Understanding Cross-Sectional Dependence in Panel Data

27 Pages Posted: 23 Apr 2018

See all articles by Gopal K. Basak

Gopal K. Basak

Indian Statistical Institute, Kolkata

Samarjit Das

Indian Statistical Institute, Kolkata

Date Written: April 23, 2018

Abstract

We provide various norm-based definitions of different types of cross-sectional dependence and the relations between them. These definitions facilitate to comprehend and to characterize the various forms of cross-sectional dependence, such as strong, semi-strong, and weak dependence. Then we examine the asymptotic properties of parameter estimators both for fixed (within) effect estimator and random effect (pooled) estimator for linear panel data models incorporating various forms of cross-sectional dependence. The asymptotic properties are also derived when both cross-sectional and temporal dependence are present. Subsequently, we develop consistent and robust standard error of the parameter estimators both for fixed effect and random effect model separately. Robust standard errors are developed (i) for pure cross-sectional dependence; and (ii) also for cross-sectional and time series dependence. Under strong or semi-strong cross-sectional dependence, it is established that when the time dependence comes through the idiosyncratic errors, such time dependence does not have any influence in the asymptotic variance of $(\hat{\beta}_{FE/RE}). $ Hence, it is argued that in estimating $Var(\hat{\beta}_{FE/RE}),$ Newey-West kind of correction injects bias in the variance estimate. Furthermore, this article lay down conditions under which $t$, $F$ and the $Wald$ statistics based on the robust covariance matrix estimator give valid inference.

Keywords: cross-sectional dependence, common factor, fixed effect model, panel data, random effect model, time series dependence

JEL Classification: C12, C33

Suggested Citation

Basak, Gopal K. and Das, Samarjit, Understanding Cross-Sectional Dependence in Panel Data (April 23, 2018). Available at SSRN: https://ssrn.com/abstract=3167337 or http://dx.doi.org/10.2139/ssrn.3167337

Gopal K. Basak

Indian Statistical Institute, Kolkata ( email )

203 B.T. Road
Kolkata, West Bengal 700108
India

Samarjit Das (Contact Author)

Indian Statistical Institute, Kolkata ( email )

203 B.T. Road
Kolkata, West Bengal 700108
India

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