How Strong is the Love of Variety?* Adina Ardelean** Santa Clara University March, 2009

Abstract This paper incorporates a more general, but still tractable, CES preference structure that nests Krugman(1980) and Armington(1969) models. The consumer has decreasing marginal valuation for an exporter’s varieties. The empirics structurally identify and estimate the consumer’s love of variety as the elasticity of imports with respect to the number of varieties. The love of variety is 44 percent lower than is assumed in Krugman’s model. An implication is that existing studies overstate the variety gains from trade liberalization. Another is that the impact of product variety on economic growth and the strength of agglomerations are smaller than is typically assumed.

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I am especially grateful to David Hummels for guidance and support. I wish to thank Jason Abrevaya, Thomas Hertel, and Chong Xiang for excellent comments. Will Martin graciously provided me access to COMTRADE data. For helpful comments and suggestions, I thank Sirsha Chatterjee, Volodymyr Lugovskyy, Georg Schaur, and seminar participants at Purdue University and Santa Clara University. All remaining errors are mine. ** Department of Economics, Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053-0385. E-mail: [email protected].

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I. Introduction First introduced in international trade theory by Krugman (1980), Dixit-Stiglitz (1977) monopolistic competition model is widely used in general equilibrium modeling of trade flows with product differentiation. In its standard form, the model employs constant elasticity of substitution (CES) preferences to gain tractability in a general equilibrium framework. Consequently, it exhibits stark predictions on the number of varieties, prices and output per variety. Krugman’s monopolistic competition model assumes each country specializes in a number of varieties that is proportional to market size. It predicts that the rate of variety expansion is proportional to the growth in country size while output and prices per variety remain constant. The prediction implies that larger economies export more only on the extensive margin (a greater range of varieties) which it is at odds with empirical evidence. Hummels and Klenow (2002, 2005) empirically exploited exporter variation and examined the relationship between the number of exported varieties and exporter’s country size. They found that the number of exported varieties represents only 59 percent of a larger country’s exports. Thus, the rate of variety growth seems to be lower than that predicted by the theory. Alternatively, Armignton’s (1969) model, which dominates Computable General Equilibrium (CGE) analyses of trade policy, assumes varieties are differentiated by country of origin. In contrast with Krugman’s model, the number of varieties is fixed. Armington’s model shuts down the variety expansion channel of larger countries. So, a country grows only through the intensive margin in the sense that it produces higher quantities of its variety sold at lower prices on the world market.

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These predictions have important welfare implications. In Krugman’s model, greater variety represents the only source of gains from trade liberalization. In Armington’s model, unilateral trade liberalization can yield unfavorable terms of trade effects since the number of varieties cannot adjust (Brown - 1987). However both terms of trade and variety gains are important consequences of trade liberalization. Thus, Armington’s model may understate the gains from trade because it lacks the variety adjustment margin while Krugman’s model may overstate them because it features no terms of trade effects. Moreover the Krugman style CES preferences introduce instability into CGE models. If product varieties are industrial inputs, then trade liberalization increases the number of input varieties that in turn increases the demand for the product, further increasing the demand for input varieties (Brown, Deardorff and Stern - 1995). The result is that these CGE models generate far greater specialization than we see in actual output patterns. This paper incorporates a more general CES preference structure1 that nests Krugman’s and Armington’s model and can explain the slower rate of variety growth seen in the data. In both models, varieties are differentiated by country of origin. In Krugman’s model the consumer also regards varieties as differentiated within an exporter country. Any two varieties originating from an exporter are equally substitutable as any two varieties from different exporters. In Armington’s model, each country produces one variety or the consumer perceives varieties originating from the same country as perfect substitutes. The general CES structure In the working paper of their seminal work, Dixit and Stiglitz(1975) proposed a general CES utility function that allows for different degrees of love of variety by introducing product diversity multiplicatively as an externality into the CES preference structure. In their specification the love of variety parameter could take positive and negative values and it could be interpreted as product diversity being a positive (public good) and negative externality (public bad) respectively. Other theoretical work used different forms of the general CES (Either – 1982, Benassy – 1996 and Montagna -1999). The specification of the general CES preference structure of this paper originates from by Brown, Deardorff and Stern(1995). 1

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generalizes the elasticity of substitution across varieties within an exporter country. Its lower and upper bounds are the elasticity of substitution in Krugman’s and Armington’s model. Intuitively, the consumer regards same country’s varieties as more substitutable than varieties originating from different countries. Thus, she has decreasing marginal valuation for varieties originating from an exporter. Put it another way, the general CES preference allows the consumer’s love of variety to be lower than is assumed by Krugman’s preference structure and higher than in Armington’s model. To give intuition for the general CES, consider two examples. The CAMIP survey2 asks car buying consumers for their second choice. It shows that conditional on buying a Japanese car, consumers’ most common second choice was also buying a Japanese car. Similarly, conditional on buying an American car, consumers’ most common second choice was also an American car (Berry, Levinshon and Pakes - 2004)3. This suggests that consumers perceive within country varieties as more similar and better substitutes. Why are varieties more similar within a country? It could be country specific comparative advantage that makes a country’s varieties more alike. For instance, Japanese car varieties might be more similar to each other than to American car varieties because of country specific technology in producing fuel efficient vehicles. French wine varieties might be more similar to each other than to Chilean wine varieties because of country specific climate, grape cultivation techniques, or methods of fermentation and ageing. In the empirics, this paper exploits a different source of variation than Hummels and Klenow (2002, 2005) to understand whether consumer’s limited love of variety explains the empirical facts. Conditional on an exporter, we exploit cross-importer variation and structurally 2

