeincountryi. Priceofintermediatecomposite in country i is given by p ci = Z ∞ 0 p mi (z) 1−η f(z)dz 1 1−η , where p mi (z) is the price, in country i, of the base good which is characterized by pro- ductivity level z. However, to deliver 1 unit of a base good from countryj to countryi, countryj must produce τ ij units of the good. Due to geographic and other barriers to trade, τ ij >1 for i 6= j. This is the standard “iceberg assumption” a la Samuelson, and τ ii = 1 for all i. I impose the triangle inequality on geographic barriers - τ ij ≤τ in τ nj , ∀ n, i.e., an upper bound on the cost of moving goods from j to i is the cost of moving them via a third country n. The importing firm in each country buys each good, x, from the lowest cost supplier of that good. Therefore, the price of good x in country i is given by: p mi (x)=Bmin j h w β j p 1−β cj k −αβ j τ ij z j (x) θ i . (3.1) Thus, given the wage vectorw, the vector of prices of the intermediate compositep c , the vectorofcapital-laborratiosk, tradecostmatrixτ andvectorofproductivityparameters 15 λ, the producer prices of individual base goods can be simulated. In the absence of distribution costs these are the retail prices of the goods. 3.1.4 Calibration Methodology This section discusses the methodology adopted to solve for the vector of wages w and the vector of prices of the intermediate composite p c and the calibration of vector of productivity parametersλ, given the matrix of estimated trade costsτ and the vector of labor endowments L and the vector of capital endowment k. I start by discussing the estimation of trade costs. Let X i be the per capita expenditure of country i on tradable goods. Define D ij as the share of country i’s per capita spending on tradables that is spent on goods from countryj. For countryj to supply goodx to countryi,j must be the lowest price seller of good x to i. Then, D ij =(AB) −1/θ w β j p 1−β cj k −αβ j τ ij p ci ! −1/θ λ j , (3.2) and P n j=1 D ij = 1. The steps taken to arrive at this expression for D ij are explained in Appendix A. I follow Eaton and Kortum (2002) in estimating the trade costs,τ ij . Eq. (3.2) implies that the share of country j in country i’s total expenditure on tradables, normalized by country i’s share in its own total expenditure on tradables, is given by: D ij D ii = w β j p 1−β cj k −αβ j τ ij −1/θ λ j w β i p 1−β ci k −αβ i −1/θ λ i . Let Ξ i = w β i p 1−β ci k −αβ i −1/θ λ i , and S i =ln(Ξ i ). ⇒ln D ij D ii =S j −S i − 1 θ lnτ ij . (3.3) The left-hand side of this equation is calculated from data on bilateral trade and gross output. The methodology used to calculate the left-hand side is explained in Appendix B. Trade costs are obtained by estimating Eq. (3.3). Since τ ij is not observable, I follow 16 the gravity equation literature to proxy trade barriers by distance, language, border and membership of free trade regions. Specifically, lnτ ij =dist T +brdr+lang+tblk R +dest i +ǫ ij , (3.4) where dist T (T = 1,...,6) is the effect of distance between i and j lying in the Tth interval, brdr is the effect of i and j sharing a border, lang is the effect of i and j sharing a language, tblk R (M = 1,2) is the effect of i and j belonging to trading area R, and dest i (i = 1,...,N) is a destination effect. The error term ǫ ij captures trade barriers due to all other factors, and is orthogonal to the regressors. The six distance intervals (in miles) are: [0,375); [375,750); [750,1500); [1500,3000); [3000,6000) and [6000,maximum]. The two trading areas are the European Union (EU) and the North- American Free Trade Agreement (NAFTA) area. S i is captured as the coefficient on source-country dummies. Eq. (3.1) implies that the price of the intermediate composite is given by p ci =AB   N X j=1 w β j p 1−β cj k −αβ j τ ij −1/θ λ j   −θ , (3.5) where A = R ∞ 0 h θ(1−η) e −h dh 1 1−η . The integral in brackets is the Gamma function Γ(ξ) evaluated at ξ = 1+θ(1−η). Convergence of this integral requires that 1+θ(1−η)> 0, which I assume holds throughout this paper. The derivation of p ci is explained in Appendix A. Thevectorofwagesisdeterminedbyimposingbalancedtrade-therevenueofcountry i must equal its expenditure. N X j=1 L j X j D ji =L i X i . In the base goods sector L i w i l mi = β(1−α) P N j=1 L j X j D ji = β(1−α)L i X i . Since l mi =1−l yi =1−ρ, ∀ i, the balanced trade condition can be written as N X j=1 L j w j D ji =L i w i . (3.6) 17 I take a stand on the endowment of labor and capital of each country by taking them from the data. Then, given the estimated trade cost matrix τ, Eq. (3.5) and Eq. (3.6) are used to solve for the equilibrium w and p c for a given initial guess for λ. The guess for λ is updated by using Eq. (3.2), for j =i. λ i =(AB) 1/θ w i p ci β/θ k −αβ/θ i D ii . (3.7) Therefore, Eq. (3.5), Eq. (3.6) and Eq. (3.7) form a system of 3N equations in 3N unknowns. In solving this system of equations, bilateral expenditure shares D ij are replaced by the bilateral expenditure shares computed from the data, b D ij . This implies that the vector of productivity parameters, λ, is a function of bilateral trade shares observed in the data, adjusted for differences in endowments of labor and capital. A similar calibration strategy is adopted by Waugh (2007). Alvarez and Lucas (2007) calibrateλbymatchingtherelativepriceofnon-tradables. Iadoptadifferentcalibration strategy for two reasons. First, since I am interested in characterizing the behavior of prices implied by the model, I do not want to use information on prices to calibrate λ. Second, and more importantly, one of the objectives of the paper is to evaluate whether the degree of market segmentation implied by flows of goods across borders can explain the deviations from the LOOP in prices of individual goods. By computing λ and τ as functions of bilateral trade shares, I impose the discipline on the model needed to answer this question. 3.1.5 Variance of LOOP Deviations Given the endowment of capital, k i , the equilibrium wage, w i , the equilibrium price of the intermediate composite, p ci , estimated trade costs, τ ij , and the calibrated productivityparameter,λ i ,Isimulatethepricesofbasegoods. UsingEq.(3.1),theprices aresimulated100timesfor3000goods. Foreachgood,x, acostvector(z 1 (x),...,z N (x)) is drawn, where N is the number of countries, from the joint density function f(z) = Q N i=1 λ i exp{− P N i=1 λ i z i }. ThedeviationfromtheLOOPforagoodincountryiiscomputedasthelogdeviation of the price of the good in country i from the geometric-average (across countries) price of the good. Q mi (x)=logp mi (x)− P N j=1 logp mj (x) N , x={1,...,3000} . (3.8) 18 The variance of LOOP deviations is measured as the cross-country dispersion in LOOP deviations in Crucini et al. (2005). This is denoted by Var(Q mi (x)|x). Good-by-good price dispersion is the square root of the variance of LOOP deviations. 3.1.6 Parameterization There are 22 OECD countries in the sample 2 . The set of countries I examine is larger than that examined by Crucini et al. (2005). In addition to the 13 EU countries included in Crucini et al. (2005), I include 9 other countries. Using only the 13 EU countries would not take into account all major trading partners of the countries. This will result in underestimation of total trade volume, which will affect the estimates of trade costs. Therefore, I choose a broader set of countries to account for as large a share of total trade as possible, but at the same time, I ensure that the chosen countries have similar levels of per capita GDP as the 13 EU countries in Crucini et al. (2005). The model is calibrated to the year 1996. The choice of the year is driven by the availability of data on capital-labor ratios. Although the data used by Crucini et al. (2005) are for 1975,1980,1985and1990,theaveragegood-by-goodpricedispersionandthevariationin good-by-goodpricedispersion(asmeasuredbyIQR)areverystableovertime. Therefore, the averages over the four years, of average good-by-good price dispersion and variation in good-by-good price dispersion can be compared with results of the model. Agriculture, hunting, forestry and fishing, mining and quarying, and manufacturing are treated as the traded goods sector. All other sectors form the final good sector. Following Alvarez and Lucas (2007), θ, which controls the variability of the national idiosyncratic component of productivity, is 0.15 andη, which is the substitution parame- ter, is 2. The choice of η is important only for the convergence of the gamma function and it does not have any implications for the results of the model. Theparameterβ iscalibratedastheshareofvalueaddedingrossoutputofthetraded goods sector. The data used to compute this ratio come from the OECD Structural Analysis (STAN) database. Details of the data and the methodology are provided in Appendix B. For the sample of countries β is 0.36. α is the share of capital in GDP. Gollin (2002) finds that the share of labor in value added for a wide cross-section of countries is around 2/3, which implies thatα is 0.33. ρ is the share of value added in the grossoutputofthefinalgoodsector. Sincethevalueoftheoutputofthefinalgoodsector 2 Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Mexico, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, United King- dom, United States. 19 is the GDP of a country,ρ is calibrated as one minus the share of traded goods sector in GDP. Using data from the OECD STAN database I find that the share of traded goods sector in GDP is 0.25 which implies thatρ is 0.75. β andρ are computed as averages for the period 1995-1997, in order to remove any potential idiosyncrasies in value added and gross output in the year 1996. The labor force vector L = (L 1 ,...,L N ) and the vector of capital-labor ratios k = (k 1 ,...,k N )aretakenfromthedatainCaselli(2005). AppendixBexplainstheprocedure used to calculate these vectors. Table 3.1 reports estimated coefficients for the geographic barriers, the corresponding standard error and the implied effect on cost relative to home sales. An increase in distance has a negative effect on trade. A country in the closest distance category faces 76 percent higher costs relative to home sales whereas a country in the farthest distance category faces a 171 percent higher trade cost. On the other hand, sharing a border with a trade partner reduces trade costs by 9 percent, while sharing a language reduces it by 4 percent. EU and NAFTA membership do not play an important role. The destination effectshowsthatitcosts36percentlesstoexporttotheUnitedStatesthantotheaverage country and it costs 55 percent more to export to Greece than to the average country. The costs imposed by trade barriers are comparable to the costs obtained by Eaton and Kortum (2002) both, quantitatively and qualitatively. Since I include all traded goods - agricultural goods, fuels and mining goods and manufacturing goods - in computing bilateral trade shares, whereas Eaton and Kortum (2002) consider only manufacturing goods, I get slightly higher estimates of costs imposed by trade barriers. Table 3.1: Geographic Barriers Implied % Variable Denoted by Coefficient Std. Error Effect on Cost Distance [0,375) - 1 θ dist1 -3.76 0.16 75.85 Distance [375,750) - 1 θ dist2 -3.91 0.13 79.80 Distance [750,1500) - 1 θ dist3 -4.25 0.12 89.09 Distance [1500,3000) - 1 θ dist4 -4.47 0.17 95.43 Distance [3000,6000) - 1 θ dist5 -6.26 0.08 155.67 Distance [6000,maximum] - 1 θ dist6 -6.65 0.09 171.15 Shared Border - 1 θ brdr 0.65 0.13 -9.34 Shared Language - 1 θ lang 0.30 0.10 -4.41 EU - 1 θ tblk1 0.19 0.14 -2.88 NAFTA - 1 θ tblk2 -0.39 0.35 6.01 Destination Country 20 Table 3.1: (continued) Implied % Variable Denoted by Coefficient Std. Error Effect on Cost Australia - 1 θ dest1 1.03 0.24 -14.38 Austria - 1 θ dest2 -1.45 0.18 24.31 Belgium - 1 θ dest3 0.74 0.18 -10.55 Canada - 1 θ dest4 1.42 0.24 -19.13 Denmark - 1 θ dest5 -0.69 0.18 10.90 Finland - 1 θ dest6 -1.21 0.18 19.86 France - 1 θ dest7 0.08 0.18 -1.12 Germany - 1 θ dest8 1.07 0.18 -14.85 Greece - 1 θ dest9 -2.92 0.18 55.07 Ireland - 1 θ dest10 -0.76 0.17 12.01 Italy - 1 θ dest11 0.06 0.18 -0.85 Japan - 1 θ dest12 2.20 0.21 -28.11 Mexico - 1 θ dest13 -0.63 0.22 9.89 Netherlands - 1 θ dest14 0.95 0.18 -13.29 New Zealand - 1 θ dest15 0.03 0.24 -0.43 Norway - 1 θ dest16 -0.62 0.23 9.82 Portugal - 1 θ dest17 -2.26 0.18 40.34 Spain - 1 θ dest18 -0.64 0.17 10.01 Sweden - 1 θ dest19 0.01 0.17 -0.16 Switzerland - 1 θ dest20 -0.60 0.22 9.44 United Kingdom - 1 θ dest21 1.10 0.18 -15.25 United States - 1 θ dest22 3.09 0.45 -37.06 Note: Given an estimated coefficient, b, the implied percentage effect on cost is estimated as 100(e −θb −1). 