Abstract

Testing cross-sectional independence in panel data models is of fundamental importance in econometric analysis with high-dimensional panels. Recently, econo-

metricians began to turn their attention to the problem in the presence of serial

dependence. The existing procedure for testing cross-sectional independence with

serial correlation is based on the sum of the sample cross-sectional correlations,

which generally performs well when the alternative has dense cross-sectional correlations, but suffers from low power against sparse alternatives. To deal with

sparse alternatives, we propose a test based on the maximum of the squared

sample cross-sectional correlations.

Furthermore, we propose a combined test

to combine the p-values of the max based and sum based tests, which performs

well under both dense and sparse alternatives. The combined test relies on the

asymptotic independence of the max based and sum based test statistics, which

we show rigorously. We show that the proposed max based and combined tests

have attractive theoretical properties and demonstrate the superior performance

via extensive simulation results.

We demonstrate the practicality of the proposed tests through two empirical applications.

Information

Preprint No.SS-2023-0348
Manuscript IDSS-2023-0348
Complete AuthorsHongfei Wang, Binghui Liu, Long Feng, Yanyuan Ma
Corresponding AuthorsLong Feng
Emailsflnankai@nankai.edu.cn

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Acknowledgments

We express our sincere gratitude to the editor, associate editor, and anonymous reviewers for their invaluable guidance, support, and constructive

feedback. Wang and Liu’s research was partially supported by National

Natural Science Foundation of China grant 12171079 and the China National Key R&D Program grant 2020YFA0714100. Long Feng is partially

supported by Shenzhen Wukong Investment Company, the Open Research

Fund of Key Laboratory of Advanced Theory and Application in Statistics

and Data Science (East China Normal University), Ministry of Education,

Tianjin Science Fund for Outstanding Young Scholar (23JCJQJC00150),

the Fundamental Research Funds for the Central Universities under Grant

No. ZB22000105 and 63233075, the China National Key R&D Program

(Grant Nos. 2019YFC1908502, 2022YFA1003703, 2022YFA1003802, 2022YFA1003803)

and the National Natural Science Foundation of China Grants (Nos. 12271271,

11925106, 12231011, 11931001 and 11971247). Ma’s research was partially

supported by grants from national institute of health. Binghui liu and Long

Feng are co-corresponding authors and contributed equally to this paper.

Supplementary Materials

The Supplementary Material contains some additional numerical results,

an additional empirical application and the technical proofs.

Supplementary materials are available for download.