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Survey conducted on behalf of General Motors for 1993 See Table 4 4

identify consumer’s love of variety as the elasticity of imports with respect to the number of varieties. To do this we first derive a measure of variety that is consistent with the underlying utility structure. The extensive margin represents the cross-section equivalent of the variety growth measure derived by Feenstra (1994) extended to the general CES case. The general CES variety adjusted price index nests Feenstra’s price index when love of variety is the highest. We employ UN’s COMTRADE data for 1999 that reports trade for many bilateral pairs and more than 5000 6 digit Harmonized System categories. We estimate that consumer love of variety is, on average, lower by 44 percent than it is assumed in Krugman’s model. The estimates reinforce Hummels and Klenow (2002, 2005)’s results and suggest that consumer’s limited love of variety could explain the patterns of the number of traded varieties observed in the data. This work relates and adds to three lines of research. First, it relates to the literature that develops richer models of product differentiation that predict a slower rate of variety growth. The literature employs two preference structures characterized by variable price elasticity of demand: quadratic utility function (Ottaviano and Thisse - 1999, Ottaviano et al. - 2000) and the ideal variety approach (Lancaster- 1979, Hummels and Lugovskyy - 2005). A monopolistic competition model with variable price elasticity of demand predicts that the variety price decreases and the variety output increases in importer’s market size. Thus, the economy expands not only on the extensive margin, but also on the intensive margin yielding a less than proportional relationship between the number of varieties and country size. Variable price elasticity of demand makes these models harder to work with in a general equilibrium framework or in empirical applications, and as a result there are only a few trade applications

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of these models. The general CES preferences could generate the slower variety growth while maintaining the tractability of the widely employed CES. Second, my work builds on and adds to the literature that calibrates or estimates the welfare impact of traded varieties in the CES framework. In a simple calibration, Romer (1994) shows that trade liberalization that increases the number of traded varieties yields large welfare gains. Feenstra (1994) constructs theoretically consistent price indices in the presence of consumer love of variety and shows that increased product variety lowers the price indices even if the prices for each variety remain constant. Recently, Broda and Weinstein (2006) applies Feenstra(1994)’s method to a larger set of commodities to estimate the impact of new imported varieties on U.S. welfare and finds that greater product variety increased U.S. consumer’s welfare by 2.6% of U.S. GDP from 1972 to 2001. Considering the paper’s estimate of U.S. love of variety, that is lower than in Krugman’s model, the recent study overstates the U.S. variety gains by 43%. Third, Head and Ries (2001) investigate whether the relationship between a country’s share of production is more or less than proportional to its share of demand in order to empirically distinguish increasing returns (Krugman) and national product differentiation (Armington) models. They found that the evidence for U.S. and Canada is mostly consistent to Armington’s model. This paper proposes an alternative structural test to home market effects and the findings reject both models and provide evidence for a model that blends together features of both Krugman and Armington. The rest of the paper is organized as follows. Section II describes the general CES preferences and builds on Feenstra(1994)’s method to derive the relative general CES demand.

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Section III identifies and estimates consumer’s love of variety. Section IV provides some robustness check exercises and section V concludes. II. Diminishing Returns to National Varieties 2.1. Preference Structure The representative consumer’s preferences are identical in all M countries and are represented by the following Cobb-Douglas utility function across differentiated products h: H

(1) U i = ! Dih µh , where h =1

H

!µ h =1

h

= 1.

We define the composite differentiated product h Di as a nested general CES utility function4: #

+ M ! "1 % nij # "1 ( . # "1 (2) Di = - $ nij # ' $ xijl# * 0 -, j =1 & l =1 ) 0/ The parameter ! > 1 represents the elasticity of substitution across exporters j; xijl , pijl and nij denote the quantity, prices per variety, and number of varieties bought from country j (including domestic varieties bought from country i ). The parameter ! " [0,1] represents the consumer’s love of variety – the marginal valuation of an exporter’s variety. To build some intuition on the general CES and the love of variety parameter we simplify the preferences for ! = 1 and ! = 0 . We further assume that all imported varieties are symmetric in quantities ( xijl = x ), and the number of imported varieties is the same across source-countries. At ! = 1 the consumer enjoys variety growth equally regardless of its source as in Krugman (1980): 4

We drop the subscript h in the rest of the section.

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!

! "1 ! "1 xij = x;nij = n $M ' U i = & # nij xij ! ) = Mn &% j =1 )(

( )

! ! "1

x (Krugman style preferences);

At ! = 0 the consumer values adding a new exporter to the consumption bundle but places no value on additional varieties produced by an existing exporter. That is, she regards all varieties within the same exporter as identical or perfect substitutes as in Armington(1969): $M U i = & # nij xij &% j =1

(

)

! "1 !

!

! ' ! "1 xij = x;nij = n ! "1 = M nx (Armington style preferences). ) )(

( )

The general CES demand for exporter j’s variety is5: (3)

x jl =

p !jl" n#j !1 % nj ( # !1 1! " n p $ j ' $ jl * j =1 & l =1 ) M

Yi

where Yi represents the importer i’s income. For ! = 1 the demand becomes the Krugman’ s CES demand. For any values of ! < 1 , the consumer faces a trade-off between the quantity per variety and the number of varieties imported. In other words, as an exporter’s varieties become less valuable at the margin than in the Krugman’s CES framework, the consumer would rather buy a higher quantity per variety than more varieties. For ! = 0 an increase in the number of varieties is exactly offset by a decrease in the quantity per variety. That is, the consumer becomes indifferent between buying more varieties or more per variety from an exporter as long as the total quantity stays the same. Taking sum across all varieties exported by country j and k in (3) and rearranging, we obtain the imports bought from exporter j relative to exporter k:

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We drop the importer subscript i in the rest of the section. 8

1 % 1" # ! "1 % n j ( ' 1" # 1" # ' n j ' $ p jl * Mj ' & l =1 ) = 1 M k ' ! "1 nk 1" # % ( ' 1" # 1" # ' nk ' $ pkl * '& & l =1 )

(4)

( * * * * * * *)

1" #

%P( +' j* & Pk )

1" #

,

where Pj and Pk represent the minimum unit-cost function of utility (2) or the CES price indexes. If we assume all varieties originating from a country are symmetric in prices, the relative total import demand simplifies to: 1#!

$p % (5) =& j ' M k ( pk ) Mj

"

$ nj % & ' . ( nk )

From (5) we can easily see that the elasticity of relative imports with respect to the relative number of varieties equals the consumer’s love of variety. An increase in the number of varieties exported by j, ceteris paribus, yields a less than proportional increase in relative imports for any ! < 1 . 2.2. General CES Price Index Decomposition In section III we structurally identify and estimate consumer’s love of variety and test whether it is different than implicitly assumed in Krugman’s or Armington’s model. To obtain reliable estimates, we need to estimate the general CES with asymmetric quantities and prices as given by (4). The logarithm of relative import demand (4) is non-linear in the number of varieties and thus requires burdensome estimation techniques. To employ linear estimation techniques, this section extends Feenstra (1994)’s method to derive the relative import demand by decomposing the relative general CES price index into a price and a number of varieties component.