3.2 Results: Ricardian Model Table 3.2 compares the model generated good-by-good price dispersion with that observed in Crucini et al. (2005). Remarkably, this multi-country ricardian model can account for 85 percent of the average good-by-good price dispersion observed in the data; the model generates average price dispersion of 23.7 percent while it is 28.8 percent in the data. How does the model fair with respect to the variation in good-by-good price dispersion? In terms of the IQR, the model can generate 21 percent of the variation observed in the data. The model does a little better in terms of P90 - P10 as it can generate about 24 percent of the variation observed in the data, which suggests that the distribution of good-by-good price dispersion generated by the model exhibits some 21 skewness. This becomes clear from the empirical distribution of the good-by-good price dispersion obtained from the model, shown in Figure 3.1. The distribution exhibits some positive skewness. Table 3.2: Good-by-Good Price Dispersion: Model Versus Data Model Data Model as ratio of Data Avg. 0.2365 0.2778 0.8513 IQR 0.0341 0.1595 0.2138 P90 - P10 0.0708 0.3008 0.2354 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Price Dispersion Probability Data Pooled 80 − 90 Ricardian Model Figure 3.1: Distribution of Var(Q mi (x)|x) 1/2 : Ricardian Model So,thestandardricardianmodeldoeswellinmatchingtheaveragegood-by-goodprice dispersion, but it is not able to generate the variation in good-by-good price dispersion observed in the data. This suggests that, for the average retail good, the degree of goods’ market segmentation implied by trade barriers is fairly consistent with the degree of segmentation implied by dispersion of LOOP deviations. However, the trade barriers implied by observed bilateral trade volumes are not large enough to account for the average price dispersion fully. More importantly, despite allowing for heterogeneity and asymmetry in international trade costs, a ricardian model with trade costs does poorly in matching the variation in good-by-good price dispersion observed in the data. 22 3.3 RicardianTradeModelwithALocalDistributionSector In this section I extend the benchmark multi-country ricardian trade model to account for local costs of distribution. Now, base goods, besides being used to produce theintermediatecomposite, arealsodeliveredtotheconsumersasretailgoods. However, every base good, x, whether imported or produced domestically, requires some units of distribution services to be delivered to the consumers. Thus, a retail good is produced by combining distribution services and a base good. Distribution services and retail goods are not traded. Individual retail goods are combined to produce a composite retail good. Each country also produces a homogeneous non-traded good. The final good that consumers consume in each country is a composite of the homogeneous non-traded good and the composite retail good. 3.3.1 Production and Consumption The production technology of base goods is unchanged. However, now, the amount of base good x bought by the importing firm, m i (x), is divided into two parts. m i (x)=m ci (x)+m qi (x) . m ci (x)isusedtoproducetheintermediatecompositeincountryiandm qi (x)isboughtby theretailerofgoodxincountryi. Theproductiontechnologyforintermediatecomposite good also remains unchanged. c i = Z ∞ 0 m ci (z) 1− 1 η f(z)dz η η−1 . The retailer of good x combines m qi (x) with distribution services to deliver the base good to the consumer in the form of a retail good. Retail good,x, is denoted bym qi (x). Distribution services, d i , are produced using Cobb-Douglas technology with labor, l di , capital, k di , and intermediate composite, c di , as the inputs. d i =[k α di l 1−α di ] δ c 1−δ di . To deliver 1 unit of base goodx to the consumer, φ i (x) units of distribution services are required, φ i (x)=ζ i u(x) ν , 23 where ζ i denotes the units of distribution services required to deliver any good to the consumer in country i, and reflects country i’s efficiency in distribution of goods, and u is a random draw from a common density function g = exp(1). The draws are assumed to be independent across goods. For a given base good, x, u and z (random cost draw for base good x) are assumed to be independent. Bringing one unit of a base good to the consumer requires a fixed proportion of dis- tribution services. This assumption is made in the spirit that production and retailing are complements, and consumers consume them in fixed proportions. Erceg and Levin (1996),Bursteinetal.(2003)andCorsettiandDedola(2005)alsoadoptthesameproduc- tion structure for retail goods. However, I allow the units of distribution services used to deliveraunitofagoodtovaryacrossgoods,aswellascountries,whereasthesestudiesdo not. Furthermore, these studies, for simplicity, do not differentiate between nontradable consumption goods, which directly enter the agents’ utility, and nontraded distribution services,whicharejointlyconsumedwithtradedgoods. However, Imakethisdistinction. This is necessary because the parametersν andζ i , which govern heterogeneity in the use of distribution services, are calibrated using the data on distribution margins and not from the data on all services. It also ensures that the distribution sector does not get more weight in GDP in the model than that observed in the data, and thereby helps to map the model clearly into the data. Therefore, in addition to producing distribution serviceseach country also produces a homogeneous non-traded good. Production of the non-traded good also combines labor, l si , capital, k si , and the intermediate composite, c si , using a Cobb-Douglas technology. s i =[k α si l 1−α si ] γ c 1−γ si . The consumer in country i therefore consumes a final good y, y i =q μ i s 1−μ i , where q i is a composite retail good. q i = Z 1 0 m qi (x) 1− 1 η dx η η−1 . Notice that now the final good consumed is a composite of a homogeneous non-traded good, and a composite retail good. 24 3.3.2 Market Clearing The intermediate composite is used as an input in the production of base goods, distribution services and the homogeneous non-traded good. Therefore, market clearing requires that Z 1 0 c i (x)dx | {z } c mi +c di +c si ≤c i , where c mi is the number of units of the intermediate composite used in the production of all base goods. The total units of distribution services required to deliver base goods to the consumer cannot exceed the output of distribution services. Z 1 0 φ i (x)m qi (x)dx≤d i . The labor market as well as the capital market must clear; Z 1 0 l i (x)dx | {z } l mi +l di +l si ≤1 , Z 1 0 k i (x)dx | {z } k mi +k di +k si ≤k i , where l mi is the share of base goods sector in the labor force, k mi is the share of base goods sector in the capital stock, and k i is the capital-labor ratio of country i. 3.3.3 Retail Prices The price at which the importing firm buys good x, p mi (x), remains unchanged and is given by Eq. (3.1). However, now I am going to refer to this as the producer price of goodx. Since delivering 1 unit of base goodx to the consumer requiresφ i (x) units of distribution services, the retail price of base good x is the sum of the producer price of good x and the value of distribution services used to deliver 1 unit of the good. p mi (x)=p mi (x)+φ i (x)p di , (3.9) 25 where the price of distribution services, p di , is given by p di =Cw δ i p 1−δ ci k −αδ i , and (3.10) C =δ −δ (1−δ) (δ−1) α −αδ (1−α) δ(α−1) (α/(1−α)) αδ . Eq.(3.9)showsthattheretailpriceofgoodxisgoingtodifferacrosscountriesfortwo reasons: (i) the producer price can be different across countries because of the presence of trade costs, and (ii) the costs of distribution can be different across countries because of differences in the price of distribution services, and differences in the number of units of distribution services used. Since p mi (x) is unchanged, it implies that the price of intermediate composite is also unchanged and is given by Eq. (3.5). 3.3.4 Calibration Methodology With the inclusion of a distribution sector, the share of the base goods sector in the labor force, l mi = 1−l di −l si = 1−μδϑ i −γ(1−μ). ϑ i is the ratio of value of distribution services and retail value of base goods in country i. It comes from the zero profit condition in the retail goods sector, which is given by: L i V mi =L i V mi +L i p di d i . V mi isthepercapitaretailvalueofallbasegoods,andV mi isthepercapitaproducerprice value of all base goods., where the second term on the right-hand side of the expression for V mi is total value of distribution services in country i. V mi = (1−ϑ i ) ϑ i p di d i . (3.11) Appendix A discusses the derivation of the sectoral shares of labor, capital and the intermediate composite. Now, the balanced trade condition is given by: N X j=1 L j w j l mj D ji =L i w i l mi . (3.12) 26 The solution methodology remains the same; I take the endowment of labor and capital from data, and estimate trade costs from the gravity equation, Eq. (3.3), solve forw i and p ci using Eq. (3.12) and Eq. (3.5), and calibrate λ i using Eq. (3.7). 3.3.5 VarianceofLOOPDeviationsandDistributionMarginsforIndividual Goods In order to compute the retail prices I simulate the producer prices and the units of distribution services used. The prices are simulated 100 times for 3000 goods. For each good, x, a cost vector (z 1 (x),...,z N (x)) is drawn, where N is the number of countries, from the joint density function f(z) = Q N i=1 λ i exp{− P N i=1 λ i z i }. Using Eq. (3.1), I calculateproducerpricesofgoods. Then,foreachcountryi,avector(u i (1),...,u i (3000)) is drawn from the density function g = e −u . Each element of the vector represents the units of distribution services used in delivering goodx to the consumer. The retail price of each good is calculated using Eq. (3.9). The deviation from the LOOP, (Q mi (x)|x), is computed using Eq. (3.8), but for retail prices. Good-by-good price dispersion is given by Var(Q mi (x)|x) 1/2 . The distribution margin for good x is calculated as: dm i (x)=1− p mi (x) p mi (x) . (3.13) 3.3.6 Parameterization The sample of countries and the year to which the model is calibrated are the same as those in the ricardian model. As in the ricardian model, agriculture, hunting, forestry and fishing, mining and quarying, and manufacturing are treated as the traded goods sector. Wholesale trade, retail trade and transport and storage form the distribution services sector. All other sectors form the non-traded good sector. The calibrated values of β, α, η and θ remain unchanged. δ and γ are calibrated as theshareofvalueaddedingrossoutputofdistributionservicessectorandthenon-traded good sector, respectively. μ is the share of the composite retail good in value of output of the final good sector. Since the value of output of the final good sector is the GDP of a country,μ is computed as one minus the share of the non-traded good sector (all services except retail trade, wholesale trade and transport and storage) in GDP. The data used to compute these parameters come from the OECD STAN Structural Analysis database. Details of the data and the methodology are provided in Appendix B. For the sample 27 of countries δ is 0.58, γ is 0.62 and μ is 0.42. Again, these are averages for the period 1995-1997. The vectors of labor force and capital-labor ratio, as well as estimates of trade costs remain unchanged. The parameterν, controls the variance in the number of units of distribution services required to deliver 1 unit of a base good to the consumers, irrespective of the country. Heterogeneity in distribution margins is used as a target in calibrating ν. First, using the model simulated distribution margins, the standard deviation of distribution margins across all goods in each country is computed. Then, an average of these country-specific standard deviations is computed. ν is chosen so that this model generated average stan- dard deviation is equal to its data counterpart. I find ν to be 0.75. ζ i represents the units of distribution services required to deliver 1 unit of a base good to the consumer in country i, irrespective of the good. ζ i is chosen so that the average of the simulated distributionmarginsofallgoodsincountryiequalstheaverageofdistributionmarginsof allgoodsincountryiobservedinthedata. Theaveragedistributionmarginforcountries with missing data (Canada, Mexico and Switzerland) is replaced by the sample average in the data. Table 3.3 gives the calibrated ζ for each country. Table 3.3: Country-Specific Distribution Parameter: ζi Country ζ Country ζ Australia 0.33 Japan 0.37 Austria 0.21 Mexico 0.23 Belgium 0.11 Netherlands 0.14 Canada 0.22 New Zealand 0.16 Denmark 0.19 Norway 0.20 Finland 0.15 Portugal 0.17 France 0.14 Spain 0.19 Germany 0.17 Sweden 0.12 Greece 0.23 Switzerland 0.17 Ireland 0.06 United Kingdom 0.18 Italy 0.18 United States 0.30 The data on distribution margins for majority of the countries are for 1995 whereas the data on trade volumes used to compute trade costs, the data on gross output and value added used to compute the parameters of the model, and the data on endowment of labor and capital are for 1996. This inconsistency is not important for two reasons. First, for the countries for which I have data over multiple years, I find that distribution 28 margins do not change significantly from one year to another for individual product categories. Second, the average distribution margin (across all products) of each country and the average of country-specific standard deviation of distribution margins (across goods), used to calibrate ν and ζ i , are going to be even more stable over time than the distribution margins for individual product categories. 