Kernel-based specification testing with skewed and heavy-tailed data
In this work, we revisit some of the most common nonparametric specification tests and assess their robustness to real world economic data. Most nonparametric econometric theory is based on a compact support assumption of the data, that is, that the data are well behaved and uniform. In economics, this assumption is regularly violated and the consequences of which are unknown. The intent of this research is twofold. First, we investigate what kind of inference practitioners are obtaining when they apply nonparametric specification tests to economic data. Then, having found that this leads to questionable inference, we modify test statistics and suggest other practices to further improve inference with such data. In the first chapter, we modify a nonparametric test for heteroskedasticity by removing the random denominator in the test statistic, an issue that can be exacerbated when applied to skewed and/or heavy tailed data. We find improvements using our modified test and suggest other methods to improve inference for practitioners applying kernel-based specification tests. In the second chapter, we propose a consistent local-linear test for variable significance that has an asymptotically standard normal distribution. Local-linear estimators are generally the dominant and preferred choice in theoretical and applied kernel regression; however, local-constant estimators are typically employed to construct test statistics. Through Monte Carlo simulations and empirical illustrations, we assess the finite sample performance of the proposed test as compared to a local-constant version. The simulations show that our local-linear test performs well, even with skewed and heavy-tailed regressors and errors, and generally outperforms the local-constant version using a wide range of data generating processes. In the third chapter, using two nonparametric kernel-based specification tests, we investigate the relative performance various auxiliary distributions used to implement the wild bootstrap in the presence of skewed and heavy-tailed regressors. Using a data driven method we identify the most appropriate auxiliary distribution for a given sample. Through Monte Carlo simulations, we show that contrary to popular practice, the Rademacher distribution provides better asymptotic refinements than that of the most commonly employed skew-corrected wild bootstrap for these tests.