The literature on purchasing power parity (PPP) relates free trade to price equalization.

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1 Price Equalization Does Not Imply Free Trade Piyusha Mutreja, B Ravikumar, Raymond G Riezman, and Michael J Sposi In this article, the authors demonstrate the possibility of price equalization in a to-country orld ith barriers to international trade For price equalization to occur hen the countries are asymmetric, the country ith higher productivity must also be the one ith the loer trade barrier A corollary of the authors result is that small departures from purchasing poer parity do not necessarily imply that orld trade is mostly integrated (JEL F, F3, F4) Federal Reserve Bank of St Louis Revie, Fourth Quarter 05, 97(4), pp The literature on purchasing poer parity (PPP) relates free trade to price equalization Based on a no-arbitrage argument, PPP suggests that a price inde constructed ith multiple goods in each country should be the same across countries hen there are no barriers to international trade Our focus is on the reverse direction: Does price inde equalization across countries necessarily imply that there is free trade? Our anser is negative: Price equalization does not imply free trade We illustrate our result in the to-country model of Dornbusch, Fischer, and Samuelson (977) We sho that many equilibria eist ith price inde equalization, even if there is no free trade Put differently, there eist many trade barrier combinations for hich the price indees are equal Hence, price equalization by itself does not guarantee zero trade barriers; information on trade flos is crucial to determine hether there are no barriers to trade A corollary of our result is that departures from price equalization are not sufficient to pin don departures from free trade that is, small deviations from PPP do not necessarily imply that orld trade is mostly integrated In our model, each country is endoed ith immobile labor that is the only factor of production There is a continuum of tradable intermediate goods, all of hich are used to produce a composite intermediate good The technology for producing each intermediate Piyusha Mutreja is an assistant professor at Syracuse University B Ravikumar is deputy director of research at the Federal Reserve Bank of St Louis Raymond G Riezman is the C Woody Thompson Research Professor of Economics at the Tippie College of Business, University of Ioa Michael J Sposi is a research economist at the Federal Reserve Bank of Dallas The authors thank YiLi Chien and Fernando Martin for their comments and Valerie Grossman and Lin Shao for research assistance 05, Federal Reserve Bank of St Louis The vies epressed in this article are those of the author(s) and do not necessarily reflect the vies of the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks Articles may be reprinted, reproduced, published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included Abstracts, synopses, and other derivative orks may be made only ith prior ritten permission of the Federal Reserve Bank of St Louis Federal Reserve Bank of St Louis REVIEW Fourth Quarter 05 33

2 Figure Price of Producer Durables (005 international $) Price (US ) Income Per Worker (US ) SOURCE: 005 Benchmark study of the Penn World Table The sample size is 43 good differs across the to countries Trade beteen the to countries is subject to eport barriers in the form of iceberg costs The presence of trade barriers implies that the to countries are not completely specialized in production that is, some intermediate goods in the continuum are not traded but are produced by both countries The aggregate price (over the continuum of intermediate goods) is a composite of both the prices of intermediate goods that are traded and the prices of intermediate goods that are not traded For symmetric countries, it is easy to sho that the aggregate price is the same in both countries We also sho that the trade flo beteen the to countries depends on the trade barriers: Large barriers imply a small trade volume, hile small barriers imply a large trade volume Thus, information on trade flos is necessary to infer the magnitude of the trade barriers For asymmetric countries, e sho numerically that there eist trade barriers such that the aggregate price is the same in both countries The price equalization in this case depends on a negative relationship beteen barriers and technology: The country ith higher productivity must have a loer eport barrier As in the symmetric case, e sho that each trade 34 Fourth Quarter 05 Federal Reserve Bank of St Louis REVIEW