3.4 Results: Ricardian Model with Distribution Accountingforthedifferencesincostsofdistributionacrossgoodsandacrosscoun- tries helps the model to better match the data. The model can match the average price dispersion very well. Table 3.4 shows that the model accounts for 96.5 percent of the average price dispersion observed in the data. Furthermore, the model can account for 32 percentoftheIQR(inter-quartilerange)observedinthedata. Ascomparedtothebench- mark ricardian model, the ricardian model with heterogeneity in distribution brings 13 percentimprovementinmatchingaveragepricedispersion,anda48percentimprovement in matching the variation in good-by-good price dispersion as measured by IQR. Table 3.4: Good-by-Good Price Dispersion: Model Versus Data Model Data Model as ratio of Data Avg. 0.2680 0.2778 0.9648 IQR 0.0505 0.1595 0.3167 P90 - P10 0.0978 0.3008 0.3251 These differences are reflected in Figure 3.2, which plots the empirical distribution of good-by-good price dispersion generated by the ricardian model with distribution, as well as that generated by the benchmark ricardian model. Notice that the distribution generated by the ricardian model with distribution is more symmetric than the distri- bution generated by the benchmark ricardian model. This is due to the fact that the improvement in matching the data brought about by including distribution generates a 38 percent improvement in matching P90 - P10, which is lower than the 48 percent improvement in accounting for IQR. Accountingforlocaldistributioncostsandincorporatingheterogeneityindistribution services requirement of goods in the benchmark ricardian model results in a significant improvement in the model’s ability to match the data. Furthermore, distribution costs play a more important role in matching the variation in good-by-good price dispersion 29 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Price Dispersion Probability Ricardian Model with Distribution Ricardian Model Data Pooled 80 − 90 Figure 3.2: Distribution of Var(Q mi (x)|x) 1/2 : Ricardian Model with Distribution Costs than in matching the average good-by-good price dispersion in retail prices observed in the data. 3.4.1 Role of Heterogeneity in Distribution In order to evaluate the role of heterogeneity in distribution costs in matching the data, I consider a simpler version of the model in which there is no heterogeneity in distribution services requirement of goods. So,φ i (x)=φ∀x, ∀i. Using the model sim- ulated distribution margins, I calculate the average of distribution margins over all goods in each country, to compute the average distribution margin for each country. Then, an average of the average country distribution margins is computed, to arrive at an average cross-country distribution margin. φ is calibrated so that the model generated average cross-country distribution margin is equal to the average cross-country distribution mar- gin in the data. Consequently, φ is set at 0.15. Table 3.5 shows that the average good-by-good price dispersion generated by this variant of the model is 23 percent. This implies that the model can explain 83 percent of theaveragedispersionobservedinthedata. TheIQRgeneratedbythemodelis22percent ofthatobservedinthedata. Relativetothemodelwithheterogeneityindistribution,this represents a 16 percent decline in the model’s ability to match the average good-by-good price dispersion and a 44 percent decline in the model’s ability to match the variation 30 in good-by-good price dispersion. Therefore, ignoring the heterogeneity in distribution costs, by assuming that all goods use the same amount of non-traded inputs, adversely affectsthemodel’sperformanceinmatchingthedata,especiallyinmatchingthevariation in good-by-good price dispersion. This is illustrated by Figure 4.3, which plots the empirical distribution generated by the model without heterogeneity in distribution, as well as that generated by the model with heterogeneity in distribution. Table 3.5: Good-by-Good Price Dispersion: Model Versus Data Model Data Model as ratio of Data Avg. 0.2311 0.2778 0.8320 IQR 0.0350 0.1595 0.2197 P90 - P10 0.0661 0.3008 0.2197 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Price Dispersion Probability Heterogeneous Distribution Homogeneous Distribution Figure3.3: DistributionofVar(Q mi (x)|x) 1/2 : RoleofHeterogeneityinDistributionCosts Interestingly, the average good-by-good price dispersion explained by the model with- out heterogeneity in distribution is actually lower than that explained by the benchmark ricardian model. In addition, the IQR generated by the model is only slightly higher than the IQR generated by the benchmark ricardian model. However, the latter can account for a higher proportion of P90 - P10 observed in the data. The restriction that all goods in every country require the same number of units of distribution services to 31 be delivered to the consumer dampens the difference in the value of distribution services used to deliver the same good in different countries. This, in turn, reduces cross-border differences in the retail price of the same good. Since the model with no heterogeneity in distribution accounts for a higher proportion of IQR but a lower proportion of P90 - P10 than the benchmark ricardian model, it suggests that the dampening effect of the con- stancy in units of distribution services used primarily affects the tails of the distribution of good-by-good price dispersion. Comparing the empirical distribution of good-by-good price dispersion generated by the model without heterogeneity with the distribution generated by the benchmark ricar- dianmodel,showninFigure3.1,revealsthatthetwodistributionshaveidenticallefttails butthe righttailofthe latterismoreskewedthanthatoftheformer. Thus, thedampen- ing effect works on the right tail of the distribution, reducing the average good-by-good price dispersion. 3.4.2 Role of Trade Costs In this section I examine the role of trade costs in driving good-by-good price dispersion. Istartbyremovingtheheterogeneityintradecosts-allcountriesfaceuniform trade costs as in Alvarez and Lucas (2007), i.e. τ ij =τ ∀i6=j. Using the matrix of trade cost parameters estimated in the benchmark ricardian model, I calculate the average trade cost an exporter faces in exporting to any other country. τ is calculated as the average of these exporter specific trade costs. I find τ to be 2.19. Note that this trade barrier does not apply when a country buys a good from its own producers rather than importing it, i.e. τ ij = 1, i =j. The next (obvious) question to ask is how important is the magnitude of trade cost in driving good-by-good price dispersion? For this purpose, I setτ at lower value of 1.33. This is the uniform trade cost estimate used in Alvarez and Lucas (2007) for a much larger set of countries. As the last step, trade costs are reduced to zero, i.e. τ ij =1∀ i,j. In conducting these experiments,ν andζ i must be recalibrated so that (i) the OECD average standard deviation of distribution margins (the average of country-specific stan- dard deviations of distribution margins) generated by the model is the same as that in the data, and (ii) the average of the distribution margins of all goods in country i gen- erated by the model equals the average of distribution margins of all goods in country i 32 observed in the data. This ensures that the magnitude of, and heterogeneity in, distri- bution margins is the same as that in the model with heterogeneity in distribution and trade costs. Table 3.6: Role of Trade Costs Avg. IQR P90 - P10 Model with heterogeneity 0.2680 0.0505 0.0978 in trade costs and distribution Uniform Trade Costs 0.2483 0.0507 0.0991 τij = τ = 2.19∀ i6= j Alvarez-Lucas Trade Costs 0.1753 0.0533 0.1033 τij = τ = 1.33∀ i6= j Zero Trade Costs 0.1647 0.0542 0.1053 τij = 1∀ i = j Data 0.2778 0.1595 0.3008 Table 3.6 reveals that removing the heterogeneity in trade costs, but with a uniform averagetradecost,thereisasmalldeclineintheaveragegood-by-goodpricedispersionto 0.2483comparedtothemodelwithheterogeneityintradecostsanddistribution(0.2680). The model with uniform trade costs can generate 89 percent of average price dispersion observedinthedata,comparedto96.5percentexplainedbythemodelwithheterogeneity in trade costs and distribution. The variation in good-by-good price dispersion increases by a negligible amount. Reducingthelevelofuniformtradecostsfrom2.19to1.33resultsinasharpdeclinein the average good-by-good price dispersion to 0.1753. With the lower uniform trade cost, the model can account for only 63 percent of the average good-by-good price dispersion. On the other hand, variation in good-by-good price dispersion increases marginally. As comparedtothefallinaveragepricedispersion, theincreaseinvariationingood-by-good price dispersion is very small - the model with lower uniform trade costs can account for 33 percent of IQR observed in the data as compared to 32 percent explained by the model with higher uniform trade costs. For P90 - P10, the corresponding numbers are 34 percent and 33 percent. Finally, reducing trade costs to zero reveals the same qualitative trend. Average good-by-good price dispersion declines further (the proportion accounted for by the model falls to 59 percent) and there is a very small increase in the variation in good-by-good price dispersion. Essentially, as trade costs decline, the distribution of good-by-good price dispersion shifts to the left, without any significant change in the variation in good-by-good price dispersion. Thus, the level of trade costs determines 33 the location of the distribution of good-by-good price dispersion. Figure 3.4 shows the leftward shift of the distribution in response to a decline in trade costs. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.005 0.01 0.015 0.02 0.025 0.03 Price Dispersion Probability Heterogenous Trade Cost Avg. Trade Cost Lucas−Alvarez Trade Cost Zero Trade Cost Figure 3.4: Effect of Trade Costs on Empirical Distribution of Var(Q mi (x)|x) 1/2 The experiments show that heterogeneity in trade costs plays a very small role in determining the average price dispersion. Removal of heterogeneity in trade costs, by assuming that trade cost between countryi and countryj (i6=j) is equal to the average trade cost for the OECD countries, leads to a small decline in average price dispersion. Furthermore, it has no significant impact on the variation in good-by-good price disper- sion. It is the magnitude of trade costs which is important for the model’s ability to match average price dispersion. A decline in the level of trade costs, from the uniform average trade cost computed for the OECD countries to the uniform trade cost used in Alvarez and Lucas (2007), results in a decline in the average good-by-good price dis- persion and a comparatively negligible increase in the variation in good-by-good price dispersion. Basically, a decline in trade costs reduces the producer price of a good. It also reduces the heterogeneity in producer price across countries. However, since trade costsarecountryspecificandnotgoodspecific,areductionintradecostsaffectsallgoods symmetrically. Therefore, all goods experience a decline in cross-country heterogeneity in producer prices. This is what causes the distribution of good-by-good price dispersion to shift to the left, without any significant change in the variance of good-by-good price dispersion. 34 3.5 Conclusion This chapter poses two questions. First, given that the new multi-country ricar- dian trade models, which allow for trade costs, can account well for the “quantity” of goods traded across international borders, what are the implications of these models for deviations from the LOOP in the prices of goods? Second, can accounting for differences in local costs of distribution across goods and across countries, help to better match the data on LOOP deviations? With respect to the first question, I find that the degree of market segmentation im- pliedbyinternationaltradebarriersisnotenoughtoaccountforgood-by-gooddispersion in LOOP deviations observed in the data. The benchmark multi-country ricardian trade model, featuring heterogeneous and asymmetric trade costs, does a good job of matching the average good-by-good price dispersion, but it is not able to generate the variation in good-by-good price dispersion observed in the data. It can explain 85 percent of average price dispersion, but only 21 percent of the variation in price dispersion. With respect to the second question, I find that accounting for differences in costs of distribution across goods and across countries significantly improves the model’s perfor- mance in matching the data. The model does a very good job of matching the average price dispersion - it explains 96.5 percent of the average price dispersion. And, it can explain32percentofthevariationinpricedispersion. Thisimpliesa13percentimprove- ment in explaining average good-by-good price dispersion and 48 percent improvement in explaining variation in good-by-good price dispersion over the benchmark ricardian model. Furthermore, imposing the assumption that all goods in all countries require the same amount of distribution services to be delivered to consumers severely limits the model’s ability to match the data, especially the variation in good-by-good price disper- sion. Therefore, heterogeneity in distribution costs plays an important role in matching the variation in good-by-good price dispersion. On the other hand, heterogeneity in trade costs does not play an important role in driving good-by-good price dispersion. Removal of heterogeneity in trade costs, keeping the average trade cost for the sample unchanged, leads to a small decline in average price dispersionandhasnosignificantimpactonthevariationingood-by-goodpricedispersion. The level of trade costs is important, however, for average good-by-good price dispersion. As the level of trade costs declines the distribution of good-by-good price dispersion shifts to the left, implying a decline in average good-by-good price dispersion, without any significant change in the variation in good-by-good price dispersion. With zero trade 35 costs, the model can explain only 59 percent of the average price dispersion observed in the data. The two sources of market segmentation - international trade costs and local costs of distribution - can explain the dispersion in LOOP deviations for an “average” retail product very well. By contrast, they can account for only one-third of the variation in dispersion in LOOP deviations observed in the data across a broad spectrum of re- tail products. Although, heterogeneity in distribution costs is crucial in explaining the variation in good-by-good price dispersion, it is clearly not enough. 36 Chapter 4 A First Step Toward Investigating the Role of Market Structure 4.1 Ricardian Model with Bertrand Competition Consider a world with N countries. Country i (i = 1,...,N) has L i consumers and each consumer has 1 unit of labor, which is supplied inelastically (all variables are expressed in per capita terms) and k i units of capital. 