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Consistent noisy independent component analysis

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  • Bonhomme, Stphane
  • Robin, Jean-Marc

Abstract

We study linear factor models under the assumptions that factors are mutually independent and independent of errors, and errors can be correlated to some extent. Under the factor non-Gaussianity, second-to-fourth-order moments are shown to yield full identification of the matrix of factor loadings. We develop a simple algorithm to estimate the matrix of factor loadings from these moments. We run Monte Carlo simulations and apply our methodology to data on cognitive test scores, and financial data on stock returns.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 149 (2009)
Issue (Month): 1 (April)
Pages: 12-25

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Handle: RePEc:eee:econom:v:149:y:2009:i:1:p:12-25

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Independent Component Analysis Factor Analysis High-order moments Noisy ICA;

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References

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  1. Forni, Mario & Reichlin, Lucrezia, 1998. "Let's Get Real: A Factor Analytical Approach to Disaggregated Business Cycle Dynamics," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 453-73, July.
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  4. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
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  7. Stéphane Bonhomme & Jean-Marc Robin, 2010. "Generalized Non-Parametric Deconvolution with an Application to Earnings Dynamics," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 491-533.
  8. Chudik, Alexander & Pesaran, M. Hashem, 2007. "Infinite Dimensional VARs and Factor Models," IZA Discussion Papers 3206, Institute for the Study of Labor (IZA).
  9. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, April.
  10. 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.
  11. James J. Heckman & Jora Stixrud & Sergio Urzua, 2006. "The Effects of Cognitive and Noncognitive Abilities on Labor Market Outcomes and Social Behavior," NBER Working Papers 12006, National Bureau of Economic Research, Inc.
  12. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-73, September.
  13. Ab Mooijaart, 1985. "Factor analysis for non-normal variables," Psychometrika, Springer, vol. 50(3), pages 323-342, September.
  14. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer, vol. 23(3), pages 187-200, September.
  15. Pal, Manoranjan, 1980. "Consistent moment estimators of regression coefficients in the presence of errors in variables," Journal of Econometrics, Elsevier, vol. 14(3), pages 349-364, December.
  16. John M. Barron & Mark C. Berger & Dan A. Black, 2006. "Selective Counteroffers," Journal of Labor Economics, University of Chicago Press, vol. 24(3), pages 385-410, July.
  17. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  18. Carneiro, Pedro & Hansen, Karsten & Heckman, James, 2003. "Estimating distributions of treatment effects with an application to the returns to schooling and measurement of the effects of uncertainty on college choice," Working Paper Series 2003:9, IFAU - Institute for Evaluation of Labour Market and Education Policy.
  19. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221.
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Citations

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Cited by:
  1. Manuel Arellano & Stéphane Bonhomme, 2009. "Identifying distributional characteristics in random coefficients panel data models," CeMMAP working papers CWP22/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Stéphane Bonhomme & Jean-Marc Robin, 2010. "Generalized Non-Parametric Deconvolution with an Application to Earnings Dynamics," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 491-533.
  3. Matteo Barigozzi & Alessio Moneta, 2012. "Identifying the Independent Sources of Consumption Variation," LEM Papers Series 2012/16, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  4. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2013. "Nonparametric estimation of finite mixtures," Sciences Po Economics Discussion Papers 2013-09, Sciences Po Departement of Economics.
  5. Susanne Schennach, 2012. "Measurement error in nonlinear models- a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Stephane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric estimation of finite measures," CeMMAP working papers CWP11/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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