  This paper introduces a maximum likelihood estimator of the value of job
amenities and labor productivity in a single matching market based on the
observation of equilibrium matches and wages. The estimation procedure
simultaneously fits both the matching patterns and the wage curve. While our
estimator is suited for a wide range of assignment problems, we provide an
application to the estimation of the Value of a Statistical Life using
compensating wage differentials for the risk of fatal injury on the job. Using
US data for 2017, we estimate the Value of Statistical Life at \$ 6.3 million
(\$2017).