4.1.1 Production and Consumption Each country produces a continuum of base goods, indexed byx∈[0,1], which are traded. In each country, there are multiple potential producers of each good. Potential producers of the same good differ from each other in the level of technical efficiency with which they can produce the good. The hth most efficient producer of base good x, in country i, produces m h i (x) units of good x using a Cobb-Douglas technology. m h i (x)=Z h i (x) h k h i (x) α l h i (x) 1−α i β c h i (x) 1−β . k h i (x), l h i (x) and c h i (x) are the amounts of capital, labor and intermediate composite, respectively, used to produce base good x in country i, by hth most efficient producer who is characterized by Z h i (x) level of technical efficiency. Countries trade base goods. In each country there is a representative importing firm that buys m i (x) of each base good x, at the lowest price. Base goods are combined to 37 produce an intermediate composite,c i , which is a Spence-Dixit-Stiglitz (SDS) aggregator with an elasticity of substitution, η. c i = Z 1 0 m i (x) 1− 1 η dx η η−1 . The representative consumer in countryi consumes a non-traded final goody, which is produced using a Cobb-Douglas technology: y i = h k α yi l 1−α yi i ρ c 1−ρ yi , wherel yi ,k yi andc yi is the amount of labor, capital and intermediate composite used to produce the final good. 4.1.2 Market Clearing The intermediate composite is used as an input in the production of base goods and the final good, so that the market clearing for intermediate composite yields Z 1 0 c i (x)dx | {z } c mi +c yi ≤c i , where c mi is the number of units of the intermediate composite used in the production of all base goods. The labor market, as well as the market for services of capital, must clear; Z 1 0 l i (x)dx | {z } l mi +l yi ≤1 , Z 1 0 k i (x)dx | {z } k mi +k yi ≤k i , where l mi is the share of base goods sector in the labor force, k mi is the share of base goods sector in the capital stock, and k i is the capital-labor ratio of country i. 4.1.3 Trade, Market Structure and Retail Prices in Base Goods Sector Trading base goods is subject to trade costs - to deliver 1 unit of a base good from country j to country i, country j must produce τ ij units of the good. Due to geographic 38 andotherbarrierstotrade,τ ij >1fori6=j. Thisisthestandard“icebergassumption” a la Samuelson, andτ ii =1 for alli. I impose the triangle inequality on geographic barriers - τ ij ≤ τ in τ nj , ∀ n, i.e., an upper bound on the cost of moving goods from j to i is the cost of moving them via a third country n. Labor and capital are mobile within countries, but immobile across countries. Profit maximization implies that the return to capital in country i is r i = (α/(1−α))w i k −1 i , wherew i is the wage. Then, the cost of producing base goodx in countryi forhth most efficient producer is B w β i p 1−β ci k −αβ i Z h i (x) ! , where B =β −β (1−β) (β−1) α −αβ (1−α) β(α−1) α 1−α αβ and p ci is the price of intermediate composite in country i. hth most efficient producer of good x in country j can deliver a unit of the good to country i at a cost: K h ij (x)=B w β i p 1−β ci k −αβ i Z h i (x) ! τ ij . (4.1) Then, the lowest cost at which country i can obtain good x is: K 1 i (x)=min j K 1 ij (x) . (4.2) Under perfect competition the lowest cost supplier of good x to country i captures the market, and therefore price of good x in country i is given by Eq. (4.2). Even under bertrand competition each market i is captured by the lowest cost supplier of each good good x, but this supplier can charge a price less than or equal to the second-lowest cost of supplying to market i. The second lowest costs of supplying good x to country i is given by K 2 i (x)=min K 2 ij ∗(x),min j6=j ∗ K 1 ij (x) , (4.3) wherej ∗ issatisfiesK 1 ij ∗(x)=K 1 i (x),i.e.,j ∗ isthecountryoflow-costsuppliertocountry i. Therefore, the second lowest-cost supplier to country i is either (i) the second lowest- cost supplier fromj ∗ or (ii) the low-cost supplier from a country other thanj ∗ . However, 39 the low-cost supplier would not charge a markup higher than ω =η/(η−1) for η > 1 1 . Therefore, the price of good x in country i is given by p mi (x)=min K 2 i (x),ωK 1 i (x) , (4.4) which in the absence of distribution costs is the retail prices of the good. Even though there are many potential producers of each good in each country, to determinethepriceofagoodxinagivencountryallthatisneededistheleveloftechnical efficiency of the low-cost producer in each country i, Z 1 i (x), and the level of technical efficiency of the second-lowest cost supplier in the low-cost source, Z 2 i (x). Following Bernard et al. (2003), I assume that the highest efficiency Z 1 i (x) and the second-highest efficiency Z 2 i (x) of producing good x in country i are realizations of random variables with the following joint distribution function: F i (z 1 ,z 2 )=Pr Z 1 i ≤z 1 ,Z 2 i ≤z 2 = h 1+λ i z −θ 2 −z −θ 1 i e −λ i z −θ 2 , (4.5) for 0 ≤ z 2 ≤ z 1 , drawn independently across countries and goods. The parameter θ governs the heterogeneity of efficiency, with higher values of θ implying less variability. Givenθ,λ i governs the average efficiency level in countryi. Thus,θ determines the gains from trade due to comparative advantage, whereas λ i determines the gains from trade due to absolute advantage. Using Eq. (4.1), Eq. (4.2) and Eq. (4.3), the joint distribution of efficiency draws can be transformed into the joint distribution of lowest cost K 1 i and second-lowest cost K 2 i of supplying a good to country i (Appendix C). G i (κ 1 ,κ 2 )=Pr K 1 i ≤κ 1 ,K 2 i ≤κ 2 =1−e −Ω i κ θ 1 −Ω i κ θ 1 e −Ω i κ θ 2 , (4.6) for κ 1 ≤ κ 2 , where Ω i = P N j=1 λ j Bw β j p 1−β cj k −αβ j .τ ij −θ . Even though the distribution of costs differs across destinations, the distribution of markups is the same in any des- tination. The markup M i (x) = p mi (x)/K 1 i (x), has Pareto distribution truncated at the monopoly markup (Appendix C). H i (ω)=Pr[M i ≤ω] = ( 1−ω −θ 1≤ω<ω ; 1 ω≥ω . 1 For η < 1, set ω =∞. 40 Since the distribution is independent of source country attributes, it implies that a more competitive (due to higher average efficiency, lower input costs, or lower trade costs) source country does not sell at systematically higher markups. Instead, as it will be shown later, greater competitiveness leads to a wider range of exports. The price of intermediate composite in country i is given by p ci = Z 1 0 p mi (x) 1−η dx 1 1−η , which, given the joint distribution of costs and the distribution of markups in country i implies that (Appendix C): p ci =AΩ −1/θ i , (4.7) where A= Γ 1−η+2θ θ 1+ η−1 θ−(η−1) ω θ 1/(1−η) . The existence of the gamma function (on the right-hand side) requires that η < 1+θ, which is assumed to hold throughout this chapter. 4.1.4 AggregateTradeShares,TradeCostsandShareofCostsinRevenues The probability that country j is the low-cost supplier of any good x to country i is given by (Appendix C): D ij = λ j Bw β j p 1−β cj k −αβ j .τ ij −θ Ω i . (4.8) Since this is independent of the good in question, aggregating across goods implies that D ij is also the fraction of goods for which countryj is the low-cost supplier to countryi. Therefore, as j becomes more competitive in destination i, due to either higher average efficiency , lower input costs, or lower costs of delivering goods to country i, it exports a wider range of goods to i. Furthermore, G i (κ 1 ,κ 2 ) is not only the distribution of the lowestandthesecond-lowestcostofsupplyingagoodtocountryiregardlessofthesource, but also the distribution of those costs conditional on the low-cost supplier j (Appendix C). As a result prices in any destination i have the same distribution regardless of the 41 source country j, and therefore, the share of total per capita expenditure of country i that goes toward goods from country j is also D ij . Hence D ij = X ij X i , where X ij is the per capita expenditure of country i on goods from country j and X i is the total per capita expenditure of country i on traded goods. I follow Eaton and Kortum (2002) to estimate the trade costs, τ ij . Eq. (4.8) implies that the share of country j in country i’s total expenditure on tradables, normalized by country i’s share in its own total expenditure on tradables, is given by: D ij D ii = w β j p 1−β cj k −αβ j τ ij −θ λ j w β i p 1−β ci k −αβ i −θ λ i . Let Ξ i = w β i p 1−β ci k −αβ i −θ λ i , and S i =ln(Ξ i ). ⇒ln D ij D ii =S j −S i −θlnτ ij . (4.9) The left-hand side of this equation is calculated from data on bilateral trade and gross output. The methodology used to calculate the left-hand side is explained in Appendix B. Trade costs are obtained by estimating Eq. (4.9). Since τ ij is not observable, I follow the gravity equation literature to proxy trade barriers by distance, language, border and membership of free trade regions. Specifically, lnτ ij =dist T +brdr+lang+tblk R +dest i +ǫ ij , (4.10) where dist T (T = 1,...,6) is the effect of distance between i and j lying in the Tth interval, brdr is the effect of i and j sharing a border, lang is the effect of i and j sharing a language, tblk R (R = 1,2) is the effect of i and j belonging to trading area R, and dest i (i = 1,...,N) is a destination effect. The error term ǫ ij captures trade barriers due to all other factors, and is orthogonal to the regressors. The six distance intervals (in miles) are: [0,375); [375,750); [750,1500); [1500,3000); [3000,6000) and [6000,maximum]. The two trading areas are the European Union (EU) and the North- American Free Trade Agreement (NAFTA) area. S i is captured as the coefficient on source-country dummies. 42 Given that the suppliers of traded goods earn non-zero profits, what is the share of variable costs in the per capita expenditure of a country on traded goods? Let X i (x) be the expenditure incurred by country i in purchasing goods x. Then, given that the markup on good x in country i is M i (x), the costs of producing good x for country i is I i (x)= X i (x) M i (x) , where X i (x)=X i p mi (x) p ci 1−η . Averaging over all goods gives: I i X i = θ 1+θ , (4.11) which is the share of production and delivery costs in the per capita expenditure of countryi (Appendix C). Since the distribution of prices in countryi does not depend on the source θ/(1+θ) is also the share of costs of country j in producing and delivering goods to country i in the per capita expenditure of country i on country j’s goods. 4.1.5 Calibration Methodology Simulating the retail prices of goods requires a wage vectorw, a vector of prices of the intermediate composite p c , the vector of capital-labor ratios k, trade cost matrix τ and vector of productivity parameters λ. Thevectorofwagesisdeterminedbyimposingbalancedtrade-therevenueofcountry i must equal its expenditure. N X j=1 L j X j D ji =L i X i . FromEq.(4.11)X ji =((1+θ)/θ)I ji andsinceX j D ji =X ji , thebalancedtradecondition implies that: 1+θ θ N X j=1 L j I ji =L i X i . In the base good sector in country i, L i w i l mi =β(1−α) P N j=1 L j I ji = (θ/(1+θ))L i X i . Substituting this result in the balanced trade condition gives L i w i l mi = N X j=1 L j w j l mj D ji , 43 where the share of labor force employed in the base good sector,l mi =1−l yi =1−ρ, ∀i. Therefore, the balanced trade condition is reduced to: L i w i = N X j=1 L j w j D ji , (4.12) I take a stand on the endowment of labor and capital of each country by taking them from the data. Then, given the estimated trade cost matrix τ, Eq. (4.7) and Eq. (4.12) are used to solve for the equilibrium p c and w for a given initial guess for λ. The guess for λ is updated by using Eq. (4.8), for j =i. λ i =(AB) θ w i p ci βθ k −αβθ i D ii . (4.13) Therefore, Eq. (4.7), Eq. (4.12) and Eq. (4.13) form a system of 3N equations in 3N unknowns. In solving this system of equations, bilateral expenditure shares D ij are replaced by the bilateral expenditure shares computed from the data, b D ij . This implies that the vector of productivity parameters, λ, is a function of bilateral trade shares observed in the data, adjusted for differences in endowments of labor and capital. A similar calibration strategy is adopted by Waugh (2007). Alvarez and Lucas (2007) calibrateλbymatchingtherelativepriceofnon-tradables. Iadoptadifferentcalibration strategy for two reasons. First, since I am interested in characterizing the behavior of prices implied by the model, I do not want to use information on prices to calibrate λ. Second, and more importantly, one of the objectives of the paper is to evaluate whether the degree of market segmentation implied by flows of goods across borders can explain the deviations from the LOOP in prices of individual goods. By computing λ and τ as functions of bilateral trade shares, I impose the discipline on the model needed to answer this question. 4.1.6 Simulating Retail Prices and Good-by-Good Price Dispersion In order to compute the prices a simple transformation simplifies the simulation algorithm. Define Ψ 1 i (x)=λ i (Z 1 i (x)) −θ , Ψ 2 i (x)=λ i (Z 2 i (x)) −θ . 44 Using the joint distribution of efficiencies, Eq. (4.5), it can be shown (Appendix C) that the transformed variables are drawn from the following distributions: Pr Ψ 1 i ≤ψ 1 =1−exp −ψ 1 , (4.14) Pr Ψ 2 i ≤ψ 2 |Ψ 1 i =ψ 1 =1−exp −ψ 2 +ψ 1 . (4.15) Combining the transformations with Eq. (4.8) results in the following expressions for the lowest and second-lowest cost of delivering good x from country j to country i: K 1 ij (x)= " Ψ 1 j (x) D ij Φ i # 1/θ , (4.16) K 2 i (x)= " Ψ 2 j (x) D ij Φ i # 1/θ . (4.17) Icarryout100simulationsfor3000goods. Foreachgood,x,avector(Ψ 1 1 (x),...,Ψ 1 N (x)) is drawn, where N is the number of countries, from the parameterless exponential dis- tribution given by Eq. (4.14). Then another vector (Υ 1 (x),...,Υ N (x)) is drawn from a parameterlessexponentialdistributionforeachgoodx,andthevector(Ψ 2 1 (x),...,Ψ 2 N (x)) is computed as Ψ 2 i (x)=Ψ 1 i (x)+Υ i (x). The lowest and second-lowest costs of good x in countryi is obtained using Eq. (4.16), Eq. (4.17), Eq. (4.2) and Eq. (4.3). Eq. (4.4) gives the retail prices of goods. The deviation from the LOOP is given by: Q mi (x)=logp mi (x)− P N j=1 logp mj (x) N , x={1,...,3000} . (4.18) The variance of LOOP deviations is measured as the cross-country dispersion in LOOP deviations, Var(Q mi (x)|x). Good-by-good price dispersion is the square root of the variance of LOOP deviations. 4.1.7 Parameterization There are 22 OECD countries in the sample 2 . The set of countries I examine is larger than that examined by Crucini et al. (2005). In addition to the 13 EU countries included in Crucini et al. (2005), I include 9 other countries. Using only the 13 EU 2 Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Mexico, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, United King- dom, United States. 