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OLS and 2SLS in Randomized and Conditionally Randomized Experiments

Author

Listed:
  • Ansel Jason

    (GoDaddy.com, LLC, Kirkland, Washington)

  • Hong Han

    (Department of Economics, Stanford University, Stanford, California)

  • Jessie Li and

    (Department of Economics, University of California, Santa Cruz, California)

Abstract

We investigate estimation and inference of the (local) average treatment effect parameter when a binary instrumental variable is generated by a randomized or conditionally randomized experiment. Under i.i.d. sampling, we show that adding covariates and their interactions with the instrument will weakly improve estimation precision of the (local) average treatment effect, but the robust OLS (2SLS) standard errors will no longer be valid. We provide an analytic correction that is easy to implement and demonstrate through Monte Carlo simulations and an empirical application the interacted estimator’s efficiency gains over the unadjusted estimator and the uninteracted covariate adjusted estimator. We also generalize our results to covariate adaptive randomization where the treatment assignment is not i.i.d., thus extending the recent contributions of Bugni, F., I.A. Canay, A.M. Shaikh (2017a), Inference Under Covariate-Adaptive Randomization. Working Paper and Bugni, F., I.A. Canay, A.M. Shaikh (2017b), Inference Under Covariate-Adaptive Randomization with Multiple Treatments. Working Paper to allow for the case of non-compliance.

Suggested Citation

  • Ansel Jason & Hong Han & Jessie Li and, 2018. "OLS and 2SLS in Randomized and Conditionally Randomized Experiments," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 238(3-4), pages 243-293, July.
    • Handle: RePEc:jns:jbstat:v:238:y:2018:i:3-4:p:243-293:n:3
    DOI: 10.1515/jbnst-2018-0016
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    References listed on IDEAS

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    2. Jun Shao & Xinxin Yu & Bob Zhong, 2010. "A theory for testing hypotheses under covariate-adaptive randomization," Biometrika, Biometrika Trust, vol. 97(2), pages 347-360.
    3. 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.
    4. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    5. 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.
    6. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, October.
    7. Han Hong & Denis Nekipelov, 2010. "Semiparametric efficiency in nonlinear LATE models," Quantitative Economics, Econometric Society, vol. 1(2), pages 279-304, November.
    8. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
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    Cited by:

    1. Jian, L. & Linton, O. B. & Tang, H. & Zhang, Y., 2023. "Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance," Cambridge Working Papers in Economics 2366, Faculty of Economics, University of Cambridge.
    2. Jiang, Liang & Phillips, Peter C.B. & Tao, Yubo & Zhang, Yichong, 2023. "Regression-adjusted estimation of quantile treatment effects under covariate-adaptive randomizations," Journal of Econometrics, Elsevier, vol. 234(2), pages 758-776.
    3. Jian, L. & Linton, O. B. & Tang, H. & Zhang, Y., 2023. "Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance," Janeway Institute Working Papers 2315, Faculty of Economics, University of Cambridge.
    4. Liang Jiang & Oliver B. Linton & Haihan Tang & Yichong Zhang, 2022. "Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance," Papers 2201.13004, arXiv.org, revised Jun 2023.
    5. Hvidman, Charlotte & Koch, Alexander K. & Nafziger, Julia & Nielsen, Søren Albeck & Rosholm, Michael, 2024. "An intensive, school-based learning camp targeting academic and non-cognitive skills evaluated in a randomized trial," Labour Economics, Elsevier, vol. 88(C).
    6. Bugni, Federico A. & Gao, Mengsi, 2023. "Inference under covariate-adaptive randomization with imperfect compliance," Journal of Econometrics, Elsevier, vol. 237(1).

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    More about this item

    Keywords

    big data; data science;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments

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