Variety Gains and the Extensive Margin of Trade

ABSTRACT

Findings from the literature suggest that previous estimates of the variety gains from trade are too small because of the imprecise measurement of the imported variety set under the Armington assumption. In this contribution, the lambda ratios as presented in Feenstra (1994) are first modified by assuming that all import variations are due to extensive margin adjustments. Under this extreme assumption, variety gains increase by a factor of six compared with the baseline Armington product-country variety differentiation case. Second, results from the literature on multi-product firms are used to obtain a more realistic magnitude of the extensive margin of imports by accounting for the entry and exit of firms as well as for product turnover within firms. It is found that welfare gains still increase by a factor of 2.5 compared with the Armington baseline case.

Keywords:

• margins of trade
• welfare gains from trade
• multi-product firm

JEL Classifications:

• F10
• F12
• F14

Acknowledgements

I am grateful to two anonymous referees for valuable suggestions. I thank Robert C. Feenstra, Ulf Lewrick and Christian Rutzer for helpful comments. I am furthermore very grateful to Rolf Weder for constant advice on the project. I also thank my colleagues at the University of Basel, the participants of the ETSG meeting in Warsaw, the FIW conference in Vienna, the YSEM in Berne, the SMYE in Istanbul and the annual congress of the SSES in Geneva for helpful comments and fruitful discussions. In addition, the author acknowledges the financial support of the WWZ Forum Basel and the Swiss National Science Foundation (project no. 100014-124975). This paper contains parts of an earlier working paper with the title ‘Globalization and the Gains from Variety: The Case of a Small Open Economy’.

Notes

¹In this paper, I focus on the identification of the variety gains from trade. A different objective is pursued by, for example, Arkolakis, Costinot, and Rodrìguez-Clare (2012). These authors argue that total gains from trade can be inferred from two simple statistics, the import penetration rate and the elasticity of imports with respect to trade costs. These welfare gains then include any possible trade gains that may be identified by different micro models; e.g., variety gains, productivity gains through firm selection or scale economies.

²Evidence on the importance of the multi-product dimension of firms is, for example, found in Arkolakis and Muendler (2010), Bernard, Jensen, Redding, and Schott (2007), Bernard, Redding, and Schott (2011), Bernard, Jensen, Redding, and Schott (2009a), and Bernard, Jensen, and Schott (2009c).

³Another aspect of the discussion on the magnitude of variety gains concerns the CES utility specification chosen by Broda and Weinstein (2006). Montagna (1999) argues that the standard Dixit-Stiglitz model incorporates a maximum love of variety. Feenstra and Shiells (1996) compare the CES framework to the translog case and conclude that new varieties have a larger impact using the former specification. Hummels and Lugovskyy (2005), based on Lancaster (1979), argue that the less than proportional increase in imported varieties with respect to market size can be explained by the falling marginal benefit of importing additional varieties. In their model, this is due to ‘crowding’ in the variety space, an effect that is absent in the CES case. Taking a somewhat different approach, Ardelean (2009) argues that the standard Krugman (1980) model overstates the love of variety, since it assumes that larger countries export more only at the extensive margin, while models in the vein of Armington (1969) assume that countries’ exports grow only at the intensive margin. By nesting Krugman- and Armington-style models, she concludes that the love of variety is 44% lower than in Krugman's CES model. These contributions imply that Broda and Weinstein (2006) may even overestimate the imported GFV. In my paper I leave this issue to one side and use the CES specification. I argue, however, that the main result of this paper, namely larger variety gains from trade due to a more realistic extensive margin definition, carry over to other modelling approaches.

⁴These two analyses are not restricted to imported variety. In my paper, I concentrate on imported variety. However, the concept presented below can, in principle, be applied to domestic production, for example by using the modelling approach of Ardelean and Lugovskyy (2010).

⁵Broda and Weinstein (2006) find variety gains of 2.6% in terms of GDP for the period from 1972 to 2001. However, the largest part of these overall gains is due to developments in the earlier years as the authors note (Broda & Weinstein, 2006, p. 576). For the years 1990 to 2001, the authors find welfare gains of 0.8% in terms of GDP.

⁶In 1990, over 14,000 products were imported into the United States, stemming from more than 150 countries and resulting in a total of more than 180,000 varieties, see Table A1.

⁷Alternatively, assume that the second term on the right-hand side is a function with well-defined derivatives (i.e., that the number of varieties included in the common sets is very large). Let I_g→∅. Applying l'Hôpital's rule, this yields the same result as found above:

⁸Note that the issue of inflation is not present in the lambda ratio of equation (3). The lambda ratio divides expenditure shares, and not expenditures, and thus general price increases cancel one another out.

