Consistent estimation of panel data sample selection models

Zusammenfassung

We analyse the properties of classical (fixed e↵ect, first-di↵erences and random e↵ects) as well as generalised method of moments-instrumental variables estimators in either static or dynamic panel data sample selection models. We show that the correlation of the unobserved errors is not sufficient for non-consistency to arise, but the presence of common (and/or nonindependent) non-deterministic covariates in the selection and outcome equations is generally necessary. When both equations do not have covariates in common and independent of each other, we show the consistency of fixed e↵ects and random e↵ects estimators in static models with exogenous covariates. Furthermore, the first-di↵erenced generalised method of moments estimator uncorrected for sample selection of Arellano and Bond (1991) as well as the instrumental variables estimator of Anderson and Hsiao (1982) are consistent for autorregressive models even with endogenous covariates. The same results hold when theboth equations have no covariates in common but they are correlated, once we account for such correlation. Under the same circumstances, the system generalised method of moments estimator (Arellano and Bover, 1995, and Blundell and Bond, 1998) has a moderate bias. Alternatively, when both equations have covariates in common we suggest the appropriate correction method, being the serial correlation of the errors a key determinant of the choice. The finite sample properties of the proposed estimators and solutions are evaluated using a Monte Carlo study. We also do two di↵erent applications to log earning equations for females using the Panel Study of Income Dynamics and to tobacco consumption models using the Spanish Continuous Family Expenditure Survey.