Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-25T08:49:12.219Z Has data issue: false hasContentIssue false
  • English
  • Français

TESTS FOR PARAMETER INSTABILITY IN DYNAMIC FACTOR MODELS

Published online by Cambridge University Press:  15 September 2014

Xu Han  and
Atsushi Inoue
Xu Han*
Affiliation:
City University of Hong Kong
Atsushi Inoue*
Affiliation:
Vanderbilt University and Tohoku University
*
*Address correspondence to Xu Han, Department of Economics and Finance, City University of Hong Kong, Kowloon, Hong Kong SAR; e-mail: xuhan25@cityu.edu.hk or to Atsushi Inoue, Department of Economics, Vanderbilt University, Nashville, TN 37235, USA; email: atsushi.inoue@vanderbilt.edu.
*Address correspondence to Xu Han, Department of Economics and Finance, City University of Hong Kong, Kowloon, Hong Kong SAR; e-mail: xuhan25@cityu.edu.hk or to Atsushi Inoue, Department of Economics, Vanderbilt University, Nashville, TN 37235, USA; email: atsushi.inoue@vanderbilt.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we develop tests for structural breaks of factor loadings in dynamic factor models. We focus on the joint null hypothesis that all factor loadings are constant over time. Because the number of factor loading parameters goes to infinity as the sample size grows, conventional tests cannot be used. Based on the fact that the presence of a structural change in factor loadings yields a structural change in second moments of factors obtained from the full sample principal component estimation, we reduce the infinite-dimensional problem into a finite-dimensional one and our statistic compares the pre- and postbreak subsample second moments of estimated factors. Our test is consistent under the alternative hypothesis in which a fraction of or all factor loadings have structural changes. The Monte Carlo results show that our test has good finite-sample size and power.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 5 , October 2015 , pp. 1117 - 1152
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andrews, D.W.K. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821–856.CrossRefGoogle Scholar
Andrews, D.W.K. & Ploberger, W. (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383.CrossRefGoogle Scholar
Bai, J. (1997) Estimating multiple breaks one at a time. Econometric Theory 13, 315–352.CrossRefGoogle Scholar
Bai, J. (2003) Inferential theory for factor models of large dimensions. Econometrica 71, 135–172.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2002) Determining the number of factors in approximate factor models. Econometrica 70, 191–221.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2010) Instrumental variable estimation in a data rich environment. Econometric Theory 26, 1577–1606.CrossRefGoogle Scholar
Banerjee, A. & Marcellino, M. (2008) Forecasting Macroeconomic Variables Using Diffusion Indexes in Short Samples with Structural Change. CEPR Working paper 6706.CrossRefGoogle Scholar
Bates, B., Plagborg-Moller, M., Stock, J., & Watson, M. (2012) Consistent factor estimation in dynamic factor models with structural instability. Journal of Econometrics, forthcoming.Google Scholar
Bernanke, B.S., Boivin, J., & Eliasz, P. (2005) Measuring the effects of monetary policy: A Factor-Augmented Vector Autoregressive (FAVAR) approach. Quarterly Journal of Economics 120, 387–422.Google Scholar
Boivin, J. & Giannoni, M. (2006) DSGE Models in a Data-Rich Environment. NBER Working paper no. 12772.Google Scholar
Breitung, J. & Eickmeier, S. (2011) Testing for structural breaks in dynamic factor models. Journal of Econometrics 163, 71–84.CrossRefGoogle Scholar
Chen, L., Dolado, J., & Gonzalo, J. (2012) Detecting Big Structural Breaks in Large Factor Models. MPRA Working paper.Google Scholar
Cheng, X., Liao, Z., & Schorfheide, F. (2013) Shrinkage Estimation of Dynamic Factor Models with Structural Instabilities. Manuscript, University of Pennsylvania.CrossRefGoogle Scholar
Choi, I. (2012) Efficient estimation of factor models. Econometric Theory 28, 274–308.CrossRefGoogle Scholar
Eickmeier, S., Lemke, W., & Marcellino, M. (2011) Classical Time-Varying FAVAR Models – Estimation, Forecasting and Structural Analysis. CEPR Discussion paper DP8321.CrossRefGoogle Scholar
Hall, A.R. (2000) Covariance matrix estimation and the power of the overidentifying restrictions test. Econometrica 68, 1517–1527.CrossRefGoogle Scholar
Han, X. & Inoue, A. (2014) Tests for Parameter Instability in Dynamic Factor Models. Manuscript, City University of Hong Kong and Southern Methodist University. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2314338.Google Scholar
Ledoit, O. & Wolf, M. (2004) A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis 88, 365–411.CrossRefGoogle Scholar
Newey, W.K. & West, K.D. (1994) Automatic lag selection in covariance matrix estimation. The Review of Economic Studies 61(4), 631–653.CrossRefGoogle Scholar
Onatski, A. (2010) Determining the number of factors from empirical distribution of eigenvalues. The Review of Economics and Statistics 92(4), 1004–1016.CrossRefGoogle Scholar
Sargent, T.J. & Sims, C.A. (1977) Business cycle modelling without pretending to have too much a-priori economic theory. In Sims et al. . (eds.), New Methods in Business Cycle Research. Federal Reserve Bank of Minneapolis.Google Scholar
Stock, J.H. & Watson, M.W. (1996) Evidence on structural instability in macroeconomic time series relations. Journal of Business and Economic Statistics 14, 11–30.Google Scholar
Stock, J.H. & Watson, M.W. (2002a) Macroeconomic forecasting using diffusion indexes. Journal of Business and Economic Statistics 20, 147–162.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2002b) Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association 97, 1167–1179.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2005) Implications of Dynamic Factor Models for VAR Analysis. NBER Working paper no. 11467.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2009) Forecasting in dynamic factor models subject to structural instability. In Castle, J. & Shephard, N. (eds.), The Methodology and Practice of Econometrics, A Festschrift in Honour of Professor David F. Hendry. Oxford University Press.Google Scholar
White, H. (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 817–838.CrossRefGoogle Scholar