Market-size effects, across places and over time

The dividing line between neoclassical trade models and the now-quite-dated “new trade theory” is economies of scale. Neoclassical models feature constant (or decreasing) returns. Free trade is efficient in such settings. With the introduction of increasing returns, Brander, Spencer, Krugman, Helpman, and others “open[ed] the possibility that government intervention in trade via import restrictions, export subsidies, and so on may under some circumstances be in the national interest after all” (Krugman 1987).

The fact that “size matters” in new trade theory (size can influence the pattern of specialization because there are economies of scale) while it does not in neoclassical models became the basis for empirical investigations trying to distinguish these theories. Davis and Weinstein (2003) describe the idea behind this research strategy:

A fundamental divide may be identified between two classes of models. In the first class, unusually strong demand for a good, ceteris paribus, makes a country an importer of a good. An example would be a conventional two-sector neoclassical model with strictly downward sloping import demands. However, there is an alternative tradition within the trade literature which emphasizes an important interaction between demand conditions and production opportunities in which the production response to local demand conditions is so powerful that strong local demand for a product leads a country to export that product. When such conditions exist, the literature terms it a home market effect.

Stepping away from trade, there’s a very different economic context in which the role of market size is also crucial: the literature on innovation. The idea dates at least to Schmookler (1966) who memorably titled two of his chapters “The amount of invention is governed by the extent of the market.” It’s also key to endogenous growth theory. Acemoglu and Linn (2004) provided empirical evidence that market size influenced innovation in a particular sector:

This paper investigates the effect of (potential) market size on entry of new drugs and pharmaceutical innovation. Focusing on exogenous changes driven by US demographic trends, we find a large effect of potential market size on the entry of nongeneric drugs and new molecular entities… Our results show that there is an economically and statistically significant response of the entry of new drugs to market size. As the baby boom generation aged over the past 30 years… the data show a corresponding decrease in the rate of entry of new drugs in categories mostly demanded by the young and an increase for drugs mostly consumed by the middle-aged.

In “The Determinants of Quality Specialization“, I showed that high-income cities manufacture higher-priced, higher-quality goods in part because they are home to more high-income households who demand such products. Quantitatively, I found that the home-market effect plays at least as large a role as the factor-abundance mechanism in quality specialization across cities of different income levels.

What does this have to do with Acemoglu and Linn (2004)? I didn’t see much of a connection when I was writing my paper. Pharmaceuticals were just one of many industries in my data on US manufacturing plants, and pharmaceutical pills are probably less sensitive to trade costs than most goods. But I now see a closer relationship between looking for home-market effects in the cross section and looking for market-size effects in the time series.

The primary bridge is a recent QJE article by Costinot, Donaldson, Kyle and Williams. They used variation in disease burdens across countries as a source of variation in demand for drugs to look for home-market effects in international pharmaceuticals production. I’ve blogged about that paper before.

The latest connection is a paper by Xavier Jaravel called “The Unequal Gains from Product Innovations: Evidence from the U.S. Retail Sector”. His article investigates the time-series analog of my cross-sectional results on quality specialization. In recent decades, income growth has been concentrated at the top of the income distribution. Did the increase in the relative size of the affluent market benefit the affluent beyond the straightforward income gains? With economies of scale, increases in demand could induce supply-side responses that favor affluent-demanded goods. That’s the home-market-effect story for why high-income cities are net exporters of high-quality products: due to increasing returns, greater demand elicits a more-than-proportionate production response. Jaravel documents the time-series equivalent for national outcomes: “(1) the relative demand for products consumed by high-income households increased because of growth and rising inequality; (2) in response, firms introduced more new products catering to such households; (3) as a result, the prices of continuing products in these market segments fell due to increased competitive pressure.”

As a result, a two-by-two matrix neatly summarizes these contributions to the empirical literature on market-size effects:

Pharmaceuticals Vertically differentiated consumer goods
Time series Acemoglu & Linn (2004) Jaravel (forthcoming)
Cross section Costinot, Donaldson, Kyle, Williams (2019) Dingel (2017)

There’s an obvious relationship between the AL and CDKW papers, as explained by CDKW:

In their original article, Acemoglu and Linn (2004) exploit such demographic variation over time within the United States to estimate the impact of market size on innovation. Here, we employ the spatial analog of this strategy, drawing on cross-sectional variation in the demographic composition of different countries in a given year, to explore how exogenous variation in demand may shape the pattern of trade.

With the benefit of hindsight, some more subtle connections between the four cells of this two-by-two matrix seem pretty clear. For example, Jaravel’s adoption of the Acemoglu (2007) terminology for “weak bias” and “strong bias” in his footnote 3 mirrors the distinction between the weak and strong versions of the home-market effect introduced by Costinot, Donaldson, Kyle, and Williams (2019).

In summary, market-size effects seem to be important for understanding both innovation outcomes and the geographic pattern of specialization. We’ve found market-size effects in the time series and in the cross section, for both the pharmaceutical sector and vertically differentiated manufactured goods.