“Innovation, Firm Dynamics, and International Trade” by Andrew Atkeson
We present a general equilibrium model of the decisions of firms to innovate and to engage in international trade. We use the model to study the changes in aggregate productivity and welfare that arise as firms' exit, export, process- and product innovation decisions respond to a change in the marginal cost of international trade. We first consider three important special cases of our model that we can solve analytically. In the first special case, all firms export. In the second special case, as in the model of Melitz (2003), only the most productive firms export but firms have no productivity dynamics after entry. In the third special case, firms have endogenous productivity dynamics but exit and export decisions are independent of size. We then extend our results to parameterized specifications of the model we must solve numerically. Our central finding is that, despite the fact that a change in trade costs can have a substantial impact on individual firms' exit, export, and process innovation decisions, the firms' free-entry condition places a constraint on the overall response of aggregate productivity to the change in trade costs. In particular, we show that the steady-state response of product innovation largely offsets the impact of changes in firms exit, export, and process innovation decisions on aggregate productivity. We also find that the dynamic welfare gains from a reduction in trade costs are very similar to the welfare gains that arise directly from the reduction in trade costs. Our results suggest that micro evidence on individual firms' responses to changes in international trade costs may not be informative about the macroeconomic implications of changes in these trade costs for aggregate productivity and welfare.