# General diagnostic tests for cross-sectional dependence in panels

## Author

Listed:
• M. Hashem Pesaran

() (University of Southern California
Trinity College)

## Abstract

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, 0. "General diagnostic tests for cross-sectional dependence in panels," Empirical Economics, Springer, vol. 0, pages 1-38.
• Handle: RePEc:spr:empeco:v::y::i::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.
2. Robert J. Barro, 1998. "Determinants of Economic Growth: A Cross-Country Empirical Study," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262522543.
3. Swamy, P A V B, 1970. "Efficient Inference in a Random Coefficient Regression Model," Econometrica, Econometric Society, vol. 38(2), pages 311-323, March.
4. Pesaran M.H. & Schuermann T. & Weiner S.M., 2004. "Modeling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 129-162, April.
5. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 239-253.
6. Baltagi, Badi H. & Song, Seuck Heun & Koh, Won, 2003. "Testing panel data regression models with spatial error correlation," Journal of Econometrics, Elsevier, vol. 117(1), pages 123-150, November.
7. Lee, Kevin & Pesaran, M Hashem & Smith, Ron, 1997. "Growth and Convergence in Multi-country Empirical Stochastic Solow Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(4), pages 357-392, July-Aug..
8. N/A, 1973. "A Correction," The Indian Economic & Social History Review, , vol. 10(2), pages 207-207, April.
9. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
10. Ahn, Seung Chan & Hoon Lee, Young & Schmidt, Peter, 2001. "GMM estimation of linear panel data models with time-varying individual effects," Journal of Econometrics, Elsevier, vol. 101(2), pages 219-255, April.
11. M. Hashem Pesaran, 2003. "Estimation and Inference in Large Heterogenous Panels with Cross Section Dependence," CESifo Working Paper Series 869, CESifo.
Full references (including those not matched with items on IDEAS)

### Keywords

Cross-sectional dependence; Spatial dependence; Diagnostic tests; Dynamic heterogenous panels; Empirical growth;

### 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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