Variety Gains from Trade Integration in Europe

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1 Variety Gains from Trade Interation in Europe d Artis Kancs a,b,c,, Damiaan Persyn a,b,d a IPTS, European Commission DG Joint Research Centre, E Seville, Spain b LICOS, University of Leuven, B-3000, Leuven, Belium c EERI, Economics and Econometrics Research Institute, B-1160 Brussels, Belium d VIVES, University of Leuven, B-3000, Leuven, Belium Abstract This is the first paper that investiates the welfare ains from trade interation in the CEE after the fall of the iron curtain, and the role of variety rowth in determinin the manitude of those ains. We apply the methodoloy of Feenstra 1994), Broda and Weinstein 2006) and Soderbery 2013) to international trade data for Latvia for the period The estimated variety ains are substantial, ranin from 0.874% to 2.890% of GDP per year. Keywords: Variety ains, trade interation, CEE, heteroeneous firms. JEL code: C68, F12, F14, F17, R12, R23. The authors acknowlede helpful comments from Marton Csilla, Aleksandra Parteka, Jan Van Hove and participants of the Workshop on Firm and Product Heteroeneity in International Trade in Leuven. We are rateful to Smirnov Serey Oleovich and Laila Ekharde for their help in accessin the OKP data for Latvia. The authors are solely responsible for the content of the paper. The views expressed are purely those of the authors and may not in any circumstances be rearded as statin an official position of the European Commission. Correspondin author address: d'artis.kancs@ec.europa.eu d Artis Kancs)

2 1. Introduction The fall of the iron curtain in the beinnin of the nineties has led to one of the larest trade interation shocks in the postwar history. It made it possible for the interation of forein trade in around a dozen of former centrally planned communist countries in Central and Eastern Europe CEE) into the world tradin system. Such examples of abrupt and rapid trade interation provide an interestin laboratory for a quantitative assessment of the welfare ains from trade interation. This paper uses the example of Latvia s breakout of the politically imposed isolation and provides the first estimates of variety ains from CEE s interation into the world tradin system, by comparin the immediate period before and after the fall of the iron curtain. Kruman 1980) was amon the first, who noticed that an enhanced set of differentiated varieties may increase the economic welfare. Since then, both the methodoloy Romer, 1994; Feenstra, 1994; Feenstra and Kee, 2004; Broda and Weinstein, 2006; Arkolakis et al., 2008; Soderbery, 2013), and the empirical evidence Broda and Weinstein, 2004; Hummels and Klenow, 2005; Broda and Weinstein, 2010; Kancs, 2010; Blonien and Soderbery, 2010) have improved sinificantly. Most of the existin empirical studies have calculated variety ains from imports in developed economies usually the USA and the EU and find substantial welfare ains ranin between 0.1 and 0.5 percent of GDP per year. These variety ains from trade are in addition to the traditional ains from trade, suestin that the true ains from trade interation, particularly in cases of lare and sudden trade interation shocks such as the fall of the iron curtain in the CEE, miht be even hiher than commonly assumed. Given that variety ains from trade are substantial in developed economies Broda and Weinstein, 2004; Hummels and Klenow, 2005; Broda and Weinstein, 2010; Blonien and Soderbery, 2010), where forein trade is widely liberalised, likely, they are even hiher when autarkic economies open their markets to forein trade. A prominent example in the postwar history is the fall of the iron curtain in the CEE, where trade with the West was prohibited for politically-ideoloical reasons. Durin the Soviet period, the quantity and the variety of oods produced, traded and consumed were not decided by the relative prices and consumer preferences, but instead, by central planners, who in many cases rationed both the quantity and the variety of traded oods. The openin of the CEE to trade and the launch of restructurin of centrally planned economies to free market economies chaned production, trade and consumption patterns sinificantly in the beinnin of the nineties. On the one hand, consumers and producers ained access 1