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The CES price index Pjk = Pj Pk (i.e. variety-adjusted price index) can be decomposed into the traditional price index R jk and extensive margin (i.e. a weighted count of the number of varieties) following Feenstra (1994)’s method. The methodology separates the extensive margin and the traditional price index without assuming that an exporter’s varieties have equal prices and quantities. Feenstra (1994) shows the consumer perceives the introduction of new varieties as a decrease in prices such that the CES price index decreases in the number of varieties. If varieties are more substitutable, they have a lower impact on the price index and the variety adjusted price index becomes closer to the traditional price index. If the set of varieties is the same across exporters (j and k), the cross section equivalent of the CES price index equals the traditional price index and can be written as6:

(6)

!p $ R jk = ( # jl & l 'I " pkl %

where srl ( I ) "

) jl ( I )

prl xrl for r = j , k ; # prl xrl l!I

# s jl ( I ) % skl ( I ) $ && '' ln s ( I ) % ln s ( I ) jl kl ) . ! jl ( I ) * ( # s jl ( I ) % skl ( I ) $ && '' + l"I ( ln s jl ( I ) % ln skl ( I ) )

The weights used in constructing the price index are the logarithmic mean of the cost shares of each variety l in country j’s exports. But, the traditional price index is not appropriately defined if the set of varieties varies across exporters. For a pair of countries, some varieties are in the common set (I) and some varieties are outside the common set. In this case, the traditional price index needs to be adjusted by the relative share of varieties outside the common set. The construction of the variety-adjusted price index requires two conditions. First, exporter j and k Sato(1976) and Vartia(1976) show that the CES price index equals the traditional price index for a fixed set of varieties. 6

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should export at least one common variety ( I ! " ). Second, the varieties in the common set should be identical such that the relative variety prices in (6) are meaningful. That is, any demand shifter should affect proportionally the varieties originating from different countries in the common set. Proposition 1 formalizes the extension of Feenstra (1994)’s method for decomposing the general CES price index. Proposition 1:7 If b jl = bkl for l ! I " ( I j # I k ), I $ % , then the general CES price index can (

" ! % ) *1 be written as Pjk = R jk $ j ' # !k & where b jl , bkl - unobservable demand shifters and (7) !r #

$p

x

$p

x

l"I

l"I r

rl rl

for r = j , k !

rl rl

We define the extensive margin as:

(8)

" EM jk ! k = "j

$p

jl

x jl

$p

$p

x kl kl

$p

l #I j

l #I k

l #I

l #I

jl

x jl

x kl kl

.

If the set of varieties imported from j is a subset of the set of varieties imported from k ( I = I j ), then the extensive margin simplifies to: (9)

EM jk =

"p

l !I j

x

kl kl

"p

l !I k

x .

kl kl

The extensive margin of country j represents the weighted count of varieties relative to exporter k’s varieties. The varieties are weighted by their importance in k’s exports. If each

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The proof of the proposition can be found in the Appendix.

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variety weighs equally, the extensive margin represents the simple count of varieties exported by j to importer i as a share of the number of varieties exported by k. From proposition 1, the variety-adjusted price index can be written as follows: (10)

(

Pjk = EM jk

)

! 1" #

R jk .

In the extension, the new varieties lower the price index at a rate that depends on both ! and ! . A lower love of variety, ceteris paribus, dampens the effect of new varieties on the price index. That is, if the consumer values new varieties less at the margin, they have a lesser effect on the price index. 2.3. Relative Import Demand with Asymmetric Varieties Using decomposition (10) we can re-write equation (4) as: (11)

(

M j M k = EM jk

) (R ) !

1" #

jk

.

The observed relative bilateral imports are a function of relative bilateral varietyadjusted price indexes. Equation (11) is the asymmetric equivalent of (5). An increase in the number of imported varieties acts in the same way as a decrease in prices: it will draw resources towards the exporter’s products and the higher is the love of variety the larger the shift. The love of variety parameter represents the elasticity of relative imports with respect to extensive margin. The price elasticity of demand remains 1 " ! as in the standard CES framework. III. Cross – Importer Love of Variety In this section we structurally identify consumer’s love of variety by estimating (11) for each product.

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3.1. Data We employ data from UN’s COMTRADE data for 1999. The COMTRADE data was obtained through UNCTAD/ World Bank WITS data system, which yields bilateral import data collected by the national statistical agencies of 143 importing countries, covering 224 exporters and 5015 6 digit level Harmonized System (HS) classification categories. After merging it with great circle distance data from Head and Mayer (2002), we obtain a dataset covering 141 importers and 211 exporters for a total of 4,407,355 data points. We define a product as a two digits level HS category (denoted by h) and a variety as a six digits level HS category (denoted by l) within a two digits level HS category8. The variety definition is limited by data availability. Ideally we would like to observe more commodity detail in trade data but it is unavailable for many importers. Other empirical work on product variety in trade has defined a variety at the same level of disaggregation (Hummels and Klenow – 2002, 2005). However the robustness check exercises in section IV show that the choice of variety at six-digits HS level does not alter the main results. For each bilateral pair in each 2 digits HS category, we construct the relative imports, extensive margin and prices according to the decomposition methodology outlined in section 2.2. All three variables vary considerably across importers for each exporter (j) – 2 digits HS (h). In the cross-section we observe a large dispersion of the extensive margin for an exporter and product (see Table 1). This gives us substantial variation to estimate the love of variety as the elasticity of relative imports with respect to the extensive margin.

