Determining the Number of Primitive Shocks in Factor Models
- 1 January 2007
- journal article
- Published by Taylor & Francis Ltd in Journal of Business & Economic Statistics
- Vol. 25 (1), 52-60
- https://doi.org/10.1198/073500106000000413
Abstract
A widely held but untested assumption underlying macroeconomic analysis is that the number of shocks driving economic fluctuations, q, is small. In this article we associate q with the number of dynamic factors in a large panel of data. We propose a methodology to determineq without having to estimate the dynamic factors. We first estimate a VAR in r static factors, where the factors are obtained by applying the method of principal components to a large panel of data, then compute the eigenvalues of the residual covariance or correlation matrix. We then test whether their eigenvalues satisfy an asymptotically shrinking bound that reflects sampling error. We apply the procedure to determine the number of primitive shocks in a large number of macroeconomic time series. An important aspect of the present analysis is to make precise the relationship between the dynamic factors and the static factors, which is a result of independent interest.Keywords
This publication has 18 references indexed in Scilit:
- The Generalized Dynamic Factor ModelJournal of the American Statistical Association, 2005
- Forecasting Using Principal Components From a Large Number of PredictorsJournal of the American Statistical Association, 2002
- Macroeconomic Forecasting Using Diffusion IndexesJournal of Business & Economic Statistics, 2002
- The Generalized Dynamic-Factor Model: Identification and EstimationThe Review of Economics and Statistics, 2000
- TESTS OF RANKEconometric Theory, 2000
- Inferring the rank of a matrixJournal of Econometrics, 1997
- On the Asymptotic Properties of LDU-Based Tests of the Rank of a MatrixJournal of the American Statistical Association, 1996
- Testing the Rank and Definiteness of Estimated Matrices With Applications to Factor, State-Space and ARMA ModelsJournal of the American Statistical Association, 1992
- Alternative explanations of the money-income correlationCarnegie-Rochester Conference Series on Public Policy, 1986
- Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal DistributionsThe Annals of Mathematical Statistics, 1951