3 to a considerably larer variety of Western oods, which were unavailable under the central plannin. On the other hand, fiercer competition from Western firms reduced the scope and scale of domestic firms operatin in the CEE, decreasin in such a way the number of domestically produced varieties. In addition, consumption patterns were affected also by centrifual shifts in the distribution of real income across income roups of population. The present paper attempts to quantify the variety ains from trade interation in the CEE by calculatin and comparin the variety-adjusted exact price indices for imports from the West before and after the fall of the iron curtain. In the empirical analysis we employ a detailed seven diit trade data on domestic sales and imports in Latvia from 1990 until 1994, usin the methodoloies developed by Feenstra 1994); Broda and Weinstein 2006); Soderbery 2013). We define varieties as product lines at 7-diit level, because this is the only data available for Latvia for the period before and after fall of the iron curtain. We estimate the cumulative welfare ains from import variety rowth durin the analysed five year period are equal to % of GDP, which corresponds to an averae annual variety ain of 2.068% of GDP. These results are new, no directly comparable estimates are available in the literature. To our knowlede the two closest studies to ours are Levchenko and Zhan 2012) and Berlinieri 2013). Levchenko and Zhan 2012) estimate the welfare ains from trade interation in a hypothetical scenario, with a baseline assumption of preservin the iron curtain. The authors obtain substantial cumulative welfare ains for the CEE economies ranin up to 15% of GDP in Latvia and 20% of GDP in Estonia. Berlinieri 2013) estimates variety ains associated with the fall of the iron curtain for tradin partners in the West, and finds substantial variety ains from trade liberalisation with the CEE, e.. the cumulative variety ains for the UK are estimated at 2% of GDP. In liht of these findins, our cumulative estimates of around 10% of Latvian GDP seem to be reasonable. In the context of previous empirical findins for developed economies Broda and Weinstein, 2004; Hummels and Klenow, 2005; Broda and Weinstein, 2010; Blonien and Soderbery, 2010), these estimates are rather lare. However, they need to be seen in liht of the initial pattern of forein trade in Latvia, which was heavily biased and restricted towards the West. To the best of our knowlede, this is the first paper to estimate the variety ains from trade interation associated with the fall of the iron curtain in the CEE in the beinnin of the nineties. Our findins are important not only for the assessment of the true 2

4 benefits from the CEE interation into the world tradin system, but they also provide an important laboratory feedback about the behaviour of estimators of variety ains also in extreme trade liberalisation scenarios, such as the fall of the iron curtain. 2. Methodoloy for estimatin variety ains 2.1. Love of variety Followin Broda and Weinstein 2006), we assume a two-tier utility function, where, at the first tier, consumers decide how much to consume domestic and imported oods accordin to Cobb-Doulas preferences, and, at the second tier, how much to consume of each variety of these oods accordin to CES preferences. 1 Suppose that I is the set of imported varieties of some ood available to consumers and i I is a variety of ood. As shown by Dixit and Stilitz 1977), an asymmetric second tier sub-utility function for imports can be represented by: U t = 1 σ 1 σ dit x σ it i I t σ σ 1 1) where σ > 1 is the elasticity of substitution between varieties of ood, x it is the quantity consumed of variety i in period t, and d it is a taste or quality parameter, which can be asymmetric across varieties. Assume that quantities, x t, 2 are optimally chosen such as to minimise i I p it x it subject to achievin utility U x t, d t ) = 1. As shown by Diewert 1976), the solution to this minimisation problem yields the correspondin minimum unit cost function: c t pt, d t ) = d it p 1 σ it i I t where p it is the price of variety i. The minimum unit cost function 2) is decreasin in the number of consumed varieties, and in taste for a particular variety. The unit cost is 1 1 σ increasin in price and the elasticity of substitution between varieties. 2) 1 Given that the structure of domestic and import nests is identical, we spell out only one of the two for imports. 2 Throuhout the paper we use bold face to denote vectors of varieties. 3

5 Differentiatin 2) yields expenditure shares, s it, implied by taste parameters d t : 2.2. Conventional exact price index s it = ln c p t, d t ) / ln pit = c p t, d t ) 1 σ d it p 1 σ it 3) First, we derive a benchmark price index aainst which to measure the variety ains. Followin Diewert 1976), we assume that there are two periods, t 1 and t, and that the quantity vectors x t and x t 1 are the cost-minimisin bundles of ood s varieties iven the prices of all varieties in both periods, p t and p t 1, and the vectors of variety tastes d t and d t 1. Followin Diewert 1976), we define the exact price index as the ratio of expenditures needed to obtain a fixed level of utility at two different prices: 3 P CEPI pt, p t 1, x t, x t 1 ) = c t pt, d t ) c t 1 pt 1, d t ) 4) Followin Sato 1976) and Vartia 1976), we assume CES unit cost function with constant tastes, d it = d it 1 = d i, and a constant set of available product varieties available in both periods, I t = I t 1 = I, which allows us to derive a conventional exact price index, P CEPI : P CEPI ) wit ) pit pt, p t 1, x t, x t 1 = = c ) t pt, d t ) 5) p i I it 1 c t 1 pt 1, d t where the ideal lo-chane weihts, w it, functions of expenditure shares, s it 1 and s it are equal to the ratio of unit costs: 4 w it = sit s it 1 ln s it ln s it 1 ) / i I s it s it 1 6) ln s it ln s it 1 3 The cost-of-livin price index is called exact, because the cost-of-livin price index, P CEPI, exactly matches chanes in the minimum unit-costs, c. 4 Accordin to Sato 1976) and Vartia 1976) 1976), w it captures the share of differences in cost shares over time normalised by the difference in loarithmic cost shares over time in the areate differences in cost shares over time normalised by the difference in loarithmic cost shares over time. 4