3 barrier combination implies a different volume of trade Hence, to infer the presence or absence of trade barriers one needs to kno the cross-country trade flos Is our result empirically relevant? After all, there is a large literature documenting deviations from PPP (see Taylor and Taylor, 004, for a summary) There is also a body of ork on a stark violation of PPP the border puzzle (see McCallum, 995, and Anderson and van Wincoop, 003) One might be tempted to conclude from the literature that since price equalization is not observed in practice, our theoretical result price equalization does not imply free trade is empirically irrelevant Producer durables trade, hoever, offers a contrast Using data from the 005 Penn World Table, Figure illustrates that the aggregate price of producer durables is roughly equal across countries The slope of the best-fitting line for the scatterplot in Figure is an estimate of the (crosscountry) income elasticity of the price of producer durables; the estimate for 005 in our sample of 43 countries is 00 Hsieh and Kleno (007) illustrate similar price equalization using 996 data (see Figure 4, p 576) The elasticity for 996 (a sample of 3 countries) is 00 Going as far back as 975, ith a sample of only 33 countries in the Penn World Table, the elasticity is 00 Does the observed price equalization documented above imply that there is free trade in producer durables? Our anser is no In a model calibrated to deliver the observed trade flos, Mutreja et al (04) obtain the price equalization observed in Figure and sho that there are substantial barriers to producer durables trade If the anser had been yes, one could assume that there are no barriers to trade in producer durables, as in Armenter and Lahiri (0) Hoever, as Mutreja et al (04) sho, the assumption of free trade in producer durables implies a volume of trade in producer durables that is inconsistent ith the observed volume Alternatively, one could conclude, as Hsieh and Kleno (007) do, that barriers to trade in producer durables are not systematically related to the level of economic development since the price of producer durables is roughly the same across countries Again, Mutreja et al (04) estimate that productivity is negatively correlated ith trade barriers in a model that is consistent ith both observed price equalization and observed trade in producer durables The rest of the article is organized as follos The net section describes the to-country model In a separate section, e demonstrate that it is possible to have price equalization in the presence of barriers to trade A TWO-COUNTRY MODEL We use the frameork of Dornbusch, Fischer, and Samuelson (977; henceforth DFS) There are to countries, indeed by i, Country i is endoed ith labor L i, the only factor of production Labor is not mobile across countries (Some of the results that follo are ell knon; they are illustrated here purely for completeness) Production In each country there is a continuum of tradable intermediate goods; the goods are indeed by [0,] The technology in country i for producing intermediate good is as Federal Reserve Bank of St Louis REVIEW Fourth Quarter 05 35

4 follos: It takes a i () units of labor to produce unit of good All intermediate goods are used to produce a composite intermediate good using the technology (), η η Qi qi d 0 here η is the elasticity of substitution beteen any to individual intermediate goods and q i () is the quantity of good used by country i The final good production technology is linear in the composite intermediate good: η () Y Q i i The final good is consumed by representative households in the to countries Both representative households have the same preferences Trade barriers take the form of iceberg costs Let i be the trade barrier for eporting a unit from country i That is, for unit to arrive in country, country must eport units There is no cost for a country to eport unit to itself All markets are competitive Labor is paid the value of its marginal product, hich is denoted by i The marginal cost of producing unit of good in country i is i a i () So for country to supply unit of good to country, the cost is a () Specialization and Trade Let p ij () be the price, in country i, of good, hen the good as produced in country j Each country purchases each good from the country that can deliver it at the loest price Hence, the price in country i of any good is simply p i () min[p i (),p i ()] At this point, it is useful to recall the implications for specialization in the DFS model Define and order the intermediate goods so that A() is decreasing in ; that is, the goods are ordered in terms of declining comparative advantage for country In the interval [0,], country is more productive than country in goods close to 0 and less productive in goods close to Goods Produced by Country Country ill produce any good so long as Solving this equation e obtain a value such that country produces all goods [0, ] Figure A illustrates the choice of for >, given the factor prices and ( ) ( ) a A, a p p a a A 36 Fourth Quarter 05 Federal Reserve Bank of St Louis REVIEW

