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This article considers the evaluation of discretely distributed treatments when outcomes are only observed for a subpopulation due to sample selection or outcome attrition. For identification, we combine a selection-on-observables assumption for treatment assignment with either selection-on-observables or instrumental variable assumptions concerning the outcome attrition/sample selection process. We also consider dynamic confounding, meaning that covariates that jointly affect sample selection and the outcome may (at least partly) be influenced by the treatment. To control in a data-driven way for a potentially high dimensional set of pre- and/or post-treatment covariates, we adapt the double machine learning framework for treatment evaluation to sample selection problems. We make use of (a) Neyman-orthogonal, doubly robust, and efficient score functions, which imply the robustness of treatment effect estimation to moderate regularization biases in the machine learning-based estimation of the outcome, treatment, or sample selection models and (b) sample splitting (or cross-fitting) to prevent overfitting bias. We demonstrate that the proposed estimators are asymptotically normal and root-n consistent and investigate their finite sample properties in a simulation study. We also apply our proposed methodology to the Job Corps data. The estimator is available in the causalweight package for the statistical software R. [ABSTRACT FROM AUTHOR]

Researchers routinely use datasets where outcomes of interest are unobserved for some cases, potentially creating a sample selection problem. Statisticians and econometricians have proposed many selection correction methods to address this challenge. We use a natural experiment to evaluate different sample selection correction methods' performance. From 2007, the state of Michigan required that all students take a college entrance exam, increasing the exam-taking rate from 64% to 99% and largely eliminating selection into exam-taking. We apply different selection correction methods, using different sets of covariates, to the selected exam score data from before 2007. We compare the estimated coefficients from the selection-corrected models to those from OLS regressions using the complete exam score data from after 2007 as a benchmark. We find that less restrictive semiparametric correction methods typically perform better than parametric correction methods but not better than simple OLS regressions that do not correct for selection. Performance is generally worse for models that use only a few discrete covariates than for models that use more covariates with less coarse distributions. [ABSTRACT FROM AUTHOR]

This article considers linear social interaction models under incomplete information that allow for missing outcome data due to sample selection. For model estimation, assuming that each individual forms his/her belief about the other members' outcomes based on rational expectations, we propose a two-step series nonlinear least squares estimator. Both the consistency and asymptotic normality of the estimator are established. As an empirical illustration, we apply the proposed model and method to National Longitudinal Study of Adolescent Health (Add Health) data to examine the impacts of friendship interactions on adolescents' academic achievements. We provide empirical evidence that the interaction effects are important determinants of grade point average and that controlling for sample selection bias has certain impacts on the estimation results. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

This article extends the standard regression discontinuity (RD) design to allow for sample selection or missing outcomes. We deal with both treatment endogeneity and sample selection. Identification in this article does not require any exclusion restrictions in the selection equation, nor does it require specifying any selection mechanism. The results can therefore be applied broadly, regardless of how sample selection is incurred. Identification instead relies on smoothness conditions. Smoothness conditions are empirically plausible, have readily testable implications, and are typically assumed even in the standard RD design. We first provide identification of the "extensive margin" and "intensive margin" effects. Then based on these identification results and principle stratification, sharp bounds are constructed for the treatment effects among the group of individuals that may be of particular policy interest, that is, those always participating compliers. These results are applied to evaluate the impacts of academic probation on college completion and final GPAs. Our analysis reveals striking gender differences at the extensive versus the intensive margin in response to this negative signal on performance. [ABSTRACT FROM AUTHOR]

In this article we introduce a test for the normality assumption in the sample selection model. The test is based on a flexible parametric specification of the density function of the error terms in the model. This specification follows a Hermite series with bivariate normality as a special case. All parameters of the model are estimated both under normality and under the more general flexible parametric specification, which enables testing for normality using a standard likelihood ratio test. If normality is rejected, then the flexible parametric specification provides consistent parameter estimates. The test has reasonable power, as is shown by a simulation study. The test also detects some types of ignored heteroscedasticity. Finally, we apply the flexible specification of the density to a travel demand model and test for normality in this model. [ABSTRACT FROM AUTHOR]

Applied economists have long struggled with the question of how to accommodate binary endogenous regressors in models with binary and nonnegative outcomes. I argue here that much of the difficulty with limited dependent variables comes from a focus on structural parameters, such as index coefficients, instead of causal effects. Once the object of estimation is taken to be the causal effect of treatment, several simple strategies are available. These include conventional two-stage least squares, multiplicative models for conditional means, linear approximation of nonlinear causal models, models for distribution effects, and quantile regression with an endogenous binary regressor. The estimation strategies discussed in the article are illustrated by using multiple births to estimate the effect of childbearing on employment status and hours of work. [ABSTRACT FROM AUTHOR]