| A general device for adjusting specification test statistics under local misspecification of unconsidered parameters is constructed. This device can be applied to any method of moments estimation procedure, including maximum likelihood and general method of moments. Size and power properties of the adjusted statistics are analyzed, and optimal size-robust test under local misspecification are constructed. In particular, it is shown that by replacing the score functions by the effective score functions (as in the Neyman's C(a) test) the power of the tests is maximized.;This methodology is used for constructing and evaluating tests for bivariate normality and for marginal normality and conditional linearity of the error terms in selection models which are robust to local distributional misspecification. This procedure is based on Lee's (Econometrica, 52, 1994, p. 843-863) test which considers bivariate Edgeworth expansions using Hermite polynomials of order 3 and 4. LM-type tests for both maximum likelihood and two-step estimation procedures are considered. Monte Carlo results show that instead of testing bivariate normality, testing marginal normality and conditional linearity separately have a better size performance. Finally, the tests procedures are applied to women's labor supply data.;Nonparametric estimators for average and quantile treatment effects are constructed using fractile graphical analysis under the identifying assumption that selection to treatment is based on observable characteristics. The proposed method has two-steps: first, the propensity score is estimated, and second, a blocking estimation procedure using this estimate is used to compute the treatment effects. In both cases, the estimators are proved to be consistent. Monte Carlo results show a better performance than other procedures based on the propensity score. Finally, these estimators are applied to a job training dataset. |