5 Figure Specialization in Production of Intermediate Goods A Specialization in Country B Specialization in Country A() 0 Produced by A() 0 Produced by A() A() Goods Produced by Country Country ill produce any good so long as p p a a A By solving this equation e obtain a value such that country produces all goods [,]; see Figure B for the case > Traded and Nontraded Goods Although all intermediate goods along the continuum are potentially tradable, goods in the range [, ] are not traded as long as there are trade barriers Country ill import all goods [0, ], hich are precisely the goods they do not produce, hile country ill import all goods [,] Put differently, specialization is not complete hen there are trade barriers (Figure 3) Under free trade, and, hence, the to curves in Figure 3 ould coincide and ould equal Equilibrium Equilibrium is characterized by a trade balance condition (3) L L, here ij is the fraction of country i s spending devoted to goods produced by country j (Recall that the labor endoment in country i is L i ) The trade shares and are Federal Reserve Bank of St Louis REVIEW Fourth Quarter 05 37

6 Figure 3 Trade Barriers and Incomplete Specialization 0 Produced by Produced by A() A() p q d, L p q d, L here i L i is the total income in country i The home trade shares are and The equilibrium price of the composite intermediate good is given by 0 (4) η η Pi pi d PRICE EQUALIZATION In this simple to-country environment, e can rite the price inde of intermediate goods in each country as the sum of three components based on the range of specialization: (5a) (5b) ( ) η η η η 0 P a d + a d + a d ( ) η η η η 0 P a d + a d + a d 38 Fourth Quarter 05 Federal Reserve Bank of St Louis REVIEW

7 The price inde is an average of the prices over three subintervals: goods produced only by country, goods produced only by country, and goods produced by both countries Con - sider first the goods produced only by country For each of these goods the price in country is equal to the price in country times the barrier of shipping from country to country A larger barrier of shipping from country to country amplifies the difference in price for each of these goods, hich in turn increases the price inde in country relative to country Second, consider the goods produced only by country Using a similar argument, a larger barrier of shipping from country to country decreases the price inde in country relative to country Finally, consider the goods produced by both countries These are the goods that are not traded The difference in the price of each of these goods is determined by the difference in the cost of inputs in this case, the age An increase in the trade barrier in either country increases the range of these nontraded goods and results in a larger increase in the price inde for the country ith a higher cost of production Symmetric Countries Suppose that the to countries are symmetric in all eogenous variables: L L,, and a () a ( ) (ie, a () is a mirror image of a ()) Given the symmetry, it is easy to see that the equilibrium specialization is given by ; that is, the range of goods produced in each country ould be the same Then, the trade flo from country to country ould be the same as that from country to country : The trade balance condition (3) then implies In Appendi A, e sho that P P Price equalization in the symmetric case depends on the assumption that and not on hether or > Hoever, the trade flos depend on the barriers To see this, suppose that there are no trade barriers that is, In this case, the specialization is complete: Country spends 50 percent of its income on goods from country and vice versa: No, suppose > In the presence of trade barriers, the specialization is incomplete: Goods in the range [, ] are produced by both countries but are not traded This, in turn, affects the trade flos: < Thus, to infer the presence or absence of trade barriers, one needs information on trade flos Asymmetric Countries Mutreja, Ravikumar, Riezman, Sposi To derive the price equalization result for to asymmetric countries, it is useful to have more structure on each country s technology for producing intermediate goods For symmetric countries, e assumed that the average productivity as the same in both countries and that productivity in country as the mirror image of that in country : a () a ( ) With the same trade barriers in the to countries, the equilibrium factor price ratio,, as equal to We used the equal factor prices to demonstrate that the price inde of intermediate goods is the same in both countries For asymmetric countries, the average productivity is Federal Reserve Bank of St Louis REVIEW Fourth Quarter 05 39

