Indirect Inference with Importance Sampling: An Application to Women’s Wage Growth

This paper has two main parts. In the first, we describe a method that smooths the objective function in a general class of indirect inference models. Our smoothing procedure makes use of importance sampling weights in estimation of the auxiliary model on simulated data. The importance sampling weights are constructed from likelihood contributions implied by the structural model. Since this approach does not require transformations of endogenous variables in the structural model, we avoid the potential approximation errors that may arise in other smoothing approaches for indirect inference. We show that our alternative smoothing method yields consistent estimates. The second part of the paper applies the method to estimating the effect of women’s fertility on their human capital accumulation. We find that the curvature in the wage profile is determined primarily by curvature in the human capital accumulation function as a function of previous human capital, as opposed to being driven primarily by age. We also find a modest effect of fertility induced nonemployment spells on human capital accumulation. We estimate that the difference in wages among prime age women would be approximately 3% higher if the relationship between fertility and working were eliminated.