⁹See http://cid.econ.ucdavis.edu/.

¹⁰Broda and Weinstein (2006) describe import data from 1990 to 2001. The qualitative findings of this analysis largely remain unchanged and are therefore omitted here. I add an updated version of Table I of Broda and Weinstein (2006) to the Appendix (Table A1).

¹¹Note that a value for sigma cannot be obtained for all product categories presented in Table A1. For some product categories, the number of observations is not sufficiently high to estimate a sigma.

¹²Alternatively, I use the Broda and Weinstein (2006) estimates. The results of the analysis presented below are not sensitive to this change.

¹³Note that for HTS-10 goods the lambda ratio is not defined if there is no common variety in the first and the last period. Where this occurs, the lambda ratio of the HTS-8 good is used for all the HTS-10 goods within this HTS-8 category. If the lambda ratio is not defined at the HTS-8 level, the HTS-6 category is used. To obtain an elasticity for these aggregated goods, the geometric mean of the sigmas of the HTS-8 goods is used. In consequence, only 858 lambda ratios are defined (and not 16,322), a combination of HTS-2, HTS-4, HTS-6, HTS-8 and HTS-10 goods. Note however, that all 16,322 sigmas are used for the calculation of the index.

¹⁴Assume, for example, that the BLS reports a price increase of 20% between 1990 and 2006 within a particular product category. Then, the ‘zero variety’ takes the value  If nominal expenditure on this product – as measured in the trade data – rises by 40%, the modified lambda ratio becomes

¹⁵Data stem from the US Linked/Longitudinal Firm Transaction Database (LFTTD). A more detailed description of the data can be found in Bernard et al. (2009c).

¹⁶Newly imported varieties tend to be unimportant in the first few years. Over time, however, these varieties acquire a larger share on total imports. For example, Bernard et al. (2009b) find that the extensive margin accounts for 50% of the time-series variation of US imports if one considers the period from 1998 to 2003. If this period is extended to 1993, then the extensive margin accounts for 76% of the variation.

¹⁷One possible variety definition at the firm level is to differentiate varieties according to different products stemming from different foreign firms. Bernard et al. (2009b), on the other hand, differentiate varieties according to importing firms instead of supplying firms.

¹⁸Total merchandise imports amount to US$460 billion in 1993. Adding the total increase of US$574 billion imports amount to US$1034 billion in 2003. Using the percentages given in Bernard et al. (2009b, p. 9), of these US$1034 billion in 2003, US$719 billion were due to new firm-product-country pairs. Of the US$460 billion in 1993, US$278 billion were lost due to vanishing firm-product-country pairs. This yields the following formula for the lambda ratio: λ_gt/λ_gt−1=([1034−719]/1034)/([460−278]/460)=0.77.

¹⁹Given the data limitations, it is not possible to calculate an aggregate lambda ratio for the full period from 1990 to 2006. Hence, since the extensive margin of imports tends to increase the longer the considered time span, an aggregate lambda ratio over the full period might even be slightly lower and the respective variety gains slightly higher than calculated for the ‘firm-product-country margin’ case below.

²⁰In other words, I use the same lambda ratio structure as in the baseline specification, i.e. replace the 858 lambda ratios by 0.77 (see Note 14) and aggregate these lambda ratio as described by equation (7). The stark assumption of one single lambda ratio is assessed in the following section.

²¹For example, Broda and Weinstein (2010) note that a large part of within-firm variety churning is due to simple labelling or marketing changes.

²²I increase (σ−1) by 50% and 100%, since σ>1 is imposed by the modelling approach.

²³Blonigen and Soderbery (2010) compare elasticities estimated from import data with elasticities estimated from more detailed market data. They find that the median of the latter estimates is approximately 17% larger. Broda and Weinstein (2006) change product definitions from SITC-3 to SITC-5 – hence inducing the varieties contained within the broader products to be more similar – and this increases the median lambda ratio by 42%. Narrowing the product definition to HTS-10, the median elasticity increases by another 23%.

²⁴An implicit assumption that is required when applying the lambda ratios in equations (4) and (5) is that inflation is the same for common, new and disappearing varieties. The results of my robustness checks indicate, however, that this issue is not crucial to the results.

²⁵For example, Boskin, Dulberger, Gordon, Griliches, and Jorgenson (1998) estimate an upward bias in the consumer price index (which also includes imports) of approximately 1% per year in the 1997 to 1998 period. However, improvements in the measurement of prices are likely to have reduced these biases since then; see for example Gordon (2000).