There is a large and rapidly growing empirical literature that has documented that a reduction in international trade costs can have a substantial impact on individual firms decisions to produce, export, and engage in research and development to improve the cost or quality of existing products. Motivated by these observations, we build a simple general equilibrium model of these decisions, and we use this model to examine the question: do considerations of the impact of a reduction in trade costs on heterogeneous firms decisions to produce, export, and innovate, lead to new answers to the macroeconomic question of the impact of a reduction in trade costs on aggregate productivity and welfare? Our answer is largely, no.
For the last several decades, research in international trade has modeled comparative advantage as an attribute of the firm. We follow this approach, and model firms as producing differentiated products that are traded subject to both a fixed and a marginal cost of exporting. Our model of innovation builds on Grilichesm(1979) knowledge capital model of firm productivity. Each firm has a stock of a firm specific factor that determines its current profit opportunities. Our model includes two forms of innovation: innovation to increase the stock of this firm specific factor in an existing firm q process innovation, and innovation to create new firms with a new initial stock of the firm specific factor q product innovation.
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. In our analysis, we find it useful to decompose the change in aggregate productivity that arises from a change in the marginal costs of trade into two components. The first component is the direct effect of a change of trade costs on productivity, holding fixed firms exit, export, process, and product innovation decisions. The magnitude of this effect is simply determined by the share of exports in production, and hence is independent of the details of our model of heterogeneous firms decisions. The second effect is the indirect effect that arises from changes in firms exit, export, process, and product innovation decisions.
What determines the magnitude of the indirect effect? An earlier theoretical literature stemming from the work of Krugman (1979), Grossman and Helpman (1991), and Rivera' Batiz and Romer (1991) looked at this question focusing only on the impact of a reduction in international trade costs on firms decisions to create new product varieties q that is to engage in product innovation. Our main finding is that the more complex models of the heterogeneous responses of firms exit, export, process and product innovation decisions that have followed this earlier work, lead to largely similar implications for the magnitude of the indirect effect of a reduction in trade costs on aggregate productivity.
To establish this finding, we first present analytical results regarding the steady state impact of a change in marginal trade costs on aggregate productivity for three important special cases of our model. In the first special case, we assume that all firms export. This specification of our model extends the work of Krugman (1979) in considering firms exit and process innovation decisions. In the second special case, only the most productive firms export, but firms have no productivity dynamics after entry, and hence this special case of our model corresponds to the model in Melitz (2003). In the third special case, which we refer to as the exogenous selection version of our model, firms have productivity dynamics due to endogenous process innovation, but exit and export decisions are independent of size. In the second and third special cases, we also assume that the real interest rate is zero. We find analytically that the indirect effect on aggregate productivity of a change in the marginal costs of trade is, to a first order approximation, the same in all three of these special cases of our model, and equal to the indirect effect found in the earlier models with only product innovation. Hence, for these special cases, the details of how a change in trade costs affects firms exit, export, and process innovation decisions do not affect at all our models implications for aggregate productivity in the steady state.
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