6 with the correspondin expenditure share, s it, on each variety s it p it x it i I p it x it 7) As shown by Sato 1976) and Vartia 1976), the conventional exact price index 5) is equal to the eometric mean of price ratios in the two periods with weihts w it. However, a critical assumption of the Sato 1976) and Vartia 1976) exact price index is that all varieties are available in both periods, i.e., the set of available varieties does not chane. Kruman 1980) was amon the first who noted that an enhanced set of horizontally differentiated varieties may contribute to an increase in economic welfare. Assumin symmetric CES preferences, d i = 1 i I, Kruman 1980) has shown that for a iven p t = p ), 5 an increase in the number of available varieties, I t, e.. throuh more types/sources of imports, reduces the minimum cost, c t : c t It ) = I 1 1 σ t p t 8) which is required to achieve a iven level of utility. Or alternatively, an increase in the number of available varieties increases the utility, which can be achieved at cost c t. Analoously to 4), the ratio of minimum unit costs can be measured by the cost-oflivin exact price index, P CEPI : P CEPI pt, p t 1, x t, x t 1, I ) = p t p t 1 = c t It ) c t 1 It 1 ). 9) Accordin to the price index 9), trade interation will not chane the number of available varieties, and hence it will not capture a fall in minimum costs, or equivalently, a rise in utility due to a variety rowth Variety-adjusted exact price index Romer 1994) proposes an extension of the Kruman 1980) model to allow for fixed 5 Assumin symmetric CES preferences, d i = 1 i I, implies that all varieties i of ood are equally priced at p. Alternatively, iven that all suppliers are symmetric, all varieties have the same price and there is no need for weihts. 6 In the model of Kruman 1980) the key source of price reductions is increasin returns to scale. As tariffs are reduced between two countries, some firms exit the market and the remainin firms expand their output and lower their averae costs throuh economies of scale. The reduction in averae costs also leads to a reduction in prices in the zero-profit equilibrium. 5

7 costs of accessin forein markets so that the number of available varieties can rise with declinin tariffs. In order to account for variety rowth, Romer 1994) multiplies the conventional exact price index, P CEPI, by the ratio of available varieties in the two periods, which yields a symmetric variety-adjusted exact price index: P VEPI pt, p t 1, x t, x t 1, I t, I t 1 ) = P CEPI It 1 I t ) 1 σ 1 10) As in Kruman 1980), the imported varieties are symmetric the same price and quantity) also in 10), implyin that the extensive import marin equals the number of imported varieties. An increase in the number of varieties, I t, in period t compared to the number of varieties, I t 1, available in period t 1 leads directly to a fall in the exact price index, P VEPI, relative to the conventional price index, P CEPI. In other words, an increasin number of varieties, I, for ood will lower the ratio of old to new varieties, I t 1 /I t, and hence the variety-adjusted exact price index, P VEPI. The downside of the Romer 1994) approach is that the variety-adjusted exact price index 10) can yield substantial bias which are different from 5)). For example, if new varieties represent only a small share of the total expenditure in a ood, then a simple count of varieties will rossly overestimate the true impact of new varieties. Feenstra 1994) provides a more eneral framework for the case when the overlappin) set of asymmetric varieties chanes between the periods. In derivin the relationship between the conventional price index without variety chanes) and the exact price index which accounts for variety chanes over time), Feenstra 1994) relaxes the symmetry assumption of Kruman 1980) and Romer 1994), and the assumption of a constant set of varieties of Kruman 1980), implyin that I t = I t 1. As above, the assumption that taste parameters are constant over time, i.e. d it = d it 1 = d i, is maintained. In line with the definition of the exact cost-of-livin price index, the asymmetric variety-adjusted price index of Feenstra 1994) equals the ratio of unit costs and uses weihts which are functions of the expenditure shares s it 1 and s it, P VEPI p, x, I ) = p it s it It ) 1 σ 1 p it 1 s it 1 It 1 ) 1 σ 1 = c t dit, I t, p it ) c t 1 dit 1, I t 1, p it 1 ) 11) Definin two new variables λ t i I p it x it / i It p it x it and 6