For instance, HS 04 category represents ‘Dairy products’ with HS 6 varieties such as: different types of milk and cream, yogurt, buttermilk, different type of cheeses etc. For apparel HS 61, we observe men and women’s dresses, pants, shirts, suits etc. For vehicles HS 87, varieties we observe are trucks, SUV’s, sedans etc. Table 4 provides the descriptions of the 2 digits HS products. 8

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3.2. Estimation and Results Since detailed data on trade costs is not readily available for many importers, we use great circle bilateral distance as a crude proxy for trade costs. We model trade costs as (where i indexes importers): (12)

" ijl = til * (dij ) . !

where til represents the ad-valorem tariff , dij represents the distance between countries i and j and ! represents the elasticity of transport costs with respect to distance. Conditional on an importer, the ad-valorem MFN tariff for a given variety can be safely assumed equal across exporting countries (Hummels and Lugovskyy - 2005). The price index becomes: ) (I )

) ( I )*

(13)

! p jl $ ijl ij ! dij $ ijl ij Rijk = ( # & . (# p & l 'I ij " d ik % l 'I " kl % !##"##$ !##"## $ Dijk

R FOB jk

where dik represents the weighted average distance of ROW exports to country i, the weights being the share of each trade partner in world trade; and the fob exporter’s prices per variety are equal across importers. We choose the ROW (rest-of-the-world) as the comparison country k. That is to say, the comparison country consists of all the exporters other than j taken together that have positive exports to importer i. The ROW is a convenient comparison country because we can exploit all the information available in the data. An additional advantage of using ROW is that, conditional on an importer, the common set of varieties between any exporter j and ROW is the set of HS 6 categories exported by j. This property allows a more intuitive construction of the extensive margin (i.e. a weighted count of varieties) as in (9) which weighs each variety with its ROW trade value.

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The estimating equation becomes: (14)

h log IMPORTSijkh = ! hj + " h log EM ijkh + # (1 $ % h ) log Dijkh + & ijk .

where each variable is constructed relative to the Rest of the World (k). Previous literature shows that the extensive margin varies both across exporters and importers. Larger and richer countries import and export a higher number of varieties (Hummels and Klenow – 2002, 2005). Also, trade barriers have a negative effect on the number of imported varieties. The above specification includes exporter fixed effects ! jh (implemented by meandifferencing) common to all importers that capture the exporters’ fob variety prices. Estimating a specification in relative terms controls for importer specific factors common to all exporters such as market size and income. Conditional on an exporter, the estimation exploits variation across importers in the extensive margin. The love of variety parameter measures the degree to which importers value an exporter’s varieties. We estimate specification (14) for each product. Pooling across products restricts the elasticity of substitution to be equal across products which based on the estimates in the literature is clearly a strong assumption (Hummels - 2001 and Broda and Weinstein- 2006). All estimates of ! h are significantly lower than that assumed in Krugman’s model and significantly higher than assumed by Armington’s model. The simple average consumer love of variety equals 0.56. All the price elasticity of demand estimates ( (1 ! " h )# ) are negative and

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significant at 5 percent level. Moreover, the average of ! h 9’s is 4.50. Table 2, figure 1, and figure 2 summarize the results by product10. IV. Robustness Checks 4.1. U.S. Love of Variety In this section we structurally identify U.S. love of variety by estimating (11) for each product. Identifying and estimating the love of variety by exploiting the time series variation in the U.S. data has some advantages. The U.S. data are more disaggregated at the commodity level that allows a finer measurement of “unique” products. Also, it provides detailed information on trade costs. 4.1.1. Data We employ U.S. data from the “U.S. Imports of Merchandise” CD-ROM for the period 1991-2005, published by the U.S. Bureau of the Census. The dataset contains U.S. imports collected from electronically submitted Customs forms, covering an average of 223 exporters and commodity detail at 10 digit level Harmonized System (HS) classification. The data includes country of origin, value, quantity, freight and duties paid. The empirical implementation defines a product as a two digits level HS category (denoted by h) and a variety as a 10 digit level HS category (denoted by l) within a two digits level HS category. For each U.S. – trade partner data point in a two digits HS category for a year, we construct the relative imports, extensive margin and prices according to the decomposition methodology outlined in section 2.2. All three variables vary across time for each exporter (j) – 2 digits HS (h) but the time variation is smaller than in the cross-section (see Table 1). calculated using !! = 0.26 (Hummels - 2001) 10 The estimates are unchanged in pooled cross-sections for 1995-2003. 9

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4.1.2. Estimation and Results The price index R jkt can be written as (where t indexes time periods): *

*

(I )

(I )

" ! jtl % jtl jt " p jl % jtl jt (15) R jkt = ) $ . ' )$ p ' l (I jt # ! ktl & l (I jt # kl & !##"##$ !##"##$ T jkt

R FOB jk

I measure the relative trade costs ( T jkt ) using ad-valorem trade costs (i.e. one plus the share of duties and freight paid in the import value) for each HS 10. For each HS 2 product, the ROW trade costs represent a weighted average of trade costs, where the weights are the share of each exporter’s variety into the ROW exports to U.S. for each time period. The estimating equation for each product h becomes: (16) log IMPORTS hjkt = ! hj + " h log EM hjkt + (1 # $ h ) logT jkth + % hjkt . We include an exporter fixed effect (implemented by mean-differencing) to capture the relative fob variety prices. By estimating a specification in relative terms, the time-shifters common to all exporters such as U.S.’s market size and income are differenced out. Conditional on an exporter, the love of variety estimation exploits time variation in the extensive margin. The love of variety estimate measures the degree to which the U.S. values new varieties and the elasticity of substitution should be greater than one ( ! h > 1 ). All U.S. ! h s are significantly lower than the love of variety assumed by Krugman’s model. The average of U.S. consumer’s love of variety equals 0.41. The time series variation in the extensive margin is noisier than the variation in cross-section and the U.S. love of variety point estimates are lower than cross-importer estimates. 99 percent of ! h are significantly

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different than unity at 5 percent level with a weighted average of 5.28. Table 2, figure 3, and figure 4 summarize the results by product. 4.2. U.S. Variety Gains - back of the envelope calculation Having the estimate of U.S. love of variety, we can extend Broda and Weinstein (2006)’s variety gains calculation. We can easily adapt the variety-adjusted price index from (10) to capture the change in the price index from period t to t-1: ( jt ( I )

,

" p jlt % " +t % - !1 (17) Pj = * $ ' $# + '& l )I # p jlt !1 & t !1 !##"##$ Rj

where R j represents the traditional price index as in defined in (6) and !r , r = t,t " 1 captures the role of the new and disappearing varieties as defined in (7). The variety gains are the ratio between the variety-adjusted price index and the traditional price index: )

# ! & * "1 (18) VG = % t ( $ !t "1 ' Broda and Weinstein (2006) find that U.S. variety gains equal to 2.6% of U.S. GDP from 1972 to 2001 using (18) when ! = 1 . For any values of ! lower than one, the calculated variety gains are lower than 2.6% of U.S. GDP. For an average ! = 0.41 across sectors, the variety gains are lower by 43% compared to Broda and Weinstein (2006)’s estimate and they are equal to 1.48% of U.S. GDP. 4.3. Hidden Variety The decomposition of the variety-adjusted price indexes into extensive margin and price index requires the existence of a common set of varieties between exporter j and k.

