Determining the Number of Primitive Shocks in Factor Models

Jushan Bai · Serena Ng

540 citations0/0 files storedJournal of Business and Economic Statistics

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Monetary Policy and Economic Impact Statistical Methods and Applications Spatial and Panel Data Analysis

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.

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References

2002Forecasting Using Principal Components From a Large Number of Predictors 2002Macroeconomic Forecasting Using Diffusion Indexes 1986Alternative Explanations of the Money-Income Correlation 2005Implications of Dynamic Factor Models for VAR Analysis 1977Business Cycle Modeling Without Pretending to Have Too Much A Priori Economic Theory 2003Monetary policy in a data-rich environment

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