Likelihood-based Analysis of Causal Effectsvia Principal Stratification: New Approach to Evaluating Job-Training Programs

Government-sponsored job-training programs must be subject to evaluation to assess whether their effectiveness justifies their cost to the public. The evaluation usually focuses on employment and total earnings, although the effect on wages is also of interest, because this effect reflects the increase in human capital due to the training program, whereas the effect on total earnings 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’’ (or less accurately ‘‘censored’’) by nonemployment, that is, they are only observed and well-defined for individuals who are employed. In this article, we develop a likelihood-based approach to estimate the wage effect of the US federally-funded Job Corps training program using ‘‘Principal Stratification’’. Our estimands are formulated in terms of: (1) the effect of the training program on wages for those who would be employed whether they were trained or not, also called the survivor average causal effect (SACE), and the proportion of people in this category; (2) the wages when trained for those who would be employed only when trained, and the proportion of people in this category; (3) the wages when not trained for those who would be employed only when not trained, and the proportion of people in this category; (4) the proportion of people who would be not employed whether trained or not. We conduct likelihood-based analysis using the EM algorithm, and investigate the plausibility of important submodels with scaled loglikelihood ratio statistics.We also conduct a sensitivity analysis with respect to specific parametric assumptions. Our results suggest that all four types of people [(1)–(4) previously] exist, which is impossible under the usual monotonicity assumptions made in traditional econometric evaluation methods.