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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