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In structural empirical models of labor market search, the distribution of wage offers is usually assumed to be exogenous. However, because in setting their wages profit-maximizing firms should consider the reservation wages of job seekers, the wage offer distribution is essentially endogenous. We investigate whether a proposed equilibrium search model, in which the wage offer distribution is endogenous, is able to describe observed labor market histories. We find that the distributions of job and unemployment spells are consistent with the data, and that the qualitative predictions of the model for the wages set by employers are confirmed by wage regressions. The model is estimated using panel data on unemployed and employed individuals. We distinguish between separate segments of the labor market, and we show that productivity heterogeneity is important to obtain an acceptable fit to the data. The results are used to estimate the degree of monopsony power of firms. Further, the effects of changes in the mandatory minimum wage are examined.

We study the asymptotic distribution of three-step estimators of a finite-dimensional parameter vector where the second step consists of one or more nonparametric regressions on a regressor that is estimated in the first step. The first-step estimator is either parametric or nonparametric. Using Newey's (1994) path-derivative method, we derive the contribution of the first-step estimator to the influence function. In this derivation, it is important to account for the dual role that the first-step estimator plays in the second-step nonparametric regression, that is, that of conditioning variable and that of argument.

We are interested in estimating the average effect of a binary treatment on a scalar outcome. If assignment to the treatment is exogenous or unconfounded, that is, independent of the potential outcomes given covariates, biases associated with simple treatment-control average comparisons can be removed by adjusting for differences in the covariates. Rosenbaum and Rubin (1983) show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates. Although adjusting for differences in the propensity score removes all the bias, this can come at the expense of efficiency, as shown by Hahn (1998), Heckman, Ichimura, and Todd (1998), and Robins, Mark, and Newey (1992). We show that weighting by the inverse of a nonparametric estimate of the propensity score, rather than the true propensity score, leads to an efficient estimate of the average treatment effect. We provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score.