Frequency-Band Estimation of the Number of Factors*

We introduce consistent estimators for the number of shocks driving large-dimensional dynamic factor models. Our estimator can be applied to single frequencies and specific frequency bands, making it suitable for disentangling shocks affecting dynamic models with a factor model representation. Noticeably, our estimator requires the time-series and cross-section size to diverge simultaneously without any constraint, and it is free of nuisance parameters, such as penalization terms. Our methodology appears ideal for macroeconomic analysis, as one can investigate how many shocks drive the business cycle or the long run, although the applicability of our methods is much wider, given the popularity of GDFMs in economics and finance. Its small-sample performance in simulations is excellent. We apply our estimator to the FRED-QD dataset, finding that the U.S. macroeconomy is driven by two shocks: an inflationary demand shock and a deflationary supply shock. Our methodology permits one to accurately estimate the number of shocks that drive medium-sized DSGE models despite their moderate cross-sectional size.

本文提出了用于估计驱动大维动态因子模型 (large-dimensional dynamic factor models) 的冲击数量的一致估计量 (consistent estimator)。该估计量可应用于单频点与特定频带场景，适用于分离具有因子模型表征形式的动态模型所受的各类冲击。值得注意的是，该估计量仅要求时间序列维度与截面维度同时趋于无穷且无额外约束，且无需引入惩罚项等冗余参数 (nuisance parameters)。鉴于广义动态因子模型 (Generalized Dynamic Factor Models, GDFMs) 在经济与金融领域的广泛应用，本文提出的方法不仅适用于宏观经济分析——可用于探究驱动经济周期或长期趋势的冲击数量，其适用范围实则更为广泛。模拟实验中的小样本表现优异。我们将该估计量应用于FRED-QD数据集，发现美国宏观经济由两类冲击驱动：通胀型需求冲击与通缩型供给冲击。即便中等规模动态随机一般均衡 (Dynamic Stochastic General Equilibrium, DSGE) 模型的截面维度适中，本文方法仍可准确估计驱动其运行的冲击数量。