8 λ t 1 i I p it 1 x it 1 / i It 1 p it 1 x it 1, 7 and usin the definition of s it iven in ) ) 7), the expenditure share on each variety can be expressed as s it It = sit I λt ) ) ) ) and s it 1 It 1 = sit 1 I λt 1. Substitutin s it I λt and s it 1 I λt 1 into equation 11), allows us to rewrite the asymmetric variety-adjusted price index as: P VEPI pt, p t 1, x t, x t 1, I t, I t 1 ) = P CEPI λt λ t 1 ) 1 σ 1 12) where λ t equals the fraction of expenditure on varieties that are available in both periods, i I p it x it, relative to the entire set of varieties available in period t, i It p it x it. Analoously, λ t 1 equals the fraction of expenditure on varieties that are available in both periods, i I p it 1 x it 1, relative to the entire set of varieties available in period t 1, i It 1 p it 1 x it 1. 8 Term ) 1/σ 1) λ t /λ t 1 measures the deviation bias) of conventional exact price index, P CEPI, variety-adjust exact price index that takes variety rowth into account, P VEPI, and it is inversely related to product variety. The inverse measure of product variety, λ t /λ t 1 ) 1/σ 1), depends on two parameters: λ and σ. First, note that λ t is decreasin in the expenditure share of new varieties. Hence, the hiher the expenditure share of new varieties, the lower is λ t, and the lower is the variety-adjusted exact price index, P VEPI, compared to the conventional exact price index, P CEPI. Second, the variety-adjusted exact price index 12) of Feenstra 1994) depends also on the ood-specific elasticity of substitution between varieties, σ. The hiher is σ, the lower is the exponent, 1/ σ 1 ), implyin that the inverse measure of product variety, λ t /λ t 1 ) 1/σ 1), approaches unity. When existin varieties are close substitutes to new or disappearin varieties, chanes in variety between t 1 and t will have a small impact on the exact price index. In contrast, when σ is small, varieties are far substitutes, consumers value new varieties a lot, and the disappear of varieties is very costly. In this case the exponent, as the whole bias term, approaches infinity implyin that the difference between the conventional price index, P CEPI, and the exact price index, P VEPI, will be lare. 7 The numerators of λ t and λ t 1 comprise the expenditure on varieties available at both time t and t 1. The set containin these varieties, I, is referred to as the common set. The denominators of λ t and λ t 1 consist of expenditures on varieties belonin to the sets I t and I t 1, respectively. In the first set, common and new varieties are included, while in the second set, common and disappearin varieties are included. Hence, hih expenditures on new varieties lower the lambda ratio, while hih expenditures on disappearin varieties increase it. 8 Alternatively, this can be interpreted as one minus the share of period t expenditure on new oods not in the set I), i It,i/ I p it x it. 7

9 2.4. Areated price index and welfare ains Areatin the variety-adjusted price indices over all product cateories yields a variety-adjusted import price index: P VEPI m ) It, I t 1 = P VEPI ) ) w t It, I t 1 13) G Price index 13) is dual for domestic varieties. In line with the Cobb-Doulas preferences at the first tier, the areated variety-adjusted exact price index is: P VEPI = ) Pd VEPI wdt + where w t and w mt are areated lo-ideal weihts. ) Pm VEPI wmt 14) An increase in the variety of oods available for consumption reduces the value of a cost-of-livin price index, and hence increases consumer standard of livin. In order to calculate the bias resultin from inorin chanes in the variety, we follow Broda and Weinstein, 2006) and take the ratio of the variety-adjusted import price index, P VEPI from section 2.3, to the areated conventional import price index, P CEPI, from section 2.2, which yields the so called endpoint ratio EPR): EPR m = PVEPI m P CEPI m It, I t 1 ) It ) = λt λ t 1 ) w t σ 1 15) Equation 15) suests that the EPR is a weihted eometric mean of the lambda ratios. Given the CES preferences at the second tier, the welfare ains from import variety rowth can be written as: 9 W m = = [ ] 1 wmt 1 EPR m i It 1 p it 1 x it 1 i I p it x it i It p it x it i I p it 1 x it 1 ) w t σ 1 wmt 1 16) where w t and w mt are areated lo-ideal weihts of Sato 1976) and Vartia 1976): 9 Applyin the same measure 16), variety rowth and the associated welfare ains can be measured both for imports and for exports, and either comparin a country set of countries) across time or comparin countries at a point of time. 8

10 w t = w mt = G s t s t 1 ln s t ln s t 1 s t s t 1 with s t = ln s t ln s t 1 i I p it x it G i I p it x it s mt s mt 1 ln s mt ln s mt 1 with s mt = G i I p it x it GDP t where G is the set of oods which remains constant over the whole period, I is the set of common varieties over the periods, p it x it is the value of imports of a particular i variety in year t, and GDP t is the ross domestic product. Accordin to equation 16), the welfare ains from import variety rowth are calculated by weihtin the inverse of the weihted areate lambda ratios with the fraction of imported oods relative to the total economic activity, w mt. Gains from variety rowth are increasin in import share in the total economic activity as, ceteris paribus, consumers care more about variety rowth in sectors that occupy lare share of consumption than in small sectors. Gains from variety are increasin in the number of new varieties. The more new varieties are imported, the larer is consumer choice and the bier are welfare ains from variety. Gains from variety are decreasin in the elasticity of substitution between varieties. If varieties of a particular ood are perfectly substitutable, then havin two varieties of that ood will have no impact on welfare. 3. Data and empirical implementation 3.1. Data sources In the present study we use the industrial and aricultural production IAP) data, which is compiled accordin to the Obshchesoyuznyy klassifikator promyshlennoy i sel skokhozyaystvennoy produktsii OKP). The OKP reroups all oods and services hierarchically into 7-diit product lines. It total, at the sevenths diit s level the IAP contains more than 2 million product lines. However, durin the period of our study the number of distinct traded product varieties does not exceed 50,000 at the 7-diit level. Hence, this is our upper level for identifyin varieties. The IAP data covers all non-military oods and services sold in Latvia Latvian Soviet Socialist Republic until 1991) from 1990 throuh Two types of variables are provided in the IAP data: the value of traded oods and the quantity of traded oods for domestic sales and imports. Dividin values by quantities allows us to construct the unit cost price) variable for each variety of all traded oods. The IAP data are confidential, 9

