Responses of Unemployment to Productivity Changes for a General Matching Technology

TL;DR

This paper extends the Diamond-Mortensen-Pissarides model to general matching technologies, showing how unemployment responds to productivity changes and highlighting differences from the Cobb-Douglas case, with implications for business-cycle analysis.

Contribution

It generalizes the response of unemployment to productivity in DMP models beyond Cobb-Douglas matching technologies, providing new insights into unemployment dynamics.

Findings

Unique steady-state exists with positive surplus from initial vacancies.

Unemployment response to productivity varies with matching technology.

Non-Cobb-Douglas matching technology increases unemployment sensitivity to productivity.

Abstract

Workers separate from jobs, search for jobs, accept jobs, and fund consumption with their wages. Firms recruit workers to fill vacancies. Search frictions prevent firms from instantly hiring available workers. Unemployment persists. These features are described by the Diamond-Mortensen-Pissarides modeling framework. In this class of models, how unemployment responds to productivity changes depends on resources that can be allocated to job creation. Yet, this characterization has been made when matching is parameterized by a Cobb-Douglas technology. For a canonical DMP model, I (1) demonstrate that a unique steady-state equilibrium will exist as long as the initial vacancy yields a positive surplus; (2) characterize responses of unemployment to productivity changes for a general matching technology; and (3) show how a matching technology that is not Cobb-Douglas implies unemployment responds more to productivity changes, which is independent of resources available for job creation, a feature that will be of interest to business-cycle researchers.