Testing for second-order cross-sectional dependence and serial dependence in large dynamic panel models

Testing for cross-sectional dependence (CD) and serial dependence (SD) is important for large dynamic panel models. By detecting the zero cross-sectional and serial covariances of model disturbances, the existing first-order tests lack the power to detect second-order CD and SD structures in the variance of model disturbances, which have been commonly documented in many empirical studies. To fill the gap, we first propose new portmanteau CD and SD tests to examine the zero values of cross-sectional and serial covariances of squared model disturbances, up to a given lag K, for large homogeneous and heterogeneous dynamic panel models. Next, we introduce new automatic portmanteau CD and SD tests that select lag K in a data-driven way. When both cross-sectional and serial dimensions diverge jointly at the same rate, we show that all proposed tests have tractable limiting null distributions of chi-square, but with a calibration about the asymptotic bias for the SD-type tests. To improve size performance when either the cross-sectional or serial dimension is not large, we further develop bootstrap procedures to obtain critical values for all proposed tests and justify their validity. Finally, we illustrate the usefulness of our proposed tests by simulations and two real examples.