45 countries would not take into account all major trading partners of the countries. This will result in underestimation of total trade volume, which will affect the estimates of trade costs. Therefore, I choose a broader set of countries to account for as large a share of total trade as possible, but at the same time, I ensure that the chosen countries have similar levels of per capita GDP as the 13 EU countries in Crucini et al. (2005). The model is calibrated to the year 1996. The choice of the year is driven by the availability of data on capital-labor ratios. Although the data used by Crucini et al. (2005) are for 1975,1980,1985and1990,theaveragegood-by-goodpricedispersionandthevariationin good-by-goodpricedispersion(asmeasuredbyIQR)areverystableovertime. Therefore, the averages over the four years, of average good-by-good price dispersion and variation in good-by-good price dispersion can be compared with results of the model. Agriculture, hunting, forestry and fishing, mining and quarying, and manufacturing are treated as the traded goods sector. All other sectors form the final good sector. Following Bernard et al. (2003),θ, which controls the variability of the national idio- syncratic component of productivity, is 3.60 and η, which is the substitution parameter, is 3.79. Bernard et al. (2003) calibrateθ andη to match two moments of U.S. plant level data - productivity advantage of exporters (value added per worker for exporters is on average 33 percent higher than that of non-exporters) and size advantage of exporters (domestic shipments of exporters are on an average 4.8 times higher than that of non- exporters). Thecalibratedvalueofθ isthesameasthelowestofthethreeestimatesfrom Eaton and Kortum (2002). The choice of η is important only for the convergence of the gamma function and it does not have any implications for the results of the model. Given the value ofθ, the parameterβ is calibrated to match the share of intermediate inputs in gross output of the traded goods sector. The share of intermediate inputs in gross output in traded good sector is (1−β)(θ/(1+θ)). The data used to compute this ratio come from the OECD Structural Analysis (STAN) database. Details of the data and the methodology are provided in Appendix B. For the sample of countries β is 0.16. αistheshareofcapitalinGDP.Gollin(2002)findsthattheshareoflaborinvalueadded for a wide cross-section of countries is around 2/3, which implies that α is 0.33. ρ is the share of value added in the gross output of the final good sector. Since the value of the output of the final good sector is the GDP of a country,ρ is calibrated as one minus the share of traded goods sector in GDP. Using data from the OECD STAN database I find that the share of traded goods sector in GDP is 0.25 which implies thatρ is 0.75. β and ρ are computed as averages for the period 1995-1997, in order to remove any potential idiosyncrasies in value added and gross output in the year 1996. 46 The labor force vector L = (L 1 ,...,L N ) and the vector of capital-labor ratios k = (k 1 ,...,k N )aretakenfromthedatainCaselli(2005). AppendixBexplainstheprocedure used to calculate these vectors. Table 4.1 reports estimated coefficients for the geographic barriers, the corresponding standard error and the implied effect on cost relative to home sales. An increase in distance has a negative effect on trade. A country in the closest distance category faces 184 percent higher costs relative to home sales whereas a country in the farthest distance category faces a 534 percent higher trade cost. On the other hand, sharing a border with a trade partner reduces trade costs by 16 percent, while sharing a language reduces it by 8 percent. EU and NAFTA membership do not play an important role. The destination effectshowsthatitcosts57percentlesstoexporttotheUnitedStatesthantotheaverage country and it costs 125 percent more to export to Greece than to the average country. Notice that the costs imposed by trade barriers are much higher than those shown in chapter 3 (and those obtained by Eaton and Kortum (2002). This is because of a smaller value of θ than that used in chapter 3. Table 4.1: Geographic Barriers Implied % Variable Denoted by Coefficient Std. Error Effect on Cost Distance [0,375) - 1 θ dist1 -3.76 0.16 184.42 Distance [375,750) - 1 θ dist2 -3.91 0.13 196.36 Distance [750,1500) - 1 θ dist3 -4.25 0.12 225.35 Distance [1500,3000) - 1 θ dist4 -4.47 0.17 245.85 Distance [3000,6000) - 1 θ dist5 -6.26 0.08 468.79 Distance [6000,maximum] - 1 θ dist6 -6.65 0.09 534.22 Shared Border - 1 θ brdr 0.65 0.13 -16.61 Shared Language - 1 θ lang 0.30 0.10 -8.02 EU - 1 θ tblk1 0.19 0.14 -5.27 NAFTA - 1 θ tblk2 -0.39 0.35 11.41 Destination Country Australia - 1 θ dest1 1.03 0.24 -24.98 Austria - 1 θ dest2 -1.45 0.18 49.63 Belgium - 1 θ dest3 0.74 0.18 -18.65 Canada - 1 θ dest4 1.42 0.24 -32.51 Denmark - 1 θ dest5 -0.69 0.18 21.11 Finland - 1 θ dest6 -1.21 0.18 39.86 France - 1 θ dest7 0.08 0.18 -2.07 Germany - 1 θ dest8 1.07 0.18 -25.75 Greece - 1 θ dest9 -2.92 0.18 125.33 47 Table 4.1: (continued) Implied % Variable Denoted by Coefficient Std. Error Effect on Cost Ireland - 1 θ dest10 -0.76 0.17 23.36 Italy - 1 θ dest11 0.06 0.18 -1.58 Japan - 1 θ dest12 2.20 0.21 -45.73 Mexico - 1 θ dest13 -0.63 0.22 19.09 Netherlands - 1 θ dest14 0.95 0.18 -23.20 New Zealand - 1 θ dest15 0.03 0.24 -0.79 Norway - 1 θ dest16 -0.62 0.23 18.93 Portugal - 1 θ dest17 -2.26 0.18 87.30 Spain - 1 θ dest18 -0.64 0.17 19.33 Sweden - 1 θ dest19 0.01 0.17 -0.29 Switzerland - 1 θ dest20 -0.60 0.22 18.17 United Kingdom - 1 θ dest21 1.10 0.18 -26.40 United States - 1 θ dest22 3.09 0.45 -57.58 Note: Given an estimated coefficient, b, the implied percentage effect on cost is estimated as 100(e −(b/θ) −1). 4.2 Results: Ricardian Model with Bertrand Competition Table 4.2 compares the model generated good-by-good price dispersion with that observedinthedata. Themulti-countryricardiantrademodelwithbertrandcompetition overpredictstheaveragegood-by-goodpricedispersionby76percent;themodelgenerates average price dispersion of 49 percent while it is 28 percent in the data. The ricardian trade model with perfectly competitive markets and no distribution costs could account for 85 percent of the average dispersion, whereas the same model with distribution costs couldaccountfor96.5percentoftheaveragegood-by-goodpricedispersion. Withrespect to the variation in good-by-good price dispersion, the current model can account for 42 percentofthevariationinpricedispersion. Thetwovariantsofthericardiantrademodel withperfectcompetitioncouldaccountfor21percent(intheabsenceofdistributioncosts) and32percent(inthepresenceofdistributioncosts)ofthevariation. Thus,inaccounting for the variation in price dispersion, the ricardian model with bertrand competition (and no distribution costs) results in a 100 percent improvement over the ricardian model with perfect competition and no distribution costs and a 32 percent improvement over the ricardain model with perfect competition and distribution costs. 48 Table 4.2: Good-by-Good Price Dispersion: Model Versus Data Model Data Model as ratio of Data Avg. 0.488 0.278 1.758 IQR 0.068 0.160 0.424 These differences are borne out in Figure 4.1, which compares the distribution of good-by-good price dispersion generated by the, current, ricardian model with bertrand competition (and no distribution costs) with those generated by the two variants of the ricardian model with perfectly competitive markets. Incorporating variable markups, by allowingcompetitioninprices, inthebasegoodssectorhelpstoaccountforamuchlarger proportion of the variation in price dispersion, but it leads to a large overprediction of average price dispersion. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Price Dispersion Probability Bertrand Competition without Distribution Perfect Competition without Distribution Perfect Competition with Distribution Data Pooled 80 − 90 Figure 4.1: Distribution ofVar(Q mi (x)|x) 1/2 : Ricardian Model with Bertrand Competi- tion The large overprediction of average good-by-good price dispersion is primarily due to a lower value of θ used in this model as compared to the models in chapter 3. Notice that in this model a lower θ implies greater heterogeneity in efficiency draws, whereas in chapter 3 it is a higher value of θ has the same effect. Thus, for comparing the two, θ used in this model is comparable to the inverse of the value used in chapter 3. This implies that value used in the model with bertrand competition is smaller than that used 49 in the models with perfect competition. The smaller value results in higher trade costs and therefore higher average good-by-good price dispersion. The other effect of the lower θ is greater heterogeneity in costs, which in turn helps the model to generate greater variation in price dispersion. 4.3 RicardianModelwithBertrandCompetitionandLocal Distribution Costs 4.3.1 Production and Consumption Asinchapter3, inthissectionIextendthemodeldevelopedintheprevioussection to account for local costs of distribution. Now, base goods, besides being used to produce theintermediatecomposite, arealsodeliveredtotheconsumersasretailgoods. However, every base good, x, whether imported or produced domestically, requires some units of distribution services to be delivered to the consumers. Distribution services and retail goods are not traded. Individual retail goods are combined to produce a composite retail good. Each country also produces a homogeneous non-traded good. The final good that consumers consume in each country is a composite of the homogeneous non-traded good and the composite retail good. The production technology of base goods is unchanged. However, now, the amount of base good x bought by the importing firm, m i (x), is divided into two parts. m i (x)=m ci (x)+m qi (x) . m ci (x) is used to produce the intermediate composite in country i and m qi (x) is bought by the retailer of goodx in countryi. The intermediate composite,c i , is a Spence-Dixit- Stiglitz (SDS) aggregator, with an elasticity of substitution, η, between goods: c i = Z 1 0 m ci (x) 1− 1 η dx η η−1 . The retailer of good x combines m qi (x) with distribution services to deliver the base good to the consumer in the form of a retail good. Retail good,x, is denoted bym qi (x). Distribution services, d i , are produced using Cobb-Douglas technology with labor, l di , capital, k di , and intermediate composite, c di , as the inputs. d i =[k α di l 1−α di ] δ c 1−δ di . 50 To deliver 1 unit of base goodx to the consumer, φ i (x) units of distribution services are required, φ i (x)=ζ i u(x) ν , where ζ i denotes the units of distribution services required to deliver any good to the consumer in countryi, and reflects countryi’s efficiency in distribution of goods, andu is a random draw from a common parameterless exponential density function, g = exp(1). The draws are assumed to be independent across goods. Bringing one unit of a base good to the consumer requires a fixed proportion of dis- tribution services. This assumption is made in the spirit that production and retailing are complements, and consumers consume them in fixed proportions. Erceg and Levin (1996),Bursteinetal.(2003)andCorsettiandDedola(2005)alsoadoptthesameproduc- tion structure for retail goods. However, I allow the units of distribution services used to deliveraunitofagoodtovaryacrossgoods,aswellascountries,whereasthesestudiesdo not. Furthermore, these studies, for simplicity, do not differentiate between nontradable consumption goods, which directly enter the agents’ utility, and nontraded distribution services,whicharejointlyconsumedwithtradedgoods. However, Imakethisdistinction. This is necessary because the parametersν andζ i , which govern heterogeneity in the use of distribution services, are calibrated using the data on distribution margins and not from the data on all services. It also ensures that the distribution sector does not get more weight in GDP in the model than that observed in the data, and thereby helps to map the model clearly into the data. Therefore, in addition to producing distribution serviceseach country also produces a homogeneous non-traded good. Production of the non-traded good also combines labor, l si , capital, k si , and the intermediate composite, c si , using a Cobb-Douglas technology. s i =[k α si l 1−α si ] γ c 1−γ si . The consumer in country i therefore consumes a final good y, y i =q μ i s 1−μ i , where q i is a composite retail good. q i = Z 1 0 m qi (x) 1− 1 η dx η η−1 . 51 Notice that now the final good consumed is a composite of a homogeneous non-traded good, and a composite retail good. 4.3.2 Market Clearing The intermediate composite is used as an input in the production of base goods, distribution services and the homogeneous non-traded good. Therefore, market clearing requires that Z 1 0 c i (x)dx | {z } c mi +c di +c si ≤c i , where c mi is the number of units of the intermediate composite used in the production of all base goods. The total units of distribution services required to deliver base goods to the consumer cannot exceed the output of distribution services. Z 1 0 φ i (x)m qi (x)dx≤d i . The labor market as well as the capital market must clear; Z 1 0 l i (x)dx | {z } l mi +l di +l si ≤1 , Z 1 0 k i (x)dx | {z } k mi +k di +k si ≤k i , where l mi is the share of base goods sector in the labor force, k mi is the share of base goods sector in the capital stock, and k i is the capital-labor ratio of country i. 4.3.3 Retail Prices The structure of trade and that of the market in the base good sector remains the same as that developed in the previous section. As a result the price at which a country i buys base good x also remains unchanged, and is given by Eq. (4.4). However, now I am going to refer to this as the producer price of good x. Since delivering 1 unit of base goodx to the consumer requiresφ i (x) units of distribution services, the retail price 52 of base good x is the sum of the producer price of good x and the value of distribution services used to deliver 1 unit of the good. p mi (x)=p mi (x)+φ i (x)p di , (4.19) where the price of distribution services, p di , is given by p di =Cw δ i p 1−δ ci k −αδ i , and (4.20) C =δ −δ (1−δ) (δ−1) α −αδ (1−α) δ(α−1) (α/(1−α)) αδ . Eq. (4.19) shows that the retail price of good x is going to differ across countries for two reasons: (i) the producer price can be different across countries because of the presence of trade costs, and (ii) the costs of distribution can be different across countries because of differences in the price of distribution services, and differences in the number of units of distribution services used. The joint distribution of the highest efficiency and the second-highest efficiency of producing good x in country i remains unchanged (Eq. (4.5)). As a result, the joint dis- tributionoflowestandandsecond-lowestcostofsupplyingagoodtocountryi(Eq.