11 and, for the purpose of this study, accessed under a special areement. Given that the data are not available in electronic format, the oriinal typewritten documents were accessed and subsequently diitalised by scannin in the archived data sheets. Areated macro-data, such as GDP by country and bilateral trade flows are drawn from the GTAP database. The evolution of imports from the OECD countries in Latvia from 1990 to 1994 is shown in Fiure 1. Accordin to the top dashed line value of trade), the areated value of imports from the OECD countries has remained rouhly at the same level over the five year period from In contrast, the averae value of imported oods from the OECD countries intensive marin) has decreased steadily between 1990 and The observed decrease in the prices for Western oods after the fall of the iron curtain can be traced back to the Soviet period, when the scarcely available Western oods were considered as luxury oods, and hence were marked-up by a luxury add-on intensive marin in Fiure 1). Moreover, if trade costs are in part fixed as in Romer 1994), see section 2.3), oods with lower value added and lower prices) will be introduced only radually over time as tanible and intanible fixed trade costs decrease. Fiure 1 indeed suests that the number of imported varieties extensive marin) has increased continuously durin the five years extensive marin). In the context of about the same areated import value from the OECD in 1990 and 1994 value of trade), an increase in the number of imported differentiated oods extensive marin) is in line with the observation that the averae value of imported ood from the OECD countries intensive marin) has decreased between 1990 and Definin the variety Usually, varieties are defined based on trade data accordin to the classification of oods, accordin to the country of oriin as in Arminton 1969), or both. Adoptin a two-way classification first, by cateories of oods and second, by countries of oriin the nest unit of observation on the import side is a certain product cateory stemmin from a particular country. A more recent firm level evidence suests that for consumers not only the country of oriin is important, but also a particular product produced by a particular firm. This implies that in addition to the set of oods and the number of tradin partners countries of oriin), also the number of active firms and the scope of available products within these firms determine the extensive marin of trade. For example, Bernard et al. 2009) show that chanes in the extensive marin resultin from the entry and exit of firms, but also from product turnover within existin firms, are mainly responsible for import and 10

12 Imports lo) Intensive marin Extensive marin Value of trade year Fiure 1: Evolution of imports from the OECD, Source: GTAP data base. export rowth over loner time spans in the United States. Amon others, Broda and Weinstein 2010) and Blonien and Soderbery 2010) adopt this definition of variety. As emphasised before, the evidence suests that the more relevant increase in varieties followin the fall of the iron curtain was not an increase in the number of source-countries from which the CEE countries could import oods, but rather the fact that truly new varieties became available, such as previously unavailable types of fruit or textiles. We therefore define varieties simply as those oods on a certain lower level of classification within a ood at a hiher level of classification. A more practical reason for definin variety accordin to the classification of oods is that this is the only data available for Latvia for the period we are interested in, i.e. before and after fall of the iron curtain. 4. Estimation of elasticities The estimation of variety ains from trade interation accordin to equation 16) is data demandin and requires, amon others, the elasticity of substitution between varieties, σ, of ood. We estimate the elasticity of substitution between varieties for each ood econometrically, usin the methodoloy of Soderbery 2013) which in turn is based on the work of Feenstra 1994) and Broda and Weinstein 2006). We start by describin the assumptions on the data eneratin process which is shared by these three 11

