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Correlation and efficiency of propensity score-based estimators for average causal effects

Author

Listed:
  • Pingel, Ronnie

    (Department of Statistics, Uppsala University)

  • Waernbaum, Ingeborg

    (IFAU - Institute for Evaluation of Labour Market and Education Policy)

Abstract

Propensity score based-estimators are commonly used to estimate causal effects in evaluation research. To reduce bias in observational studies researchers might be tempted to include many, perhaps correlated, covariates when estimating the propensity score model. Taking into account that the propensity score is estimated, this study investigates how the efficiency of matching, inverse probability weighting and doubly robust estimators change under the case of correlated covariates. Propositions regarding the large sample variances under certain assumptions of the data generating process are given. The propositions are supplemented by several numerical large sample and finite sample results from a wide range of models. The results show that the correlation may increase or decrease the variances of the estimators. There are several factors that influence how correlation affects the variance of the estimators, including the choice of estimator, the strength of the confounding towards outcome and treatment, and whether a constant or non-constant causal effect is present.

Suggested Citation

  • Pingel, Ronnie & Waernbaum, Ingeborg, 2015. "Correlation and efficiency of propensity score-based estimators for average causal effects," Working Paper Series 2015:3, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    • Handle: RePEc:hhs:ifauwp:2015_003
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    References listed on IDEAS

    as
    1. 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.
    2. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    3. Millimet, Daniel L. & Tchernis, Rusty, 2009. "On the Specification of Propensity Scores, With Applications to the Analysis of Trade Policies," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 397-415.
    4. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    5. Pingel, Ronnie, 2014. "Some approximations of the logistic distribution with application to the covariance matrix of logistic regression," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 63-68.
    6. Jinyong Hahn, 2004. "Functional Restriction and Efficiency in Causal Inference," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 73-76, February.
    7. Xavier De Luna & Ingeborg Waernbaum & Thomas S. Richardson, 2011. "Covariate selection for the nonparametric estimation of an average treatment effect," Biometrika, Biometrika Trust, vol. 98(4), pages 861-875.
    8. Halbert White & Xun Lu, 2011. "Causal Diagrams for Treatment Effect Estimation with Application to Efficient Covariate Selection," The Review of Economics and Statistics, MIT Press, vol. 93(4), pages 1453-1459, November.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Double robust; inverse probability weighting; matching; observational study;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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