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Globalization and the Gains from Variety: Size and Openness of Countries and the Extensive Margin Lukas Mohler, University of Basel July 2009 Abstract With the seminal work of Feenstra (1994) and its application

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Globalization and the Gains from Variety: Size and Openness of Countries and the Extensive Margin Lukas Mohler, University of Basel July 2009 Abstract With the seminal work of Feenstra (1994) and its application to the United States by Broda and Weinstein (2006) the gains from variety through trade as suggested by Krugman (1979) have become quantifiable. My paper adds to this literature in different respects: On the theoretical side, the Feenstra ratios are reinterpreted to allow for unobserved growth at the extensive margin. Also, the gains from variety are decomposed regarding countries of origin and industries. On the empirical side, the gains from variety are calculated for the United States and Switzerland, a small open economy. Analyzing the empirical results for these countries as well as data from other OECD economies, it is then argued that size and openness of countries as well as the (unobserved) true growth at the extensive margin are important factors in determining the welfare gains from variety. JEL classification: F12, F14; Keywords: Welfare Gains from Trade, Trade in Variety, Small Open Economy; I thank Robert C. Feenstra for helpful comments. Furthermore, I am very grateful to Rolf Weder for constant advice on the project. I also thank my colleagues at the University of Basel, the participants of the ETSG in Warsaw, the FIW in Vienna, the YSEM in Berne, the SMYE in Istanbul and the SSES in Geneva for helpful comments and fruitful discussions. I gratefully acknowledge the financial support of the WWZ Forum Basel. This paper has often been presented under the title Globalization and the Gains from Variety: The Case of a Small Open Economy. 1 1 Introduction Since the seminal contributions of Krugman (1979, 1980), economists try to quantify the gains from trade within a monopolistic competition framework. Within such a model, gains from variety stem from three sources: Price reductions due to increasing returns to scale, an increased product variety for consumers, and in more recent models, the self-selection of firms upon trade liberalization. 1 I like to motivate my paper by first revisiting some important contributions about the second source of welfare gains - the gains from variety. The models developed by Spence (1976), by Dixit and Stiglitz (1977), and, applied to trade, by Krugman (1979, 1980) have had a great impact on the theoretical as well as the empirical literature in our field. Within this monopolistic competition setting, consumers value additional varieties depending on the substitutability between varieties, captured by the elasticity of substitution. This dependence on a single parameter and the tractability explains the empirical success of these models. The first attempt to use this framework to quantify the value of new varieties upon trade liberalization is done by Romer (1994). 2 As a consequence of trade barriers and the fixed costs of introducing a new variety into a foreign market, some goods are not profitable enough to be exported and this leads to a limited variety being offered in the importing country. The gains from trade liberalization can then account for up to 20% of GDP if many goods were previously prevented from being imported. Klenow and Rodríguez-Clare (1997) provide some empirical evidence for this calibration exercise. In their paper, the gains from trade liberalization using Costa Rican data can account for up to 2% of GDP. These gains incorporate the gains from variety which raise the overall gains from trade by 50% to 300%. The most influential work to date, however, is done by Feenstra (1994). Within a CES framework, he develops a price index for imports that is corrected for new and disappearing varieties. New varieties lower the unit-costs depending on their substitutability with other varieties and their expenditure share. This allows Feenstra (1994) to quantify the upward bias in conventional import price indices that ignore changes in the set of imported varieties. This approach is used by Broda and Weinstein (2006) to estimate the gains from imported variety in the United States between 1972 and They find that the upward bias of the conventional import price index is 1.2% per year. This leads to a gain from imported variety of 2.6% of GDP over the whole period. This result of Broda and Weinstein (2006) is the topic of a recent debate. Benassy (1996) emphasizes one peculiarity of the standard Dixit-Stiglitz model: The love of variety is constant and equal to the 1 In an excellent survey, Feenstra (2006) reviews the empirical evidence for these gains from trade within monopolistic competition models. 