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

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James J. Heckman
Petra E. Todd

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Abstract

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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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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Handle: RePEc:nbr:nberwo:15179

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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  1. 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. [Downloadable!] (restricted)
  2. James J. Heckman & Sergio Urzua & Edward J. Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," NBER Working Papers 12574, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. 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, 08. [Downloadable!] (restricted)
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  4. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," Econometrica, Econometric Society, vol. 66(5), pages 1017-1098, September.
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  5. 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. [Downloadable!] (restricted)
  6. Rajeev H. Dehejia & Sadek Wahba, 2002. "Propensity Score-Matching Methods For Nonexperimental Causal Studies," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 151-161, February. [Downloadable!] (restricted)
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  7. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, 07. [Downloadable!] (restricted)
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  8. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Blackwell Publishing, vol. 65(2), pages 261-94, April. [Downloadable!] (restricted)
  9. James J. Heckman, 1989. "Choosing Among Alternative Nonexperimental Methods for Estimating the Impact of Social Programs: The Case of Manpower Training," NBER Working Papers 2861, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  10. 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. [Downloadable!] (restricted)
  11. 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.
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