Semiparametric Maximum Likelihood Sieve Estimator for Correction of Endogenous Truncation Bias

Abstract

Semiparametric correction for a sample selection bias in the presence of endogenous truncation is known to be much more difficult in the case of a binary selection variable than in the case of a continuous selection variable. This paper proposes a simple bandwidth-free semiparametric methodology to correct for a self-selection bias in a truncated sample, without any prior knowledge of the marginal density functions of the selection model’s random disturbances. Each of the unknown marginal density functions is estimated using Sieve estimator, utilizing Hermite polynomials as basis functions. The aforementioned procedure is appropriate for both binary and continuous selection variables cases under the covariate shift assumption. We consider a double hurdle model, which is a combination of two selection rules. The first is propagated by a truncation in the dependent variable of the substantive equation. The second is propagated by endogenous self-selection. The suggested correction procedure produces estimates that are of high accuracy and consistent based on Monte Carlo simulations. The random disturbances are not restricted to being symmetric and their marginal distribution functions are unknown. Thus, in the data generation process we verify the applicability of our procedure to cases in which the disturbances are neither jointly nor marginally normally distributed. These disturbances are constructed as realizations of non-symmetric distribution functions.