Semi-parametric estimation of the sample selection model

TLDR: In this article, the authors compare three types of nonparametric Maxfmum Zikelíhood estimators: Semt-nonparametrc MaxfmUM Zikellíhood, Semtnonparameter Zikeller estimators, and SingZe-equatton estimators.

Abstract: Esttmatfng a uxtge equatfon, account must be taken of the jact that ruages oj non-i,iorkers are not observed. For thts purpose, Heckman (1979) fntroduced the sample seLectfon modeL, consiating of troo equatíons: A(Línear) arage equatfon, explafning the potenttal Zog t,iage rate of every índívídual, incZudfng non-morkers, and a bfnary choice equatton, indícatíng ~uhether or not someone fs employed and the axige fa observed. TradíttonaL ML-eatfmatfon requfres a parametric specfftcatfon of the dtstributfon of the error terms, such as bivarfate normaZíty. Recently, a number of aemt-parametric estfmators have been developed mhích onZy requfre fndependence of the errors from the regressora ín both equations. We conatder three types o1 them: Semt-nonparametrtc Maxfmum Zikelíhood, ín mhich the parametera of interest and the densíty oJ the errors are eatimated afmuLtaneouaZy; 1}uo atage estfmators, generalizing the traditfonal Heckman ttoo step eatimator, míth semf-parametric estfmates o~ the bfnary chotce equatfon and a noriparametrfc correctton term added to the axige equatfon; and singZe-equatton estimators, neglecting irlJormation on non-raorkers. The estimators conaídered are asymptotícaZly normal, and aZZom Jor fnference. We preaent reaulta ,~or a sample of Dutch jemales and compare ~ith parametric !(L-estimatea. " We are grateful to the Netherlends Central Bureau of Statiatics (CBS) for providing the data. The views expressed i n this paper do not necessarily reflect the policies of the CBS. Financial support by the Netherlands Organisation of Scientific Research (NWO) and the Royal Netherlands Academy of Arts and Sciences (KNAW) is gratefully acknowledged by the first and second author, respectively. We are grateful for valuable commenta to Arie Kapteyn and seminar participants at CORE, (ironingen University, Tilburg University, and the Free University of Amsterdam.