We characterize the relationship between the distributions of two variables linked by a structural model. We then show that, in models of heterogeneous firms in monopolistic competition, this relationship implies a new demand function that we call “CREMR” (Constant Revenue Elasticity of Marginal Revenue). This demand function is the only one that is consistent with productivity and sales distributions having the same form (whether Pareto, lognormal, or Fréchet) in the cross section, and it is necessary and sufficient for Gibrat's Law to hold over time. Among the applications we consider, we use our methodology to characterize misallocation across firms; we derive the distribution of markups implied by any assumptions on demand and productivity; and we show empirically that CREMR‐based markup distributions provide an excellent parsimonious fit to Indian firm‐level data, which in turn allows us to calculate the proportion of firms that are of suboptimal size in the market equilibrium.

Abstract We study how stickiness in business relationships influences the trade impact of aggregate uncertainty. To begin, we construct a product-level index of relationship stickiness using firm-to-firm relationship duration data. We then demonstrate how relationship stickiness shapes trade dynamics in response to uncertainty shocks. We find that episodes of uncertainty lead to a decline in the overall establishment of new business relationships, with the impact varying depending on the level of stickiness. In markets characterized by high stickiness, uncertainty shocks primarily impede investments in new firm-to-firm relationships. In contrast, for nonsticky products, the adjustment to uncertainty shocks mainly manifests as the disruption of existing relationships.

In this appendix, we prove the various statements made in our paper. In Appendix A, we study the impact of market size on the FEE. Appendix B is devoted to the multisector economy, while Appendix C shows that equilibrium under the translog behaves like equilibrium under the CARA.

This paper analyzes the transfer pricing of multinational firms. Intrafirm prices may systematically deviate from arm’s-length prices for two motives: pricing to market and tax avoidance. Using French firm-level data on arm’s-length and intrafirm export prices, we find that the sensitivity of intrafirm prices to foreign taxes is reinforced once we control for pricing-to-market determinants. Most important, we find no evidence of tax avoidance if we disregard tax haven destinations. Tax avoidance through transfer pricing is economically sizable. The bulk of this loss is driven by the exports of 450 firms to ten tax havens.