Testing for error cross-sectional uncorrelatedness in a two-way error components panel data model

ABSTRACT

This paper proposes a new test for the error cross-sectional uncorrelatedness in a two-way error components panel data model based on large panel data sets. By virtue of an existing statistic under the raw data circumstance, an analogous test statistic using the within residuals of the model is constructed. We show that the resulting statistic needs bias correction to make valid inference, and then propose a method to implement feasible correction. Simulation shows that the test based on the feasible bias-corrected statistic performs well. Additionally, we employ a real data set to illustrate the use of the new test.

KEYWORDS:

• Cross-sectional dependence
• Large panels
• Two-way error components
• Uncorrelatedness

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F03

Acknowledgements

The author would like to thank an anonymous referee for providing valuable comments that lead to a significantly improved article. The author is also grateful to Liang Peng, Zongwu Cai, Chao Yang, Nianqing Liu, Hanghui Zhang, Xin Jin and Yahong Zhou for helpful suggestions at the 2016 Symposium on Financial Engineering and Risk Management and at the 2016 Spring Term Workshops held by the School of Economics of SUFE.

Notes

1 Under H₀, Srivastava (2005) estimated a⁰₂ by . However, this estimator cannot always guarantee in finite samples, which prompts us to employ the estimator . is asymptotically identical to except a bias of order , but it can ensure that is always well defined due to the Cauchy-Schwarz inequality.

2 Assumption 1 (iii) postulates that T = O(n^δ) for some δ ∈ (0, 1]. Here, to ensure the consistency of , it needs to restrict δ to be in (1/3, 1]. However, note that the consistency of does not require this restriction.

3 The eigendecomposition is not unique since given a particular Q_m, interchanging any two columns of it, the resulting matrix still satisfies and . Our analysis below will depend on the eigendecompositions of E_n and E_T. However, the final conclusions do not rely on the forms of Q_n and Q_T.

Additional information

Funding

Financial support from the Humanities and Social Sciences Youth Foundation of Ministry of Education of China (Grant No. 16YJC790074), and the Beijing Natural Science Foundation (Grant No. 1174018) are gratefully acknowledged.