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Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation

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  • Bartalotti, Otávio

    () (Iowa State University)

Abstract

In regression discontinuity design (RD), for a given bandwidth, researchers can estimate standard errors based on different variance formulas obtained under different asymptotic frameworks. In the traditional approach the bandwidth shrinks to zero as sample size increases; alternatively, the bandwidth could be treated as fixed. The main theoretical results for RD rely on the former, while most applications in the literature treat the estimates as parametric, implementing the usual heteroskedasticity-robust standard errors. This paper develops the "fixed-bandwidth" alternative asymptotic theory for RD designs, which sheds light on the connection between both approaches. I provide alternative formulas (approximations) for the bias and variance of common RD estimators, and conditions under which both approximations are equivalent. Simulations document the improvements in test coverage that fixed-bandwidth approximations achieve relative to traditional approximations, especially when there is local heteroskedasticity. Feasible estimators of fixed-bandwidth standard errors are easy to implement and are akin to treating RD estimators as locally parametric, validating the common empirical practice of using heteroskedasticity-robust standard errors in RD settings. Bias mitigation approaches are discussed and a novel, bootstrap higher-order bias correction procedure based on the fixed bandwidth asymptotics is suggested.

Suggested Citation

  • Bartalotti, Otávio, 2018. "Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation," IZA Discussion Papers 11560, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp11560
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    Keywords

    average treatment effect; locally parametric inference; local polynomial estimators; fixed bandwidth; heteroskedasticity robust standard errors; bias correction;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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