A multilevel factor model: Identification, asymptotic theory and applications
研究了包含全球因子和国家因子的多层次因子模型，提出序贯识别方法，用典型相关分析和主成分估计分别估计两类因子，并证明估计量的一致性和渐近正态性，应用于25个OECD国家识别国际商业周期。
Summary This paper studies a multilevel factor model with global and country factors. The global factors affect all individuals, whereas the country factors affect only those within each specific country. A sequential procedure to identify the global and country factors separately is proposed. In the initial step, the global factors are estimated by canonical correlation analysis. Using this initial estimator, the principal component estimators (PCEs) of the global and country factors are constructed. It is shown that the PCEs estimate the spaces of the global and country factors consistently and are normally distributed in the limit. Several information criteria that can estimate the number of country factors are proposed. The number of global factors is assumed to be known. Extensive simulation results demonstrate that the sequential procedure and information criteria work well in finite samples. The method of this paper is applied to 25 OECD countries to identify an international business cycle. It is reported that the method extracts a global factor reasonably well.