A structural analysis of the correlated random coefficient wage regression model with an application to the ols-iv puzzle

We estimate a finite mixture dynamic programming model of schooling decisions in which the log wage regression function is set within a correlated random coefficient model and we use the structural estimates to perform counterfactual experiments. We show that the estimates of the dynamic programming model with a rich heterogeneity specification, along with simulated schooling/wage histories, may be used to obtain estimates of the average treatment effects (ATE), the average treatment effects for the treated and the untreated (ATT/ATU), the marginal treatment effect (MTE) and, finally, the local average treatment effects (LATE). The model is implemented on a panel of white males taken from the National Longitudinal Survey of Youth (NLSY) from 1979 until 1994. We find that the average return to experience upon entering the labor market (0.059) exceeds the average return to schooling in the population (0.043). The importance of selectivity based on individual specific returns to schooling is illustrated by the difference between the average returns for those who have not attended college (0.0321) and those who attended college (0.0645). Our estimate of the MTE (0.0573) lies between the ATU and ATT and exceeds the average return in the population. Interestingly, the low average wage return is compatible with the occurrence of very high returns to schooling in some subpopulation (the highest type specific return is 0.13) and the simulated IV estimates (around 0.10) are comparable to those very high estimates often reported in the literature. The high estimates are explained by the positive correlation between the returns to schooling and the individual specific reactions. Moreover, they are not solely attributable to those individuals who are at the margin, but also to those individuals who would achieve a higher grade level no matter what. The structural dynamic programming model with multi-dimensional heterogeneity is therefore capable of explaining the well known OLS/IV puzzle.