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The reverse home-market effect in exports: a cross-country study of the extensive margin of exports

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Abstract

Do small countries have higher proportions of firms that export in manufacturing industries than large ones? As small countries are well known to be more open than large ones, it may appear uncontroversial to claim that the answer is yes. Nevertheless, this contradicts predictions from many standard trade models positing a home-market effect in the number of manufacturing firms and exporters. In this article, I present a theoretical model where a home-market effect in the number of firms coexists with a reverse home-market effect in the number of exporters: as in standard models, the number of firms in a small country relative to that in a large one is lower than relative income, but, in contrast to standard models, the relative number of exporters is larger. As a consequence, small countries will have higher proportions firms that export in manufacturing industries—a claim I support empirically.

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Notes

  1. The availability of firm-level data spawned a literature distinguishing between the extensive and intensive margins of trade. Changes in trade flows can be due to changes in number of units such as firms, products or countries (the extensive margin) or changes in the amount traded per unit (the intensive margin). The definition of the two margins differs in different articles, depending on the research question. See e.g. Lawless (2010) or, for an overview, Bernard et al. (2012).

  2. Manufactured goods are here defined as goods that are characterised by product differentiation and produced under IRS. I follow common practice in the HME literature and use the terms ‘IRS industries’ and ‘manufacturing industries’ interchangeably throughout the article. I acknowledge, however, that this may be imprecise, and that, for instance, many services sectors may also have the same attributes. I return to this point in Sect. 3.

  3. The HME was first introduced formally by Krugman (1980). He presented a model of trade between two different-sized countries building on the Dixit and Stiglitz (1977) framework, where consumers value variety of goods, and firms produce differentiated goods and engage in monopolistic competition. The HME was further developed in HK 1985, who introduced a sector producing a homogenous good under constant returns to scale (CRS) into the Krugman (1980) framework. In models where entry and exit of firms is impossible (or difficult), the HME can result in lower wages instead of (or in addition to) fewer firms. See e.g. Demidova and Rodríguez-Clare (2013) and the accompanying online appendix or Felbermayr and Jung (2012).

  4. The figures in parenthesis indicate the share of manufacturing exports in total exports in the countries in year 2010. I focus on low- and middle-income countries because the empirical analysis presented in Sect. 3 only includes countries like that. There are, however, also many examples of small high-income countries with a high share of manufacturing exports in total exports. Examples include Finland (0.77) and Singapore (0.73). Data is taken from the Comtrade database. For some countries export data lack. In such cases, I use mirror values (i.e. the sum of all other countries’ import from the country in question). I thank Arne Melchior for providing me with these data.

  5. Several articles have studied other conditions for the HME to occur. Other models that produce a reverse HME in the number of firms as well as in the number of exporters include Okubo and Rebeyrol (2006), who assume stronger IRS in the large country; and Yu (2005), who relaxes the commonly made assumption of a constant consumers’ expenditure share for manufactured goods. Furthermore, the HME will be dampened in a model with no homogenous good sector (see e.g. Demidova and Rodríguez-Clare 2013 and the accompanying online appendix for the case of equal firms; and Felbermayr and Jung 2012 for the case of firm-level differences in marginal costs). The HME may also disappear if trade costs accrue in both the manufacturing and the homogenous good sector and not only in the manufacturing sector, as is commonly assumed (Davis 1998). It may also disappear in a multiple country setting (Behrens et al. 2009).

  6. This mechanism is present in traditional trade models emphasising CRS, homogenous goods, and comparative advantage. These generally predict that countries will be net exporters of goods for which they have relatively low domestic demand because they have access to a relatively large foreign market (Davis and Weinstein 1999).

  7. Due to data availability, I am not able to directly test the coexistence of an HME in the number of firms and a reverse HME in the number of exporters.

  8. See the working paper version of this article, Medin (2013) for a discussion of the criteria for this to happen.

  9. Wage is the only source of income, because free entry of firms in the manufacturing sector assures that profits are driven to 0 (see below). Consequently, Y can also be interpreted as relative size of labour force.

