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Bounded Love of Variety and Patterns of Trade

Abstract

Long-run bilateral trade data exhibit four empirical regularities: (i) countries import only a small fraction of all traded varieties, (ii) per capita income and the number of imported varieties correlate positively, (iii) per capita income and trade shares correlate positively and (iv) world trade shares have markedly increased. Standard theories fail to simultaneously explain these patterns. This paper reconciles theory and data by assuming that the consumer’s marginal utility from varieties is bounded. Given this assumption, consumers do not purchase foreign varieties that bear high transport costs. With increasing incomes, however, consumers include more of the latter varieties, which generates the four patterns above.

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Fig. 1
Fig. 2
Fig. 3

Notes

  1. 1.

    This is a common definition of variety, which the present paper adopts. It thereby departs from the more accurate definition by Krugman (1980), which identifies a variety by the firm that produces it.

  2. 2.

    Hufbauer (1970) provides an early study, Francois and Kaplan (1996) a more recent empirical study. See also Ventura (2006) on the correlation between trade volumes and per capita income.

  3. 3.

    Empirical studies investigating the impact of trade on growth generally control for causal links from income growth to trade openness (see, e.g., Frankel and Romer 1999 or Alcalá and Ciccone 2004).

  4. 4.

    Among the papers mentioned in the introduction, this class comprises Anderson (1979), Baier and Bergstrand (2001), Yi (2003), Melitz (2003), Broda and Weinstein (2004, 2006), Ruhl (2005), Cuñat and Maffezzoli (2007), and Simonovska (2010).

  5. 5.

    By the same token, the set of countries from which importer purchases from, on which the definition of variety is based in Figs. 1 and 2, is constant in per capita income.

  6. 6.

    All references to equations in this subsection are to Melitz and Ottaviano (2008) and are labeled by MO.

  7. 7.

    Here and in the following, the use of Greek letters differs from that of the previous section.

  8. 8.

    The transformation \(\tilde{c}=c/\vartheta \) (ϑ > 0) implies \(\ln ( \tilde{c}+1)=\ln (1/\vartheta )+\ln (c+\vartheta )\) and shows that, as long as consumption units are free, the choice of adding unity instead of a positive constant does not mean a loss of generality.

  9. 9.

    Indeed, Anderson and van Wincoop (2004) show that trade costs are substantial; the border effect alone accounts for a tariff-equivalent of about 40%.

  10. 10.

    In line with the estimates in Haveman and Hummels (2004), preferences specified in Eq. 2 predict higher markups at higher per capita consumption levels.

  11. 11.

    These expressions incorporate the relevant conditions for \(c_{d}^{_{(\ast )}} \) to be positive.

  12. 12.

    For all i,k ∈ I there is a permutation ξ:II so that ξ(τ i ) = τ k .

  13. 13.

    Throughout the same time interval, the number of employees per firm rises by 12.3% from 17.7 to 19.9. These numbers are calculated with data from the “United States Small Business Administration.” (See http://www.sba.gov/advo/index.html.)

  14. 14.

    For comparison, the traditional Krugman (1980) model predicts that the number of firms is proportional to L/α, independently of β. In this setting, population growth between 1988 and 2006 (22%) implies that the setup cost remained constant if the observed increase in the number of firms (22%) was to be matched.

  15. 15.

    Baldwin and Harrigan (2007) observed also that the average unit value of exports is positively related to distance.

  16. 16.

    Taking the logs of N it as the dependent variable does not change the significance of the estimates but alters their interpretation. Moreover, it introduces a selection bias by eliminating observations of zero trade flows.

  17. 17.

    For Switzerland, which forms part of a collection of relatively small countries, the average distance to potential trade partners is 5,684 kilometers in 2000. The corresponding figure for New Zealand is 14,094, the longest distance to the average potential trade partner. There is little variation in time, as these values change only with foundation of new countries.

  18. 18.

    All qualitative results are preserved for other years.

