Intersection tests for the cointegrating rank in dependent panel data

Abstract

This paper takes a multiple testing perspective on the problem of determining the cointegrating rank in macroeconomic panel data with cross-sectional dependence. The testing procedure for a common rank among the panel units is based on Simes’ (1986) intersection test and requires only the p-values of suitable individual test statistics. A Monte Carlo study demonstrates that these simple tests are robust to cross-sectional dependence and have reasonable size and power properties. A multivariate version of Kendall’s tau is used to test an important assumption underlying Simes’ procedure for dependent statistics. The proposed method is illustrated by an empirical application.

Keywords:

• Common factors
• Cross-sectional dependence
• Likelihood-ratio
• Multiple testing
• Panel cointegration rank test

JEL classification:

• C12
• C15
• C33

Acknowledgments

Financial support by the German Research Foundation (DFG) through the project KA-3145/1-1 is gratefully acknowledged. The data for the empirical analysis was in part collected during a research stay of the second author at the Humboldt Universität in Berlin. The first author would like to thank Plamen Trayanov for helpful discussions. The authors are also grateful to two anonymous referees for their constructive comments and suggestions.

Notes

1 Describing Hommel’s procedure is outside the scope of this paper, but the reader is referred to Hanck (2013) for an illustration.

2 Please note that rank-transformed data refers to the pseudo-observations obtained when the true observations are replaced by their rank in the data sorted in ascending order. This is not to be mistaken with the cointegrating rank.

3 The model assumptions given here refer to the SL test, as our simulations have shown it has preferable finite-sample properties; the model for Johansen’s tests differs slightly in terms of how the deterministic terms are specified, and for details we refer to Johansen (1995).

4 Results for power against $H_0:r=1$ when the true rank is two are similar and not reported for brevity. They are available upon request.

5 This is in line with the findings of both Toda (1995) and Saikkonen and Lütkepohl (2000).

6 The corresponding results for the constant correlation and spatial dependence cases can be found in the Appendix.

7 An illustration of this point is provided by Figures 1 and 2 in the Appendix.

8 We are grateful to Christoph Hanck for providing us with the GAUSS codes.

9 For more details we refer to Hartung (1999).

10 We have used their implementations in pescadf by Piotr Lewandowski and xtunitroot in Stata. Unit root test results are available upon request.

11 Trend in relative output is visible only for Korea, Norway and the UK.

12 $H_0:r=0$ is the starting point in the sequential rank testing procedures of Johansen (1995) and Saikkonen and Lütkepohl (2000).