We present a general equilibrium model of the decisions of firms to innovate and to engage in international trade. We use the model to analyze the impact of a reduction in international trade costs on firms ’ process and product innovative activity. We first show analytically that if all firms export with equal intensity, then a reduction in international trade costs has no impact at all, in steady-state, on firms ’ investments in process innovation. We then show that if only a subset of firms export, a decline in marginal trade costs raises process innovation in exporting firms relative to that of non-exporting firms. This reallocation of process innovation reinforces existing patterns of comparative advantage, and leads to an amplified response of trade volumes and output over time. In a quantitative version of the model, we show that the increase in process innovation is largely offset by a decline in product innovation. We find that, even if process innovation is very elastic and leads to a large dynamic response of trade, output, consumption, and the firm size distribution, the dynamic welfare gains are very similar to those in a model with inelastic process innovation.

In standard monetary policy approaches, interest-rate rules often produce indeterminacy. A sophisticated policy approach does not. Sophisticated policies depend on the history of private actions, government policies, and exogenous events and can differ on and off the equilibrium path. They can uniquely implement any desired competitive equilibrium. When interest rates are used along the equilibrium path, implementation requires regime-switching. These results are robust to imperfect information. Our results imply that the Taylor principle is neither necessary nor sufficient for unique implementation. They also provide a direction for empirical work on monetary policy rules and determinacy.