×

Testing for cross-sectional dependence in a panel factor model using the wild bootstrap \(F\) test. (English) Zbl 1416.62387

Summary: This paper considers testing for cross-sectional dependence in a panel factor model. Based on the model considered by J. Bai [Econometrica 71, No. 1, 135–171 (2003; Zbl 1136.62354)], we investigate the use of a simple \(F\) test for testing for cross-sectional dependence when the factor may be known or unknown. The limiting distributions of these \(F\) test statistics are derived when the cross-sectional dimension and the time-series dimension are both large. The main contribution of this paper is to propose a wild bootstrap \(F\) test which is shown to be consistent and which performs well in Monte Carlo simulations especially when the factor is unknown.

MSC:

62J05 Linear regression; mixed models
62F03 Parametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
62G09 Nonparametric statistical resampling methods

Citations:

Zbl 1136.62354
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Andrews DWK (2005) Cross-section regression with common shocks. Econometrica 73:1551-1585 · Zbl 1153.91665 · doi:10.1111/j.1468-0262.2005.00629.x
[2] Akritas M, Arnold S (2000) Asymptotics for analysis of variance when the number of levels is large. J Am Stat Assoc 449:212-226 · Zbl 0996.62064 · doi:10.1080/01621459.2000.10473915
[3] Bai J (2003) Inferential theory for factor models of large dimensions. Econometrica 71:135-171 · Zbl 1136.62354 · doi:10.1111/1468-0262.00392
[4] Bai J (2009) Panel data models with interactive fixed effects. Econometrica 77:1229-1279 · Zbl 1183.62196 · doi:10.3982/ECTA6135
[5] Bai J, Kao C, Ng S (2009) Panel cointegration with global stochastic trends. J Econom 149:82-99 · Zbl 1429.62381 · doi:10.1016/j.jeconom.2008.10.012
[6] Bai J, Ng S (2002) Determining the number of factors in approximate factor models. Econometrica 70: 191-221 · Zbl 1103.91399
[7] Bathke A (2004) The ANOVA F test can still be used in some balanced designs with unequal variances and nonnormal data. J Stat Plan Inference 126:413-422 · Zbl 1076.62073 · doi:10.1016/j.jspi.2003.09.010
[8] Boos DD, Brownie C (1995) ANOVA and rank tests when the number of treatments is large. Stat Probab Lett 23:183-191 · Zbl 0819.62037 · doi:10.1016/0167-7152(94)00112-L
[9] Davidson R, Flachaire E (2008) Wild bootstrap, tamed at last. J Econom 146:162-169 · Zbl 1418.62183 · doi:10.1016/j.jeconom.2008.08.003
[10] Gonçalves S, Perron B (2010) Bootstrapping factor-augmented regression models. Université de Montréal, Working Paper · Zbl 1311.62040
[11] Johnson NL, Kotz S, Balakrishinan N (1995) Distributions in statistics: continuous univariate distributions. Wiley, New York
[12] Krämer W (1989) On the robustness of the F-test to autocorrelation among disturbances. Econ Lett 30:37-40 · Zbl 1328.62426 · doi:10.1016/0165-1765(89)90153-5
[13] Krämer W, Michels S (1997) Autocorrelation- and heteroskedasticity-consistent T-values with trending data. J Econom 76:141-147 · Zbl 0873.62067 · doi:10.1016/0304-4076(95)01786-0
[14] Liu RY (1988) Bootstrap procedures under some non-IID models. Ann Stat 16:1696-1708 · Zbl 0655.62031 · doi:10.1214/aos/1176351062
[15] Mammen E (1993a) When does bootstrap work?. Asymptotic results and simulations. Springer, New York · Zbl 0760.62038
[16] Mammen E (1993b) Bootstrap and wild bootstrap for high dimensional linear models. Ann Stat 21:255-285 · Zbl 0771.62032 · doi:10.1214/aos/1176349025
[17] Orme CD, Yamagata T (2006) The asymptotic distribution of the F-test statistic for individual effects. Econom J 9:404-422 · Zbl 1106.62020 · doi:10.1111/j.1368-423X.2006.00191.x
[18] Schott JR (2005) Testing for complete independence in high dimensions. Biometrika 92:951-956 · Zbl 1151.62327 · doi:10.1093/biomet/92.4.951
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.