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 with an explanatory variable matters for selection. To address this specification problem, a full information maximum likelihood (FIML) estimator and a simple two-step estimator are developed. Monte Carlo (MC) simulations illustrate that the bias of the ordinary heckit estimator is removed by these generalized estimation procedures. Along with OLS and ordinary heckit, we apply these estimators to data from a randomized trial that evaluates the effectiveness of financial incentives for reducing obesity. Estimation results indicate that the choice of the estimation procedure clearly matters.