| This dissertation investigates identification and estimation of treatment effects with non-experimental data, using instrumental variable based Heckman-Vytlacil models. First, it reconsiders Vytlacil's (2002) result of equivalence between the Local Average Treatment Effect (LATE) framework of Imbens and Angrist (1994) and Heckman-Vytlacil latent variable selection model with a single valid instrument. Adopting a measure theoretical approach, it shows that the two may not be equivalent under a broader definition of the LATE framework, establishes equivalence conditions in this more general case, and extends the equivalence proof to models with a discrete polychotomous treatment. Second, it uses Manski's (1995) bounding argument and Imbens & Angrist's differencing argument to show that in the Heckman-Vytlacil framework a class of treatment effects represented as functionals of potential outcome distributions can be identified. These functionals include the mean, the effect on which is the average treatment effect (ATE), and the quantiles, where the correspondent effect is the quantile treatment effect (QTE). The potential outcome distributions may apply to the whole population, or be conditional on various "local" sub-populations, depending on the range of the probability of selection into treatment. However, in a model with a discrete polychotomous treatment, it shows that treatment effects cannot be point-identified. Bounds are provided for effects that are not point identified. Third, this dissertation develops a generic two-step estimation procedure, to obtain estimators for ATEs in the whole population as well as for "local" sub-populations. Then a matching estimator based on the two-step procedure is constructed to approximate the ATE, and its performance is assessed by a Monte Carlo simulation exercise. Finally, the new estimator is applied to an empirical evaluation of the college wage premium. Taking the number of siblings as an instrumental variable for college education, the two-step estimator is used to obtain point estimates of the college wage premium, which are compared with results from traditional control function methods that work in special cases of the Heckman-Vytlacil model. The results show treatment effect estimates to be sensitive to whether the instrument has a strong impact on the selection probability, and to the choice of specification. |
