published in: Empirical Economics, 2021, 60, 13–50
This paper proposes simple tests of error cross section dependence which are applicable to
a variety of panel data models, including stationary and unit root dynamic heterogeneous
panels with short T and large N. The proposed tests are based on average of pair-wise
correlation coefficients of the OLS residuals from the individual regressions in the panel, and
can be used to test for cross section dependence of any fixed order p, as well as the case
where no a priori ordering of the cross section units is assumed, referred to as CD(p) and CD
tests, respectively. Asymptotic distributions of these tests are derived and their power
function analyzed under different alternatives. It is shown that these tests are correctly
centred for fixed N and T, and are robust to single or multiple breaks in the slope coefficients
and/or error variances. The small sample properties of the tests are investigated and
compared to the Lagrange multiplier test of Breusch and Pagan using Monte Carlo
experiments. It is shown that the tests have the correct size in very small samples and
satisfactory power, and as predicted by the theory, quite robust to the presence of unit roots
and structural breaks. The use of the CD test is illustrated by applying it to study the degree
of dependence in per capita output innovations across countries within a given region and
across countries in different regions. The results show significant evidence of cross
dependence in output innovations across many countries and regions in the world.
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