An application of local linear regression with asymmetric kernels to regression discontinuity designs
Estimation of causal eects in regression discontinuity designs relies on a local Wald estimator whose components are estimated via local linear regressions centred at an specic point in the range of a treatment assignment variable. The asymptotic distribution of the estimator depends on the specic choice of kernel used in these nonparametric regressions, with some popular kernels causing a notable loss of effciency. This article presents the asymptotic distribution of the local Wald estimator when a gamma kernel is used in each local linear regression. The resulting statistics is easy to implement, consistent at the usual nonparametric rate, maintains its asymptotic normal distribution, but its bias and variance do not depend on kernel-related constants and, as a result, is becomes a more effcient method. The effciency gains are measured via a limited Monte Carlo experiment, and the new method is used in a substantive application.
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