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Theoretically a variety in the common set features an equal unobservable demand shifter for both exporters which can be interpreted as the same number of hidden varieties, the same quality or taste parameter. Previous studies (Hummels-Klenow- 2005, Broda and Weinstein 2006) have empirical defined variety at different level of aggregation imposed by data availability. In the cross-importer estimation, we define the common set of varieties as the set of HS 6 categories within a HS 2 category in which both exporters have positive exports to a given importer. This issue could represent a mis-measurement problem if there are multiple hidden varieties (e.g. HS 10 categories) within each HS 6 category. But, in the paper’s specification, it does not bias the estimates if the relative number of hidden varieties is proportional to the relative number of observed varieties. However, I can use the U.S. data to test the statement. Consider that HS 10 categories represent the hidden varieties within an observed HS 6 category. For each HS 2 category, the following holds true: (19)

j j j nHS10 nHS10/HS6 N HS6 = k * k . k nHS10 nHS10/HS6 N HS6

j j j where nHS10 , nHS10/HS6 and N HS6 represent the number of HS 10 categories within an HS 2, the

number of HS 10 categories within an HS 6 category and the number of HS 6 category within an HS 2 exported for each j. Testing whether varieties defined at HS 6 level in the common set feature the same j k nHS10/HS6 = 1 ) is equivalent to number of hidden varieties for exporter j and k (i.e. nHS10/HS6 j k nHS10 testing whether the relative number of hidden varieties ( nHS10 ) is proportional to relative j k N HS6 number of observed varieties ( N HS6 ). Figure 7 confirms that hidden varieties do not

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represent a problem in the specification in relative terms and the deviations from the 45 degree line are captured by the exporter fixed effects. An alternative hidden variety robustness check is to re-estimate the U.S. love of variety by defining a variety at HS 6 commodity level and compare the estimates to the estimates obtained by defining a variety at HS 10 level. The point estimates differ on average by .06 but the mean of the estimates distribution is preserved. Figure 5 and 6 shows the distribution of the love of variety and elasticity of substitution estimates when variety is defined at HS 6 level. V. Conclusion This paper incorporates a general CES preference structure that nests Krugman’s and Armington’s model. The general CES introduces a trade-off that the consumer faces between buying more varieties or higher quantities per variety. The empirics structurally identify and estimate consumer’s love of variety as the elasticity of relative imports to extensive margin and find that it is lower than is assumed in Krugman’s model and higher than is assumed in Armington(1969). Consumer’s limited love of variety has important implications for welfare calculations. A back of the envelope calculation shows that the recent estimates of U.S. variety gains overstate the impact of the increase in the number of imported varieties on U.S. welfare by 43%. Moreover, if varieties are industrial inputs, the impact of product variety on economic growth and the strength of industrial agglomerations are smaller than it is typically assumed.

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References:

Armington, P.S. (1969), “A theory of demand for products distinguished by place of production”, International Monetary Fund Staff Papers, vol. 16, pp. 159–76. Benassy, Jean-Pascal (1996),“Taste for variety and optimum production patterns in monopolistic competition”, Economics Letters, Vol. 52. Berry, Steven, Levinsohn, James and Pakes, Ariel (2004), “Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market”, Journal of Political Economy, Vol. 112 (1) Broda, Christian and Weinstein, David E (2004), "Variety Growth and World Welfare", American Economic Review, Vol. 94(2) Broda, Christian and Weinstein, David E. (2006), “Globalization and the Gains from Variety”, Quarterly Journal of Economics, Vol. 121(2) Brown, Drusilla K. (1987), “Tariffs, the Terms of Trade, and National Product Differentiation”, Journal of Policy Modeling 9(3), 503-526 Brown, Drusilla K., Deardorff, Alan V. and Stern, Robert M. (1995), “Modeling Multilateral Trade Liberalization in Services”, Asia-Pacific Economic Review 2:21-34, April Dixit, Avinash K., Stiglitz, Joseph E. (1975), “Monopolistic competition and Optimum Product Diversity”, Warwick Economic Research paper No. 64 Dixit, Avinash K., Stiglitz, Joseph E. (1977), “Monopolistic competition and Optimum Product Diversity”, American Economic Review, Vol.67, No.3 Feenstra, Robert C. (1994), “New Product Varieties and the Measurement of International Prices”, American Economic Review, Vol. 84, No. 1 Feenstra, Robert and Kee, Hiau Looi (2004), “On the Measurement of Product Variety in Trade”, American Economic Review, Vol. 94(2) Head, Keith and Ries, John (2001), “Increasing Returns Versus National Product Differentiation as Explanation for the Pattern of U.S.- Canada Trade”, American Economic Review 91 No. 4, p. 858-876 Head, Keith & Thierry Mayer (2002) "Illusory Border Effects: Distance Mismeasurement Inflates Estimates of Home Bias in Trade," Working Papers 2002-01, CEPII research center Hummels, David (2001), “Toward a Geography of Trade Costs”, Purdue University mimeo