(4.6)) and the distribution of markups in countryi also remain unchanged. The unchanged dis- tributions together with unchanged producer price of base good x imply that the the price of intermediate composite in country i is still given by Eq. (4.7). 4.3.4 Calibration Methodology The unchanged distributions of efficiency draws and costs combined with the un- changed structure of trade costs, imply that the share of total per capita expenditure of country i that goes toward goods from country j, D ij , also remains unchanged and is given by Eq. (4.8). For the same reasons, the share of production and delivery costs in the per capita expenditure of countryi is also unaltered, and is given by Eq. (4.11). The estimation of trade costs is also the same as in the previous model. However,withtheintroductionofthedistributionsectorthebalancedtradecondition is given by L i w i l mi = N X j=1 L j w j l mj D ji , (4.21) 53 where the share of labor force employed in the base good sector, l mi , is given by: l mi = 1−γ+μ(γ−δϑ i ) βθ+δϑ i βθ . (4.22) ϑ i is the ratio of value of distribution services and retail value of base goods in country i. It comes from the zero profit condition in the retail goods sector, which is given by: L i V mi =L i V mi +L i p di d i . V mi isthepercapitaretailvalueofallbasegoods,andV mi isthepercapitaproducerprice value of all base goods, where the second term on the right-hand side of the expression for V mi is total value of distribution services in country i. ϑ i is computed from data (Appendix B). V mi = (1−ϑ i ) ϑ i p di d i . (4.23) Thesolutionmethodologyremainsthesame;Itakeastandontheendowmentoflabor and capital of each country by taking them from the data. Then, given the estimated trade cost matrix τ and the vector of labor force share of base good sector, l m from Eq. (4.22), Eq. (4.7) and Eq. (4.21) are used to solve for the equilibrium w and p c for a given initial guess for λ. The guess for λ is updated by using Eq. (4.13). 4.3.5 Simulating Retail Prices and Good-by-Good Price Dispersion In order to compute the retail prices I simulate the producer prices and the units of distribution services used. Again, 100 simulations are carried out for 3000 goods. The simulation of producer prices of this model follows the same algorithm as developed for the simulation of retail prices of the previous model. Thus, for each good x two vectors, (Ψ 1 1 (x),...,Ψ 1 N (x)) and (Ψ 2 1 (x),...,Ψ 2 N (x)), are constructed from parameterless expo- nential distributions given by Eq. (4.14) and Eq. (4.15), respectively. Then, the lowest and second-lowest costs of good x in country i is obtained using Eq. (4.16), Eq. (4.17), Eq. (4.2) and Eq. (4.3). Eq. (4.4) gives the producer prices of goods. Then, for each country i, a vector (u i (1),...,u i (3000)) is drawn from the density functiong =e −u . Each element of the vector represents the units of distribution services used in delivering good x to the consumer. The retail price of each good is calculated using Eq. (4.19). The deviation from the LOOP is given by: 54 Q mi (x)=logp mi (x)− P N j=1 logp mj (x) N , x={1,...,3000} . (4.24) The variance of LOOP deviations is measured as the cross-country dispersion in LOOP deviations, Var(Q mi (x)|x). Good-by-good price dispersion is the square root of the variance of LOOP deviations. The distribution margin for good x is calculated as: dm i (x)=1− p mi (x) p mi (x) . (4.25) 4.3.6 Parameterization The sample of countries and the year to which the model is calibrated are the same asthoseintheRicardianmodel. AsintheRicardianmodel,agriculture,hunting,forestry and fishing, mining and quarying, and manufacturing are treated as the traded goods sector. Wholesale trade, retail trade and transport and storage form the distribution services sector. All other sectors form the non-traded good sector. The calibrated values of β, α, η and θ remain unchanged. δ and γ are calibrated as theshareofvalueaddedingrossoutputofdistributionservicessectorandthenon-traded good sector, respectively. μ is the share of the composite retail good in value of output of the final good sector. Since the value of output of the final good sector is the GDP of a country,μ is computed as one minus the share of the non-traded good sector (all services except retail trade, wholesale trade and transport and storage) in GDP. The data used to compute these parameters come from the OECD STAN Structural Analysis database. Details of the data and the methodology are provided in Appendix B. For the sample of countries δ is 0.58, γ is 0.62 and μ is 0.42. Again, these are averages for the period 1995-1997. The vectors of labor force and capital-labor ratio, as well as estimates of trade costs remain unchanged. The parameterν, controls the variance in the number of units of distribution services required to deliver 1 unit of a base good to the consumers, irrespective of the country. Heterogeneity in distribution margins is used as a target in calibrating ν. First, using the model simulated distribution margins, the standard deviation of distribution margins across all goods in each country is computed. Then, an average of these country-specific standard deviations is computed. ν is chosen so that this model generated average stan- dard deviation is equal to its data counterpart. I find ν to be 0.70. ζ i represents the units of distribution services required to deliver 1 unit of a base good to the consumer 55 in country i, irrespective of the good. ζ i is chosen so that the average of the simulated distributionmarginsofallgoodsincountryiequalstheaverageofdistributionmarginsof allgoodsincountryiobservedinthedata. Theaveragedistributionmarginforcountries with missing data (Canada, Mexico and Switzerland) is replaced by the sample average in the data. Table 4.3 gives the calibrated ζ for each country. Table 4.3: Country-Specific Distribution Parameter: ζi Country ζ Country ζ Australia 9.16 Japan 7.70 Austria 7.59 Mexico 11.67 Belgium 3.40 Netherlands 4.20 Canada 4.15 New Zealand 5.03 Denmark 6.36 Norway 6.59 Finland 5.05 Portugal 6.62 France 3.96 Spain 6.39 Germany 4.48 Sweden 4.09 Greece 25.67 Switzerland 5.31 Ireland 2.20 United Kingdom 5.13 Italy 5.45 United States 5.43 4.4 Results: Ricardian Model with Bertrand Competition and Local Distribution Costs Table 4.4 shows the results for the ricardian model with bertrand competition and distribution costs. As in case of the variant without distribution costs, this augmented model overpredicts the average good-by-good price dispersion observed in the data; the model generates average price dispersion of 46 percent while it is 28 percent in the data. The average price dispersion generated by this model is marginally smaller than the that generated by the model that does not incorporate distribution costs. This somewhat counter-intuitive result occurs because Var log 1+ φ i (x)p di p mi (x) |x < 2Var Q mi (x)|x − 2Cov(log(p mi (x)+φ i (x)p di ),logp mi (x)|x) where Q mi (x) is the LOOP deviation in producer price of good x in country i. As mentioned earlier, the two variants of the ricardian model with perfectly competitive 56 markets could account for 96.5 percent (with distribution costs) and 83 percent (without distribution costs) of the average good-by-good price dispersion. Ascomparedtovariantwithoutdistributionservices,thericardianmodelwithbertrand competition and distribution costs generates slightly higher variation in price dispersion - 43.5 percent as compared to 42 percent. As compared to the two variants of the ricar- dian trade model with perfect competition, the current model represents a 107 percent improvement over the variant without distribtuion costs and 36 percent improvement over the variant with distribution costs. Figure 4.2 depicts the empirical distribution of good-by-good price dispersion generated by the current model as well as those generated by the other three models. Table 4.4: Good-by-Good Price Dispersion: Model Versus Data Model Data Model as ratio of Data Avg. 0.461 0.278 1.661 IQR 0.069 0.160 0.435 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Price Dispersion Probability Bertrand Competition with Distribution Perfect Competition with Distribution Bertrand Competition without Distribution Perfect Competition without Distribution Data Pooled 80 − 90 Figure 4.2: Distribution ofVar(Q mi (x)|x) 1/2 : Ricardian Model with Bertrand Competi- tion and Distribution Costs 57 4.4.1 Role of Heterogeneity in Distribution In order to evaluate the role of heterogeneity in distribution costs in matching the data,Iconsideraversionofthericardianmodelwithbertrandcompetitioninwhichthere is no heterogeneity in distribution services requirement of goods. So, φ i (x)=φ∀ x, ∀ i. Using the model simulated distribution margins, I calculate the average of distribution margins over all goods in each country, to compute the average distribution margin for each country. Then, an average of the average country distribution margins is computed, toarriveatanaveragecross-countrydistributionmargin. φiscalibratedsothatthemodel generated average cross-country distribution margin is equal to the average cross-country distribution margin in the data. Consequently, φ is set at 4.6. Table 4.5 shows that the average good-by-good price dispersion generated by this variant of the model is 41 percent, which is lower than that generated by the model with heterogeneity in distribution costs. The IQR generated by the current model is 35 per- cent of that observed in the data. Relative to the variant of the model with heterogeneity in distribution, this represents a 25 percent decline in the model’s ability to match the variation in good-by-good price dispersion. Therefore, ignoring the heterogeneity in dis- tribution costs, by assuming that all goods use the same amount of non-traded inputs, adverselyaffectsthemodel’sperformanceinmatchingthevariationingood-by-goodprice dispersion. This result is qualitatively similar to that obtained in case of the model with perfectly competitive market structure. The adverse impact of ignoring heterogeneity in distribution is illustrated by Figure 4.3, which plots the empirical distribution generated by the model without heterogeneity in distribution, as well as that generated by the model with heterogeneity in distribution. Table 4.5: Good-by-Good Price Dispersion: Model Versus Data Model Data Model as ratio of Data Avg. 0.413 0.278 1.486 IQR 0.055 0.160 0.348 Comparing the empirical distribution of good-by-good price dispersion generated by the model without heterogeneity with the distribution generated by the model without heterogeneityindistributionrevealsthatthetwodistributionshaveidenticallefttailsbut the right tail of the latter is more skewed than that of the former. Thus, the dampening effectofassuminghomogeneousrequirementofdistributionservicesworksontherighttail of the distribution. Given that the random draws for distribution services requirements 58 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.005 0.01 0.015 0.02 0.025 0.03 Price Dispersion Probability Bertrand with Heterogeneous Distribution Bertrand with Homogeneous Distribution Figure 4.3: Distribution of Var(Q mi (x)|x) 1/2 : Role of Heterogeneity in Distribution of goods are made from a parameterless exponential distribution, which is highly skewed to the right, it would mean that imposing homogeneity in distribution costs would affect those goods more that required more units of distribution services. Therefore, goods that showed lower price dispersion, because of fewer units of distribution services, are less affected by the imposition of homogeneity in distribution costs, whereas goods that showedhigherpricedispersion,becauseofgreaternumberofunitsofdistributionservices, are more affected by this change. This explains why the left tail of the distribution of good-by-good price dispersion remains practically unaltered and most of the dampening effect works on the right tail. 4.4.2 Role of Trade Costs In this section I examine the role of trade costs in driving good-by-good price dispersion generated by the model with bertrand competition and distribution costs. I start by removing the heterogeneity in trade costs - all countries face uniform trade costs as in Alvarez and Lucas (2007), i.e. τ ij =τ ∀i6=j. Using the matrix of estimated trade cost parameters, I calculate the average trade cost an exporter faces in exporting to any other country. τ is calculated as the average of these exporter specific trade costs. Note thatthistradebarrierdoesnotapplywhenacountrybuysagoodfromitsownproducers rather than importing it, i.e. τ ij = 1, i =j. The next (obvious) question to ask is how important is the magnitude of trade cost in driving good-by-good price dispersion? For 59 this purpose, I set τ at lower value of 1.33. This is the uniform trade cost estimate used in Alvarez and Lucas (2007) for a much larger set of countries. As the last step, trade costs are reduced to zero, i.e. τ ij =1∀ i,j. In conducting these experiments,ν andζ i must be recalibrated so that (i) the OECD average standard deviation of distribution margins (the average of country-specific stan- dard deviations of distribution margins) generated by the model is the same as that in the data, and (ii) the average of the distribution margins of all goods in country i gen- erated by the model equals the average of distribution margins of all goods in country i observed in the data. This ensures that the magnitude of, and heterogeneity in, distri- bution margins is the same as that in the model with heterogeneity in distribution and trade costs. Table 4.6: Role of Trade Costs Avg. IQR Model with heterogeneity 0.461 0.069 in trade costs and distribution Uniform Trade Costs 0.363 0.066 τij = τ = Avg.