Bai, Jushan and Wang, Peng (2012): Identification and estimation of dynamic factor models.
Download (667kB) | Preview
We consider a set of minimal identification conditions for dynamic factor models. These conditions have economic interpretations, and require fewer number of restrictions than when putting in a static-factor form. Under these restrictions, a standard structural vector autoregression (SVAR) with or without measurement errors can be embedded into a dynamic factor model. More generally, we also consider overidentification restrictions to achieve efficiency. General linear restrictions, either in the form of known factor loadings or cross-equation restrictions, are considered. We further consider serially correlated idiosyncratic errors with heterogeneous coefficients. A numerically stable Bayesian algorithm for the dynamic factor model with general parameter restrictions is constructed for estimation and inference. A square-root form of Kalman filter is shown to improve robustness and accuracy when sampling the latent factors. Confidence intervals (bands) for the parameters of interest such as impulse responses are readily computed. Similar identification conditions are also exploited for multi-level factor models, and they allow us to study the spill-over effects of the shocks arising from one group to another.
|Item Type:||MPRA Paper|
|Original Title:||Identification and estimation of dynamic factor models|
|Keywords:||dynamic factor models; multi-level factor models; impulse response function; spill-over effects|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - 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 > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General
|Depositing User:||Peng Wang|
|Date Deposited:||30. Apr 2012 01:28|
|Last Modified:||12. Feb 2013 14:38|
 D. Amengual and M. Watson. Consistent estimation of the number of dynamic factors in large N and T panel. Journal of Business and Economic Statistics, 25(1):91–96, 2007.
 T.W. Anderson. An Introduction to Multivariate Statistical Analysis. New York: Wiley, 1984.
 T.W. Anderson and H. Rubin. Statistical inference in factor analysis. In In J. Neyman (Ed.): Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability., volume 5, pages 111–150. Univ. of California Press, 1956.
 J. Bai. Inferential theory for factor models of large dimensions. Econometrica, 71(1):135–172, 2003.
 J. Bai and S. Ng. Determining the number of factors in approximate factor models. Econometrica, 70(1):191–221, 2002.
 J. Bai and S. Ng. Determining the number of primitive shocks in factor models. Journal of Business and Economic Statistics, 25(1):52–60, 2007.
 J. Bai and S. Ng. Principal components estimation and identification of the factors. Working paper, 2010.
 J.O. Berger and L.R. Pericchi. The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91(433):109–122, 1996.
 B. Bernanke, J. Boivin, and P. Eliasz. Measuring monetary policy: a factor augmented vector autoregressive (FAVAR) approach. Quarterly Journal of Economics, 120(1):387–422, 2005.
 G.J. Bierman. Factorization methods for discrete sequential estimation. Dover Books on Mathematics, Dover Publications, 1977.
 J. Breitung and J. Tenhofen. GLS estimation of dynamic factor models. Journal of the American Statistical Association, 106(495):1150–1166, 2011.
 C.K. Carter and R. Kohn. On Gibbs sampling for state space models. Biometrika, 81:541–553, 1994.
 S. Chib. Marginal likelihood from the Gibbs output. Journal of the American Statistical Association, 90 (432):1313–1321, 1995.
 I. Choi. Efficient estimation of factor models. Econometric Theory, 28(2):274–308, 2012.
 T. Cogley and T.J. Sargent. Drifts and volatilities: monetary policies and outcomes in the post WWII US. Review of Economic Dynamics, 8 (2):262–302, 2005.
 G. Connor and R. Korajzcyk. Performance measurement with the arbitrage pricing theory: a new framework for analysis. Journal of Financial Economics,15:373–394, 1986.
 M.J. Crucini, M.A. Kose, and C. Otrok. What are the driving forces of international business cycles? Review of Economic Dynamics, 14:156–175, 2011.
 M. Del Negro and C. Otrok. Dynamic factor models with time-varying parameters: measuring changes in international business cycles. Working paper, 2008.
 F.X. Diebold, C. Li, and V. Yue. Global yield curve dynamics and interactions: a generalized Nelson-Siegel approach. Journal of Econometrics, 146(2):351–363, 2008.
 C. Doz, D. Giannone, and L. Reichlin. A quasi-maximum likelihood approach for large approximate dynamic factor models. forthcoming, Review of Economics and Statistics, 2011.
 G. Evensen. Data assimilation: the ensemble Kalman filter. 2nd ed. Springer, 2009.
 M. Forni, M. Hallin, M. Lippi, and L. Reichlin. The generaized dynamic factor model: identification and estimation. Review of Economics and Statistics, 82(4):540–554, 2000.
 J.F. Geweke. The dynamic factor analysis of economic time series. In In D. J. Aigner and A. S. Goldberger (Eds.): Latent Variables in Socio-economic Models. Amsterdam: North-Holland, 1977.
 A.W. Gregory and A.C. Head. Common and country-specific fluctuations in productivity, investment, and the current account. Journal of Monetary Economics, 44(3):423–451, 1999.
 B. Junbacker and S.J. Koopman. Likelihood-based analysis for dynamic factor models. Working paper, 2008.  C. Kim and C. Nelson. State Space Models With Regime Switching: Classical and Gibbs Sampling Approaches With Applications. Massachusetts: MIT Press, 1999.
 M.A. Kose, C. Otrok, and C.H. Whiteman. International business cycles: World, region, and country-specific factors. American Economic Review, 93(4):1216–1239, 2003.
 D.N. Lawley and A.E. Maxwell. Factor Analysis in a Statistical Method. Butterworth, London, 1971.
 E. Moench, S. Ng, and S. Potter. Dynamic hierarchical factor models. Working paper, 2011.
 A. O’Hagan. Fractional Bayes factors for model comparison. Journal of the Royal Statistical Society. Series B (Methodological), 57(1):99–138, 1995.
 D. Quah and T. Sargent. A dynamic index model for large cross sections. In Business Cycles, Indicators and Forecasting, NBER Chapters, pages 285–310. National Bureau of Economic Research, Inc, December 1993.
 C.A. Sims and T. Zha. Error bands for impulse responses. Econometrica, 67(5):1113–1156, 1999.
 J.H. Stock and M.W. Watson. Diffusion indexes. NBER Working Paper 6702, 1998.
 J.H. Stock and M.W. Watson. Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97:1167–1179, 2002.
 J.H. Stock and M.W. Watson. Implications of dynamic factor models for VAR analysis. NBER Working Paper 11467, 2005.
 M.K. Tippett, J.L. Anderson, C.H. Bishop, T.M. Hamill, and J.S. Whitaker. Ensemble square root filters. Monthly Weather Review, 131:1485–1490, 2003.
 P. Wang. Large dimensional factor models with a multi-level factor structure: identification, estimation, and inference. Working paper, 2010.
 M.W. Watson and R.F. Engle. Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models. Journal of Econometrics, 23(3):385–400, 1983.
 M. West and J. Harrison. Bayesian Forecasting and Dynamic Models. Springer Series in Statistics, 1997.
 J.H. Wright. Term premia and inflation uncertainty: empirical evidence from an international panel dataset. American Economic Review, 101(4):1514–1534, 2011.
 A. Zellner. An introduction to Bayesian inference in econometrics. John Wiley and Sons, Inc, 1971.