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Acknowledgements

I would like to thank Raphael Auer, Giancarlo Corsetti, Gino Gancia, Omar Licandro, Marco Maffezzoli, Diego Puga, Morten Ravn, Karl Schlag and Jaume Ventura and two anonymous referees for many valuable comments. All remaining errors are mine.

The views expressed in this paper are mine and do not necessarily represent those of the Swiss National Bank.

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Correspondence to Philip Sauré.

Appendix: Proofs

Appendix: Proofs

Proof of Eq. 22

For I = 2 rewrite Eq. 12 as

$$ w_{1}=w_{1}\frac{L_{1}\tau _{11}(c_{11}+1)c_{11}}{\sum_{m}L_{m}\tau _{1m}(c_{m1}+1)c_{m1}}+w_{2}\frac{L_{2}\tau _{21}(c_{12}+1)c_{12}}{ \sum_{m}L_{m}\tau _{2m}(c_{m2}+1)c_{m2}} $$

Rearrange as

$$ \frac{(c_{21}+1)c_{21}}{\sum_{m}L_{m}\tau _{1m}(c_{m1}+1)c_{m1}}=\frac{w_{2} }{w_{1}}\frac{(c_{12}+1)c_{12}}{\sum_{m}L_{m}\tau _{2m}(c_{m2}+1)c_{m2}} $$

No, with w 1 = w, \(w_{2}=w^{\ast }\) and the corresponding notation, one has

$$ \begin{aligned} \frac{w^{\ast }}{w} &=\frac{c_{f}^{\ast }+1}{c_{f}+1}\frac{\tau L(c_{f}+1)+L^{\ast }\left(c_{d}^{\ast }+1\right)c_{d}^{\ast }/c_{f}}{\tau L^{\ast }\left(c_{f}^{\ast }+1\right)+L(c_{d}+1)c_{d}/c_{f}^{\ast }} \\ &=\frac{c_{f}^{\ast }+1}{c_{f}+1}\frac{\tau L+L^{\ast }c_{d}^{\ast }/c_{f}+\alpha /\left( \beta ^{\ast }c_{f}\right) }{\tau L^{\ast }+Lc_{d}/c_{f}^{\ast }+\alpha /\left(\beta c_{f}^{\ast }\right)} \end{aligned} $$

where Eq. 10 has been used in the last step.□

Proof of Eq. 25

The first country’s trade share is

$$ \begin{aligned} e &=\frac{L^{\ast }n(c_{f}^{\ast }+1)c_{f}^{\ast }\beta w}{Lw} \\ &=\gamma \frac{L^{\ast }(c_{f}^{\ast }+1)c_{f}^{\ast }}{L(c_{d}+1)c_{d}+L^{ \ast }\tau (c_{f}^{\ast }+1)c_{f}^{\ast }} \end{aligned} $$

where n from Eq. 11 has been used. Substituting c d from Eq. 21

$$ \begin{aligned} e&=\gamma \frac{L^{\ast }\left(c_{f}^{\ast }+1\right)c_{f}^{\ast }}{\left( \frac{\alpha }{\beta }+\sqrt{L\left[ \frac{\alpha }{\beta }-L^{\ast }\tau (c_{f}^{\ast })^{2}\right] }\right) +L^{\ast }c_{f}^{\ast }}\\ &=\gamma \frac{L^{\ast }\left(c_{f}^{\ast }+1\right)}{\left( \frac{\alpha }{\beta c_{f}^{\ast }}+\sqrt{L\left[ \frac{\alpha }{\beta \left(c_{f}^{\ast }\right)^{2}}-L^{\ast }\tau \right] }\right) +L^{\ast }} \end{aligned} $$

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Sauré, P. Bounded Love of Variety and Patterns of Trade. Open Econ Rev 23, 645–674 (2012). https://doi.org/10.1007/s11079-011-9207-3

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Keywords

  • Marginal utility
  • Variety

JEL Classification

  • F10
  • F13