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Properties of least squares estimator in estimation of average treatment effects

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  • Jinyong Hahn

    (UCLA)

Abstract

Treatment effects are often estimated by the least squares estimator controlling for some covariates. This paper investigates its properties. When the propensity score is constant, it is a consistent estimator of the average treatment effects if it is viewed as a semiparametric partially linear regression estimator, but it is not necessarily more efficient than the simple difference-of-means estimator. If it is literally viewed as a least squares estimator with a finite number of controls, it is equal to the weighted average of conditional average treatment effects with potentially negative weights, although the negative weight issue does not exist under semiparametric interpretation. It is shown that the negative weight issue can be avoided by use of logit specification.

Suggested Citation

  • Jinyong Hahn, 2023. "Properties of least squares estimator in estimation of average treatment effects," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 14(3), pages 301-313, December.
    • Handle: RePEc:spr:series:v:14:y:2023:i:3:d:10.1007_s13209-023-00279-x
    DOI: 10.1007/s13209-023-00279-x
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    References listed on IDEAS

    as
    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Myoung-Jae Lee, 2018. "Simple least squares estimator for treatment effects using propensity score residuals," Biometrika, Biometrika Trust, vol. 105(1), pages 149-164.
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    4. 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.
    5. Akanksha Negi & Jeffrey M. Wooldridge, 2021. "Revisiting regression adjustment in experiments with heterogeneous treatment effects," Econometric Reviews, Taylor & Francis Journals, vol. 40(5), pages 504-534, April.
    6. 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 (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    OLS; Negative weight; Efficiency;
    All these keywords.

    JEL classification:

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

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