Responses of Unemployment to Productivity Changes for a General Matching Technology

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.