Handling Distinct Correlated Effects with CCE

Stauskas, Ovidijus and De Vos, Ignace (2024): Handling Distinct Correlated Effects with CCE.

Abstract

The Common Correlated Effects (CCE) estimator is a popular method to estimate panel data regression models with interactive effects. Due to its simplicity in approximating the common factors with cross-section averages of the observables, it lends itself to a wide range of applications. They include static and dynamic models, homogeneous or heterogeneous coefficients or possibly very general types of factor structure. Despite such flexibility, with very few exceptions, CCE properties are usually examined under a restrictive assumption that all the observed variables load on the same set factors, which ensures joint identification of the factor space. In this paper, we explore an empirically relevant scenario when the dependent and explanatory variables are driven by distinct but correlated factors. In doing this, we consider panel dimensions such that T/N is finite even in large samples, which is known to induce an asymptotic bias in CCE setting. We subsequently develop a toolbox to perform asymptotically valid inference in homogeneous and heterogeneous panels.

• Item Type: MPRA Paper
• Language: English
• Keywords: Panel data, bootstrap, interactive effects, CCE, factors, information criterion
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C33 - Panel Data Models ; Spatio-temporal Models; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C38 - Classification Methods ; Cluster Analysis ; Principal Components ; Factor Models

References

Ahn, S. C. and Horenstein, A. R. (2013). Eigenvalue ratio test for the number of factors. Econometrica, 81(3):1203–1227.

Bai, J. (2009). Panel data models with interactive fixed effects. Econometrica, 77(4):1229–1279.

Bai, J. and Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica,70(1):191–221.

Blomquist, J. and Westerlund, J. (2013). Testing slope homogeneity in large panels with serial correlation. Economics Letters, 121(3):374–378.

Chudik, A., Mohaddes, K., Pesaran, M. H., and Raissi, M. (2017). Is there a debt-threshold effect on output growth? Review of Economics and Statistics, 99(1):135–150.

Chudik, A., Pesaran, M., and Tosetti, E. (2011). Weak and strong cross-section dependence and estimation of large panels. The Econometrics Journal, 14(1):C45–C90.

Cui, G., Norkute, M., Sarafidis, V., and Yamagata, T. (2022). Two-stage instrumental variable estimation of linear panel data models with interactive effects. The Econometrics Journal, 25(2):340–361.

Davison, A. C. and Hinkley, D. V. (1997). Bootstrap methods and their application. Number 1. Cambridge university press.

De Vos, I., Everaert, G., and Sarafidis, V. (2023). A method to evaluate the rank condition for cce estimators. Econometric Reviews, pages 1–33.

De Vos, I. and Stauskas, O. (2024). Cross-section bootstrap for cce regressions. Journal of Econometrics, 240(1):105648.

De Vos, I. and Westerlund, J. (2019). On cce estimation of factor-augmented models when regressors are not linear in the factors. Economics Letters, 178:5–7.

Djogbenou, A., Goncalves, S., and Perron, B. (2015). Bootstrap inference in regressions with estimated factors and serial correlation. Journal of Time Series Analysis, 36(3):481–502.

Eberhardt, M. and Presbitero, A. F. (2015). Public debt and growth: Heterogeneity and non-linearity. Journal of international Economics, 97(1):45–58.

Eberhardt, M. and Teal, F. (2011). Econometrics for grumblers: a new look at the literature on cross country growth empirics. Journal of Economic Surveys, 25(1):109–155.

Goncalves, S. and Perron, B. (2014). Bootstrapping factor-augmented regression models. Journal of Econometrics,182(1):156 – 173. Causality, Prediction, and Specification Analysis: Recent Advances and Future Directions.

Jiang, B., Yang, Y., Gao, J., and Hsiao, C. (2021). Recursive estimation in large panel data models: Theory and practice. Journal of Econometrics, 224(2):439–465.

Juodis, A. (2022). A regularization approach to common correlated effects estimation. Journal of Applied Econometrics, 37(4):788–810.

Juodis, A., Karabiyik, H., and Westerlund, J. (2021). On the robustness of the pooled cce estimator. Journal of Econometrics, 220(2):325–348.

Kapetanios, G. (2008). A bootstrap procedure for panel data sets with many cross-sectional units. Econometrics Journal, 11(2):377–395.

Karabiyik, H., Reese, S., and Westerlund, J. (2017). On the role of the rank condition in CCE estimation of factor-augmented panel regressions. Journal of Econometrics, 197(1):60 – 64.

Karavias, Y., Narayan, P. K., and Westerlund, J. (2023). Structural breaks in interactive effects panels and the stock market reaction to covid-19. Journal of Business & Economic Statistics, 41(3):653–666.

Margaritella, L. and Westerlund, J. (2023). Using information criteria to select averages in cce. The Econometrics Journal, page utad009.

Moon, H. R. and Weidner, M. (2015). Linear regression for panel with unknown number of factors as interactive fixed effects. Econometrica, 83(4):1543–1579.

Norkute, M. and Westerlund, J. (2021). The factor analytical approach in near unit root interactive effects panels. Journal of Econometrics, 221(2):569–590.

Pesaran, M. (2006). Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure. Econometrica, 74(4):967–1012.

Pesaran, M. and Tosetti, E. (2011). Large panels with common factors and spatial correlation. Journal of Econometrics, 161(2):182–202.

Pesaran, M. H. and Yamagata, T. (2008). Testing slope homogeneity in large panels. Journal of econometrics,142(1):50–93.

Phillips, P. C. and Moon, H. R. (1999). Linear regression limit theory for nonstationary panel data. Econometrica, 67(5):1057–1111.

Stauskas, O. (2022). Complete theory for cce under heterogeneous slopes and general unknown factors. Oxford Bulletin of Economics and Statistics.

Westerlund, J. (2018). Cce in panels with general unknown factors. The Econometrics Journal, 21(3):264–276. Westerlund, J. and Petrova, Y. (2018). Asymptotic collinearity in cce estimation of interactive effects models. Economic Modelling, 70:331–337.

Westerlund, J., Petrova, Y., and Norkute, M. (2019). Cce in fixed-t panels. Journal of applied econometrics, 34(5):746–761.

Westerlund, J. and Urbain, J. (2013). On the estimation and inference in factor-augmented panel regressions with correlated loadings. Economics Letters, 119(3):247–250.

Westerlund, J. and Urbain, J.-P. (2015). Cross-sectional averages versus principal components. Journal of Econometrics, 185(2):372–377.