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ASYMPTOTICALLY UNIFORMLY MOST POWERFUL TESTS FOR UNIT ROOTS IN GAUSSIAN PANELS WITH CROSS-SECTIONAL DEPENDENCE GENERATED BY COMMON FACTORS

Published online by Cambridge University Press:  29 April 2024

Oliver Wichert Open the ORCID record for Oliver Wichert [Opens in a new window] ,
I. Gaia Becheri Open the ORCID record for I. Gaia Becheri [Opens in a new window] ,
Feike C. Drost Open the ORCID record for Feike C. Drost [Opens in a new window]  and
Ramon van den Akker Open the ORCID record for Ramon van den Akker [Opens in a new window]
Oliver Wichert
Affiliation:
CHARLES RIVER ASSOCIATES
I. Gaia Becheri
Affiliation:
INDEPENDENT RESEARCHER
Feike C. Drost*
Affiliation:
TILBURG UNIVERSITY
Ramon van den Akker
Affiliation:
TILBURG UNIVERSITY
*
Address correspondence to Feike C. Drost, Econometrics Group, CentER, Tilburg University, Tilburg, The Netherlands; e-mail: F.C.Drost@tilburguniversity.edu
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Abstract

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This paper considers testing for unit roots in Gaussian panels with cross-sectional dependence generated by common factors. Within our setup, we can analyze restricted versions of the two prevalent approaches in the literature, that of Moon and Perron (2004, Journal of Econometrics 122, 81–126), who specify a factor model for the innovations, and the PANIC setup proposed in Bai and Ng (2004, Econometrica 72, 1127–1177), who test common factors and idiosyncratic deviations separately for unit roots. We show that both frameworks lead to locally asymptotically normal experiments with the same central sequence and Fisher information. Using Le Cam’s theory of statistical experiments, we obtain the local asymptotic power envelope for unit-root tests. We show that the popular Moon and Perron (2004, Journal of Econometrics 122, 81–126) and Bai and Ng (2010, Econometric Theory 26, 1088–1114) tests only attain the power envelope in case there is no heterogeneity in the long-run variance of the idiosyncratic components. We develop a new test which is asymptotically uniformly most powerful irrespective of possible heterogeneity in the long-run variance of the idiosyncratic components. Monte Carlo simulations corroborate our asymptotic results and document significant gains in finite-sample power if the variances of the idiosyncratic shocks differ substantially among the cross-sectional units.

Type
MISCELLANEA
Information
Econometric Theory , Volume 40 , Issue 5 , October 2024 , pp. 1184 - 1209
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2024. Published by Cambridge University Press