13 contributions. We then turn to a description of the different estimators which have been proposed Data eneratin process To obtain estimates of demand elasticities from observed quantities and prices, we need a model for both supply and demand, and assumptions allowin for identification. Reconsider the asymmetric CES utility function which was shown in equation 1) and is reproduced here for easy reference: U t = 1 σ 1 σ dit x σ it i I t σ σ 1. 17) As shown in equation 7), iven a CES utility function at the second tier, the share of expenditure on a sinle variety i I relative to the total expenditure on all varieties of ood equals to s it p it x it i I p it x it = pit c t ) 1 σ d it, 18) where c t is the unit cost function from equation 2). This expenditure share derived from the consumer optimisation problem will be interpreted as the demand equation. We take loarithms and difference over time to obtain lns it ) = φ t + 1 σ) lnp it ) + ɛ it, 19) where φ t = σ 1) ln [ c t d t )/c t 1 d t 1 ) ] is a random effect common to all varieties within a ood, and ɛ it = lnd it ) captures remainin idiosyncratic disturbances to demand stemmin from chanes in taste for sinle varieties. Before estimatin 19), correlation between ɛ it, prices and shares needs to be addressed. As quantities and prices are determined jointly by the intersection of demand and supply, demand shocks would simultaneously affect quantities shares) and prices, and runnin OLS on equation 19) would lead to biased estimates. To address this bias, a supply schedule is introduced as ln p it = ψ t + ω 1 + ω ln s it + δ it, 20) where ψ t = ω ln E t /1 + ω ) aain is a random effect which depends on both the 12

14 inverse supply elasticity ω homoeneous across varieties within the ood), and the total expenditure on the ood, E t. The error term δ it = lnξ it )/1 + ω t ) captures all remainin variety-specific supply shocks. Similar to how differencin over time removes cross-sectional time-invariant effects in a panel-setup, the supply and demand equations are differenced with respect to a reference variety k I to remove the ood-specific terms φ t and ψ t. Denotin this double differencin operator with k, we obtain k ln s it ln s it ln s kt = σ 1) k ln p it + ɛ k it, and k ln p it ln p it ln p kt = ω 1 + ω k ln s it + δ k it. 21) A key assumption for identification is that the remainin demand and supply shocks to varieties are independent, such that E[ɛ k it δk it ] = 0. We can write demand and supply brinin the error terms to one side, and multiply both equations to obtain or k ln p it ) 2 = θ 1 k lns it )) 2 + θ 2 k lns it ) lnp it )) 2 + ɛ k it δk it Y it = θ 1 X 1,it + θ 2 X 2,it + u it, 22) where Y, X 1, X 2 and u are appropriately defined, and θ 1 = ω 1 + ω )σ 1) and θ 2 = 1 ω σ 2) 1 + ω )σ 1). 23) Note that the variables in 23) are the second moments of chanes in prices and expenditure shares, and the error term is the cross-moment of demand and supply shocks Estimators As demand shocks are assumed to be independent, we have E[u it ] = 0. Unfortunately, the error term is correlated with both prices and expenditure shares contained in X 1 and X 2, causin direct estimation of 23) to produce biased results. 13

15 Feenstra 1994) proposes a simple method to obtain estimates for θ 1, θ 2 and thereby for the elasticities σ and ω, by time-averain equation 23) to obtain Y i = θ 1 X 1,i + θ 2 X 2,i + u i, 24) which can be estimated by OLS or usin WLS with 1/T i as weihts for increased efficiency. This between estimation provides unbiased estimates as plimu i )=0 such that the error-term and source of bias) disappears as T, under the condition that X 1 and X 2 are not proportional. This estimator is an implementation of the GMM estimator approximatin the moment condition E[u it = 0]. As arued by Broda and Weinstein 2006), however, this method frequently produces estimates of θ 1 and θ 2 which do not correspond to meaninful values for σ and ω. As a solution, they suest to run a rid search over a set of possible values for σ and ω, translate this into values for θ 1 and θ 2, evaluate the GMM objective function and choose those parameter combination which minimises it. The rid-search itself is not free from problems, however. In practice, it turns out that the simple estimator of Feenstra 1994) fails because of reasons which also cause problems for the rid-search. As a result, the rid-search will very frequently end up with solutions which are close to the boundary of the rid, with very hih or very low estimates for the elasticities as a result. As arued by Soderbery 2013), in turn, the underlyin problem of these problems is that the second step of the above estimation method, which starts from the correlation and variation of expenditure shares contained in the time-averaed variables for each variety, ives an equal weiht to each variety - apart from weihin by the number of observations. This tends to assin a lot of weiht to outliers, especially for those varieties or entire datasets) where T is small. Soderbery 2010, 2013) shows that a Limited Information Maximum Likelihood LIML) estimator is less sensitive to such small sample bias, and proposes a hybrid estimator which switches from LIML to constrained nonlinear LIML in cases where standard LIML would produce meaninless estimates of the elasticities. Given these advantaes of the LIML estimator, in the present study we follow Soderbery 2010, 2013) and use this estimator Elasticity estimates Usin the hybrid LIML estimator of Soderbery 2013), we estimated the elasticities between varieties of different oods. Fiure 2 shows the cumulative distribution function 14

