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Optimized Regression Discontinuity Designs

Author

Listed:
  • Guido Imbens

    (Stanford University)

  • Stefan Wager

    (Stanford University)

Abstract

The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting nonparametric regression models on both sides of a treatment assignment boundary and then reporting plug-in estimates for the effect of interest. In applications, however, it is often difficult to tune the nonparametric regressions in a way that is well calibrated for the specific target of inference; for example, the model with the best global in-sample fit may provide poor estimates of the discontinuity parameter, which depends on the regression function at boundary points. We propose an alternative method for estimation and statistical inference in regression discontinuity designs that uses numerical convex optimization to directly obtain the finite-sample-minimax linear estimator for the regression discontinuity parameter, subject to bounds on the second derivative of the conditional response function. Given a bound on the second derivative, our proposed method is fully data driven and provides uniform confidence intervals for the regression discontinuity parameter with both discrete and continuous running variables. The method also naturally extends to the case of multiple running variables.

Suggested Citation

  • Guido Imbens & Stefan Wager, 2019. "Optimized Regression Discontinuity Designs," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 264-278, May.
  • Handle: RePEc:tpr:restat:v:101:y:2019:i:2:p:264-278
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    References listed on IDEAS

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    8. Adam C. Sales & Ben B. Hansen, 2020. "Limitless Regression Discontinuity," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 143-174, April.
    9. Yang He & Otávio Bartalotti, 2020. "Wild bootstrap for fuzzy regression discontinuity designs: obtaining robust bias-corrected confidence intervals [Using Maimonides’ rule to estimate the effect of class size on scholastic achievemen," The Econometrics Journal, Royal Economic Society, vol. 23(2), pages 211-231.
    10. Kohei Yata, 2021. "Optimal Decision Rules Under Partial Identification," Papers 2111.04926, arXiv.org.
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