Nonlinear Search and Matching Explained

Competing explanations for the sources of nonlinearity in search and matching models indicate that they are not fully understood. This paper derives an analytical solution to a textbook model that highlights the mechanisms that generate nonlinearity and quantifies their contributions. Procyclical variation in the matching elasticity creates nonlinearity in the job finding rate, which interacts with the law of motion for unemployment. These results show the matching function choice is not innocuous. Quantitatively, the Den Haan et al. (2000) matching function more than doubles the skewness of unemployment and welfare cost of business cycles, compared to the Cobb-Douglas specification.