16 Fiure 2: Cumulative distribution function of elasticity estimates of our elasticity estimates, replacin estimates of σ in excess of The left panel shows the results when definin oods on the 2-diit level, and varieties on the 5-diit level, and compares this to the estimates when definin oods at the lower 4-diit level and varieties on the same 5-diit level. As intuition would suest, the 5-diit varieties are more heteroeneous to consumers when combinin them in a few 2-diit level oods and as a result the estimated elasticity of substitution is lower with oods defined on the 2-diit level. For example, about 20 percent of elasticities are lower than 1.5 with oods at the 4-diit level, whereas this is about 35 percent with oods at the 2-diit level. Reversely, virtually no 2-diit level ood has an estimated elasticities above 2.5, whereas about 10 percent of the 4-diit level oods do. The riht panel in Fiure 2 plots the distribution of elasticities with oods at the 2-diit level and varieties at the 5-diit level, but now compares it with oods defined at the 4-diit level and varieties at the 7-diit. Althouh, in both choices varieties are 2-levels of classification down from the oods level, we expect 7 diit varieties within 5 diit oods to be more substitutable compared to 5 diit varieties within 2-diit oods. Aain this intuition is confirmed by our estimates. 5. Results: variety ains from trade interation in Latvia 5.1. Main results We estimate the variety ains from trade interation in Latvia based on equation 16) and trade data as described in section 3. Here, which is our main specification, we define 10 This is done in order to improve the optical tractability of the Fiure. 15

17 ood at the five-diit level and varieties at the seven-diit level. The estimation results are reported in Table 1. The first column reports years ), the second column reports the conventional exact price index, Pm CEPI, calculated accordin to equation 5), the third column reports the variety-adjusted exact price index, Pm VEPI, calculated accordin to equation 16), column four reports the endpoint ratio EPR) equation 15)), and columns five and six report the bias and welfare ains due to import variety rowth, respectively. Table 1: Estimated variety ains from trade interation in Latvia, year Pm CEPI Pm VEPI EPR m bias W m Notes: Definition of ood: five-diits, definition of variety: seven-diits. Variety ains, W m, are estimated accordin to equation 16), by usin trade data described in section 3, and elasticity estimates reported in section 4.3. Variables bias and W m are measured in percent. The cumulative welfare ains from import variety rowth durin the analysed five year period are equal to % of GDP sum of column W m ), which corresponds to an averae annual variety ain of 2.068% of GDP. The estimates reported in Table 1 also suest that there is a sinificant variation in the estimated welfare ains between years and with respect to the source of ains from trade. The hihest variety ains are estimated for % of GDP), followed by % of GDP). A comparison of columns five and six suests that there is no one-to-one mappin between the bias from nelectin chanes in the variety column bias) and welfare ains from variety rowth column W m ). The ains from variety take into account also the share of imports in the GDP, which has increased steadily until These results cannot be confirmed or rejected) based on existin studies, because there are no directly comparable estimates available in the literature. To our knowlede the two closest studies to ours are Levchenko and Zhan 2012) and Berlinieri 2013). Levchenko and Zhan 2012) estimate the welfare ains from trade interation in a hypothetical scenario, with a baseline assumption of preservin the iron curtain. The authors obtain substantial cumulative welfare ains for the CEE economies ranin up to 15% of GDP in Latvia and 20% of GDP in Estonia. Berlinieri 2013) estimates variety ains associated 16

18 with the fall of the iron curtain for tradin partners in the West, and finds substantial variety ains from trade liberalisation with the CEE, e.. the cumulative variety ains for the UK are estimated at 2% of GDP. In liht of these findins, our cumulative estimates of around 10% of Latvian GDP over the five year period are considerable. In the context of previous empirical findins for developed economies Broda and Weinstein, 2004; Hummels and Klenow, 2005; Broda and Weinstein, 2010; Blonien and Soderbery, 2010), these estimates are rather lare. However, they need to be seen in liht of the initial pattern of forein trade in Latvia, which was heavily restricted and biased. As shown in Fiure 1, very few commodities were imported in Latvia from the OECD before the fall of the iron curtain 1990). In addition, iven that imports from the West were scarce, they were marked up as luxury oods. An increase in the availability of Western oods on the post-autarkic markets durin the nineties, and a decrease in prices for imported oods both contributed to a rapid increase in the demand for Western oods. Given that most of the observed trade rowth took place throuh the extensive marin of trade see Fiure 1), the estimated variety ains seem to be reasonable. Table 1 also reports the key variables which were used to compute the variety ains: the conventional exact price index, Pm CEPI, the variety-adjusted exact price index, P VEPI m, and the ratio between the two, EPR m. As expected, both prices indices Pm CEPI are above one durin the whole five-year period, implyin that consumer and Pm vepi expenditures in Latvia have increased for imports from the OECD countries. However, the variety-adjusted exact price index, Pm VEPI, consistently suests a smaller increase in the costs-of-livin than the conventional exact price index, Pm CEPI, EPR m < 1, t), suestin that nelectin variety ains would underestimate welfare ains from trade Robustness checks In this section we estimate variety ains under alternative definitions of oods and varieties. First, variety ains are calculated by definin oods at the four-diit level and varieties at the seven-diit level. Second, variety ains are calculated by definin oods defined at the six-diit level and varieties at the seven-diit level. The results are reported in Tables 2 and 3, respectively. Generally, the results reported in Tables 2 and 3 suest the same order of manitude of the estimated variety ains from trade interation in Latvia. By definin oods at the four-diit level and varieties at the seven-diit level Table 2) slihtly increases the estimated variety ains: the cumulative welfare ains are % of GDP and the annual ains are 2.298% of GDP. In contrast, by definin oods at the six-diit level and 17

