Equilibrium search models are useful tools for the evaluation oflabor market policies. Recently developed equilibrium search models of thelabor market are able to fit the wage distribution perfectly with longitudinallabor supply data, by estimating an appropriate distribution of laborproductivity across firms. This paper formally compares such structuralestimates to their directly observed counterparts in firm data. More generally,we investigate the extent to which these models are able to explain theobserved distributions of wages, productivities and firm sizes across firms, aswell as the extent to which they are able to explain the observed relationshipsbetween these variables across firms. The parameters that capture searchfrictions are estimated with worker data that are matched to the firm data.