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A Note on Adapting Propensity Score Matching and Selection Models to Choice Based Samples

  • James J. Heckman
  • Petra E. Todd

The probability of selection into treatment plays an important role in matching and selection models. However, this probability can often not be consistently estimated, because of choice-based sampling designs with unknown sampling weights. This note establishes that the selection and matching procedures can be implemented using propensity scores fit on choice-based samples with misspecified weights, because the odds ratio of the propensity score fit on the choice-based sample is monotonically related to the odds ratio of the true propensity scores.

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File URL: http://www.nber.org/papers/w15179.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15179.

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Date of creation: Jul 2009
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Publication status: published as James J. Heckman & Petra E. Todd, 2009. "A note on adapting propensity score matching and selection models to choice based samples," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages S230-S234, 01.
Handle: RePEc:nbr:nberwo:15179
Note: TWP
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  1. James Heckman & Salvador Navarro-Lozano, 2004. "Using Matching, Instrumental Variables, and Control Functions to Estimate Economic Choice Models," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 30-57, February.
  2. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2009. "Understanding Instrumental Variables in Models with Essential Heterogeneity," Working Papers 200941, Geary Institute, University College Dublin.
  3. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
  4. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 261-94, April.
  5. Heckman, J.J. & Hotz, V.J., 1988. "Choosing Among Alternative Nonexperimental Methods For Estimating The Impact Of Social Programs: The Case Of Manpower Training," University of Chicago - Economics Research Center 88-12, Chicago - Economics Research Center.
  6. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc.
  7. A. Smith, Jeffrey & E. Todd, Petra, 2005. "Does matching overcome LaLonde's critique of nonexperimental estimators?," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 305-353.
  8. 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.
  9. Rajeev H. Dehejia & Sadek Wahba, 1998. "Propensity Score Matching Methods for Non-experimental Causal Studies," NBER Working Papers 6829, National Bureau of Economic Research, Inc.
  10. Manski, Charles F., 1986. "Semiparametric analysis of binary response from response-based samples," Journal of Econometrics, Elsevier, vol. 31(1), pages 31-40, February.
  11. Rajeev H. Dehejia & Sadek Wahba, 1998. "Causal Effects in Non-Experimental Studies: Re-Evaluating the Evaluation of Training Programs," NBER Working Papers 6586, National Bureau of Economic Research, Inc.
  12. Manski, Charles F & Lerman, Steven R, 1977. "The Estimation of Choice Probabilities from Choice Based Samples," Econometrica, Econometric Society, vol. 45(8), pages 1977-88, November.
  13. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," NBER Working Papers 6699, National Bureau of Economic Research, Inc.
  14. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-20, September.
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