A robust approach to heteroskedasticity, error serial correlation and slope heterogeneity in linear models with interactive effects for large panel data

ISER DP No. 1037

86 Pages Posted: 7 Aug 2018 Last revised: 27 Jan 2022

See all articles by Guowei Cui

Guowei Cui

Huazhong University of Science and Technology

Kazuhiko Hayakawa

Hiroshima University

Shuichi Nagata

Kwansei Gakuin University - School of Business Administration; Kwansei Gakuin University - Department of Mathematical Sciences

Takashi Yamagata

University of York - Department of Economics and Related Studies; Osaka University - Institute of Social and Economic Research

Date Written: June 26, 2019

Abstract

In this paper, we propose a robust approach against heteroskedasticity, error serial correlation and slope heterogeneity in linear models with interactive effects for large panel data. First, consistency and asymptotic normality of the pooled iterated principal component (IPC) estimator for random coefficient and homogeneous slope models are established. Then, we prove the asymptotic validity of the associated Wald test for slope parameter restrictions based on the panel heteroskedasticity and autocorrelation consistent (PHAC) variance matrix estimator for both random coefficient and homogeneous slope models, which does not require the Newey-West type time-series parameter truncation. These results asymptotically justify the use of the same pooled IPC estimator and the PHAC standard error for both homogeneous-slope and heterogeneous-slope models. This robust approach can significantly reduce the model selection uncertainty for applied researchers. In addition, we propose a Lagrange Multiplier (LM) test for correlated random coefficients with covariates. This test has non-trivial power against correlated random coefficients, but not for random coefficients and homogeneous slopes. The LM test is important because the IPC estimator becomes inconsistent with correlated random coefficients. The finite sample evidence and an empirical application support the reliability and the usefulness of our robust approach.

Keywords: panel data; slope heterogeneity; interactive effects; correlated random coefficients

JEL Classification: C12, C13, C23

Suggested Citation

cui, guowei and Hayakawa, Kazuhiko and Nagata, Shuichi and Yamagata, Takashi, A robust approach to heteroskedasticity, error serial correlation and slope heterogeneity in linear models with interactive effects for large panel data (June 26, 2019). ISER DP No. 1037, Available at SSRN: https://ssrn.com/abstract=3215661 or http://dx.doi.org/10.2139/ssrn.3215661

Guowei Cui

Huazhong University of Science and Technology ( email )

Wuhan, Hubei 430074
China
18171270610 (Phone)

Kazuhiko Hayakawa

Hiroshima University ( email )

Japan

Shuichi Nagata

Kwansei Gakuin University - School of Business Administration ( email )

1-155 Uegahara-1bancho
Nishinomiya, Hyogo 662-8501
Japan

Kwansei Gakuin University - Department of Mathematical Sciences ( email )

Japan

Takashi Yamagata (Contact Author)

University of York - Department of Economics and Related Studies ( email )

Heslington
York, YO1 5DD
United Kingdom

Osaka University - Institute of Social and Economic Research ( email )

6-1, Mihogaoka
Suita, Osaka 567-0047
Japan

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