Testing for Correlation between the Regressors and Factor Loadings in Heterogeneous Panels with Interactive Effects

TY - JOUR

T1 - Testing for Correlation between the Regressors and Factor Loadings in Heterogeneous Panels with Interactive Effects

AU - Kapetanios, G.

AU - Serlenga, Laura

AU - Shin, Yongcheol

N1 - © The Author(s) 2023

PY - 2023/5/11

Y1 - 2023/5/11

N2 - A large literature on modelling cross-section dependence in panels has been developed through interactive effects. However, there are areas where research has not really caught on yet. One such area is the one concerned with whether the regressors are correlated with factor loadings or not. This is an important issue because if the regressors are uncorrelated with loadings, we can simply use the consistent two-way fixed effects (FE) estimator without employing any more sophisticated econometric methods such as the principal component(PC) or the common correlated effects estimators. We explore this issue, which has received surprisingly little attention and propose a Hausman-type test to address the matter. Further, we develop two nonparametric variance estimators for the FE and PC estimators as well as their difference, that are robust to the presence of heteroscedasticity, autocorrelation and slope heterogeneity. Under the null hypothesis of no correlation between the regressors and loadings the proposed test follows the chi-squared distribution asymptotically. Monte Carlo simulation results confirm satisfactory size and power performance of the test even in small samples. Finally, we provide extensive empirical evidence in favour of uncorrelated factor loadings. In this situation, the FE estimator would provide a simple and robust estimation strategy which is invariant to nontrivial computational issues associated with the PC estimator.

AB - A large literature on modelling cross-section dependence in panels has been developed through interactive effects. However, there are areas where research has not really caught on yet. One such area is the one concerned with whether the regressors are correlated with factor loadings or not. This is an important issue because if the regressors are uncorrelated with loadings, we can simply use the consistent two-way fixed effects (FE) estimator without employing any more sophisticated econometric methods such as the principal component(PC) or the common correlated effects estimators. We explore this issue, which has received surprisingly little attention and propose a Hausman-type test to address the matter. Further, we develop two nonparametric variance estimators for the FE and PC estimators as well as their difference, that are robust to the presence of heteroscedasticity, autocorrelation and slope heterogeneity. Under the null hypothesis of no correlation between the regressors and loadings the proposed test follows the chi-squared distribution asymptotically. Monte Carlo simulation results confirm satisfactory size and power performance of the test even in small samples. Finally, we provide extensive empirical evidence in favour of uncorrelated factor loadings. In this situation, the FE estimator would provide a simple and robust estimation strategy which is invariant to nontrivial computational issues associated with the PC estimator.

KW - Panel Data Model with Interactive Effects

KW - Correlation between the Regressors and Factor Loadings

KW - Robust Variance Estimators

KW - Hausman-type Test

U2 - 10.1007/s00181-023-02390-1

DO - 10.1007/s00181-023-02390-1

M3 - Article

SN - 0377-7332

VL - 64

SP - 2611

EP - 2659

JO - Empirical Economics

JF - Empirical Economics

ER -