Because of the increased availability of large panel data sets, common factor models have become very popular. The workhorse of the literature is the principal components (PC) method, which is based on an eigen‐analysis of the sample covariance matrix of the data. Some of its uses are to estimate the factors and their loadings, to determine the number of factors, and to conduct inference when estimated factors are used in panel regression models. The bulk of the underlying theory that justifies these uses is based on the assumption that both the number of time periods, T, and the number of cross‐section units, N, tend to infinity. This is a drawback, because in practice T and N are always finite, which means that the asymptotic approximation can be poor, and there are plenty of simulation results that confirm this. In the current paper, we focus on the typical micro panel where only N is large and T is finite and potentially very small—a scenario that has not received much attention in the PC literature. A version of PC is proposed, henceforth referred to as cross‐section average‐based PC (CPC), whereby the eigen‐analysis is performed on the covariance matrix of the cross‐section averaged data as opposed to on the covariance matrix of the raw data as in original PC. The averaging attenuates the idiosyncratic noise, and this is the reason why in CPC T can be fixed. Mirroring the development in the PC literature, the new method is used to estimate the factors and their average loadings, to determine the number of factors, and to estimate factor‐augmented regressions, leading to a complete CPC‐based toolbox. The relevant theory is established, and is evaluated using Monte Carlo simulations.

中文翻译：

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固定T面板的基于横截面平均的主成分方法

由于大型面板数据集的可用性越来越高，所以公因子模型变得非常流行。文献的主力军是主要成分（PC）方法，该方法基于数​​据样本协方差矩阵的特征分析。它的一些用途是估计因素及其负荷，确定因素的数量以及在面板回归模型中使用估计因素时进行推断。证明这些用途合理的基本理论是基于这样的假设，即时间段数T和横截面单位数N都趋于无穷大。这是一个缺点，因为实际上T和N总是有限的，这意味着渐近逼近可能很差，并且有大量仿真结果证实了这一点。在当前的论文中，我们关注于典型的微型面板，其中只有N大而T是有限的并且可能非常小，这种情况在PC文献中并未引起太多关注。提出了一种PC版本，此后称为基于横截面平均的PC（CPC），从而对横截面平均数据的协方差矩阵（而不是原始原始协方差矩阵）进行特征分析数据与原始PC相同。平均衰减特有噪声，这就是为什么在CPC T中可以解决。反映PC文献的发展，该新方法用于估算因子及其平均负荷，确定因子数量以及估算因子增强的回归，从而形成一个完整的基于CPC的工具箱。建立了相关的理论，并使用蒙特卡洛模拟对其进行了评估。