Bayesian inference in a correlated random coefficients model: Modeling causal effect heterogeneity with an application to heterogeneous returns to schooling

Combining data sets from High School and Beyond (HSB) and the 1980 Census, we illustrate our methods in practice and investigate heterogeneity in returns to education. Our analysis decomposes the impact of key HSB covariates on log wages into three parts: a “direct” effect and two separate indirect effects through educational attainment and returns to education. Our results strongly suggest that the quantity of schooling attained is determined, at least in part, by the individual's own return to education. Specifically, a one percentage point increase in the return to schooling parameter is associated with the receipt of (approximately) 0.14 more years of schooling. Furthermore, when we control for variation in returns to education across individuals, we find no difference in predicted schooling levels for men and women. However, women are predicted to attain approximately 1/4 of a year more schooling than men on average as a result of higher rates of return to investments in education.