Bai, Jushan and Li, Kunpeng and Lu, Lina (2014): Estimation and inference of FAVAR models.

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Abstract
The factoraugmented vector autoregressive (FAVAR) model, first proposed by Bernanke, Bovin, and Eliasz (2005, QJE), is now widely used in macroeconomics and finance. In this model, observable and unobservable factors jointly follow a vector autoregressive process, which further drives the comovement of a large number of observable variables. We study the identification restrictions in the presence of observable factors. We propose a likelihoodbased twostep method to estimate the FAVAR model that explicitly accounts for factors being partially observed. We then provide an inferential theory for the estimated factors, factor loadings and the dynamic parameters in the VAR process. We show how and why the limiting distributions are different from the existing results.
Item Type:  MPRA Paper 

Original Title:  Estimation and inference of FAVAR models 
Language:  English 
Keywords:  high dimensional analysis; identification restrictions; inferential theory; likelihoodbased analysis; VAR; impulse response. 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C38  Classification Methods ; Cluster Analysis ; Principal Components ; Factor Models 
Item ID:  60960 
Depositing User:  Kunpeng Li 
Date Deposited:  27. Dec 2014 05:57 
Last Modified:  27. Dec 2014 06:24 
References:  Anderson, T. W. (2003) An Introduction to Multivariate Statistical Analysis, John Wily & Sons. Anderson, T. W. and H. Rubin (1956) Statistical inference in factor analysis, In Proceedings of the third Berkeley Symposium on mathematical statistics and probability: contributions to the theory of statistics, University of California Press. Bai, J. (2003) Inferential theory for factor models of large dimensions. Econometrica, 71(1), 135171. Bai, J. and K. Li (2012a) Statistical analysis of factor models of high dimension, The Annals of Statistics, 40(1), 436465. Bai, J. and K. Li (2012b) Maximum likelihood estimation and inference for approximate factor models of high dimension, Manuscript. Bai, J. and S. Ng (2002) Determining the number of factors in approximate factor models, Econometrica, 70:1, 191221. Bai, J. and S. Ng (2013) Principal components estimation and identification of static factors, Journal of Econometrics,176, 1829. Bernanke, B. S. and J. Boivin (2003) Monetary policy in a datarich environment, Journal of Monetary Economics, 50:3, 525546. Bernanke, B. S., J. Boivin, and P. Eliasz (2005) Measuring the effects of monetary policy: a factoraugmented vector autoregressive (FAVAR) approach, The Quarterly Journal of Economics, 120:1, 387422 Bianchi, F., H., Mumtaz, and P. Surico (2009) The great moderation of the term structure of U.K. interest rates, Jounral of Monetary Economics, 56, 856871. Boivin, J., M.P. Giannoni, and I. Mihov (2009) Sticky prices and monetary policy: evidence from disaggregated US data, American Economic Review, 99:1,350384. Chamberlain, G. and M. Rothschild (1983) Arbitrage, factor structure, and meanvariance analysis on large asset markets, Econometrica, 51:5, 12811304. Christiano, L. J., M. Eichenbaum and C.L. Evans (1999) Monetary policy shocks: What have we learned and to what end? J. B. Taylor and M. Woodford (ed.), Handbook of Macroeconomics, 1, 65148. Chen, L., J. J. Dolado, and J. Gonzalo (2011): Detecting Big Structural Breaks in Large Factor Models, Manuscript, Universidad Carlos III de Madrid. Cheng, X, Z. Liao, F. Schorfheide (2013). Shrinkage estimation of highdimensional factor models with structural instabilities, Department of Economics, U. Pennsylvania. Doan, T., R.B. Litterman, and C.A. Sims (1984) Forecasting and policy analysis using realistic prior distributions, Econometric Reviews, 3, 1100. Doz, C., D. Giannone, and L. Reichlin (2012) A quasimaximum likelihood approach for large approximate dynamic factor models, Review of economics and statistics, 94(4), 10141024. Doz, C., D. Giannone, and L. Reichlin (2011), A TwoStep estimator for large approximate dynamic factor models based on Kalman filtering, Journal of Econometrics, 164:1, 188205. Fan, J. , Liao, Y., and Mincheva, M. (2011) High Dimensional Covariance Matrix Estimation in Approximate Factor Models. The Annals of Statistics, 39, 33203356. Fan, J., Y., Liao and M, Mincheva (2013) Large covariance estimation by thresholding principal orthogonal complements, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75(4), 603680. Forni, M. and L., Gambetti (2010) The dynamic effects of monetary policy: A strctural factor model approach, Jounral of Monetary Economics, 57(2), 203216. Forni, M., M. Hallin, M. Lippi and L. Reichlin (2000) The generalized dynamicfactor model: Identification and estimation. Review of Economics and Statistics, 82(4), 540554. Goncalves, S., and Perron, B. (2014) Bootstrapping factoraugmented regression models, Journal of Econometrics, 182(1), 156173. Hamiltion, J. (1994) Time series analysis, Princeton university press Princeton. Han, X. (2014) Tests for overidentifying restrictions in FactorAugmented VAR models, Journal of Econometrics, Forthcoming. Han, X., and A. Inoue (2011): Tests for Parameter Instability in Dynamic Factor Models, Manuscript, North Carolina State University. Lawley D. N. and A. E. Maxwell (1971) Factor Analysis as a Statistical Method, New York: American Elsevier Publishing Company. Leeper, E. M., C. A. Sims, and T. Zha (1996) What does monetary policy do? Brookings Papers on Economic Activity, 2, 163. Litterman, R. B. (1986) Forecasting with Bayesian vector autoregressions: five years of experience, Journal of Business and Economic Statistics, 4:2538. Ludvigson, S. C. and S. Ng (2009) Macro factors in bond risk premia, Review of Financial Studies, 22(12), 50275067. Moench, E. (2008) Forecasting the yield curve in a datarich environment: A noarbitrage factoraugmented VAR approach, Journal of Econometrics, 146(1), 2643. Quah, D. and T. Sargent (1992). A dynamic index model for large crosssection. Federal Reserve Bank of Minneapolis, Discussion Paper 77. Shintani, M., and Guo, Y. (2011) Finite sample performance of principal components estimators for dynamic factor models: Asymptotic vs. bootstrap approximations, Manuscript, Vanderbilt University. Sims, C. A. (1980) Macroeconomics and Reality, Econometrica, 48:148. Sims, C. A. (1992) Interpreting the macroeconomic time series facts: the effects of monetary policy" European Economic Review, 36, 9751000. Sims, C. A. (1993) A ninevariable probabilistic macroeconomic forecasting model, J.H. Stock and M.W. Watson, eds., Business Cycles, Indicators, and Forecasting (University of Chicago Press for the NBER, Chicago), Ch.7:179204. Stock, J. H. and M. W. Watson (2002) Forecasting using principal components from a large number of predictors, Journal of the American Statistical Association , 97, 11671179. Stock, J. H. and M. W. Watson (2005) Implications of Dynamic Factor Models for VAR Analysis, manuscript. Tsai, H., and R. S., Tsay (2010) Constrained factor models, Jounral of the American Statistical Association, 105, 15931605. Watson, M. W. and R. F., Engle (1983) Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models, Journal of Econometrics, 23(3), 385400. Yamamoto Y. (2011) Bootstrap inference of impulse response functions in factoraugmented vector regression, Manuscript. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/60960 