I estimate a function that matches vacant jobs and unemployed workers to produce new hires. Israeli law requiring vacancy registration yields unique data quality. The literature underestimates matching function coefficients because of a simultaneity bias, as the outflow of hires depletes stocks of unemployed and vacancies. Instruments and a new simulation method address this bias. A new test reveals strong evidence of heterogeneity in unemployed and vacancies. Estimates imply labor market dynamics that absorb shocks completely within only 2 months. Reductions in the hire rate of referrals can explain a 2.1 percentage point increase in unemployment between 1978 and 1990.