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Identifying the Effect of Changing the Policy Threshold in Regression Discontinuity Models

Author

Listed:
  • Yingying Dong

    (California State University, Irvine)

  • Arthur Lewbel

    (Boston College)

Abstract
Regression discontinuity models, where the probability of treatment jumps discretely when a running variable crosses a threshold, are commonly used to nonparametrically identify and estimate a local average treatment effect. We show that the derivative of this treatment effect with respect to the running variable is nonparametrically identified and easily estimated. Then, given a local policy invariance assumption, we show that this derivative equals the change in the treatment effect that would result from a marginal change in the threshold, which we call the marginal threshold treatment effect (MTTE). We apply this result to Manacorda (2012), who estimates a treatment effect of grade retention on school outcomes. Our MTTE identifies how this treatment effect would change if the threshold for retention was raised or lowered, even though no such change in threshold is actually observed.

Suggested Citation

  • Yingying Dong & Arthur Lewbel, 2010. "Identifying the Effect of Changing the Policy Threshold in Regression Discontinuity Models," Boston College Working Papers in Economics 759, Boston College Department of Economics, revised 15 Dec 2012.
    • Handle: RePEc:boc:bocoec:759
    Note: Previously circulated as "Regression Discontinuity Marginal Threshold Treatment Effects"
    as

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    Keywords

    regression discontinuity; sharp design; fuzzy design; treatment effects; program evaluation; threshold; running variable; forcing variable; marginal effects.;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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