A synthesis of the Lucas-Prescott island model and the Mortensen- Pissarides matching model of unemployment is studied. By assumption, all unmatched workers and jobs are randomly assigned to islands at the beginning of each period and the number of matches that form on a particular island is the minimum of the two realizations. When calibrated to the recently observed averages of U.S. unemployment and vacancy rates, the model fits the observed vacancy-unemployment Beveridge relationship very well and implies an implicit log linear relationship between the job finding rate and the vacancy-unemployment relationship with an elasticity near 0.5. The constrained efficient solution to the model is decentralized by a equilibrium outcome in which wages on each island are determined by a modified auction. Although the efficient solution explains only about 25% of the observed volatility in the U.S. vacancy-unemployment ratio, an equilibrium outcome in which wages are determined as the solution to a strategic bargaining game explains almost all of it.
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Mortensen, Dale T., 2009. "Island matching," Journal of Economic Theory, Elsevier, vol. 144(6), pages 2336-2353, November. citation courtesy of