When Outcome Heterogeneously matters for Selection: a Generalized Selection Correction Estimator

The classical Heckman (1976, 1979) selection correction estimator (heckit) is misspecified and inconsistent if an interaction of the outcome variable and an explanatory variable matters for selection. To address this specification problem, a full information maximum likelihood estimator and a simple two-step estimator are developed. Monte-Carlo simulations illustrate that the bias of the ordinary heckit estimator is removed by these generalized estimation procedures. Along with OLS and the ordinary heckit procedure, we apply these estimators to data from a randomized trial that evaluates the effectiveness of financial incentives for weight loss among the obese. Estimation results indicate that the choice of the estimation procedure clearly matters.