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Hummels, David and Klenow, Peter J. (2002),“The Variety and Quality of a Nation’s Trade”, NBER Working Paper #8712 Hummels, David and Klenow, Peter J. (2005), “The Variety and Quality of a Nation’s Exports”, American Economic Review 95, p704-723 Hummels, David and Lugovskyy, Volodymyr (2005), “Trade in Ideal Varieties: Theory and Evidence”, NBER Working Paper # 11828 Krugman, Paul R.(1980), “Scale Economies, Product Differentiation, and the Pattern of Trade”, American Economic Review vol. 70 (5) Lancaster, Kelvin (1979), Variety, Equity and Efficiency. New York: Columbia University Press Montagna, Catia (2001), “Efficiency Gaps, Love of Variety and International Trade”, Economica, Vol. 68 Romer, Paul M.(1994), “New goods, Old Theory, and the Welfare Costs of Trade Restrictions”, Journal of Development Economics 43, 5-38 Ottaviano, Gianmarco I.P. and Thisse, Jacques-Francois (1999), “Monopolistic Competition, Multiproduct Firms and Optimum Product Diversity”, Core discussion paper No. 9919 Ottaviano, Gianmarco I.P. and Thisse, Jacques-Francois (2000), “Agglomeration and Trade Revisited”, International Economic Review, Vol. 43(2) Sato, Kazuo (1976), “The Ideal Log-Change Index Number”, Review of Economics and Statistics, Vol. 58, No. 2 Vartia, Yrjo O.(1976), “Ideal Log-Change Index Numbers”, Scandinavian Journal of Statistics 3(3), p. 121-126 U.S. Bureau of the Census (1991-2005), “U.S. Imports of Merchandise” CD-ROM

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Table 1: Variation in Relative Imports, Extensive Margin, and Price Indexes Coefficient of Variation Mean Standard error Median Min Max

IMPORTSijk

EMijk

2.25 1.23 1.98 0.003 10.45

0.95 0.38 0.92 0 3.64

Dijk 0.87 0.37 0.82 0 5.5

Data Source: United Nations' Comtrade dataset (1999) Coefficient of Variation Mean Standard error Median Min Max

IMPORTsUsjkt

EMUSjkt

0.88 0.52 0.82 0 3.6

0.64 0.47 0.58 0 3.52

TUSjkt 0.07 0.09 0.04 0 1.54

Data Source: U.S. Bureau of Census (1991-2005), "US Imports of Merchandise" Note: For each exporter(j) - HS 2(h), calculate the coefficient of variation CoV( xijkh )=stdev( xijkh )/mean( xijkh ). The table reports summary statistics for the coefficient of variation over all exporters and HS 2 products.

23

Table 2: Love of Variety and Elasticity of Substitution Estimates by 2 digits HS Summary Statistics Specification

Cross-importer (using distance) LoV EoS 0.54 5.12 0.56 4.5 0.57 4.62 0.13 0.89 0.19 2.09 0.88 6.13

Weighted Mean Simple Mean Median Std. Deviation Min. Max.

U.S. (using trade costs) LoV EoS 0.39 5.28 0.41 4.68 0.4 4.55 0.14 1.71 0.12 1.16 0.77 9.21

Table 3: Consumer’s choice of cars’ varieties Consumers Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 8 Group 9 Group 10

st

1 choice Chevrolet Metro Chevrolet Cavalier Ford Escort Cadillac Seville Ford Taurus Toyota Corolla Nissan Sentra Honda Accord Acura Legend Toyota Lex LS400

2nd choice of the highest # of consumers Ford Escort Ford Escort Ford Tempo Cadillac Deville Toyota Camry Honda Civic Toyota Corolla Toyota Camry Toyota Lex ES300 Cadillac Deville

2nd choice of the next highest # of consumers Geo Storm Chrysler LeBaron Ford Taurus Lincoln MK8 Mercury Sable Toyota Camry Honda Civic Ford Taurus Toyota Lex SC300 Infiniti Q45

Data Source: CAMIP – propriety survey conducted on the behalf of General Motors for 1993 (Berry, Levinsohn and Pakes – 2004)

24

Figure 1: Love of Variety Estimates across HS2 - weighted by value-

.2

.4

.6

.8

1

Figure 2: Elasticity of Substitution Estimates across HS2 - weighted by value -

2

3

4

5

6

elasticity of transport costs w.r.t distance = 0.267 Hummels(2001)

25

Figure 3: U.S. Love of Variety Estimates across HS2 - weighted by value -

0

.2

.4

.6

.8

Variety defined at HS 10 commodity level

Figure 4: U.S. EoS Estimates across HS2 - weighted by value -

0

2

4

6

8

10

Variety defined at HS 10 commodity level

26

Table 4: Cross-Importer Love of Variety Estimates HS 2 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

Description Live Animals Meat and Edible Meat Fish, Crustaceans & Aquatic Invertebrates Dairy Prods; Birds Eggs; Honey; Ed Animal Pr Nesoi Products of Animal Origin, Nesoi Live Trees, Plants, Bulbs etc.; Cut Flowers etc. Edible Vegetables & Certain Roots & Tubers Edible Fruit & Nuts; Citrus Fruit or Melon Peel Coffee, Tea, Mate & Spices Cereals Milling Products; Malt; Starch; Inulin; Wht Gluten Oil Seeds etc.; Misc Grain, Seed, Fruit, Plant etc. Lac; Gums, Resins & Other Vegetable Sap & Extract Vegetable Plaiting Materials & Products Nesoi Animal or Vegetable Fats, Oil etc. & Waxes Edible Preparations of Meat, Fish, Crustaceans etc. Sugars and Sugar Confectionary Cocoa and Cocoa Preparations Prep Cereal, Flour, Starch or Milk; Bakers Wares Prep Vegetables, Fruit, Nuts or Other Plant Parts Miscellaneous Edible Preparations Beverages, Spirits and Vinegar Food Industry Residues & Waste; Prep Animal Feed Tobacco and Manufactured Tobacco Substitutes Salt; Sulfur; Earth & Stone; Lime & Cement Plaster Ores, Slag and Ash Mineral Fuel, Oil etc.; Bitumin Subst; Mineral Wax Inorg Chem; Prec & Rare-Earth Met & Radioact Compd Organic Chemicals Pharmaceutical Products Fertilizers Tanning & Dye Ext etc.; Dye, Paint, Putty etc., Inks Essential Oils etc., Perfumery, Cosmetic etc. Preps Soap etc.; Waxes, Polish etc.; Candles; Dental Preps Albuminoidal Subst; Modified Starch; Glue; Enzymes Explosives; Pyrotechnics; Matches; Pyro Alloys etc. Photographic or Cinematographic Goods Miscellaneous Chemical Products Plastics and Articles Thereof Rubber and Articles Thereof Raw Hides and Skins (No Furskins) and Leather Leather Art; Saddlery etc., Handbags etc.; Gut

LoV Coeff

S.e.

