Firm Entry and Exit with Unbounded Productivity Growth

TL;DR

This paper extends the firm entry-exit model by removing productivity bounds, demonstrating that under broad conditions, firm size distributions follow a power law tail, aligning better with empirical data.

Contribution

It introduces a generalized model allowing unbounded productivity growth, provides conditions for stationary equilibria, and characterizes the firm size distribution as a power law tail.

Findings

Firm size distribution exhibits a power law tail under broad productivity growth conditions.

New representations of entry rates and aggregate supply are derived.

A Lyapunov function approach is used to establish equilibrium existence.

Abstract

In Hopenhayn's (1992) entry-exit model productivity is bounded, implying that the predicted firm size distribution cannot match the power law tail observable in the data. In this paper we remove the boundedness assumption and, in this more general setting, provide an exact characterization of existence of stationary equilibria, as well as a novel sufficient condition for existence based on treating production as a Lyapunov function. We also provide new representations of the rate of entry and aggregate supply. Finally, we prove that the firm size distribution has a power law tail under a very broad set of productivity growth specifications.