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I develop Bayesian estimation approaches to the simultaneous equation model with ordered probit and two\u2010limit censored regression and the bivariate duration model, accounting for the heterogeneity in returns to education and the nonlinearity in the effects of compulsory attendance. I find substantial variability in returns to education across schools and evidence of diminishing marginal effects of compulsory attendance on high school completion. The simulation results suggest that increasing the compulsory attendance age raises the probability of completing high school and reduces the proportion of time the individuals are unemployed. These effects are much more pronounced for disadvantaged students but less pronounced for advantaged students, suggesting the potential effects of compulsory attendance on reducing the inequality in education and employment. 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