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Exponent of Cross-sectional Dependence for Residuals

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  • Natalia Bailey
  • George Kapetanios
  • M. Hashem Pesaran

Abstract

In this paper we focus on estimating the degree of cross-sectional dependence in the error terms of a classical panel data regression model. For this purpose we propose an estimator of the exponent of cross-sectional dependence denoted by α; which is based on the number of non-zero pair-wise cross correlations of these errors. We prove that our estimator, ᾶ; is consistent and derive the rate at which ᾶ approaches its true value. We evaluate the finite sample properties of the proposed estimator by use of a Monte Carlo simulation study. The numerical results are encouraging and supportive of the theoretical findings. Finally, we undertake an empirical investigation of α for the errors of the CAPM model and its Fama-French extensions using 10-year rolling samples from S&P 500 securities over the period Sept 1989 - May 2018.

Suggested Citation

  • Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2018. "Exponent of Cross-sectional Dependence for Residuals," CESifo Working Paper Series 7223, CESifo.
    • Handle: RePEc:ces:ceswps:_7223
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    References listed on IDEAS

    as
    1. Pesaran, M. H. & Yamagata, T., 2012. "Testing CAPM with a Large Number of Assets (Updated 28th March 2012)," Cambridge Working Papers in Economics 1210, Faculty of Economics, University of Cambridge.
    2. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
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    4. Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2016. "Exponent of Cross‐Sectional Dependence: Estimation and Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(6), pages 929-960, September.
    5. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    6. A. Chudik & G. Kapetanios & M. Hashem Pesaran, 2018. "A One Covariate at a Time, Multiple Testing Approach to Variable Selection in High‐Dimensional Linear Regression Models," Econometrica, Econometric Society, vol. 86(4), pages 1479-1512, July.
    7. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    8. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
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    11. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    12. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 45-90, February.
    13. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-1323, September.
    14. Eugene F. Fama & Kenneth R. French, 2004. "The Capital Asset Pricing Model: Theory and Evidence," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 25-46, Summer.
    15. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    16. Pesaran, M. Hashem & Yamagata, Takashi, 2012. "Testing CAPM with a Large Number of Assets," IZA Discussion Papers 6469, Institute of Labor Economics (IZA).
    17. Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
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    Cited by:

    1. Arnab Bhattacharjee & Jan Ditzen & Sean Holly, 2022. "Spatial and Spatio-Temporal Error Correction, Networks and Common Correlated Effects," Advances in Econometrics, in: Essays in Honor of M. Hashem Pesaran: Panel Modeling, Micro Applications, and Econometric Methodology, volume 43, pages 37-60, Emerald Group Publishing Limited.
    2. Keil, Sascha, 2024. "Competing for manufacturing value added: How strong is competitive cost pressure on sectoral level?," Structural Change and Economic Dynamics, Elsevier, vol. 69(C), pages 197-212.
    3. Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2021. "Measurement of factor strength: Theory and practice," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 587-613, August.
    4. Telila, Henok Fasil, 2023. "Frontier markets sovereign risk: New evidence from spatial econometric models," Finance Research Letters, Elsevier, vol. 58(PD).
    5. Ge, S., 2020. "Text-Based Linkages and Local Risk Spillovers in the Equity Market," Cambridge Working Papers in Economics 20115, Faculty of Economics, University of Cambridge.
    6. Arnab Bhattacharjee & Tapabrata Maiti, 2019. "P. C. Mahalanobis in the Context of Current Econometrics Research," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-11, September.
    7. Yu-Ke, Chen & Hassan, Muhammad Shahid & Kalim, Rukhsana & Mahmood, Haider & Arshed, Noman & Salman, Muhammad, 2022. "Testing asymmetric influence of clean and unclean energy for targeting environmental quality in environmentally poor economies," Renewable Energy, Elsevier, vol. 197(C), pages 765-775.
    8. Tullio Gregori & Marco Giansoldati, 2023. "Do current and capital account liberalizations affect economic growth in the long run?," Empirical Economics, Springer, vol. 65(1), pages 247-273, July.
    9. Ge, Shuyi & Li, Shaoran & Linton, Oliver, 2023. "News-implied linkages and local dependency in the equity market," Journal of Econometrics, Elsevier, vol. 235(2), pages 779-815.
    10. Henok Fasil Telila, 2024. "Frontier markets sovereign risk: New evidence from spatial econometric models," French Stata Users' Group Meetings 2024 10, Stata Users Group.
    11. Valizadeh, Pourya & Fischer, Bart L. & Bryant, Henry L., 2022. "Investigating the Differential Effects of the Economy on SNAP Participation: A Factor Model Approach," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322367, Agricultural and Applied Economics Association.
    12. Floros Flouros & Victoria Pistikou & Vasilios Plakandaras, 2022. "Geopolitical Risk as a Determinant of Renewable Energy Investments," Energies, MDPI, vol. 15(4), pages 1-21, February.
    13. Kapetanios, G. & Pesaran, M.H. & Reese, S., 2021. "Detection of units with pervasive effects in large panel data models," Journal of Econometrics, Elsevier, vol. 221(2), pages 510-541.

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    More about this item

    Keywords

    pair-wise correlations; cross-sectional dependence; cross-sectional averages; weak and strong factor models; CAPM and Fama-French factors;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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