8 different in the to countries, so the equilibrium factor prices need not be the same in the to countries By imposing more structure on the productivities in the to countries e can determine the equilibrium factor price ratio and, hence, the prices of intermediate goods We assume that the comparative advantage function, a A a here the average labor productivity in country i is proportional to the parameter i and the parameter governs the coefficient of variation in productivity (The epression for A() can be derived by folloing Eaton and Kortum, 00 The details are provided in Appendi B) Trade Shares The trade share ij is the fraction of country i s total spending on intermediate goods that ere produced by country j We sho in Appendi B that (6a) (6b) + + The trade shares in equations (6a) and (6b) are clearly beteen 0 and ; that is, each country ill specialize in some goods in the continuum Equations (6a) and (6b) are intuitive For instance, > implies loer If country is more productive than country, then the trade flo from country to country ill be less than it ould be if country is as productive as country Similarly, a larger eport barrier in country implies less trade flo from country to country Prices The trade shares in (6a) and (6b), together ith the trade balance condition (3), determine the equilibrium factor price ratio : (7) + L L + It is clear that there eists a unique relative age that satisfies equation (7) Using equation (4) and the analytical epression for prices p i () (see Appendi B), the relative price beteen the to countries is given by 330 Fourth Quarter 05 Federal Reserve Bank of St Louis REVIEW

9 (8) P P + + If there are no trade barriers, then all goods are traded and PPP holds that is, if, then and P P regardless of the equilibrium relative age (see Figure 3 for the determination of and ) Hoever, in the presence of trade barriers, the relative price ill depend on the relative age, hich is pinned don by equation (7) Suppose that andor L L Is it possible to obtain price equalization ith trade barriers? As it turns out, the anser is yes There are many combinations of > and > that deliver price equalization Hoever, each combination implies a different volume of trade For instance, suppose that to pairs of barriers (, ) and (, ) both generate price equalization If (, ) > (, ), then the volume of trade under (, ) ill be greater than the volume under (, ) Put differently, given price equalization, information on trade flos pins don the trade barriers Numerical Eample Assume that, L L, and 0 What are the 4 combinations of and that deliver price equalization? The trivial case is free trade: The combination and leads to price equalization This is easy to see from equation (8) Free trade implies (see Figure 3 for an illustration of specialization by the to countries) Even though, free trade does not imply Country specializes in a larger range of goods: > The trade flos are given by 04 and 076 Note, hoever, that the factor prices and are not equalized A close look at equation (7) reveals that if > and if, then > Country is, on average, more productive than country No consider the case ith barriers One of the combinations that leads to price equalization is and 5 As noted earlier, since country is more productive than country and its eport cost is loer, must be greater than Barriers to trade imply incomplete specialization, so there is a range of intermediate goods that are not traded The trade flos in this case are given by (9) For price equalization to occur ith asymmetric countries, the eport barrier for the lessproductive country must be larger than the eport barrier for the more-productive country (Figure 4A) The locus of {(, ) P P } lies above the 45-degree line since country is more Federal Reserve Bank of St Louis REVIEW Fourth Quarter 05 33

10 Figure 4 Trade Barriers and Trade Flos Consistent ith Price Equalization A Trade Barrier Combinations Country s Eport Barrier: Free Trade {(, ) P P } 45º Country s Eport Barrier: B Trade Flos Trade Flos from Country to Country : {(, ) P P } 45º Free Trade Trade Flos from Country to Country : 33 Fourth Quarter 05 Federal Reserve Bank of St Louis REVIEW

11 productive The corresponding trade flos are illustrated in Figure 4B by the locus of {(, ) P P } Each barrier combination in Figure 4A corresponds to a unique trade flo combination in Figure 4B Larger barriers imply smaller trade flos All of these combinations deliver price equalization Hoever, each barrier combination corresponds to a distinct set of trade flos beteen the to countries These trade barrier combinations and productivities are in the empirically plausible range Mutreja et al (04) estimate the average productivity,, in producer durables for a sample of 88 countries in 005 In the cross-country distribution of average productivity, the country in the 85th percentile is 38 times as productive as the country in the 5th percentile The trade-eighted eport barrier in the 85th percentile country is 3, and the corresponding barrier in the 5th percentile country is 40 (74 percent higher) In our numerical eample, country is four times as productive as country and the barrier in country is 3 percent higher Testable Implication Since price equalization occurs ith barriers as ell as ith free trade, an obvious question at this stage is ho ould one test hether barriers to trade eist The relevant empirical case is the one ith asymmetric countries For this case, e shoed earlier that it is possible to obtain price equalization even hen there are barriers to trade, provided the country ith the higher average productivity is also the one ith the loer eport barrier In other ords, price equalization in our model implies a negative correlation beteen and Note that if price equalization implies free trade, then for all countries, so the correlation beteen and ould be zero Under the eaker inference in Hsieh and Kleno (007) that the barriers to trade in producer durables are not systematically related to the level of economic development, the correlation beteen and ould again be zero One problem is that the productivity parameter is not directly observable, so e have to use an observable proy to test the implication A convenient proy for in our model is L i i real GDP per orker Real GDP in our model is, so real GDP per orker is P y i Higher productivity (ie, higher ) implies a higher age rate and, ith price equalization, a higher real GDP per orker Another problem is that empirically observable trade costs cannot deliver the observed trade flos, so e cannot use the observed trade costs in our test Hoever, e can use the model-implied relationship beteen trade flos and trade barriers and construct a testable implication In Appendi B, e sho that for to asymmetric countries i i P i Mutreja, Ravikumar, Riezman, Sposi (0a) P P and Federal Reserve Bank of St Louis REVIEW Fourth Quarter

