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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.

Suggested Citation

  • Andrew Chesher & Erich Battistin, 2004. "The Impact of Measurement Error on Evaluation Methods Based on Strong Ignorability," Econometric Society 2004 North American Summer Meetings 339, Econometric Society.
    • Handle: RePEc:ecm:nasm04:339
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    References listed on IDEAS

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    1. Andrew Chesher & Christian Schluter, 2002. "Welfare Measurement and Measurement Error," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 357-378.
    2. 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, July.
    3. 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.
    4. Wickens, Michael R, 1972. "A Note on the Use of Proxy Variables," Econometrica, Econometric Society, vol. 40(4), pages 759-761, July.
    5. 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.
    6. 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, February.
    7. 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.
    8. repec:adr:anecst:y:2008:i:91-92:p:11 is not listed on IDEAS
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    Cited by:

    1. Klein, Tobias J., 2010. "Heterogeneous treatment effects: Instrumental variables without monotonicity?," Journal of Econometrics, Elsevier, vol. 155(2), pages 99-116, April.
    2. Klein, T.J., 2010. "Heterogeneous treatment effects : Instrumental variables without monotonicity?," Other publications TiSEM 0ec85b01-ab6a-4c2a-9e23-1, Tilburg University, School of Economics and Management.
    3. Thomas Siedler, 2007. "Does Parental Unemployment Cause Right-Wing Extremism?," Discussion Papers of DIW Berlin 666, DIW Berlin, German Institute for Economic Research.
    4. Siedler, Thomas, 2006. "Family and Politics: Does Parental Unemployment Cause Right-Wing Extremism?," IZA Discussion Papers 2411, Institute of Labor Economics (IZA).

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    More about this item

    Keywords

    potential outcomes; small sigma asymptotics; treatment effects;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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