  10. Since there is no G in HK1985, that model does not distinguish between exporters and non-exporters—either all firms or no firms export. As a consequence, the extensive margin of export in that model is either 0 or 1. Note that, as pointed out by Medin (2003), introducing fixed export costs into the HK 1985 framework is alone not sufficient to render possible an equilibrium where exporters and non-exporters coexist—more structure has to be added to the model. In BF 2010 as well as in Medin (2003) more structure is added to the supply side. In Venables (1994) more structure is added to the demand side, and in the present model, more structure is added to both the supply and the demand side. In an appendix in Medin (2003), a Venables (1994) model with asymmetric countries is outlined, but the full model is not written out. There is no HME in domestic sales in that model-outline, as it only allows for an equal number manufacturing industries in the two countries (see Sect. 2 for discussion). In all these models, except for BF (2010) firms are initially equal.

  11. Conceptually this is not different from the fact that in all trade models based on the Dixit and Stiglitz (1977) combination of CES utility and monopolistic competition, there is a potential number of Ω firms (goods) in the economy, but the market is not big enough for all of them; thus, in equilibrium, only a subset will actually produce (be produced).

  12. Even though I depart from todays’ common practice in modelling Melitz (2003) type firm-level differences in φ, it is not my intention to claim that firms do not differ in their marginal production costs. However, Melitz-type models generally focus on firm differences in explaining why some firms become exporters while others do not. The main determinant of whether or not a firm exports is its productivity. But it is not surprising that different firms behave differently. Here, I wish to highlight export-market conditions, rather than firm-level differences, as determinants of firms' export status, and I believe that introducing firm-level differences in φ would unnecessarily complicate the model without giving more insight into the central issues of the article.

  13. One might be led to believe that the HME in exports in HK 1985 is due to an undesired side-effect of the model’s inability to distinguish between exporting and non-exporting firms (see footnote 10). This is not the case, since also in BF 2010 the extensive margin of manufacturing export is independent of the size of the home- and export-market (despite that it can be lower than 1). Consequently, the HME in the number firms translates into an HME in the number of exporters, also in that model.

  14. Also see discussion in Baldwin et al. (2003, ch. 10.2).

  15. Similar nested CES functions are frequently used in models of multiproduct firms to distinguish goods produced by the same firm from goods produced by different firms. See e.g. Bernard et al. (2011).

  16. There are not enough degrees of freedom in the model to endogenise both the number of firms and the number of industries.

  17. See the working paper version of this article, Medin (2013), for details on the derivation. Note that since firms and industries are symmetric, we can disregard indexing them. It is sufficient to characterise a firm and an industry by country of origin. Consequently, we can write C i (k j ) = C ji , and c i (k j ,ω i ) = c ji .

  18. For non-exporters, z ij will of course be 0.

  19. The key to solving the equilibrium is to divide (11) by (10). The working paper version of this article, Medin (2013), provides further details.

  20. See e.g. Melitz (2003), BF 2010, or Felbermayr and Jung (2012) for a similar measure and condition. Note that T β t β < 1 is a necessary but not sufficient condition for the existence of some non-exporters in both countries. It seems reasonable as empirical evidence generally shows that only a proportion of firms export (see e.g. Bernard et al. 2012).

  21. From the sign of the derivatives we see that MN is largest for M close to 1 and t β T β close to 0. Setting M = 1 and/or t β T β = 0 in Eq. (13) yield MN = Y. Also note that the lower bound of MN is defined by setting M = Y and t β T β = 1, which yields MN = Y 2.

  22. From the sign of the derivatives we see that MN * is smallest for M = Y and t β T β close to 0. Setting Y = M and t β T β = 0 in Eq. (15) yield MN * = Y. Also note that the upper bound of MN * defined by setting M = 1 in Eq. 15, which yields MN* = Y −1.