12 (0b) P P Free trade implies and P P Thus, both ratios, and, must equal In our numerical eample, this implication is confirmed The matri of trade flos under free trade is With barriers to trade, our numerical eample has price equalization along ith the implications that is less than and is less than That is, country has a higher GDP per orker, higher, and loer trade barriers In a model ith more than to countries, a general version of equations (0a) and (0b) is j jj Pj P j, here j denotes any country that eports to country For producer durables, since the price inde is roughly the same across countries, the above equation can be ritten as ln j jj ln j Thus, a testable implication of our model is that the higher the GDP per orker in country j j relative to that in country, the higher the ratio Fiing country to be the United States jj and using the sample of 88 countries from Mutreja et al (04) for the year 005, the correlation beteen ln and ln is almost 60 percent The real GDP per orker in Austria is j y j jj y j 86 percent of that in the United States, hile the ratio for Austria is 0 The corresponding numbers for Chile are 7 percent and 006 and for Laos are 5 percent and 000 jj Note that under free trade and under the inference that barriers are uncorrelated ith economic development, should be uncorrelated ith country j s relative GDP per orker j jj 334 Fourth Quarter 05 Federal Reserve Bank of St Louis REVIEW

13 CONCLUSION Mutreja, Ravikumar, Riezman, Sposi We sho theoretically, using a simple to-country model, that the eistence of equal price indees across countries does not imply that there is free trade Information on trade flos is important in determining the magnitude of the trade barriers When there are barriers to trade, e demonstrate that price equalization implies that countries ith higher average productivity must have loer trade barriers n APPENDIXES A Price Equalization for Symmetric Countries To sho that P P for symmetric countries, recall that and a () a ( ) implies a symmetric equilibrium that is characterized by a mirror image specialization,, and equal ages, Using equations (5a) and (5b), the price inde in each country is given by η η η η ( ) 0 ( ) ( ) P a d + a d + a d, η η η η ( ) 0 ( ) ( ) P a d + a d + a d Consider the first component of the price inde in country : η η η 0 0 a d a d a z dz, here the first equality uses the mirror image specialization property and the last equality is due to a change of variables z Note that the last term in the above equation and the third term in the epression for the price inde in country are eactly the same Net, consider the second component in the price inde in country Using analogous logic, η η η a d a d a z dz Note that the last term in the above equation equals the second component in the epression for the price inde in country Finally, consider the third component in the price inde in country : η η η 0 a d a d a z dz The last term in the above equation equals the first component in the epression for the price inde in country Thus, the price indees are equalized in the symmetric equilibrium: P P Federal Reserve Bank of St Louis REVIEW Fourth Quarter