0.79 0.58 0.65 0.65 0.46 0.40 0.62 0.59 0.52 0.56 0.53 0.49 0.32 0.44 0.65 0.62 0.59 0.64 0.66 0.70 0.45 0.60 0.49 0.63 0.63 0.60 0.63 0.66 0.51 0.58 0.65 0.73 0.71 0.88 0.68 0.51 0.66 0.51 0.63 0.64 0.43 0.42

(0.06) (0.04) (0.02) (0.03) (0.03) (0.04) (0.03) (0.03) (0.02) (0.03) (0.02) (0.03) (0.04) (0.06) (0.02) (0.03) (0.03) (0.05) (0.03) (0.03) (0.03) (0.03) (0.04) (0.03) (0.02) (0.03) (0.03) (0.02) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.05) (0.03) (0.04) (0.03) (0.04) (0.03) (0.04) (0.04)

Nobs 2,553 2,453 4,694 3,702 2,502 2,913 4,289 4,959 5,277 2,986 2,794 4,411 2,626 1,480 4,121 3,600 4,212 3,328 4,286 4,774 4,998 5,145 3,231 3,267 4,759 1,934 3,967 5,179 5,523 6,008 2,748 5,282 5,532 4,938 3,968 2,136 3,552 5,629 8,150 6,925 3,257 5,325

R2 0.55 0.50 0.58 0.54 0.53 0.60 0.59 0.57 0.51 0.48 0.53 0.51 0.51 0.29 0.58 0.45 0.51 0.54 0.58 0.60 0.54 0.59 0.48 0.44 0.53 0.47 0.54 0.63 0.69 0.62 0.50 0.69 0.67 0.63 0.58 0.38 0.68 0.65 0.70 0.70 0.49 0.63

27

Table 4: Cross-Section Love of Variety Estimates – cont’d HS 2 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 78 79 80 81 82 83 84 85 86

Description Furskins and Artificial Fur; Manufactures Thereof Wood and Articles of Wood; Wood Charcoal Cork and Articles of Cork Mfr of Straw, Esparto etc.; Basketware & Wickerwrk Wood Pulp etc.; Recovd (Waste & Scrap) Ppr & Pprbd Paper & Paperboard & Articles (Inc Papr Pulp Artl) Printed Books, Newspapers etc.; Manuscripts etc. Silk, including Yarns and Woven Fabric Thereof Wool & Animal Hair, including Yarn & Woven Fabric Cotton, including Yarn and Woven Fabric Thereof Veg Text Fib Nesoi; Veg Fib & Paper Yns & Wov Fab Manmade Filaments, including Yarns & Woven Fabrics Manmade Staple Fibers, incl Yarns & Woven Fabrics Wadding, Felt etc; Sp Yarn; Twine, Ropes etc. Carpets and other Textile Floor Coverings Spec Wov Fabrics; Tufted Fab; Lace; Tapestries etc. Impregnated etc. Text Fabrics; Tex Art for Industry Knitted or Crocheted Fabrics Apparel Articles and Accessories, Knit or Crochet Apparel Articles and Accessories, not Knit etc. Textiles Art Nesoi; Needlecraft Sets; Worn Text Art Footwear, Gaiters etc. and Parts Thereof Headgear and Parts Thereof Umbrellas, Walking-Sticks, Riding-Crops etc., Parts Prep Feathers, Down etc.; Artif Flowers; H Hair Art Art of Stone, Plaster, Cement, Asbetos, Mica etc. Ceramic Products Glass and Glassware Nat etc. Pearls, Prec. etc. Stones, Pr Met etc.; Coin Iron and Steel Articles of Iron or Steel Copper and Articles Thereof Nickel and Articles Thereof Aluminum and Articles Thereof Lead and Articles Thereof Zinc and Articles Thereof Tin and Articles Thereof Base Metals Nesoi; Cerments; Articles Thereof Tools, Cutlery etc. of Base Metal & Parts Thereof Miscellaneous Articles of Base Metal Nuclear Reactors, Boilers, Machinery etc.; Parts Electric Machinery etc.; Sound Equip; TV Equip Pts; Railway or Tramway Stock etc; Traffic Signal Equip

LoV Coeff

S.e.

0.52 0.67 0.57 0.22 0.51 0.74 0.51 0.45 0.56 0.59 0.38 0.53 0.57 0.44 0.52 0.48 0.47 0.42 0.51 0.58 0.49 0.61 0.19 0.50 0.37 0.60 0.73 0.71 0.70 0.69 0.55 0.59 0.70 0.67 0.74 0.68 0.68 0.42 0.58 0.74 0.35 0.48 0.80

(0.06) (0.03) (0.06) (0.07) (0.05) (0.03) (0.03) (0.07) (0.04) (0.03) (0.04) (0.03) (0.03) (0.03) (0.04) (0.03) (0.03) (0.05) (0.02) (0.02) (0.03) (0.03) (0.04) (0.04) (0.05) (0.03) (0.03) (0.03) (0.03) (0.02) (0.04) (0.04) (0.07) (0.04) (0.05) (0.04) (0.09) (0.05) (0.03) (0.03) (0.03) (0.02) (0.06)

Nobs

R2

1,775 6,773 1,371 2,081 1,640 6,692 6,388 1,494 2,687 5,435 2,270 4,446 4,675 4,108 3,791 3,974 3,736 2,941 6,829 7,326 6,237 5,695 3,811 2,221 1,977 4,886 5,632 6,083 4,519 5,300 7,355 4,329 1,695 5,512 1,497 2,085 1,505 1,872 6,050 5,650 10,555 10,050 2,456

0.46 0.64 0.48 0.44 0.53 0.70 0.65 0.51 0.55 0.60 0.48 0.62 0.61 0.56 0.58 0.63 0.61 0.54 0.65 0.67 0.59 0.60 0.51 0.49 0.46 0.66 0.66 0.66 0.64 0.68 0.68 0.63 0.56 0.61 0.46 0.47 0.41 0.53 0.71 0.69 0.76 0.76 0.49 28

Table 4: Cross-Section Love of Variety Estimates – cont’d HS 2 87 88 89 90 91 92 93 94 95 96

Description

LoV

Vehicles, except Railway or Tramway, and Parts etc. Aircraft, Spacecraft, and Parts Thereof Ships, Boats and Floating Structures Optic, Photo etc., Medic or Surgical Instruments etc. Clocks and Watched and Parts Thereof Musical Instruments; Parts and Accessories Thereof Arms and Ammunition; Parts and Accessories Thereof Furniture; Bedding etc.; Lamps Nesoi etc.; Prefab Bd. Toys, Games & Sport Equipment; Parts & Accessories Miscellaneous Manufactured Articles

Coeff

S.e.