  23. Some other models can also serve as alternative explanations, but not all of these seem equally fit. Chaney (2008) and Felbermayr and Jung (2012) develop Melitz-type model with asymmetric countries. In the first, the number of firms is set exogenously proportional to country income, and, although not the focus in the article, the model produces a reverse HME in exports (but no HME in domestic sales). In the second, the small country’s share of the world’s mass of firms is lower than its share of income, so there is an HME with respect to the mass of firms. As in the model presented here, the extensive margin of export is larger in the small country. Nevertheless, it is not possible to solve for the relative mass of exporting firms, so we cannot know whether there is a reverse HME in the mass of exporters.

  24. Then an equal number of imported and domestic composite industry goods will enter the utility function, regardless of how small home is. If home is say 100 times smaller than foreign, and there are no export costs, foreign’s demand towards goods produced in home will be 100 times higher than home’s demand towards goods produced in foreign.

  25. From the sign of the derivatives we see that N */N is largest for t β T β and M close to 1. Setting t β T β = 1 and/or M = 1 in Eq. (17) yields N */N = Y −2, which defines the upper bound of N */N. Setting t β T β = 0 and M = Y, yields N */N = 1, which defines the lower bound.

  26. The data also covers some other countries, but for these I do not have sufficient information to include them in the regression analysis presented below.

  27. The information is based on data from the Comtrade database for year 2010. Also see Footnote 4.

  28. The data are stratified, and I applied sampling weights to ensure unbiasedness of these measures.

  29. Most of them are from year 2014. Many are also from years 2009 and 2010.

  30. Note that in the theoretical analysis it was assumed that no firms exported without also selling in the domestic market. In the data there are a few firms (0.7 %) that export all their output. These are counted among n ii in the empirical analysis. Also other studies find that very few firms export without also selling in their domestic market. For example, Eaton, Kortum, and Kramarz (2011) find that <1 % of French firms do this.

  31. GDP is measured in constant (year 2005) USD. For each country, I construct relative home-market size based on GDP figures for the year corresponding to the year the country appears in the Enterprise Survey dataset. GDP data are taken from the World Development Indicators (2013).

  32. Liberia in year 2009 and Vanuatu in year 2009.

  33. Note that in the equations, variable (τ) and fixed (G) export costs are embedded in t and T respectively.

  34. See Baldwin and Harrigan (2011) for a discussion of the measure. Its advantage over alternative measures is that it does not put too much weight on very small and distant countries. This is important, as our sample consists of many such countries. Data for distance between pairs of countries come from the CEPII database dist_cepii (Mayer and Zignago 2011). I use the Great Circle distance measured in kilometres between largest cities (the dist variable). Internal distance d ii is set equal to the square root of the country’s area multiplied by about 0.4, according to Head and Mayer (2000).

  35. In the model, productivity is given by 1/φ times the wage, and the wage is normalised to 1.

  36. Using the Stata 14 command fracreg logit (StataCorp. 2014). Also see Wooldridge (2012), pp. 748–753, for a textbook discussion on fractional dependent variables and Ramalho et al. (2011) for a recent discussion.

  37. Ideally, I should also have included industry dummies, but unfortunately information on more disaggregated industry affiliation than “manufacturing” and “services” is not available for many countries. However, I do include a dummy for the services industry in the sensitivity analysis where that industry is included.

  38. The effect of an independent variable on the dependent variable is calculated for all observed variables of the other independent variables. Thereafter, the average of all calculated effects is reported. See the margins, dxdy command in the Stata14 manual for more information.

  39. Weights are equal to the share of the exporter’s total export value of manufacturing goods that is shipped to each destination country.

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Acknowledgments

I am grateful to Ragnhild Balsvik, Kjetil Bjorvatn, Pao-Li Chang (associate editor of this journal), Jan I. Haaland, Per Botolf Maurseth, Arne Melchior, Andreas Moxnes, and anonymous referees for valuable comments. Copyediting by Susan Høivik is highly appreciated. Research funding was provided by the Research Council of Norway, Project 139982/510 ‘Globalization and Internationalization of the Norwegian Economy’ and Project 233836 ‘Traders in the food value chain: Firm size and international food distribution.’

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    Hege Medin

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Medin, H. The reverse home-market effect in exports: a cross-country study of the extensive margin of exports. Rev World Econ 153, 301–325 (2017). https://doi.org/10.1007/s10290-016-0269-6

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