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The Impact of Measurement Error on Evaluation Methods Based on Strong Ignorability

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  • Andrew Chesher
  • Erich Battistin

Abstract

When selection bias can purely be attributed to observables, several estimators have been discussed in the literature to estimate the average effect of a binary treatment or policy on a scalar outcome. Identification typically exploits the unconfoundedness of the treatment, which is verified if the participation status is independent of potential outcomes conditional on observable covariates. Assuming unconfoundedness, the average effect of the treatment can be estimated by matching, differencing within subpopulation averages of treated and untreated units, or by propensity score methods under an additional condition on the support of the covariates exploited. The latter condition, together with unconfoundedness, makes participation into the treatment group strongly ignorable, as defined by Rosenbaum and Rubin (1983). This paper derives conditions for identification and estimation of treatment effects when observable covariates relevant to unconfoundedness are measured with error. An expression for the measurement error bias is derived, and conditions are discussed for this to be zero. A bias correction procedure is also presented, which uses non-parametric estimates of functionals of the distribution of observed covariates.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 339.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:339

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Keywords: potential outcomes; small sigma asymptotics; treatment effects;

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References

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  1. 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.
  2. Guido Imbens, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometric Society World Congress 2000 Contributed Papers 1166, Econometric Society.
  3. Heckman, James J. & Lalonde, Robert J. & Smith, Jeffrey A., 1999. "The economics and econometrics of active labor market programs," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 31, pages 1865-2097 Elsevier.
  4. Chesher, Andrew & Schluter, Christian, 2002. "Welfare Measurement and Measurement Error," Review of Economic Studies, Wiley Blackwell, vol. 69(2), pages 357-78, April.
  5. Wickens, Michael R, 1972. "A Note on the Use of Proxy Variables," Econometrica, Econometric Society, vol. 40(4), pages 759-61, July.
  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.
  7. Michael LECHNER, 2008. "A Note on the Common Support Problem in Applied Evaluation Studies," Annales d'Economie et de Statistique, ENSAE, issue 91-92, pages 217-235.
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Cited by:
  1. Klein, T.J., 2008. "Heterogeneous Treatment Effects: Instrumental Variables Without Monotonicity?," Discussion Paper 2008-45, Tilburg University, Center for Economic Research.
  2. repec:ese:iserwp:2006-51 is not listed on IDEAS
  3. Siedler, Thomas, 2006. "Family and Politics: Does Parental Unemployment Cause Right-Wing Extremism?," IZA Discussion Papers 2411, Institute for the Study of Labor (IZA).
  4. Thomas Siedler, 2007. "Does Parental Unemployment Cause Right-Wing Extremism?," Discussion Papers of DIW Berlin 666, DIW Berlin, German Institute for Economic Research.

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