Sciences Po Economics Discussion Papers Welfare and Trade Without Pareto∗

Heterogeneous firm papers that need parametric distributions—most of the liter-ature following Melitz (2003)—use the Pareto distribution. The use of this distribu-tion allows a large set of heterogeneous firms models to deliver the simple gains from trade (GFT) formula developed by Arkolakis et al. (2012) (hereafter, ACR). This implication is closely tied to the fact that Pareto allows for a constant elasticity of substitution import system.1 Three important criteria have motivated researchers to select the Pareto distribu-tion for heterogeneity. The first is tractability. Assuming Pareto makes it relatively easy to derive aggregate properties in an analytical model. Users of the Pareto distri-bution also justify it on empirical and theoretical grounds. For example, ACR argue that the Pareto provides “a reasonable approximation for the right tail of the ob-served distribution of firm sizes ” and is “consistent with simple stochastic processes for firm-level growth, entry, and exit...” This paper investigates the consequences of replacing the assumption of Pareto heterogeneity with log-normal heterogeneity. This case is interesting because it (a) maintains some desirable analytic features of Pareto, (b) fits the complete distribution of firm sales rather than just approximating the right tail, and (c) can be generated under equally plausible processes (see online appendix). The log-normal is reasonably tractable but its use sacrifices some “scale-free ” properties conveyed by the Pareto distribution. Aspects of the the calibration that do not matter under Pareto lead to important differences in the gains from trade under log-normal