Sales and Markup Dispersion: Theory and Empirics

Models of monopolistic competition with heterogeneous firms have provided a fertile laboratory for studying a range of problems relating to the process of globalization. Much of this work to date has assumed special forms for preferences and technology, usually CES preferences on the demand side, and a Pareto distribution of firm productivity on the supply side.

These assumptions have been justified on the grounds that they imply a Pareto distribution for firm sales. While the Pareto matches well the right-tail of the firm size distribution, recent empirical evidence points to the fact that the overall distribution is rather lognormal. Furthermore, the assumption of CES preferences in a monopolistically competitive market structure, can not explain the observed dispersion of markups across firms within the same industry.

In this paper, we provide a general characterization of the problem of explaining the distribution of firm size and firm markups, given particular assumptions about the structure of demand and the distribution of firm productivities. We present two different kinds of results. On the one hand, we present exact conditions under which specific assumptions about the distribution of firm productivity are consistent with a particular form of the distribution of sales revenue, output, or markups. On the other hand, we use the Kullback-Leibler divergence from information theory to quantify the information loss when a predicted distribution fails to match the actual one.

Among the theoretical results we derive is a characterization of the demand functions which are necessary and sufficient for productivity and sales to exhibit the same distribution from a wide family which includes Pareto, log-normal and Fréchet. We show that this property is implied by a new family of demands, a generalization of the CES, which we call “CREMR” for “Constant Revenue Elasticity of Marginal Revenue.” This new family generates variable markups across firms that differ in their productivity.

Using French and Indian firm-level data, we find that, to explain sales and markups, the choice between Pareto and log-normal productivity distributions matters less than the choice between CREMR and other demands.

Authors: joint with M. Mrazova and P. Neary.