Determining the Number of Primitive Shocks in Factor Models
提出一种无需估计动态因子即可确定宏观经济冲击数量的方法，通过估计静态因子的VAR模型并检验残差协方差矩阵的特征值，应用于大量宏观经济时间序列数据。
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.