2 Note that many authors have quantifed the value of new varieties using quite different approaches: Examples are Hausman (1997a, 1997b and 1999), based on Hicks (1940). Another example is Petrin (2002) using a random utility specification. However, these approaches require very detailed micro data. 2 mark-up of firms. Based on this work, Montagna (1999) uses a more general model and shows that the standard Dixit-Stiglitz model incorporates a maximum of love of variety. Furthermore, Hummels and Lugovskyy (2005), based on Lancaster (1979), argue that the less than proportional increase in imported varieties with respect to market size can be explained by the falling marginal benefit of importing additional varieties. In their model, this is due to crowding in the variety space. Taking a somewhat different approach, Ardelean (2009) also argues that the standard Krugman (1980) model overstates the love of variety since it assumes that larger countries export more only at the extensive margin, while models in the vein of Armington (1969) assume that countries exports grow only at the intensive margin. She develops a more general model that nests Krugman and Armington style models and concludes that the love of variety is 44% lower than in Krugman s CES model. These contributions imply that Broda and Weinstein (2006) may overestimate the gains from variety. On the other hand, in many contributions it is argued that the disaggregated trade date used in Broda and Weinstein (2006) misses out on some variety growth. For example, Schott (2004) shows that trade data is consistent with vertically differentiated varieties within disaggregated product groups. He shows empirically that those varieties differ regarding capital or skill intensity and therefore differ in quality. Similarly, Hummels and Klenow (2005) argue that the unobserved varieties within HS product categories - both horizontally and vertically differentiated - will affect the extensive margin positively. Hallak and Schott (2008) also emphasize the horizontal and vertical differentiation within trade data, set up a model that can account for these unobserved varieties and estimate those differences. Finally, Blonigen and Soderbery (2009), using very detailed market data, show for the automobile market of the United States that the trade data underestimate the growth in variety by as much as 50%. The detailed firm-level data that has become available recently provides more evidence: In the literature that explores firm-level data, the destination of products, the entry and exit of firms and the number of products per firm are all determinants of the extensive margin. Bernard et al. (2006) argue that much of the change in trade is due to the change within firms. This is also found in Bernard et al. (2009), where multi-product firm level data is analyzed with respect to the intensive and extensive margins and it is found that the extensive margin resulting from entry and exit of firms, but also from new and disappearing products per firm is substantial in the United States. These results are confirmed by Arkolakis and Muendler (2009) for Brazil and Chile. All these contributions imply that Broda and Weinstein (2006) may even underestimate the gains from variety. It is one main objective of my paper to analyze the effect of this unobserved growth at the extensive margin on the gains from variety. 3 I approach this issue by extending Feenstra (1994). I reinterpret the 3 Note that detailed firm-level data is still not available for all the imports of a country. Therefore, to quantify the total gains from imported variety as in Broda and Weinstein (2006), one still relies on the disaggregated trade data. 3 seminal lambda ratios and propose two bounds for the gains from variety: A first case where growth is only possible at the intensive margin of an Armington variety - this is the benchmark case originally proposed by Feenstra (1994) - and a second case where all growth in the expenditure of imports happens at the extensive margin of the Armington varieties. Since the true magnitude of the extensive margin is unobserved, I will argue that the true gains from variety lie within these bounds. I then calculate these two bound empirically for Switzerland, a small open economy, and the United States: For the period from 1990 to 2006, these welfare gains lie between 0.3% and 5.0% of GDP in Switzerland. In the United States, the gains account for between 0.5% and 4.7% of GDP. These results imply that the gains from variety estimated in Broda and Weinstein (2006) are a lower bound and may be even higher if some unobserved growth at the extensive margin is taken into account. As a further theoretical contribution, I provide a decomposition of the gains from variety regarding countries of origin and product categories. This allows me to compare the structure of trade between countries regarding the gains from variety. The empirical results of this decomposition exemplify the different geographical, geopolitical and economic positions of countries: For example, while Switzerland depends heavily on its three large EU neighbours regarding the gains from variety, the