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Linear regression for panel with unknown number of factors as interactive fixed effects

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  • Hyungsik Roger Moon
  • Martin Weidner

    (Institute for Fiscal Studies and UCL)

Abstract

In this paper we study the least sqares (LS) estimator in a linear panel regression model with interactive fixed effects for asymptotics where both the number of time periods and the number of cross-sectional units go to infinity. Under appropriate assumptions we show that the limiting distribution of the LS estimator for the regression coefficients is independent of the number of interactive fixed effects used in the estimation, as long as this number does not fall below the true number of interactive fixed effects present in the data. The important practical implication of this result is that for inference on the regression coefficients one does not necessarily need to estimate the number of interactive effects consistently, but can rely on an upper bound of this number to calculate the LS estimator. Supplementary material for this paper is available here.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP49/13.

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Date of creation: Oct 2013
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Handle: RePEc:ifs:cemmap:49/13

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  1. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
  2. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, 07.
  3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  4. Chudik, Alexander & Pesaran, Hashem & Tosetti, Elisa, 2009. "Weak and strong cross section dependence and estimation of large panels," Working Paper Series 1100, European Central Bank.
  5. Bai, Z. D. & Silverstein, Jack W. & Yin, Y. Q., 1988. "A note on the largest eigenvalue of a large dimensional sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 166-168, August.
  6. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, vol. 56(6), pages 1371-95, November.
  7. Silverstein, Jack W., 1989. "On the eigenvectors of large dimensional sample covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 1-16, July.
  8. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
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Cited by:
  1. Alexander Chudik & M. Hashem Pesaran, 2013. "Common Correlated Effects Estimation of Heterogeneous Dynamic Panel Data Models with Weakly Exogenous Regressors," CESifo Working Paper Series 4232, CESifo Group Munich.
  2. Hyungsik Roger Moon & Matthew Shum & Martin Weidner, 2012. "Estimation of random coefficients logit demand models with interactive fixed effects," CeMMAP working papers CWP08/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Laurent Gobillon & Thierry Magnac, 2013. "Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls," PSE Working Papers halshs-00849071, HAL.
  4. repec:hal:wpaper:halshs-00849071 is not listed on IDEAS
  5. Iván Fernández-Val & Martin Weidner, 2013. "Individual and time effects in nonlinear panel models with large N,T," CeMMAP working papers CWP60/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Bai, Jushan, 2013. "Likelihood approach to dynamic panel models with interactive effects," MPRA Paper 50267, University Library of Munich, Germany.
  7. Stéphane Bonhomme & Elena Manresa, 2012. "Grouped Patterns Of Heterogeneity In Panel Data," Working Papers wp2012_1208, CEMFI.
  8. Hyungsik Roger Moon & Martin Weidner, 2013. "Dynamic linear panel regression models with interactive fixed effects," CeMMAP working papers CWP63/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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