You have likley already seen “Comparative Advantage and Heterogeneous Firms,” as Andrew Bernard, Stephen Redding, and Peter Schott worked on it for more than four years. If you haven’t, now is the time. The paper was finally published early this year in the Review of Economic Studies (journal pdf; older ungated pdf). It’s a fabulous piece of theory that introduces heterogeneous firms (via a Pareto distributed productivity term) and fixed trade costs to the classic 2x2x2 monopolistic competition model of trade.
Here’s the abstract:
This paper examines how country, industry, and firm characteristics interact in general equilibrium to determine nations’ responses to trade liberalization. When firms possess heterogeneous productivity, countries differ in relative factor abundance, and industries vary in factor intensity, falling trade costs induce reallocations of resources both within and across industries and countries. These reallocations generate substantial job turnover in all sectors, spur relatively more creative destruction in comparative advantage industries than in comparative disadvantage industries, and magnify ex ante comparative advantage to create additional welfare gains from trade. The improvements in aggregate productivity as countries liberalize dampen and can even reverse the real-wage losses of scarce factors.
This is clearly an improvement over existing models of trade with hetereogeneous firms, which often feature a numeraire that pins down the wage and labor as the only input. Now we get to talk about wage effects and comparative advantage! Unfortunately, the resulting mathematical complexity is such that closed-form solutions don’t exist for some of the endogeneous variables. The authors have to resort to numerical simulations to describe some areas of interest. Nonetheless, I really like this paper.