Testing for cross-sectional dependence in panel-data models

Testing for cross-sectional dependence in panel-data models

2006 | Rafael E. De Hoyos, Vasilis Sarafidis
The article introduces a new Stata command, `xtcsd`, which tests for cross-sectional dependence in panel-data models. Cross-sectional dependence refers to correlations between the error terms of different cross-sectional units in a panel dataset. The command implements three tests: Pesaran's CD test, Friedman's test, and Frees' test. These tests are particularly useful when the number of cross-sectional units $N$ is large and the number of time periods $T$ is small, which is common in many empirical applications. The article explains that cross-sectional dependence can arise from common shocks, unobserved components, spatial dependence, or idiosyncratic pairwise dependence. It highlights the importance of testing for cross-sectional dependence because it can significantly affect the efficiency and consistency of estimators, especially in dynamic panel models. For example, if cross-sectional dependence is ignored, the efficiency gains from pooling data may be lost. The `xtcsd` command is designed to complement existing tests like the Breusch-Pagan LM test, which is suitable for different scenarios of $N$ and $T$. The command is applicable to both balanced and unbalanced panels and provides a straightforward way to perform three popular tests for cross-sectional dependence. The article also includes an empirical example using a dataset of U.S. states to illustrate the use of the command. The results show that cross-sectional dependence is present in the data, as indicated by the rejection of the null hypothesis of cross-sectional independence by all three tests. The article concludes that these tests are complementary and should be used together to ensure robustness in the analysis of panel data.The article introduces a new Stata command, `xtcsd`, which tests for cross-sectional dependence in panel-data models. Cross-sectional dependence refers to correlations between the error terms of different cross-sectional units in a panel dataset. The command implements three tests: Pesaran's CD test, Friedman's test, and Frees' test. These tests are particularly useful when the number of cross-sectional units $N$ is large and the number of time periods $T$ is small, which is common in many empirical applications. The article explains that cross-sectional dependence can arise from common shocks, unobserved components, spatial dependence, or idiosyncratic pairwise dependence. It highlights the importance of testing for cross-sectional dependence because it can significantly affect the efficiency and consistency of estimators, especially in dynamic panel models. For example, if cross-sectional dependence is ignored, the efficiency gains from pooling data may be lost. The `xtcsd` command is designed to complement existing tests like the Breusch-Pagan LM test, which is suitable for different scenarios of $N$ and $T$. The command is applicable to both balanced and unbalanced panels and provides a straightforward way to perform three popular tests for cross-sectional dependence. The article also includes an empirical example using a dataset of U.S. states to illustrate the use of the command. The results show that cross-sectional dependence is present in the data, as indicated by the rejection of the null hypothesis of cross-sectional independence by all three tests. The article concludes that these tests are complementary and should be used together to ensure robustness in the analysis of panel data.
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