gains in the United States are more evenly distributed among its numerous major trading partners in the world. I will then argue that size and openness of countries are, together with the (unobserved) growth at the extensive margin, important factors in determining the welfare gains from variety in countries: First, considering the fact that many SOEs have import shares that are several times larger than the one of the United States, one could imagine larger gains from variety for these economies. Second, SOEs are often supposed to have disadvantages associated with the import of new varieties: Romer (1994) and many others argue that fixed costs limit the number of goods available in an economy. For SOEs, such fixed costs constitute natural barriers to trade: Since the domestic market is small in these economies, fixed costs are more important relative to larger economies and consequently prevent more goods from being imported. 4 My empirical results imply that SOEs in the OECD experience a lower growth in imported variety over time. For Switzerland, I show that this lower imported variety growth compared to the United States results in a large welfare loss for consumers. Despite the lower growth in imported varieties, the gains from variety may be higher in Switzerland due to its much higher import share. I argue in this paper that the higher the assumed growth at the extensive margin, the higher are the gains from variety in Switzerland relative to the gains in the United States due to the much higher import share. Thus, the magnitude of the extensive margin seems not only to be important for the total size of the gains 4 This also is an interesting issue in the light of current theoretical trade literature: A very modern approach to capture variety effects in models is Melitz (2003). In his and other models, heterogeneous firms face fixed costs for exporting and decide whether to enter a foreign market or not. 4 from variety but also for the relative gains between countries. OECD data is used to show that this may hold quite generally for other small and large OECD economies. The paper is structured as follows: Section 2 first reviews the methodology used to determine the gains from imported variety, mainly referring to Feenstra (1994) and Broda and Weinstein (2006). In the second part of this section, the extensions of the model are proposed. Section 3 presents the empirical gains from variety in Switzerland and the United States for the period from 1990 to In Section 4, Switzerland is compared to the United States, and the reasons for the differences in the gains from variety are analyzed. In addition, it is argued that similar results hold for other OECD countries. Section 5 concludes. 2 Modelling, Empirical Strategy, and Estimation In this section, the methodology used to estimate the gains from imported variety as developed by Feenstra (1994) and Broda and Weinstein (2006) is reviewed first. In the second part of the section some extensions to the standard methodology are proposed. 2.1 Review of the Standard Model Imported varieties c are grouped into goods g using the following CES utility function: M gt = ( c C d 1/σg gct m (σg 1)/σg gct ) σg/(σ g 1) ; σ g 1 g G. (1) where σ g is the elasticity of substitution between the varieties of good g. G is the set of goods and C is the set of all potential varieties. d gct is a taste or quality parameter. Utility is separable and homothetic. The unit-cost function for every good g is: ( φ M gt (I gt, d gt ) = d gct p 1 σg gct c I t ) 1/(1 σg), (2) where I gt is the set of varieties available at time t and p gct is the unit price of an imported variety. These unit cost functions are the building blocks for the price index. More specifically, a cost of living index (COLI) is set up. It measures the total cost to the consumer in order to achieve the highest possible utility level given his level of income. With homothetic preferences the cost function for every consumer is independent of the level of income: Diewert (1976) defines an exact price index as the fraction of unit costs: 5 P M g ( p gt, p gt 1, x gt, x gt 1, I g ) = φm gt (I g, d g ) φ M gt 1 (I g, d g ). (3) Note that for the moment a constant set of varieties, I g, henceforth called the common set, is used. 5 Sato (1976) and Vartia (1976) have derived the exact price index for the CES unit-cost function: P g ( p gt, p gt 1, x gt, x gt 1, I g ) = ( pgct p gct 1 c I g ) wgct, (4) where w gct (I g ) = s gct (I g ) = (s gct s gct 1 )/(ln s gct ln s gct 1 ) c I g ((s gct s gct 1 )/(ln s gct ln s gct 1 )), p gct x gct c I g p gct x gct. Thus, the price index is the geometric mean of all price changes. The weights depend on the expenditure shares s gct. The exact price index defined above demands that all the varieties are available at all periods. It is due to Feenstra (1994) that the exact price index for a non-constant set of varieties, I gt, is known: π g ( p gt, p gt 1, x gt, x gt 1, I g ) = φm gt (I gt, d g ) φ M gt 1 (I gt 1, d g ), (5) = P g ( p gt, p gt 1, x gt, x gt 1, I