Test for the covariance matrix in time-varying coefficients panel data models with fixed effects
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Online ISSN 2005-2863 Print ISSN 1226-3192
RESEARCH ARTICLE
Test for the covariance matrix in time‑varying coefficients panel data models with fixed effects Yuping Hu1 · Sanying Feng1 · Jing Zhao2 Received: 7 December 2019 / Accepted: 2 November 2020 © Korean Statistical Society 2020
Abstract This paper proposes tests for the null of sphericity and identity matrix for nonparametric time-varying coefficient panel data models with fixed effects. Firstly, based on the local linear smoothing technique, the estimators of the unknown coefficient functions and model residuals are obtained. Secondly, proper test statistics are proposed aiming at tests for sphericity or identity matrix with a large number of crosssectional units and time series observations. In addition, the limiting distributions of the proposed test statistics are derived based on random matrix theory. At last, some simulation studies are conducted to examine the finite sample performance for the proposed test statistics and a real data example is analyzed. Keywords Sphericity · Covariance matrix · Time-varying coefficients panel data models · Local linear estimation · Cross-sectional dependence
1 Introduction In the traditional linear panel model it is generally assumed that the error terms are cross-sectional or sequential independent and homoscedasticity in order to obtain the best linear unbiased estimation of parameters. It is also true for applied panel data work given the numerous applications that report fixed effects estimates ignoring cross-sectional dependence or heteroscedasticity. However, in most real cases, the error terms don’t satisfy these assumptions. As is typical in economics, the cross-sectional variability and temporal variation often exist. Unlike heteroscedasticity, certain types of cross-sectional dependence in the data may result in the inconsistency of ordinary least square estimators. One can see Andrews (2005) for a factor model example and Lee (2002) for a spatial autoregressive model example. In
* Jing Zhao [email protected] 1
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
2
China National Institute of Standardization, Beijing 100191, China
13
Vol.:(0123456789)
Journal of the Korean Statistical Society
a word, in the presence of heteroscedasticity or cross-sectional dependence, ignoring these effects will result in failure of parameter estimation and hypothesis testing results. Many factors, such as the omission of some important explanatory variables in the model, the inaccurate model setting, sample data with measurement error, the differences of cross sectional individuals, etc, may result in heteroscedasticity. Cross-sectional dependence is also frequently discussed in econometrics. In fact, in economic activity, there are many cases that are related to contemporaneous correlation. In various kinds of asset pricing model, for example, because assets are in the same market environment and will be jointly influenced by factors such as policy and market environme
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