Does size matter? In international trade, market size can influence the pattern of specialization when there are economies of scale. A number of papers written in the late 1990s and early 2000s, surveyed by Keith Head and Thierry Mayer in a 2004 Handbook chapter, looked at the connection between market size and the pattern of specialization and trade, using countries’ total expenditure as the relevant measure of size.
The recent literature linking patterns of trade to countries’ income levels has spurred a number of economists to pay more attention to the role of product quality and non-homothetic preferences in international trade. In particular, relative country size and relative demand are only necessarily synonymous when preferences are homothetic. When expenditure shares vary with income levels, the composition of income influences the composition of demand. Two places with the same number of consumers will have very different demands for high-quality products if one place is populated by high-income households and the other is not. In elegant theoretical settings, Fajgelbaum, Grossman, and Helpman (2011) and Matsuyama (2015) show that economies of scale and trade costs can cause higher-income locations to specialize in the income-elastic products that are in greater relative demand.
Whether a country’s income level influences its product mix and export basket through this demand channel is a classic question in international trade. The hypothesis dates to a monograph by Staffan Burenstam Linder published in 1961. He wrote “the range of exportable products is determined by internal demand. It is a necessary, but not a sufficient condition, that a product be consumed (or invested) in the home country for this product to be a potential export product.” “The level of average income… has… a dominating influence on the structure of demand.” Linder’s economic mechanism – entrepreneurial discovery in bringing products to market – was not presented as a mathematical model, but he made clear empirical predictions about the pattern of trade that could be taken to data: “The more similar the demand structure of two countries, the more intensive, potentially, is the trade between these two countries.”
A formal model in which the pattern of demand influenced the pattern of production did not arrive until 1980, when Paul Krugman introduced a very special model in which there are “home market” effects on the pattern of trade. Consider two countries with identical technologies, homothetic preferences, and different population sizes. Suppose there are two sectors, one producing with increasing returns and trade costs, the other producing with constant returns and costless trade. Krugman (1980) and Krugman and Helpman (1985) showed that “if two countries have the same composition of demand, the larger country will be a net exporter of the products whose production involves economies of scale.”
There are important differences between Linder (1961) and Krugman (1980). En route to formal results, the role of income levels was lost. With homothetic preferences, market size and total expenditure are synonymous. Thus, the empirical work summarized by Head and Mayer used this notion of size. Fajgelbaum, Grossman, and Helpman (2011) bridged this gap between Linder and Krugman by using a demand system in which the composition of income matters for market size. My job-market paper, now available at the Review of Economic Studies, showed that better market access to higher-income consumers results in manufacturing plants specializing in higher-quality products.
There is another gap between Linder (1961) and Krugman (1980). Linder said internal demand was necessary for production and thus exporting. Krugman (1980) predicts that greater demand elicits such a strong production response that the location is a net exporter. Following Linder, I focused on the pattern of specialization and exports in early drafts of my JMP. Some discussants and referees told me that they wanted an empirical result for net exports because “the home-market effect is a prediction about net exports.” I found that proximity to higher-income consumers predicts the composition of exports but not the composition of imports, so my results did characterize net exports. But I remained a bit puzzled by the gap between Linder and Krugman.
A new paper by Costinot, Donaldson, Kyle, and Williams, which Dave presented at last week’s SCID-IGC conference, has now cleared up this confusion about “the home-market effect”. They introduce a “distinction between the weak home-market effect, which focuses on gross exports, and the strong home-market effect, which focuses on net exports.” Economies of scale are necessary for both. “By lowering the price of goods with larger domestic markets, economies of scale can instead create a positive relationship between exports and domestic demand.” “A strong home-market effect arises if economies of scale are strong enough to dominate the direct effect of domestic demand on imports.”
Why has this distinction not been stated previously? It turns out that the formal models in Krugman (1980) and other accounts assume functional forms such that any home-market effect is always strong. The notion of a weak home-market effect, stated very clearly in Linder’s 1961 book, disappeared due to a modeling choice. We can now see it again, in clear mathematical terms, thanks to CDKW.
Simplifying assumptions are a double-edged sword. The role of market access only received its due attention after Krugman’s formalization, for which he won a Nobel Prize. But there were elements in Linder’s account of home-market effects that we are only recovering half a century later. Fajgelbaum, Grossman, and Helpman (2011) revived the role of income composition, and now CDKW have revived the weak home-market effect.
No one appreciates these trade-offs in modeling more than Paul Krugman himself. As he wrote in his 1980 contribution: “The analysis in this section has obviously been suggestive rather than conclusive. It relies heavily on very special assumptions and on the analysis of special cases.” Unfortunately, economists have spent many, many years using only this special case. The weak home-market effect was lost due to assumptions embedded in the very tractable functional forms Krugman employed.
In particular, the weak home-market effect was lost to a modeling quirk that linked economies of scale with the price elasticity of demand. Peter Neary warned about this particular assumption in his great 2001 JEL piece, “Of Hype and Hyperbolas“. Section 4, “Limitations of the Model”, describes “a number of special features that make it less suitable for addressing some issues” and the fact that consumers’ elasticity of substitution and price elasticity of demand winds up as an index of returns to scale is first on his list. With hindsight, we know that the weak home-market effect was one of those issues left unaddressed.
This seems a classic case of a phenomenon Krugman highlighted in his meditation on economic methodology: “an extended period in which improved technique actually led to some loss in knowledge”. Gradually, though, the rigor of formal theory leads to better understanding. Now we have home-market effects, weak and strong.