g ) ( λgt λ gt 1 ) 1/(σg 1), (6) where λ gt = λ gt 1 = c I g p gct x gct c I gt p gct x gct, (7) c I g p gct 1 x gct 1 c I gt 1 p gct 1 x gct 1. (8) Hence, the exact or corrected price index with variety change is a conventional price index times an additional term, henceforth called the lambda or Feenstra ratio. Note that the numerators of λ gt and λ gt 1 comprise the expenditure on the common varieties; i.e., those varieties that are available at t and t 1. In the denominator of λ gt the new varieties are included additionally while in the denominator of λ gt 1, the disappearing varieties are included additionally. Thus, the lambda ratio gets smaller if there 5 It is a remarkable feature that the price index does not depend on taste parameters. The intuition for this result shown by Diewert (1976) is that all the information contained in the taste parameters is captured by the expenditure shares. 6 are many new varieties, and it gets larger if there are many disappearing varieties. This is determined entirely by the expenditure on these new and disappearing varieties. This ratio is then weighted by a term negatively related to the elasticity of substitution. Thus, there is a greater correction in the price index if the elasticity is low. If the elasticity is high however, the lambda ratio converges to one. Now that the exact price indices for the imported goods are known, they are aggregated into the aggregate exact import price index: Π M ( p t, p t 1, x t, x t 1, I) = g G [ P g (I g ) = CIP I(I) g G ( λgt λ gt 1 ( λgt λ gt 1 ) 1/(σg 1) ] w gt, (9) ) wgt/(σ g 1), (10) where CIP I(I) is a conventional import price index that does not account for the change in varieties. The ratio of the corrected import price index and the conventional price index expresses the bias from ignoring the change in variety. This ratio is called the end-point ratio (EPR) and it is defined as EP R = ΠM CIP I(I) = CIP I(I) CIP I(I) g ( λgt λ gt 1 ) wgt/(σ g 1) = g ( λgt λ gt 1 ) wgt/(σ g 1). (11) Thus, the EPR is the weighted average of the lambda ratios weighted by a term incorporating the elasticity of substitution. Assuming a simple Krugman (1980) structure, the overall price index of the economy can be written as ( p D Π = t p D t 1 ) w D t (Π M ) wm t, (12) where w M t is the log-change weight of the imports, w D t is the weight of the domestic sector and p D t is the price of the domestic good. Since this structure admits a separation between the domestic and the import markets, the gains from imported variety result in 6 GF V = [ ] w M 1 t 1. (13) EP R Hence, the welfare gains can be calculated by weighting the inverse of the weighted aggregate lambda ratios with the fraction of imported goods relative to total economic activity. To calculate the gains, the elasticity of substitution has to be estimated for every product group. The stochastic model is derived by Feenstra (1994) and is omitted here. 6 This can be derived by using the ratio of the conventional and the corrected price index of the whole economy: ( ) w GF V = Πcon p Π cor 1 = D D ( ) t w t p D D [ t / t CIP I(I) wm t ( ) ] M λgt wgt /(σ w g 1) t 1 = g 1 = [ ] 1 w M t λ gt 1 EP R 1. p D t 1 p D t 1 (Π M ) wm t 7 2.2 Extension I: Proposing Two Bounds for the Gains from Variety As will become clear in the empirical section below, the gains from variety depend heavily on the definition of a variety and so do the relative gains between countries: Using disaggregated trade data sets, varieties are always defined as a particular good stemming from distinct countries of origin. This Armington (1969) definition, although widely used, is special and has its weaknesses: One country continually provides one variety of a specific good. There is no growth at the extensive margin at the level of an Armington variety. Or as Blonigen and Soderbery (2009) put it, The Armington assumption hides substantial variety change. More specifically, if rising expenditures are observed for the imports of a particular Armington variety, this can have two reasons: Either there is growth at the intensive margin (i.e., existing varieties are imported at higher values) or there is growth at the extensive margin (i.e., more actual 7 varieties are imported). The Armington definition of a variety only allows for growth at the intensive margin. In this section I will propose the opposite case: I will set up slightly different lambda ratios that can be interpreted as allowing full growth at the extensive margin. 8 It is then argued that the true gains from variety lie between these two polar cases. This fundamental issue is already adressed by Feenstra (1994). 9 He shows that the lambda ratios as described in the section above do not provide the true correction of the import price index if there is a change in the number of actual varieties. An example can be used to illustrate this point: One variety using this data may be toys from China. In reality however, many actual varieties of toys are imported from China. If this

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