Theory and Practice of Inference in Regression Discontinuity: A Fixed-Bandwidth Asymptotics Approach

Otavio Bartalotti

No 1302, Working Papers from Tulane University, Department of Economics

Abstract: In regression discontinuity design (RD), researchers use bandwidths around the discontinuity. For a given bandwidth, one can estimate asymptotic variance based on the assumption that the bandwidth shrinks to zero as sample size increases (the traditional approach) or, alternatively, that the bandwidth is fixed. The main theoretical results for RD rely on the former, while most applications in the literature treat the estimates as parametric. This paper develops the "fixed-bandwidth" alternative asymptotic theory for local polynomial estimators, bridging the gap between theorists and practitioners and shedding light on implicit assumptions on both approaches. The fixed-bandwidth approach provides alternative formulas, i.e. alternative approximations, for the bias and variance of RD estimators. Simulations indicate that fixed-bandwidth approximations are usually better than traditional approximations, and improvements are nontrivial when there is heteroskedasticity. When there is no heteroskedasticity, both approximations are shown to be equivalent under some additional mild conditions. Feasible estimators of fixed-bandwidth standard errors are easy to implement and improve coverage of confidence intervals compared to the traditional approach, especially in the presence of heteroskedasticity. Fixed-bandwidth approximations are akin to treating RD estimators as locally parametric, providing theoretical justification for the common empirical practice of using heteroskedasticity-robust standard errors in RD settings.

Keywords: regression discontinuity design; average treatment effect; fixed bandwidth asymptotics; local polynomial estimators (search for similar items in EconPapers)
JEL-codes: C12 C21 (search for similar items in EconPapers)
Pages: 61 pages
Date: 2013-01, Revised 2013-11
New Economics Papers: this item is included in nep-ecm
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http://repec.tulane.edu/RePEc/pdf/tul1302.pdf Second Version, January 2013 (application/pdf)

Related works:
Working Paper: Theory and Practice of Inference in Regression Discontinuity: A Fixed-Bandwidth Asymptotics Approach (2014)
Working Paper: Theory and practice of inference in regression discontinuity: a fixed-bandwidth asymptotics approach (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:tul:wpaper:1302

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