We study the welfare gains from trade in an economy with heterogeneous firms, variable markups and endogenous growth. Variable markups arise from oligopolistic competition, and cost-reducing innovation is the engine of long-run growth. Trade liberalisation stiffens competition by reducing markups, generating tougher firm selection and increasing the aggregate productivity level. Selection increases firms' incentives to innovate, thereby leading to a higher aggregate productivity growth rate. Endogenous productivity growth boosts the selection gains from trade, leading to substantial welfare improvements. A calibrated version of the model shows that growth doubles the welfare gains obtainable in models with static firm-level productivity.If the gains from trade are small, is it worth facing the potentially disruptive distributional consequences of globalisation?1 Assessing the size and identifying the sources of gains from trade is a long-standing challenge for economists. In recent decades, a new line of research introducing firm heterogeneity in trade models has uncovered a new source of welfare gains. Trade-induced reallocations of market shares from low to highly productive firms within the same industries increase sectorial efficiency, leading to improvements in aggregate productivity and to potentially large welfare gains. However, selection also carries welfare losses that can possibly outweigh the gains: firms' exit has a negative effect on welfare by reducing the variety of goods available in the economy.Theoretical and quantitative analyses assessing the contribution of the selection margin have mainly featured market structures with perfect or monopolistic competition, focused on static models or on dynamic economies without long-run productivity growth. The goal of this article is to fill these gaps by providing a theory of trade with heterogeneous firms under oligopolistic competition and innovationdriven productivity growth. On the one hand, because of 'cross-hauling' of identical goods, oligopoly trade is potentially wasteful, therefore representing a more difficult environment in which to obtain welfare gains. On the other hand, trade reduces markups thereby generating pro-competitive effects which are absent in environments where firms' market power is constant. Moreover, innovation-driven growth can potentially magnify the gains from selection, as market share reallocations can affect not only the productivity level but also its growth rate. We show that the new gains due

This paper introduces idiosyncratic …rm e¢ ciency shocks into a continuous-time general equilibrium model of trade with heterogeneous …rms. The presence of sunk export entry costs and e¢ ciency uncertainty gives rise to hysteresis in export market participation. A …rm will enter into the export market once it achieves a given size, re ‡ecting its e¢ ciency, but may keep exporting even after its e¢ ciency has fallen below its initial entry level. Some exporters will not be selling as much in the domestic market as other …rms that never entered the foreign market. The model captures the qualitative features of …rm birth, growth, export market entry and exit, and death found in the empirical literature. We calibrate the model to match relevant statistics of …rms'turnover and export dynamics in the United States, and show that the mode of globalization (a reduction in sunk costs as opposed to overhead costs), matters for a …rm's selection and persistence in export status. Trade liberalization via a reduction in sunk export entry costs reduces a …rm's export status persistence, while the opposite happens when liberalization takes place through a reduction in overhead export costs.JEL Codes: F10, L11

In the early 1970s U.S. firms were the uncontested world leaders in R&D investment in most manufacturing sectors. Later, led by Japan and Europe, foreign firms began to challenge American R&D leadership in many sectors of the economy. This period of increasing technological competition is contemporaneous with a substantial increase in U.S. R&D subsidies. What is the effect of the observed increase in international competition on U.S. welfare? How does foreign competition affect the optimal R&D subsidy in the United States, and, consequently, how far is this from the subsidy observed in the data? This article addresses these questions in a two-country quality ladder growth model.

How do import tariffs and R&D subsidies help domestic firms compete globally? How do these policies affect aggregate growth and economic welfare? To answer these questions, we build a dynamic general equilibrium growth model where firm innovation endogenously determines the dynamics of technology, and, therefore, market leadership and trade flows, in a world with two large open economies at different stages of development. Firms' R&D decisions are driven by (i) the defensive innovation motive, (ii) the expansionary innovation motive, and (iii) technology spillovers. The theoretical investigation illustrates that, statically, globalization (defined as reduced trade barriers) has ambiguous effects on welfare, while, dynamically, intensified globalization boosts domestic innovation through induced international competition. Accounting for transitional dynamics, we use our model for policy evaluation and compute optimal policies over different time horizons. The model suggests that the introduction of the Research and Experimentation Tax Credit in 1981 proves to be an effective policy response to foreign competition, generating substantial welfare gains in the long run. A counterfactual exercise shows that increasing tariffs as an alternative policy response improves domestic welfare only when the policymaker cares about the very short run, and only when introduced unilaterally. Tariffs generate large welfare losses in the medium and long run, or when there is retaliation by the foreign economy. Protectionist measures generate large dynamic losses by distorting the impact of openness on innovation incentives and productivity growth. Finally, our model predicts that a more globalized world entails less government intervention, thanks to innovation-stimulating effects of intensified international competition.