References

REFERENCES

Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59, 817–858.CrossRefGoogle Scholar
Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70, 191–221.CrossRefGoogle Scholar
Bai, J., & Ng, S. (2004). A PANIC attack on unit roots and cointegration. Econometrica , 72, 1127–1177.CrossRefGoogle Scholar
Bai, J., & Ng, S. (2010). Panel unit root tests with cross-section dependence: A further investigation. Econometric Theory , 26, 1088–1114.CrossRefGoogle Scholar
Baltagi, B. H., & Kao, C. (2000). Nonstationary panels, cointegration in panels and dynamic panels: A survey. In Baltagi, B. H., Fomby, T. B., & Hill, R. C. (Eds.), Nonstationary panels, panel cointegration, and dynamic panels (pp. 7–51). Emerald.CrossRefGoogle Scholar
Banerjee, A. (1999). Panel data unit roots and cointegration: An overview. Oxford Bulletin of Economics and Statistics , 61, 607–629.CrossRefGoogle Scholar
Becheri, I. G., Drost, F. C., & Van den Akker, R. (2015a). Asymptotically UMP panel unit root tests—The effect of heterogeneity in the alternatives. Econometric Theory , 31, 539–559.CrossRefGoogle Scholar
Becheri, I. G., Drost, F. C., & Van den Akker, R. (2015b). Unit root tests for cross-sectionally dependent panels: The influence of observed factors. Journal of Statistical Planning and Inference , 160, 11–22.CrossRefGoogle Scholar
Breitung, J., & Pesaran, M. H. (2008). Unit roots and cointegration in panels. In Mátyás, L., & Sevestre, P. (Eds.), The econometrics of panel data (pp. 279–322). Springer.CrossRefGoogle Scholar
Brockwell, P. J., & Davis, R. A. (1991). Time series: Theory and methods . Springer Series in Statistics. Springer.CrossRefGoogle Scholar
Choi, I. (2006). Nonstationary panels. In Hassani, H., Mills, T. C., & Patterson, K. (Eds.), Palgrave handbook of econometrics (pp. 511–539). Palgrave Macmillan.Google Scholar
Choi, I. (2015). Almost all about unit roots: Foundations, developments, and applications . Cambridge University Press.CrossRefGoogle Scholar
Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica , 64, 813–836.CrossRefGoogle Scholar
Gengenbach, C., Palm, F. C., & Urbain, J. P. (2010). Panel unit root tests in the presence of cross-sectional dependencies: Comparison and implications for modelling. Econometric Reviews , 29, 111–145.CrossRefGoogle Scholar
Gutierrez, L. (2006). Panel unit-root tests for cross-sectionally correlated panels: A Monte Carlo comparison. Oxford Bulletin of Economics and Statistics , 68, 519–540.CrossRefGoogle Scholar
Jansson, M. (2008). Semiparametric power envelopes for tests of the unit root hypothesis. Econometrica , 76, 1103–1142.Google Scholar
Juodis, A., & Westerlund, J. (2019). Optimal panel unit root testing with covariates. Econometrics Journal , 22, 57–72.CrossRefGoogle Scholar
Moon, H. R., Perron, B., & Phillips, P. C. B. (2007). Incidental trends and the power of panel unit root tests. Journal of Econometrics , 141, 416–459.CrossRefGoogle Scholar
Moon, H. R., Perron, B., & Phillips, P. C. B. (2014). Point-optimal panel unit root tests with serially correlated errors. Econometrics Journal , 17, 338–372.CrossRefGoogle Scholar
Moon, H. R., & Perron, B. (2004). Testing for a unit root in panels with dynamic factors. Journal of Econometrics , 122, 81–126.CrossRefGoogle Scholar
Müller, U. K., & Elliott, G. (2003). Tests for unit roots and the initial condition. Econometrica , 71, 1269–1286.CrossRefGoogle Scholar
Newey, W. K., & West, K. D. (1994). Automatic lag selection in covariance matrix estimation. Review of Economic Studies , 61, 631–653.CrossRefGoogle Scholar
O’Connell, P. (1998). The overvaluation of purchasing power parity. Journal of International Economics , 44, 1–19.CrossRefGoogle Scholar
Patterson, K. (2011). Unit root tests in time series, Volume 1: Key concepts and problems . Palgrave Macmillan.CrossRefGoogle Scholar
Patterson, K. (2012). Unit root tests in time series, Volume 2: Extensions and developments . Palgrave Macmillan.CrossRefGoogle Scholar
Pesaran, M. H., Smith, L. V., & Yamagata, T. (2013). Panel unit root tests in the presence of a multifactor error structure. Journal of Econometrics , 175, 94–115.CrossRefGoogle Scholar
Phillips, P. C. B., & Magdalinos, T. (2007). Limit theory for moderate deviations from a unit root. Journal of Econometrics , 136, 115–130.CrossRefGoogle Scholar
Phillips, P. C. B., & Moon, H. R. (1999). Linear regression limit theory for nonstationary panel data. Econometrica , 67, 1057–1111.CrossRefGoogle Scholar
Phillips, P. C. B., & Sul, D. (2003). Dynamic panel estimation and homogeneity testing under cross section dependence. Econometrics Journal , 6, 217–259.CrossRefGoogle Scholar
Phillips, P. C. B., & Sul, D. (2007). Bias in dynamic panel estimation with fixed effects, incidental trends and cross section dependence. Journal of Econometrics , 137, 162–188.CrossRefGoogle Scholar
Van den Akker, R., Werker, B. J. M., & Zhou, B. (2023). Hybrid rank-based panel unit root tests. Forthcoming in: Festschrift in honour of Marc Hallin. Available at SSRN: https://ssrn.com/abstract=4613034 CrossRefGoogle Scholar
Van der Vaart, A. W. (2000). Asymptotic statistics . Cambridge University Press.Google Scholar
Westerlund, J. (2015). The power of PANIC. Journal of Econometrics , 185, 495–509.CrossRefGoogle Scholar
Westerlund, J., & Breitung, J. (2013). Lessons from a decade of IPS and LLC. Econometric Reviews , 32, 547–591.CrossRefGoogle Scholar
Yamamoto, Y., & Horie, T. (2023). A cross-sectional method for right-tailed panic tests under a moderately local to unity framework. Econometric Theory , 39, 389–411.CrossRefGoogle Scholar
Zhou, B., Van den Akker, R., & Werker, B. J. M. (2019). Semiparametrically optimal hybrid rank tests for unit roots. Annals of Statistics, 47, 2601–2638.CrossRefGoogle Scholar
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