We survey the microfoundations, empirical evidence and estimation issues underlying the aggregate matching function. Several microeconomic matching mechanisms have been suggested in the literature with some successes but none is generally accepted as superior to all others. Instead, an aggregate matching function with hires as a function of vacancies and unemployment has been successfully estimated for several countries. The Cobb-Douglas restrictions with constant returns to scale perform well. Recent work has utilized disaggregated data to go beyond aggregate estimates, with many refinements and suggestions for future research.

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I model and simulate the effects of employment tax cuts on unemployment and wages in four equilibrium models: competitive, union bargaining, search and efficiency wages. I find that if the ratio of unemployment compensation to wages is fixed, the effect of the tax cut is mainly on wages. But if income out of work is fixed in real terms, there are substantial employment effects. When wages are determined by bargaining, revenue-neutral reforms that make the tax more progressive also reduce unemployment. Thus, policy towards unemployment compensation and tax structure are key influences on the effect of taxes on unemployment.

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