We develop a monopolistically competitive model of trade with firm heterogeneity -in terms of productivity differences -and endogenous differences in the 'toughness' of competition across markets -in terms of the number and average productivity of competing firms. We analyze how these features vary across markets of different size that are not perfectly integrated through trade; we then study the effects of different trade liberalization policies. In our model, market size and trade affect the toughness of competition, which then feeds back into the selection of heterogeneous producers and exporters in that market. Aggregate productivity and average markups thus respond to both the size of a market and the extent of its integration through trade (larger, more integrated markets exhibit higher productivity and lower markups). Our model remains highly tractable, even when extended to a general framework with multiple asymmetric countries integrated to different extents through asymmetric trade costs. We believe this provides a useful modeling framework that is particularly well suited to the analysis of trade and regional integration policy scenarios in an environment with heterogeneous firms and endogenous markups.

We develop a stochastic, general equilibrium, two-country model of trade and macroeconomic dynamics. Productivity differs across individual, monopolistically competitive firms in each country. Firms face a sunk entry cost in the domestic market and both fixed and per-unit export costs. Only relatively more productive firms export. Exogenous shocks to aggregate productivity and entry or trade costs induce firms to enter and exit both their domestic and export markets, thus altering the composition of consumption baskets across countries over time. In a world of flexible prices, our model generates endogenously persistent deviations from PPP that would not exist absent our microeconomic structure with heterogeneous firms. It provides an endogenous, microfounded explanation for a Harrod-Balassa-Samuelson effect in response to aggregate productivity differentials and deregulation. Finally, the model successfully matches several moments of U. S. and international business cycles.

We show that endogenous firm selection provides a new welfare margin for heterogeneous firm models of trade (relative to homo geneous firm models). Under some parameter restrictions, the trade elasticity is constant and is a sufficient statistic for welfare, along with the domestic trade share. However, even small deviations from these restrictions imply that trade elasticities are variable and differ across markets and levels of trade costs. In this more general setting, the domestic trade share and endogenous trade elasticity are no longer sufficient statistics for welfare. Additional empirically observable moments of the micro structure also matter for welfare.

In a class of trade models which satisfy a constant elasticity gravity equation, the welfare gains from trade can be computed using the open economy domestic trade share and a constant trade elasticity. The measured welfare gains from trade from this quantitative approach are typically relatively modest. In this paper, we suggest a channel for welfare gains that this quantitative approach typically abstracts from: trade-induced changes in domestic productivity. Using a model of sequential production, in which trade induces a reorganization of production that raises domestic productivity, we show that the welfare gains from trade can become arbitrarily large.

We document how demand shocks in export markets lead French multiproduct exporters to reallocate the mix of products sold in those destinations. In response to positive demand shocks, French firms skew their export sales toward their best-performing products. We develop a theoretical model of multiproduct firms and derive the specific demand conditions (with endogenous price elasticities) needed to generate these product-mix reallocations. Under those demand conditions, the increased competition from demand shocks in export markets also induces productivity changes within the firm. We empirically test for this connection between demand shocks and the productivity of multiproduct firms. We find that this connection is economically substantial.

This paper builds a framework for the analysis of macroeconomic fluctuations that incorporates the endogenous determination of the number of producers and products over the business cycle. Economic expansions induce higher entry rates by prospective entrants subject to sunk investment costs. The sluggish response of the number of producers generates a new and potentially important endogenous propagation mechanism for business cycle models. The return to investment determines household saving decisions, producer entry, and the allocation of labor across sectors. Our framework replicates several features of business cycles and predicts procyclical profits even for preference specifications that imply countercyclical markups.

We analyze how demand conditions faced by a firm in its export markets affect its innovation decisions. We exploit exogenous firm-level export demand shocks and find that firms respond by patenting more; furthermore, this response is driven by the subset of initially more productive firms. The patent response arises two to five years after the shock, highlighting the time required to innovate. In contrast, the demand shock raises contemporaneous sales and employment for all firms regardless of their productivity. This skewed innovation response to common demand shocks arises naturally from a model of endogenous innovation and competition with firm heterogeneity.