# General diagnostic tests for cross-sectional dependence in panels

## Author

Listed:
• M. Hashem Pesaran

(University of Southern California
Trinity College)

## Abstract

This paper proposes simple tests of error cross-sectional 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 the 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-sectional dependence of any fixed order p, as well as the case where no a priori ordering of the cross-sectional units is assumed, referred to as $$\hbox {CD}(p)$$ CD ( p ) and $$\hbox {CD}$$ CD tests, respectively. Asymptotic distribution of these tests is 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, they are quite robust to the presence of unit roots and structural breaks. The use of the $$\hbox {CD}$$ 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.

## Suggested Citation

• M. Hashem Pesaran, 2021. "General diagnostic tests for cross-sectional dependence in panels," Empirical Economics, Springer, vol. 60(1), pages 13-50, January.
• Handle: RePEc:spr:empeco:v:60:y:2021:i:1:d:10.1007_s00181-020-01875-7
DOI: 10.1007/s00181-020-01875-7
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## References listed on IDEAS

as
1. Pesaran, M. Hashem & Timmermann, Allan, 2005. "Small sample properties of forecasts from autoregressive models under structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 183-217.
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### Keywords

Cross-sectional dependence; Spatial dependence; Diagnostic tests; Dynamic heterogenous panels; Empirical growth;
All these keywords.

### JEL classification:

• C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
• C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
• C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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