0.55 0.50 0.71 0.46 0.37 0.53 0.59 0.69 0.42 0.57

(0.03) (0.04) (0.04) (0.03) (0.03) (0.04) (0.04) (0.03) (0.04) (0.03)

Nobs 7,611 2,824 2,589 7,869 3,724 3,174 1,928 7,152 5,729 5,631

R2 0.71 0.57 0.49 0.77 0.63 0.68 0.51 0.69 0.68 0.68

Figure 5: U.S. Love of Variety Estimates across HS2 - weighted by value -

0

.2

.4

.6

.8

Variety defined at HS 6 commodity level

29

Figure 6: U.S. EoS Estimates across HS2 - weighted by value -

0

2

4

6

8

10

Variety defined at HS 6 commodity level

30

Appendix: Price index decomposition11 The general CES utility function:

(1) U = n j

" #1 ! #1

!

" ! #1 & ! #1 % '' + b !jl x jl! (( ) l$I j *

The minimum cost of obtaining one unit of utility from varieties l of a product corresponding to the above utility function: 1

(2) P = n j j

! "1 1" #

& ) 1" # ! 1" # ( % bjl p jl + ' l $I j *

where ! is the elasticity of substitution between varieties and I j = {1,..., N j } is the set of imported varieties from country j with the quantity per variety x jl > 0

! l " I j , prices p jl > 0 !l " I j and the unobservable demand

shifter b jl > 0 . This setup is equivalent to Feenstra(1994)’s when ! = 1 corresponding to the upper bound of the “love of variety” parameter. We preserve Feenstra(1994)’s notation for the minimum cost of obtaining one unit of utility from varieties l of a product when ! = 1 with lower case c. In the following, we extend the price index decomposition derived by Feenstra(1994) to allow for different degrees of preference for variety. First, we define the variety-adjusted price index based on the assumption that the number of varieties is identical between country j and k ( I j = I k = I ) and the unobservable demand shifter is the same for the common set of varieties ( b jl = bkl = b !l " I ). The price index can be defined as:

(3) R = jk

(

Pj p j , I,b

) = c ( p , I,b)

Pk ( pk , I,b)

j

j

ck ( pk , I,b)

The second equality comes from plugging (2) into (3) and using the assumption that the number of varieties is the same in both countries. Sato(1976)12 shows that the price index corresponding to the CES unit cost function can be written as:

11 12

The notation is adapted to this paper even though we follow closely Feenstra(1994). We adapt the time series result to cross section.

31

!p $ (4) R = ( # jl & jk l 'I " pkl %

) jl ( I )

which is a geometric mean of variety prices with weights ! jl ( I ) . The weights are defined as follows:

# s jl ( I ) % skl ( I ) $ && ' ln s jl ( I ) % ln skl ( I ) ') (5) ! ( I ) * ( , where the cost shares s jl ( I ) are: jl # s jl ( I ) % skl ( I ) $ && '' + l"I ( ln s jl ( I ) % ln skl ( I ) ) (6) srl ( I ) "

prl xrl for r = j , k . p x # rl rl l!I

(

" ! % ) *1 Proposition 1: If b jl = bkl for l ! I " ( I j # I k ), I $ % , then = R jk $ j ' Pk # !k & Pj

where (7) ! # r

$p $p l"I

l"I r

x

rl rl

for r = j , k

x

rl rl

Proof: The expenditure shares of each variety l of country r=j,k can be derived as the elasticity of unit cost function with respect to the price of variety l: (8) slr ( I r ) =

$Pr ( pr , nr , I r ) $prl

prl ! #1 = cr ( pr , nr , I r ) brl " prl1#! for r = j , k Pr ( pr , nr , I r )

Rearranging, we can obtain: !

1

(9) cr ( pr , nr , I r ) = srl (I r )" #1 brl 1#" prl for r = j , k The price index associated with the general CES unit cost function can be written using (9) as:

(

Pj p j ,bj , I j (10)

(

Pk pk ,bk , I k

)= n

! "1 1" # j j ! "1 1" # k k

)

n

for l $I

=

! "1

c ( p j ,bj , I j )

(

c pk ,bk , I k

n

! "1 1" # j jl

s

! "1 1" # k kl

n

s

(I )

1 # "1

(I )

1 # "1

j

k

)

=

( )

1 # "1

(I )

1 # "1

# n1" s jl I j j ! "1 1" # k kl

n

s

k

! # b1" p jl jl ! 1" # kl

b

for l $I

=

pkl

p jl pkl

32

The expenditure shares of each variety can be written:

prl xrl # p x rl rl l " I (11) srl (I r ) = for r = j , k prl xrl # prl xrl # l"I l"I r ! "#" $! "#" $ srl (I )

!r

We can define the number of varieties as:

(12)

nj nk

#p

!

l "I j

jl

#p

l "I k

x jl x

kl kl

#p l "I

#p l "I

jl

x jl x

kl kl

=

$k $j

Rewriting the variety expenditure shares as in (11) and using (12), (10) becomes: "

(13)

Pj Pk

=

() (I)

! #j $1 s jl I !

" # $1 k kl

s

1 # $1 1 # $1

p jl pkl

Taking the geometric mean across varieties in (13) and using the weights ! jl ( I ) , we get: (

P " ! % ) *1 ! (14) j = $ j ' Pjk Pk # !k &

() ()

"s I % - $ s jl I ' l ,I # kl &

+ jl ( I ) ) *1

It is easy to prove that the product in (14) equals 1. q.e.d The CES price index can be written as: (

" ! % ) *1 (15) =$ j' R jk Pk # !k & Pj

The price index defined by (15) is equivalent to the CES price index derived by Feenstra(1994) when ! = 1 .

33