Nonlinear Search and Matching Explained
AbstractPrevailing wisdom suggests the matching function choice is innocuous in search and matching models. We show this is not the case. Using a closed-form global solution, we derive conditions under which the matching function generates nonlinear dynamics. Gross complementarity between vacancies and unemployed workers generates procyclical variation in the matching elasticity and negatively skewed job finding rate dynamics.
Quantitatively, this implies that 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 matching function. However, the data supports the latter specification.