Abstract
This article provides several tests for skewness and kurtosis for the error terms in a one-way fixed-effects varying coefficient panel data model. To obtain these tests, estimators of higher-order moments of both error components are obtained as solutions of estimating equations. Additionally, to obtain the nonparametric residuals, a local constant estimator based on a pairwise differencing transformation is proposed. The asymptotic properties of these estimators and tests are established. The proposed estimators and test statistics are augmented by simulation studies, and they are also illustrated in an empirical analysis regarding the technical efficiency of European Union companies.
Highlights
Testing for skewness and kurtosis is a relevant topic in many fields in economics, among others in finance and productivity analysis
A test for skewness in this second error component is of great interest because it is equivalent to a test for inefficiency at firm levels
This paper extends the contributions in Cox and Hall (2002) and Wu et al (2012); we propose estimators of higher-order moments and tests of skewness and kurtosis for the different components of a fixed-effects panel data model where the regression function has the form of a nonparametric varying coefficient model
Summary
Testing for skewness and kurtosis is a relevant topic in many fields in economics, among others in finance and productivity analysis. This paper extends the contributions in Cox and Hall (2002) and Wu et al (2012); we propose estimators of higher-order moments and tests of skewness and kurtosis for the different components of a fixed-effects panel data model where the regression function has the form of a nonparametric varying coefficient model. We would like to emphasize that our proposal to estimate higher-order moments and the battery of tests could be based on root-N consistent residuals obtained from a fully parametric model. To our knowledge, this simpler specification has not been studied yet. The detailed mathematical proofs of the main results and additional Monte Carlo results are collected in the supplement, Appendix C
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