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Treatment effects in sample selection models and their nonparametric estimation

  • Lee, Myoung-jae

In a sample-selection model with the ‘selection’ variable Q and the ‘outcome’ variable Y∗, Y∗ is observed only when Q=1. For a treatment D affecting both Q and Y∗, three effects are of interest: ‘participation’ (i.e., the selection) effect of D on Q, ‘visible performance’ (i.e., the observed outcome) effect of D on Y≡QY∗, and ‘invisible performance’ (i.e., the latent outcome) effect of D on Y∗. This paper shows the conditions under which the three effects are identified, respectively, by the three corresponding mean differences of Q, Y, and Y|Q=1 (i.e., Y∗|Q=1) across the control (D=0) and treatment (D=1) groups. Our nonparametric estimators for those effects adopt a two-sample framework and have several advantages over the usual matching methods. First, there is no need to select the number of matched observations. Second, the asymptotic distribution is easily obtained. Third, over-sampling the control/treatment group is allowed. Fourth, there is a built-in mechanism that takes into account the ‘non-overlapping support problem’, which the usual matching deals with by choosing a ‘caliper’. Fifth, a sensitivity analysis to gauge the presence of unobserved confounders is available. A simulation study is conducted to compare the proposed methods with matching methods, and a real data illustration is provided.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 167 (2012)
Issue (Month): 2 ()
Pages: 317-329

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Handle: RePEc:eee:econom:v:167:y:2012:i:2:p:317-329
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  1. Myoung-jae Lee & Sang-jun Lee, 2007. "Sensitivity Analysis Of Job-Training Effects On Reemployment For Korean Women," Discussion Paper Series 0720, Institute of Economic Research, Korea University.
  2. Myoung-jae Lee, 2000. "Median treatment effect in randomized trials," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 595-604.
  3. Fair, Ray C, 1978. "A Theory of Extramarital Affairs," Journal of Political Economy, University of Chicago Press, vol. 86(1), pages 45-61, February.
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  8. David (David Patrick) Madden, 2006. "Sample selection versus two-part models revisited : the case of female smoking and drinking," Working Papers 200604, School of Economics, University College Dublin.
  9. Lee, Myoung-jae, 2005. "Micro-Econometrics for Policy, Program and Treatment Effects," OUP Catalogue, Oxford University Press, number 9780199267699, July.
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  13. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  14. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, 01.
  15. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
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