Chen, Liang (2012): Identifying observed factors in approximate factor models: estimation and hypothesis testing.
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Despite their popularities in recent years, factor models have long been criticized for the lack of identification. Even when a large number of variables are available, the factors can only be consistently estimated up to a rotation. In this paper, we try to identify the underlying factors by associating them to a set of observed variables, and thus give interpretations to the orthogonal factors estimated by the method of Principal Components. We first propose a estimation procedure to select a set of observed variables, and then test the hypothesis that true factors are exact linear combinations of the selected variables. Our estimation method is shown to able to correctly identity the true observed factor even in the presence of mild measurement errors, and our test statistics are shown to be more general than those of Bai and Ng (2006). The applicability of our methods in finite samples and the advantages of our tests are confirmed by simulations. Our methods are also applied to the returns of portfolios to identify the underlying risk factors.
|Item Type:||MPRA Paper|
|Original Title:||Identifying observed factors in approximate factor models: estimation and hypothesis testing|
|English Title:||Identifying observed factors in approximate factor models: estimation and hypothesis testing|
|Keywords:||factor models; observed factors; estimation; hypothesis testing; Fama-French three factors|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General
C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics
|Depositing User:||Liang Chen|
|Date Deposited:||20. Mar 2012 18:58|
|Last Modified:||18. Feb 2013 16:43|
Altug, S. (1989). Time-to-build and aggregate fluctuations: some new evidence. International Economic Review, 889–920.
Andrews, D. (2003). Tests for parameter instability and structural change with unknown change point: a corrigendum. Econometrica, 395–397.
Andrews, D. W. K. (1993). Tests for parameter instability and structural change with unknown change point. Economet-rica 61(4), pp. 821–856.
Bai, J. (2003). Inferential theory for factor models of large dimensions. Econometrica 71(1), 135–171.
Bai, J. (2009). Panel data models with interactive fixed effects. Econometrica 77(4), 1229–1279.
Bai, J. and S. Ng (2002). Determining the number of factors in approximate factor models. Econometrica 70(1), 191–221.
Bai, J. and S. Ng (2006). Evaluating latent and observed factors in macroeconomics and finance. Journal of Economet-rics 131(1-2), 507–537.
Bernanke, B., J. Boivin, and P. Eliasz (2005). Measuring the effects of monetary policy: a factor-augmented vector autoregressive (favar) approach. The Quarterly Journal of Economics 120(1), 387.
Boivin, J. and M. Giannoni (2006). Dsge models in a data-rich environment. Technical report, National Bureau of Economic Research.
Breitung, J. and S. Eickmeier (2011). Testing for structural breaks in dynamic factor models. Journal of Economet- rics 163(1), 71 – 84.
Chamberlain, G. and M. Rothschild (1983). Arbitrage, factor structure, and mean-variance analysis on large asset mar-kets. Econometrica 51(5), 1281–1304.
Chen, L., J. Dolado, and J. Gonzalo (2011). Detecting big structural breaks in large factor models. manuscript, Universidad Carlos III de Madrid.
Chen, N., R. Roll, and S. Ross (1986). Economic forces and the stock market. Journal of Business, 383–403.
Fama, E. and K. French (1993). Common risk factors in the returns on stocks and bonds. Journal of financial eco- nomics 33(1), 3–56.
Forni, M., D. Giannone, M. Lippi, and L. Reichlin (2009). Opening the black box: Structural factor models with large cross-sections. Econometric Theory 25(5), 1319–1347.
Han, X. and A. Inoue (2011). Tests for parameter stability in dynamic factor models. manuscript, NC State Univserity. Kryshko, M. (2011). Data-rich dsge and dynamic factor models.
Lewbel, A. (1991). The rank of demand systems: theory and nonparametric estimation. Econometrica: Journal of the Econometric Society, 711–730.
Onatski, A. (2009a). Asymptotics of the principal components estimator of large factor models with weak factors. manuscript, Columbia University.
Onatski, A. (2009b). Testing hypotheses about the number of factors in large factor models. Econometrica 77(5), 1447–1479.
Onatski, A. (2010). Determining the number of factors from empirical distribution of eigenvalues. The Review of Economics and Statistics 92(4), 1004–1016.
Pesaran, M. (2006). Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74(4), 967–1012.
Sargent, T. (1989). Two models of measurements and the investment accelerator. The Journal of Political Economy, 251–287.
Shanken, J. and M. Weinstein (2006). Economic forces and the stock market revisited. Journal of Empirical Fi- nance 13(2), 129–144.
Stock, J. and M. Watson (2002a). Forecasting using principal components from a large number of predictors. Journal of the American statistical association 97(460), 1167–1179.
Stock, J. and M. Watson (2003). Has the business cycle changed and why?
Stock, J. and M.Watson (2009). Forecasting in dynamic factor models subject to structural instability. The Methodology and Practice of Econometrics. A Festschrift in Honour of David F. Hendry, 173–205.
Stock, J. H. and M. W. Watson (2002b). Macroeconomic forecasting using diffusion indexes. Journal of Business and Economic Statistics 20(2), 147–162. 3