A widely held but untested assumption underlying macroeconomic analysis is that the number of shocks driving economic fluctuations, q, is small. In this paper, we associate q with the number of dynamic factors in a large panel of data. We propose a methodology to determine q without having to estimate the dynamic factors. Our analysis is based on the residuals of a VAR in r static factors, where the factors are themselves obtained by applying the method of principal components to a large panel of data. Our algebraic tests are based on a spectral decomposition of the covariance matrix of the residuals of a VAR. The tests are exact if the residuals were observable. Because of sampling variability fromhaving to estimate the VAR, the tests are accurate up to an error that vanishes asymptotically. We show how this error depends on the rate of convergence of the sample covariance to the population covariance of the true innovations. An important aspect of the present analysis is to make precise the relation between the dynamic factors and the static factors, which is a result of independent interest.
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