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Treatment effects in sample selection models and their nonparametric estimation

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  • Lee, Myoung-jae

Abstract

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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Bibliographic Info

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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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Treatment effect; Sample selection; Matching; U-statistic; Sensitivity analysis;

References

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  1. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
  2. David Madden, 2006. "Sample Selection Versus Two-Part Models Revisited: the Case of Female Smoking and Drinking," Health, Econometrics and Data Group (HEDG) Working Papers 06/12, HEDG, c/o Department of Economics, University of York.
  3. Myoung-Jae Lee, 2004. "Selection correction and sensitivity analysis for ordered treatment effect on count response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(3), pages 323-337.
  4. 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.
  5. Alberto Abadie & Joshua Angrist & Guido Imbens, 1999. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Working papers 99-16, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Lee, Myoung-jae, 2005. "Micro-Econometrics for Policy, Program and Treatment Effects," OUP Catalogue, Oxford University Press, number 9780199267699.
  7. Leung, S.F. & Yu, S., 1992. "On the Choice Between Sample Selection and Two-Part Models," RCER Working Papers 337, University of Rochester - Center for Economic Research (RCER).
  8. Fair, Ray C, 1978. "A Theory of Extramarital Affairs," Journal of Political Economy, University of Chicago Press, vol. 86(1), pages 45-61, February.
  9. 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.
  10. Curt Wells, 2003. "Retesting Fair's (1978) model on infidelity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(2), pages 237-239.
  11. 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.
  12. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers 0118, National Bureau of Economic Research, Inc.
  13. 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.
  14. QI Li & Jeff Racine, 2004. "Predictor relevance and extramarital affairs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(4), pages 533-535.
  15. McDonald, John F & Moffitt, Robert A, 1980. "The Uses of Tobit Analysis," The Review of Economics and Statistics, MIT Press, vol. 62(2), pages 318-21, May.
  16. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  17. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053, April.
  18. repec:cup:cbooks:9780521496032 is not listed on IDEAS
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Cited by:
  1. Lee, M-J; & Kim, Y-S.;, 2011. "Effects of Informal Family Care on Formal Health Care: Zero-Inflated Endogenous Count for Censored Response," Health, Econometrics and Data Group (HEDG) Working Papers 11/10, HEDG, c/o Department of Economics, University of York.

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