∀ i6= j Alvarez-Lucas Trade Costs 0.158 0.055 τij = τ = 1.33∀ i6= j Zero Trade Costs 0.156 0.059 τij = 1∀ i = j Data 0.278 0.160 Table4.6revealsthatremovingtheheterogeneityintradecosts,byimposingauniform averagetradecost,thereisasharpdeclineintheaveragegood-by-goodpricedispersionto 0.36comparedtothemodelwithheterogeneityintradecostsanddistribution(0.46). The variation in good-by-good price dispersion decreases by a negligible amount. Reducing trade costs to a lower (uniform) level, as used by Alvarez and Lucas (2007), results in a sharper decline in average price dispersion, with the variation in price dispersion also declining, but by a comparatively much smaller magnitude. As the last step, decreasing trade costs to zero reduces average good-by-good price dispersion to 0.156 and increases variation in price dispersion marginally. Changing the structure of trade costs from heterogeneous to uniform and zero, ad- verselyaffectstheabilityofthemodeltomatchtheaveragegood-by-goodpricedispersion - from more than 100 percent (about 166 percent) to 56 percent. The variation in price dispersion accounted for by the model also declines, but by a much smaller margin - from 60 43.5 percent to 37 percent. Essentially, as trade costs decline, the distribution of good- by-good price dispersion shifts to the left, without a significant change in the variation in good-by-good price dispersion. Figure 4.4 shows the leftward shift of the distribution in response to a decline in trade costs. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Price Dispersion Probability Heterogenous Trade Cost Avg. Trade Cost Lucas−Alvarez Trade Cost Zero Trade Cost Figure 4.4: Effect of Trade Costs on Empirical Distribution of Var(Q mi (x)|x) 1/2 The experiments show that both, heterogeneity in trade costs and level of trade costs, play an important role in determining the average price dispersion, but the level of trade costs is more important than heterogeneity in trade costs. However, the two are not important in determining the variation in price dispersion. Furthermore, the decline in average good-by-good price dispersion in response to the removal of heterogeneity in tradecostsislargerthanthedeclineinresponsetoremovalofheterogeneityindistribution servicesrequirementofgoods. Ontheotherhand, variationinpricedispersionaccounted for by the model falls more in response to the removal of heterogeneity in distribution costs than in response to the removal of heterogeneity in trade costs. 4.5 Conclusion In this chapter I take the first step towards introducing imperfect competition into the model developed in chapter 3. I modify the perfectly competitive market structure of the base good sector, developed in chapter 3, to an environment where producers of base goods compete in prices, ala bertrand. This change is is motivated by strong 61 empirical evidence on the characteristics of exporters relative to non-exporters. Bertrand competition results in strategic behavior among producers of goods, and hence gives rise to good-specific markups. The question I pose is the following: Can this change in market structure help to explain a greater proportion of the variation in good-by-good price dispersion (more than two-third of the variation remained unexplained in chapter 3)? The ricardian trade model with bertrand competition generates average price disper- sionof49percentwhileitis28percentinthedata-anoverpredictionby76percent. The ricardian trade model with perfectly competitive markets and no distribution costs could account for 85 percent of the average dispersion. The same model, when augmented by distributioncostscouldaccountfor96.5percentofaveragepricedispersion. Withrespect to the variation in good-by-good price dispersion, the current model can account for 42 percent of the variation in price dispersion. This implies a 100 percent improvement over the ricardian model with perfect competition and no distribution costs and a 32 percent improvement over the ricardain model with perfect competition and distribution costs. Therefore, incorporating competition in prices improves the performance of the model in accounting for the variation in good-by-good price dispersion. Incorporating distribution costs into the ricardian model with bertrand competition does not lead to a significant improvement in the model performance. It results in a marginal decline in the extent of overprediction of the average price dispersion - model generates average price dispersion of 46 percent. As compared to the variant without distribution services, the current model can account for a slightly higher proportion of the variation in price dispersion observed in the data - 43.5 percent as compared to 42 percent. Hence,ascomparedtothetwovariantsofthericardiantrademodelwithperfect competition, this model results in a 107 percent improvement over the variant without distribution costs and 36 percent improvement over the variant with distribution costs. Heterogeneity in distribution costs is important in matching the data. But, it is more important in explaining the variation in good-by-good price dispersion than the average price dispersion. On the other hand, trade costs play a more important role in driving average good-by-good price dispersion. Both, heterogeneity in trade costs and level of trade costs, play an important role in determining the average price dispersion, but the level of trade costs is more important than heterogeneity in trade costs. The importance ofheterogeneityintradecostsindrivingaveragepricedispersionstandsinsharpcontrast withtheimportanceofheterogeneityintradecostsinchapter3. Inchapter3itisthelevel 62 of trade costs, and not the heterogeneity in trade costs, that is important in determining the average good-by-good price dispersion. In chapter 3, I investigated the importance of two sources of market segmentation - internationaltradecostsandlocaldistributioncosts-inexplainingthedispersionoflawof oneprice(LOOP)deviations. Inthischapter,Iaddathirdsourceofmarketsegmentation - pricing-to-market, which results in variable markups. Though, incorporating this third factor leads to a large overprediction of average price dispersion, it also results in a significant improvement in accounting for the variation in price dispersion. However, at the end of the day, even with variable markups, about 56 percent of the variation in good-by-good price dispersion remains unexplained. 63 Bibliography Alvarez, Fernando and Robert E. Lucas, “General Equilibrium Analysis of the Eaton-Kortum Model of International Trade,” Journal of Monetary Economics, Sep- tember 2007, 54, issue 6, 1726–1768. Atkeson, Andrew and Ariel Burstein, “Pricing-to-Market, Trade Costs, and Inter- national Relative Prices,” Working Paper, 2007. Aw,BeeYan,ChungSukkyun,andMarkJ.Roberts,“ProductivityandTurnover in the Export Market: Micro Evidence from Taiwan and South Korea,” World Bank Economic Review, Jan 2000, 14 (1), 65–90. Bergin, Paul R. and Reuven Glick, “Endogenous Tradability and Macroeconomic Implications,” Federal Reserve Bank of San Francisco, Working Paper Series. Working Paper 2003-09, 2006. Bernard, Andrew B. and Bradford J. Jensen, “Exporters, Jobs, and Wages in U.S. Manufacturing: 1976-1987,” Brookings Papers on Economic Activity: Microeconomics, 1995, pp. 67–119. and , “Exceptional Exporter Performance: Cause, Effect, or Both?,” Journal of International Economics, Feb 1999, 47 (1), 1–25. , Jonathan Eaton, Bradford J. Jensen, and Samuel Kortum, “Plants and Productivity in International Trade,” American Economic Review, 2003, 93 (4), 1268– 1290. Betts, Caroline M. and Timothy J. Kehoe, “Tradability of Goods and Real Ex- changeRateFluctuations,” FRB Minneapolis Research Department Staff Report, 2001. Burstein, Ariel T., Joao C. Neves, and Sergio Rebelo, “Distribution Costs and Real Exchange Rate Dynamics during Exchange-Rate-Based Stabilizations,” Journal of Monetary Economics, 2003, 50, 1189–1214. Caselli, Francesco, “Accounting for Cross-Country Income Differences,” Handbook of Economic Growth, 2005. ed. by P. Aghion, and S. Durlauf. Clerides, Sofronis, Saul Lach, and James R. Tybout, “Is Learning by Exporting Important? Micro-DynamicEvidencefromColombia,MexicoandMorocco,”Quarterly Journal of Economics, Aug 1998, 113 (3), 903–947. 64 Corsetti, Giancarlo and Luca Dedola, “A Macroeconomic Model of International Price Discrimination,” Journal of International Economics, 2005, 67, 129–155. Crucini, Mario J., Chris I. Telmer, and Marios Zachariadis, “Understanding European Real Exchange Rates,” American Economic Review, June 2005, 95 (3), 724– 738. Cumby, Robert E., “Forecasting Exchange Rates and Relative Prices with the Ham- burger Standard: Is What You Want What You Get with McParity,” National Bureau of Economic Research, Inc., NBER Working Papers: No. 5675, 1996. Dornbusch, Rudiger, Stanley Fischer, and Paul A. Samuelson, “Comparative Advantage, Trade, and Payments in a Ricardian Model with a Continuum of Goods,” The American Economic Review, Dec 1977, 67 (5), 823–839. Eaton,JonathanandSamuelKortum,“Technology,Geography,andTrade,”Econo- metrica, 2002, 70 (5), 1741–1779. Engel, Charles and John H. Rogers, “European Product Market Integration after the Euro,” Economic Policy, 2004, 19 (39), 347–384. Erceg, Christopher J. and Andrew T. Levin, “Structures and the Dynamic Behav- ior of the Real Exchange Rate.,” Mimeo, Board of Governors of the Federal Reserve System., 1996. Feenstra, Robert C., Robert E. Lipsey, Haiyan Deng, Alyson C. Ma, and Hengyong Mo, “World Trade Flows: 1962-2000,” National Bureau of Economic Re- search, Inc., NBER Working Papers: No. 11040, January 2005. Ghosh, Atish R. and Holger C. Wolf, “Pricing in International Markets: Lessons from The Economist,” National Bureau of Economic Research, Inc., NBER Working Papers: No. 4806, 1994. Giovannini, Alberto, “Exchange Rates and Traded Goods Prices,” Journal of Inter- national Economics, February 1988, 24 (1/2), 45–68. Goldberg,LindaandJoseManuelCampa,“DistributionMargins,ImportedInputs, and the Sensitivity of the CPI to Exchange Rates,” National Bureau of Economic Research, Inc., NBER Working Papers: 12121, 2006. Gollin, Douglas, “Getting Income Shares Right,” Journal of Political Economy, 2002, 110, 458–474. Haskel, Jonathan and Holger Wolf, “The Law of One Price - A Case Study,” Scan- dinavian Journal of Economics, 2001, 103 (4), 545–58. Heston, Alan, Robert Summers, and Bettina Aten, “Penn World Table Version 6.1,” Centre for International Comparisons at the University of Pennsylvania, 2002. Isaard, Peter, “How Far Can We Push the Law of One Price?,” American Economic Review, December 1977, 67 (5), 942–948. 65 Knetter, Michael M., “Price Discrimination by U.S. and German Exporters,” Ameri- can Economic Review, March 1989, 79 (1), 198–210. , “International Comparisons of Price-to-Market Behavior,” American Economic Re- view, June 1993, 83 (3), 473–486. Lutz,Matthias,“PricinginSegmentedMarkets,ArbitrageBarriers,andtheLawofOne Price: Evidence from The European Car Market,” Review of International Economics, 2004, 12 (3), 456–75. Melitz, Marc, “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,” Econometrica, 2003, 71, 1695–1725. Roberts, Mark J. and James R. Tybout, “The Decision to Export in Colombia: An Empirical Model of Entry with Sunk Costs,” The American Economic Review, Sep 1997, 87 (4), 545–564. Rogers, John H., “Price Level Convergence, Relative Prices, and Inflation in Europe,” Board of Governors of the Federal Reserve System (U.S.), International Finance Dis- cussion Papers: No. 699, 2001. Sanyal, Kalyan K. and Ronald W. Jones, “The Theory of Trade in Middle Prod- ucts,” American Economic Review, March 1982, 72 (1), 16–31. Waugh, Michael E., “International Trade and Income Differences,” June 2007. 66 Appendix A Appendix to Chapter 3 A.1 Price of Intermediate Composite Relabeling good x by its productivity level z p mi (z) 1/θ =B 1/θ min j w β j p 1−β cj k −αβ j τ ij 1/θ z j Two properties of the exponential distribution are useful here: (i) if v∼ exp(κ)⇒av∼ exp(κ/a). If v 1 and v 2 are independent, with v 1 ∼ exp(κ 1 ) and v 2 ∼ exp(κ 2 ), and s=min(v 1 ,v 2 )⇒s∼exp(κ 1 +κ 2 ). Then p mi (z) 1/θ ∼exp   B −1/θ N X j=1 ψ ij   , where ψ ij = w β j p 1−β cj k −αβ j τ ij −1/θ λ j Since the price of the intermediate composite is given by p 1−η ci = Z ∞ 0 p mi (z) 1−η f(z)dz where f(z) = N Y i=1 λ i ! exp − N X i=1 λ i z i ! Let R =p mi (z) 1/θ and S =p mi (z) 1−η , and therefore R =S 1/(θ(1−η)) . Then p 1−η ci =   B −1/θ N X j=1 ψ ij   −θ(1−η) Z ∞ 0 h θ(1−η) e −h dh 67 where R ∞ 0 h θ(1−η) e −h dh is a Gamma function. Let A = R ∞ 0 h θ(1−η) e −h dh 1 1−η . Substi- tuting for ψ ij gives p ci =AB   N X j=1 w β j p 1−β cj k −αβ j τ ij −1/θ λ j   −θ A.2 Expenditure Shares D ij =Pr p mj (x)≤min k6=j p mk (x) Usingthetwopropertiesofexponentialdistributiondiscussedearlierandathirdproperty, which says that: if v 1 ∼ exp(κ 1 ) and v 2 ∼ exp(κ 2 ) and v 1 and v 2 are independent then Pr{v 1 ≤v 2 }= κ 1 κ 1 +κ 2 , we get D ij = ψ ij P N k=1 ψ ik Combining this with Eq. (3.5) and substituting for ψ ij gives: D ij =(AB) −1/θ w β j p 1−β cj k −αβ j τ ij p ci ! −1/θ λ j A.3 Sectoral Allocations of Inputs in the Ricardian Model with Distribution Sector The first order conditions with respect to labor and intermediate composite in the base goods sector, distribution services sector and non-traded good sector give the following relations between sectoral labor allocations: l di = δ(1−β) β(1−δ) c di c mi l mi (A.1) l si = γ(1−β) β(1−γ) c si c mi l mi (A.2) Substituting these in the market clearing condition for labor implies l mi 1+ δ(1−β) β(1−δ) c di c mi + γ(1−β) β(1−γ) c si c mi =1 (A.3) The importing firm in each country makes zero profit. L i p ci c i +L i V mi =L i X i 68 SubstitutingforV mi fromEq.