Evaluating the effects of job training programs on wages through principal stratification

In an evaluation of a job training program, the causal effects of the program on wages are often of more interest to economists than the program's effects on employment or on income. The reason is that the effects on wages reflect the increase in human capital due to the training program, whereas the effects on total earnings or income may be simply reflecting the increased likelihood of employment without any effect on wage rates. Estimating the effects of training programs on wages is complicated by the fact that, even in a randomized experiment, wages are truncated by nonemployment, i.e., are only observed and well-defined for individuals who are employed. We present a principal stratification approach applied to a randomized social experiment that classifies participants into four latent groups according to whether they would be employed or not under treatment and control, and argue that the average treatment effect on wages is only clearly defined for those who would be employed whether they were trained or not. We summarize large sample bounds for this average treatment effect, and propose and derive a Bayesian analysis and the associated Bayesian Markov Chain Monte Carlo computational algorithm. Moreover, we illustrate the application of new code checking tools to our Bayesian analysis to detect possible coding errors. Finally, we demonstrate our Bayesian analysis using simulated data.