14 B Prices and Trade Flos for Asymmetric Countries We follo Eaton and Kortum (00) and assume that and follo indepena ( ) a ( ) dent, country-specific Fréchet distributions The distributions are characterized by a countryspecific location parameter, i, and common shape parameter, The epected value of a i () is proportional to i, so the average labor productivity in country i across the continuum of intermediate goods is proportional to i Then A since a a a Further more, is distributed Fréchet ith parameters ( i,), a i () is distributed eponentially ith parameter i In this section, e sho ho to derive analytical epressions for price indees and trade shares for asymmetric countries Our derivations rely on three properties of the eponential distribution: Property u ~ ep(α) and k > 0 ku ~ ep(αk) Property u ~ ep(α ) and u ~ ep(α ) min{u,u } ~ ep(α + α ) α Property 3 u ~ ep(α ) and u ~ ep(α ) Pr(u u ) α+ α Price Indees We derive the price inde, P, for the composite intermediate good in country The derivation for P is analogous Country purchases each good from the least-cost supplier, so the price of good is Since a j () ~ ep( j ), it follos from Property that Then, Property implies that No let μ ( ) + ( ) Then p min ( ) a ( ),( ) a ( ) a ( ) ~ ep( ) and ( ) a ep + a, a min ep Finally, appealing to Property again, p ( ) ep( + ( ) ) 336 Fourth Quarter 05 Federal Reserve Bank of St Louis REVIEW

15 Apply a change of variables so that ω μ t and obtain Let γ Γ( + ( η)) ( η), here Γ() is the gamma function Therefore, Using analogous logic, the price inde in country can be epressed as η η P μ t ep μ t dt ( ) η η η P μ ω ep ω d ω P γ μ γ + γ + P γ μ γ + γ + Using the epressions for price indees, the relative price beteen the to countries is (B) + P + P Trade Flos We no derive the trade shares ij, the fraction of country i s total spending on goods that ere obtained from country j As in the Eaton and Kortum (00) setup, ij is also the probability that country j is the least-cost supplier of an arbitrary good For instance, Pr{ } p p Cost minimization by producers of good in country i implies that the cost of each unit of labor is equal to the age rate i Perfect competition implies that the price in country of intermediate good, hen purchased from country, equals the unit cost in country times the trade barrier Hence, Federal Reserve Bank of St Louis REVIEW Fourth Quarter

16 Similarly, Testable Implication From the epression for, e can infer as Hence, From epression (B) for the relative price, it is easy to see that (B) To deliver price equalization in our model, is negatively correlated ith Thus, for an importing country i, e can compute the ratio for all countries j that eport to country i and test hether this ratio is positively correlated ith j { } { } + + Pr a a Pr a a (by Properties and 3) P P ij jj Mutreja, Ravikumar, Riezman, Sposi 338 Fourth Quarter 05 Federal Reserve Bank of St Louis REVIEW

17 NOTE Mutreja, Ravikumar, Riezman, Sposi In equilibrium, each country ill produce only a subset of the goods and import the rest Therefore, average measured productivity ill depend on the range of goods produced and ill be endogenous REFERENCES Anderson, James and van Wincoop, Eric Gravity ith Gravitas: A Solution to the Border Puzzle American Economic Revie, March 003, 93(), pp 70-9 Armenter, Roc and Lahiri, Amartya Accounting for Development Through Investment Prices Journal of Monetary Economics, October 0, 59(6), pp Dornbusch, Rudiger; Fischer, Stanley and Samuelson, Paul A Comparative Advantage, Trade, and Payments in a Ricardian Model ith a Continuum of Goods American Economic Revie, December 977, 67(5), pp Eaton, Jonathan and Kortum, Samuel Technology, Geography, and Trade Econometrica, September 00, 70(5), pp Hsieh, Chang-Tai and Kleno, Peter J Relative Prices and Relative Prosperity American Economic Revie, June 007, 97(3), pp McCallum, John National Borders Matter: Canada-US Regional Trade Patterns American Economic Revie, June 995, 85(3), pp 65-3 Mutreja, Piyusha; Ravikumar, B; Riezman, Raymond and Sposi, Michael J Price Equalization, Trade Flos, and Barriers to Trade European Economic Revie, August 04, 70, pp Taylor, Alan M and Taylor, Mark P The Purchasing Poer Parity Debate Journal of Economic Perspectives, Fall 004, 8(4), pp Federal Reserve Bank of St Louis REVIEW Fourth Quarter

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