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Moving the Goalposts: Addressing Limited Overlap in the Estimation of Average Treatment Effects by Changing the Estimand

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Author Info
Richard K. Crump
V. Joseph Hotz
Guido W. Imbens
Oscar A. Mitnik

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Abstract

Estimation of average treatment effects under unconfoundedness or exogenous treatment assignment is often hampered by lack of overlap in the covariate distributions. This lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification. In such cases researchers have often used informal methods for trimming the sample. In this paper we develop a systematic approach to addressing such lack of overlap. We characterize optimal subsamples for which the average treatment effect can be estimated most precisely, as well as optimally weighted average treatment effects. Under some conditions the optimal selection rules depend solely on the propensity score. For a wide range of distributions a good approximation to the optimal rule is provided by the simple selection rule to drop all units with estimated propensity scores outside the range [0.1,0.9].

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0330.

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Date of creation: Oct 2006
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Handle: RePEc:nbr:nberte:0330

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Find related papers by JEL classification:
C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens, 2006. "Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand," IZA Discussion Papers 2347, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  2. Guido W. Imbens & Whitney Newey & Geert Ridder, 2006. "Mean-squared-error Calculations for Average Treatment Effects," IEPR Working Papers 06.57, Institute of Economic Policy Research (IEPR). [Downloadable!]
  3. Michael Lechner, 2005. "Some practical issues in the evaluation of heterogeneous labour market programmes by matching methods," Labor and Demography 0505006, EconWPA. [Downloadable!]
    Other versions:
  4. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 1-21, June. [Downloadable!]
  5. Michael Lechner, 2002. "Program Heterogeneity And Propensity Score Matching: An Application To The Evaluation Of Active Labor Market Policies," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 205-220, May. [Downloadable!] (restricted)
  6. 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.
    Other versions:
  7. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2006. "Nonparametric Tests for Treatment Effect Heterogeneity," IZA Discussion Papers 2091, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  8. 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)
  9. repec:cup:etheor:v:10:y:1994:i:2:p:233-53 is not listed on IDEAS
  10. 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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  11. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July. [Downloadable!] (restricted)
  12. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, vol. 93(2), pages 126-132, May. [Downloadable!]
  13. 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)
  14. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March. [Downloadable!] (restricted)
    Other versions:
  15. Heckman, James J & Ichimura, Hidehiko & Todd, Petra E, 1997. "Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme," Review of Economic Studies, Blackwell Publishing, vol. 64(4), pages 605-54, October. [Downloadable!] (restricted)
  16. 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. [Downloadable!] (restricted)
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  17. 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. [Downloadable!] (restricted)
  18. 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. [Downloadable!] (restricted)
  19. Guido W. Imbens & Whitney Newey & Geert Ridder, 2005. "Mean-square-error Calculations for Average Treatment Effects," IEPR Working Papers 05.34, Institute of Economic Policy Research (IEPR). [Downloadable!]
  20. Joshua D. Angrist, 1998. "Estimating the Labor Market Impact of Voluntary Military Service Using Social Security Data on Military Applicants," Econometrica, Econometric Society, vol. 66(2), pages 249-288, March.
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  21. Richard Blundell & Monica Costa Dias, 2002. "Alternative approaches to evaluation in empirical microeconomics," CeMMAP working papers CWP10/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  22. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, 06. [Downloadable!] (restricted)
    Other versions:
  23. 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.
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2006. "Nonparametric Tests for Treatment Effect Heterogeneity," NBER Technical Working Papers 0324, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Onur Baser, 2007. "Propensity Score Matching with Limited Overlap," Economics Bulletin, Economics Bulletin, vol. 9(8), pages 1-8. [Downloadable!]
  3. Foucault, Thierry & Themar, David & Sraer, David, 2008. "Individual investors and volatility," Les Cahiers de Recherche 899, HEC Paris. [Downloadable!]
    Other versions:
  4. Stefano DellaVigna & Ethan Kaplan, 2006. "The Fox News Effect: Media Bias and Voting," NBER Working Papers 12169, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Zhong Zhao, 2005. "Sensitivity of Propensity Score Methods to the Specifications," IZA Discussion Papers 1873, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  6. de Brauw, Alan & Hoddinott, John, 2008. "Must conditional cash transfer programs be conditioned to be effective?: The impact of conditioning transfers on school enrollment in Mexico," IFPRI discussion papers 757, International Food Policy Research Institute (IFPRI). [Downloadable!]
  7. Wagstaff, Adam & Lindelow, Magnus & Gao Jun & Xu Ling & Qian Juncheng, 2007. "Extending health insurance to the rural population : an impact evaluation of China's new cooperative medical scheme," Policy Research Working Paper Series 4150, The World Bank. [Downloadable!]
    Other versions:
  8. Wagstaff, Adam, 2007. "Health insurance for the poor : initial impacts of Vietnam's health care fund for the poor," Policy Research Working Paper Series 4134, The World Bank. [Downloadable!]
  9. DellaVigna, Stefano & Kaplan, Ethan, 2006. "The Fox News Effect: Media Bias and Voting," Seminar Papers 748, Stockholm University, Institute for International Economic Studies. [Downloadable!]
  10. Allcott, Hunt & Ortega, Daniel E., 2009. "The performance of decentralized school systems : evidence from Fe y Alegría in Venezuela," Policy Research Working Paper Series 4879, The World Bank. [Downloadable!]
  11. Sudhanshu Handa & John Maluccio, 2008. "Matching the gold standard: Comparing experimental and non-experimental evaluation techniques for a geographically targeted program," Middlebury College Working Paper Series 0813, Middlebury College, Department of Economics. [Downloadable!]
  12. Deininger, Klaus & Liu, Yanyan, 2008. "Economic and Social Impacts of Self-Help Groups in India," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6482, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]
  13. Ciro Biderman & João Manoel Pinho de Mello & Alexandre A Schneider, 2006. "Dry law and homicides: evidence from the São Paulo metropolitan area," Textos para discussão 518, Department of Economics PUC-Rio (Brazil), revised Oct 2008. [Downloadable!]
  14. Matias Busso & Patrick Kline, 2008. "Do Local Economic Development Programs Work? Evidence from the Federal Empowerment Zone Program," Cowles Foundation Discussion Papers 1639, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  15. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens, 2006. "Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand," IZA Discussion Papers 2347, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  16. Chen, Shaohua & Mu, Ren & Ravallion, Martin, 2008. "Are there lasting impacts of aid to poor areas ? Evidence from rural China," Policy Research Working Paper Series 4084, The World Bank. [Downloadable!]
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