A Structural Analysis of the Correlated Random Coefficient Wage Regression Model

We estimate a …nite mixture dynamic programming model of schooling decisions in which the log wage regression function is set in a random coe¢ cient framework. We also analyze the determinants of 3 counterfactual experiments (a college attendance subsidy, a high school graduation subsidy and an overall decrease in the rate of time preference) and examine a proposition often claimed in the “Average Treatment E¤ects” literature; that the discrepancy between OLS and IV estimates of the returns to schooling may be explained by the relatively higher returns experienced by those a¤ected by exogenous policy changes. We …nd that the average return to experience upon entering the labor market (0.0863) exceeds the average return to schooling (0.0576) and we …nd more cross-sectional variability in the returns to experience than in the returns to schooling. Labor market skills (as opposed to taste for schooling) appear to be the prime factor explaining schooling attainments. We …nd little evidence in favor of a positive correlation between reactions induced by an exogenous experiment and the individual speci…c returns to schooling. Key Words: Random Coe¢ cient, Returns to Schooling, Comparative Advantages, Dynamic Programming, Dynamic Self-Selection. JEL Classi…cation: J2-J3. 1 Introduction and Objectives In this paper, we investigate the empirical properties of the correlated random coe¢ cient wage regression model (CRCWRM) using a structural dynamic programming model.1 The term “correlated random coe¢ cient wage regression model”refers to the standard Mincerian log wage regression function in which the coe¢ cients may be arbitrarily correlated with the regressors (education and experience). While the comparative advantages representation of the labor market is far from being new (Roy, 1951, Becker and Chiswick, 1966 and Willis and Rosen, 1979), economists have only recently paid particular attention to the speci…cation and the estimation of linear wage regression models set in a random coe¢ cient framework (Heckman and Vitlacyl (1998, 2000), Wooldridge (1997, 2000), Angrist and Imbens (1994), Card (2000) and Meghir and Palme (2001)). In this recent branch of the literature, it is customary to estimate the log wage regression function using Instrumental Variable (IV) techniques and interpret the estimates in a framework where the returns to schooling are individual speci…c. This surge of new research is understandable. In a context where schooling is understood as the outcome of individual decision making within a dynamic framework, rational individuals base their schooling decisions partly on absolute and comparative advantages in the labor market and partly on their taste for schooling. As a consequence, the random coe¢ cients (the returns to schooling and experience), as opposed to only the individual speci…c intercept terms, will normally be correlated with individual schooling attainments. In a linear wage regression, individual di¤erences in the intercept term represent a measure of absolute advantage in the labor market while di¤erences in slopes re‡ect individual comparative advantages in human capital acquisition via schooling and experience. While it might be tempting to focus solely on heterogeneity in the returns to schooling (and assume homogeneous returns to experience), this approach is likely to be unsatisfactory. If the returns to schooling and experience are truly correlated, ignoring individual di¤erences in the return to labor market experience is likely to a¤ect the estimates of the returns to schooling as well as the causal link between labor market ability and schooling (dynamic self-selection). Modeling wage regressions in a random coe¢ cient framework therefore requires the allowance for 1The term “correlated random coe¢ cient wage regression model”is also used in Heckman and Vitlacyl (1998).