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A1195
Title: Variance properties of local polynomial density estimators at the boundary: Application to manipulation testing Authors:  Yuta Okamoto - Kyoto University (Japan) [presenting]
Shunsuke Imai - Kyoto University - Graduate School of Economics (Japan)
Abstract: Variance properties of the local polynomial density estimator at the boundary points are investigated. Asymptotic and theoretical non-asymptotic analyses reveal that kernel selection is crucial in contrast to common sense in nonparametric statistics. In particular, it is shown that the estimation accuracy can be devastatingly poor with the most used kernel functions, including the uniform and triangular kernels. More seriously, this finding also applies to the performance of the manipulation testing based on the estimator, which is the most accepted method in empirical economics. It is shown that the test has only disappointing statistical power and often fails to detect the unbalance in a running variable. However, these problematic natures are drastically resolved just by changing the kernel function to a less-known one. Numerous simulations and empirical applications are provided to highlight the empirical relevance, and these results strongly support the use of a carefully chosen kernel function.