19 Table 2: Estimated variety ains from trade interation in Latvia, year Pm CEPI Pm VEPI EPR m bias W m Notes: Definition of ood: four-diits, definition of variety: seven-diits. Variety ains, W m, are estimated accordin to equation 16), by usin trade data described in section 3, and elasticity estimates reported in section 4.3. Variables bias and W m are measured in percent. Table 3: Estimated variety ains from trade interation in Latvia, year Pm CEPI P VEPI m EPR m bias W m Notes: Definition of ood: six-diits, definition of variety: seven-diits. Variety ains, W m, are estimated accordin to equation 16), by usin trade data described in section 3, and elasticity estimates reported in section 4.3. Variables bias and W m are measured in percent. varieties at the seven-diit level Table 3) slihtly reduces the estimated variety ains: the cumulative welfare ains are 9.554% of GDP and the annual ains are 1.911% of GDP. 6. Conclusions The fall of the iron curtain in the beinnin of the nineties led to one of the larest episodes of abrupt trade interation in the postwar history. This is the first paper that estimates the welfare ains from trade interation in the CEE after the fall of the iron curtain, and the role of variety rowth in determinin the manitude of those ains. We apply the methodoloy of Feenstra 1994), Broda and Weinstein 2006) and Soderbery 2013) to international trade data for Latvia for the period The estimated variety ains are substantial, ranin from 0.874% to 2.890% of GDP per year. Over the period , the extensive marin of trade has contributed to additional % increase in welfare ains from trade interation in Latvia. These findins suest 18

20 that the true ains from trade interation in the CEE after the fall of the iron curtain are likely to be hiher than it is usually assumed. References Arkolakis, C., Demidova, S., Klenow, P. J. and Rodriuez-Clare, A. 2008). Endoenous variety and the ains from trade. American Economic Review, 98 2), Arminton, P. 1969). A theory of demand for products distinuished by place of production. IMF Staff Papers, 16, Berlinieri, G. 2013). Variety Growth, Welfare Gains and the Fall of the Iron Curtain. Unpublished manuscript, London School of Economics. Bernard, A. B., Jensen, J. B., Reddin, S. J. and Schott, P. K. 2009). The marins of US trade. American Economic Review, 99 2), Blonien, B. A. and Soderbery, A. 2010). Measurin the benefits of forein product variety with an accurate variety set. Journal of International Economics, 82 2), Broda, C. and Weinstein, D. E. 2004). Variety rowth and world welfare. American Economic Review, 94 2), and 2006). Globalization and the ains from variety. Quarterly Journal of Economics, 121 2), and 2010). Product creation and destruction: Evidence and price implications. American Economic Review, 100 3), Diewert, W. E. 1976). Exact and superlative index numbers. Journal of Econometrics, 4 2), Dixit, A. K. and Stilitz, J. E. 1977). Monopolistic competition and optimum product diversity. American Economic Review, 67 3), Feenstra, R. and Kee, H. L. 2004). On the measurement of product variety in trade. American Economic Review, 94 2), Feenstra, R. C. 1994). New product varieties and the measurement of international prices. American Economic Review, 84 1), Hummels, D. and Klenow, P. J. 2005). The variety and quality of a nation s exports. American Economic Review, 95 3), Kancs, D. 2010). Structural Estimation of Variety Gains from Trade Interation in Asia. Australian Economic Review, 43 3), Kruman, P. 1980). Scale economies, product differentiation, and the pattern of trade. American Economic Review, 70 5), Levchenko, A. A. and Zhan, J. 2012). Comparative advantae and the welfare impact of european interation. Economic Policy, 27 72), Romer, P. 1994). New oods, old theory, and the welfare costs of trade restrictions. Journal of Development Economics, 43 1), Sato, K. 1976). The ideal lo-chane index number. Review of Economics and Statistics, 58 2), Soderbery, A. 2010). Investiatin the asymptotic properties of import elasticity estimates. "Economics Letters", 109 2), ). Estimatin Import Supply and Demand Elasticities: Analysis and Implications. Unpublished manuscript, Purdue University. 19

21 Vartia, Y. O. 1976). Ideal lo-chane index numbers. Scandinavian Journal of Statistics, 3 3),

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