The intensive margin in trade

Is the variation in bilateral trade flows across countries primarily due to differences in the number of exporting firms (the extensive margin) or in the average size of an exporter (the intensive margin)? And how does this affect the estimation and quantitative implications of the Melitz (2003) trade model? The benchmark Melitz model with Pareto-distributed firm productivity and fixed costs of exporting, predicts that, conditional on the fixed costs of exporting, all variation in exports across trading partners should occur on the extensive margin. We subject this theoretical prediction to a reality check drawing upon the World Banks Exporter Dynamics Database (EDD) which has firm-level exports from 50 developing countries to all destinations. We find that around 50 percent of the variation in exports across trading partners is along the intensive margin, contradicting the benchmark Melitz-Pareto model. We find that moving from a Pareto to a lognormal distribution of firm productivity allows the Melitz model to successfully match the role of the intensive margin evident in the EDD. We then study the implications of our findings for quantitative trade theory. Using likelihood methods and the EDD, we estimate a generalized Melitz model with a joint lognormal distribution for firm productivity, fixed costs and demand shifters, and use exact hat algebra to quantify the counterfactual effects of a decline in trade costs on trade flows and welfare in the estimated model. Finally, we compare these effects to those that would be predicted by the Melitz-Pareto model, with the Pareto shape parameter chosen to match the average trade elasticity implied by our estimated Melitz-lognormal model. We find that the effects on welfare turn out to be quite close to those in the standard Melitz-Pareto model even though the effects on trade flows remain different.