Is the matching function Cobb-Douglas?

We study the theoretical properties that particular matching functions must satisfy to represent a frictional labor market within a general equilibrium random matching model. We analyze Cobb-Douglas, CES and other functional forms of the matching function. Our findings establish restrictions on the parameters of these matching functions to ensure that the equilibrium is interior. These restrictions provide both theoretical reasons to choose among several functional forms and model misspecification tests for empirical work.