(3.11),usingtherelationsp ci c di =(1−δ)p di d i andp ci c mi = (1−β)X i to substitute forp di d i andX i and employing the market clearing condition for intermediate composite gives c si c mi = β (1−β) − c di c mi (1−δϑ i ) ϑ i (1−δ) (A.4) Since GDP equals factor income and p ci c si =(1−γ)p si s i , it implies that (1−α)p ci c si = (1−μ)(1−γ)w i . Combining this with Eq. (A.3) and using the relation that w i l mi = (β(1−α)/(1−β))p ci c mi implies c si c mi 1−γ(1−μ) (1−γ)(1−μ) = β (1−β) − c di c mi δ (1−δ) (A.5) Using Eq. (A.4) and Eq. (A.5) to solve for the two ratios -c di /c mi andc si /c mi - and using Eq. (A.3) gives the share of labor force employed in the base goods sector. l mi =1−μδϑ i −γ(1−μ) Substituting for l mi in Eq. (A.1) and Eq. (A.2) gives the share of distribution services sector and non-traded good sector in labor force, respectively. l di =μδϑ i l si =γ(1−μ) Since r i = (α/(1−α))w i k −1 i , the first order conditions from firms’ profit maximiza- tion in base goods sector, distribution services sector and non-traded good sector imply that a sector’s capital share is proportional to its labor force share where the factor of proportionality is the country’s capital-labor ratio. k mi =k i l mi , k di =k i l di , k si =k i l si . The first order conditions with respect to labor and intermediate composite in the base goods sector, distribution services sector and non-traded good sector give the fol- lowing relations between sectoral labor allocations and sectoral allocation of intermediate composite: l di = δ(1−β) β(1−δ) c di c mi l mi l si = γ(1−β) β(1−γ) c si c mi l mi c mi , c di and c si are determined by combining these two conditions with the market clearing condition for intermediate composite and market clearing condition for labor. 69 Appendix B Data for Parameterization and Parameterization Methodology B.1 Data on Gross Output and Value Added The data used to compute the share of value added in gross output of the three sectors come from the OECD STAN Structural Analysis database 1 . Value added and gross output of the sub sectors are added to get the data at the sectoral level, i.e. for traded good sector, distribution services sector and non-traded good sector. Ratio of value added and gross output is calculated for each country in each sector for three years - 1995, 1996 and 1997, and then averaged over three years to remove any idiosyncrasies associated with the year 1996. The ratios are then averaged across countries for each sector to get the sector’s value added as a ratio of gross output. Australia and Ireland are not included in this exercise because of missing data on gross output. The share of traded goods sector in GDP is calculated as the value added in traded good sector as a ratio of the total value added in a country. The share of non-traded good sector in GDP is computed in the same manner. Again, both ratios are averages for the period 1995-1997. B.2 Bilateral Trade Data and Expenditure Shares Data on bilateral trade volumes for the 22 OECD countries is obtained from the NBER-United Nations Trade Data, 1962-2000. Feenstra et al. (2005) provide the doc- umentation for the data. The data are organized by the 4 digit Standard International Trade Classification, revision 2. Imports of each country in the sample from the other 21 countries are extracted for the year 1996. To compute the expenditure shares, I follow Eaton and Kortum(2002). Summing the exports of a country across all trading partners gives the country’s total exports. Using the OECD STAN database, gross output of the traded goods sector for the year 1996 is obtained by adding gross output of the sub sectors. Gross output is expressed in nominal local currency units. Nominal yearly exchange rates with respect to the U.S. dollar for the year 1996 are used to convert local currency units into U.S. dollars. Data on nominal exchange rates come from OECD Economic Outlook, June, 2003, Annex Table 37. Then, 1 STAN Industry, ISIC Rev. 2 Vol 1998 release 01 70 subtracting total exports of a country from its gross output gives each country’s home purchases. Addinghomepurchasesandtotalimportsofacountrygivesthecountry’stotal expenditure on traded goods. Normalizing home purchases and imports of an importing country from its trading partners by the importer’s total expenditure on traded goods creates expenditure shares that are used in the model. Thedataondistance,borderandlanguageusedintheestimationoftradecostscomes fromCentreD’EtudesProspectivesEtD’InformationsInternationales(http://www.cpeii.fr). B.3 Labor Force and Capital-Labor Ratio Capital-laborratiodataareobtainedfromCaselli(2005),andareconstructedusing the perpetual inventory method which uses purchasing power parity investment rates in Heston et al. (2002). Data on labor force also come from Caselli (2005), and are again based on Heston et al. (2002). Since the data for Germany are missing, capital-labor ratio is computed as the average of capital-labor ratios of other countries. Missing data on labor force were replaced by data from World Development Indicators (WDI). The data are for the year 1996. B.4 BasicPriceValueofTradedGoodsasaratioofPurchaser Price Value of Traded Goods ϑ i is computed from the data as 1 minus the ratio of basic price value of all traded goods and purchaser price value of all traded goods. These data come from the use tables of the countries. The basic price value of all traded goods is calculated as the sum of the supply of the 29 categories of goods valued in basic prices. The purchaser price value of alltradedgoodsiscalculatedasthesumofthesupplyofthe29categoriesofgoodsvalued in purchaser prices. Since data for Canada, Mexico and Switzerland are not available, ϑ for these countries is assumed to be the average of ϑs of the remaining 19 countries. 71 Appendix C Appendix to Chapter 4 C.1 The Joint Distribution of Lowest and Second-Lowest Cost Define complimentary distribution, e G ij as: e G ij (κ 1 ,κ 2 )=Pr K 1 ij ≥κ 1 ,K 2 ij ≥κ 2 . Eq. (4.1) implies that e G ij (κ 1 ,κ 2 ) = Pr Z 1 i ≤W i τ ij /κ 1 ,Z 2 i ≤W i τ ij /κ 2 = F i W i τ ij /κ 1 ,W i τ ij /κ 2 , where W i =Bw β i p 1−β ci k −αβ i . The property that F (z 1 ,z 2 ;T) = h 1+λ i z −θ 2 −z −θ 1 i e −λ i z −θ 2 ⇒F (Δz 1 ,Δz 2 ;T) = F z 1 ,z 2 ;TΔ θ , implies e G ij (κ 1 ,κ 2 )=F κ −1 1 ,κ −1 2 ;T W i τ ij −θ , for κ 1 ≤κ 2 . The next step is to derive the complimentary distribution of lowest and second-lowest cost irrespective of source j, i.e. e G i (κ 1 ,κ 2 )=Pr K 1 i ≥κ 1 ,K 2 i ≥κ 2 . There are two possibilities: 1. K 1 ij >κ 2 , ∀ j =1,...,N. 2. κ 1 ≤K 1 ij ≤κ 2 , K 2 ij >κ 2 , ∀ j =1,...,N and K 1 in >κ 2 , n6=j. 72 This implies that e G i (κ 1 ,κ 2 )= N Y j=1 e G ij (κ 2 ,κ 2 )+ N X j=1 h e G ij (κ 1 ,κ 2 )− e G ij (κ 2 ,κ 2 ) i Y n6=j e G in (κ 2 ,κ 2 ) , which reduces to e G i (κ 1 ,κ 2 )=F κ −1 1 ,κ −1 2 ;Ω i . In order to obtain the joint distribution, G i (κ 1 ,κ 2 ), consider all possible values of K 1 i and K 2 i : 1. K 1 i ≤κ 1 , K 2 i ≤κ 1 →G i (κ 1 ,κ 1 ). 2. K 1 i ≤κ 1 , κ 1 ≤K 2 i ≤κ 2 →G i (κ 1 ,κ 2 )−G i (κ 1 ,κ 1 ). 3. K 1 i ≤κ 1 , K 2 i ≥κ 2 → e G i (0,κ 2 )− e G i (κ 1 ,κ 2 ). 4. κ 1 ≤K 1 i ≤κ 2 , K 2 i ≤κ 1 → not possible. 5. κ 1 ≤K 1 i ≤κ 2 , κ 1 ≤K 2 i ≤κ 2 → e G i (κ 1 ,κ 1 )− e G i (κ 1 ,κ 2 ). 6. κ 1 ≤K 1 i ≤κ 2 , K 2 i ≥κ 2 → e G i (κ 1 ,κ 2 )− e G i (κ 2 ,κ 2 ). 7. K 1 i ≥κ 2 , K 2 i ≥κ 2 → e G i (κ 2 ,κ 2 ). Then G i (κ 1 ,κ 2 )=1− e G i (0,κ 2 )− e G i (κ 1 ,κ 1 )+ e G i (κ 1 ,κ 2 ) , ⇒G i (κ 1 ,κ 2 )=1−e −Ω i κ θ 1 −Ω i κ θ 1 e −Ω i κ θ 2 . C.2 The Distribution of Markups Define markup in country ‘i’ for good ‘x’ M i (x)= p mi (x) K 1 i , where p mi (x)=min K 2 i (x),ωK 1 i (x) . Define ´ M i = K 2 i /K 1 i . Then M i = min{ ´ M i ,ω}. Consider the distribution of ´ M i , given K 2 i =κ 2 , for any ´ ω≥1: Pr h ´ M i ≤ ´ ω|K 2 i =κ 2 i = Pr h κ 2 ´ ω ≤K 1 i ≤κ 2 |K 2 i =κ 2 i ⇒Pr h ´ M i ≤ ´ ω|K 2 i =κ 2 i = R κ 2 κ 2 ´ ω g i (κ 1 ,κ 2 )dκ 1 R κ 2 0 g i (κ 1 ,κ 2 )dκ 1 , where g i (κ 1 ,κ 2 )= ∂ 2 G i (κ 1 ,κ 2 ) ∂κ 1 ∂κ 2 =θ 2 Ω 2 i κ θ−1 1 κ θ−1 2 e −Ω i κ θ 2 . 73 Then H i (´ ω) = Pr h ´ M i ≤ ´ ω|K 2 i =κ 2 i = κ θ 2 −(κ 2 /´ ω) θ κ θ 2 ⇒H i (´ ω) = 1− ´ ω −θ . Since the conditional distribution of ´ M i does not depend on κ 2 , it implies that the un- conditional distribution of ´ M i is the same - Pareto. Therefore, H i (ω)=Pr h ´ M i ≤ ´ ω i = 1− ´ ω −θ 1≤ ´ ω<ω ; 1 ´ ω≥ω . C.3 Price Index in a Destination p ci = Z 1 0 p mi (x) 1−η dx 1 1−η . Therefore, p ci = E h p 1−η mi i 1/(1−η) , and E p mi 1−η = Z ∞ 1 E h p mi 1−η | ´ M i = ´ ω i dH i (´ ω) . Now, p mi (x)=K 1 i (x)min{´ ω,ω}. Therefore, E p mi 1−η =   R ω 1 E h K 2 i 1−η | ´ M i = ´ ω i θ´ ω −(θ+1) d´ ω + R ∞ ω E h ω.K 2 i /´ ω 1−η | ´ M i = ´ ω i θ´ ω −(θ+1) d´ ω   , and since ´ M i is independent of K 2 i , it implies that E p mi 1−η = Z ω 1 h K 2 i 1−η i θ´ ω −(θ+1) d´ ω+ Z ∞ ω E h ω 1−η K 2 i 1−η ´ ω η−1 i θ´ ω −(θ+1) d´ ω . Now, Z ω 1 h K 2 i 1−η i θ´ ω −(θ+1) d´ ω =E h K 2 i 1−η i (1−ω −θ ) , and Z ∞ ´ ω E h ω 1−η K 2 i 1−η ´ ω η−1 i θ´ ω −(θ+1) d´ ω =ω 1−η E h K 2 i 1−η i E ´ ω η−1 ´ ω −θ . Define ˜ ω = ´ ω η−1 Using the distribution of markups, the density function of ˜ ω is given by ˜ f i (˜ ω)= θ η−1 ˜ ω − θ η−1 +1 74 Therefore E p mi 1−η =E h K 2 i 1−η i 1−ω −θ +ω −θ . θ 1+θ−η , where E h K 2 i 1−η i = Z ∞ 0 κ 2 1−η g 2 i (κ 2 )dκ 2 . g 2 i (κ 2 ) = R κ 2 0 g i (κ 1 ,κ 2 )dκ 1 . Define ˜ κ 2 = κ 1−η 2 . Then the density function of ˜ κ 2 is given by ˜ g i (˜ κ 2 )= θ 1−η Ω 2 i ˜ κ 2 2θ−1+η 1−η e −Ω i ˜ κ 2 θ 1−η . Therefore E h κ 2 i 1−η i =Ω −(1−η)/θ i .Γ 1−η+2θ θ , and E h p 1−η mi i = Γ 1−η+2θ θ 1+ η−1 θ−(η−1) ω −θ Ω −(1−η)/θ i , where Γ(.) is a gamma function. Then p ci = E h p 1−η mi i 1/(1−η) ⇒p ci =AΩ −1/θ i , where A= Γ 1−η+2θ θ 1+ η−1 θ−(η−1) ω θ 1/(1−η) . C.4 Probability that Country j is Lowest-Cost Supplier to Country i For country j to be the low-cost supplier of good x to country i: K 1 i (x)=min j K 1 ij (x) (C.1) The marginal distribution ofK 1 i isG 1 i (κ 1 )=1−e −Ω i κ θ 1 . Then if firms in countryj were exporting to country i, it would imply that G 1 ij (κ 1 )=1−e −λ j(W j τ ij) −θ κ θ 1 . Then the probability that country j is low-cost supplier of good x is given by: D ij = Z ∞ 0 Y n6=j 1−G 1 in (c) dG 1 in (c) 75 ⇒D ij = λ j Bw β j p 1−β cj k −αβ j .τ ij −θ Ω i ,∀x∈[0,1]. C.5 Distribution of Costs Conditional on Source Country j The complimentary distribution of costs in country i conditional on the source being country j is given by: ˜ G i (κ 1 ,κ 2 |j)= 1 D ij " R ∞ κ2 Q n6=j 1−G 1 in (c) dG 1 in (c) + h ˜ G ij (κ 1 ,κ 2 )− ˜ G ij (κ 2 ,κ 2 ) i Q n6=j ˜ G in (κ 2 ,κ 2 ) # , which simplifies to ˜ G i (κ 1 ,κ 2 |j)=F κ −1 1 ,κ −1 2 ;Ω i = ˜ G i (κ 1 ,κ 2 ) . Therefore, the conditional complimentary distribution is the same as the unconditional complimentary distribution, which then implies that the conditional distribution of costs is the same as the unconditional distribution of costs. C.6 Share of Production and Delivery Costs in Per Capita Expenditure of Country i Let X i (x) be the per capita expenditure of country i on good x, and let M i (x) be the markup on good x in country i. Then, X i (x) = M i (x)I i (x), where I i (x) is the cost of producing and delivering good x to country i. Since X i (x)= p mi (x) p ci 1−η X i ⇒I i (x)=X i p mi (x) 1−η M i (x) −1 p 1−η ci . Averaging over all goods implies that I i X i = E h p 1−η mi M −1 i i p 1−η ci . E h p 1−η mi M −1 i i = Z ∞ 1 E h p mi 1−η | ´ M i = ´ ω i θ´ ω −(θ+1) ´ ω −1 d´ ω ⇒E h p 1−η mi M −1 i i = Z ω 1 E h K 2 i 1−η i θ´ ω −(θ+2) d´ ω+ Z ∞ ω E h ω.K 2 i /´ ω 1−η i θ´ ω −(θ+1) ´ ω −1 d´ ω 76 ⇒E h p 1−η mi M −1 i i = θ θ+1 E h K 2 i 1−η i 1+ω −(θ+1) η 1+θ−η . Using the expressions derived for p ci and E h p 1−η mi i , one gets the relation that I i X i = θ θ+1 . 77

Abstract (if available)

Abstract Observed trade flows provide one metric to gauge the degree of international goods market segmentation. Deviations from the law of one price provide another. New survey data on retail prices for a broad cross section of goods across 13 EU countries, compiled by Crucini, Telmer and Zachariadis (2005), show that (i) the average dispersion of law of one price (LOOP) deviations across all goods is 28 percent and (ii) the range of that dispersion across goods is large, varying from 2 percent to 83 percent. Quantitative multi-country ricardian models, a la Eaton and Kortum, use data on bilateral trade volumes to estimate international trade barriers or trade costs. I find that a multi-country ricardian model with perfectly competitive markets, in which heterogeneous and asymmetric trade costs are carefully calibrated to match observed bilateral trade volumes, can account for 85 percent of the average dispersion but only 21 percent of the variation in price dispersion.

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Essays on the econometric analysis of cross-sectional dependence

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Creator Giri, Rahul (author)

Core Title Explaining the cross-sectional distribution of law of one price deviations

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 08/04/2008

Defense Date 04/30/2008

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Bertrand competition,distribution costs,imperfect competition,international trade costs,law of one price,OAI-PMH Harvest,trade

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Betts, Caroline M. (committee chair), Joines, Doug (committee member), Kim, Yong (committee member), Quadrini, Vincenzo (committee member)

Creator Email rahul.giri@gmail.com,rgiri@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1375

Unique identifier UC174496

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