Identification of Unknown Common Factors: Leaders and Followers

This article has the following contributions. First, this article develops a new criterion for identifying whether or not a particular time series variable is a common factor in the conventional approximate factor model. Second, by modeling observed factors as a set of potential factors to be identified, this article reveals how to easily pin down the factor without performing a large number of estimations. This allows the researcher to check whether or not each individual in the panel is the underlying common factor and, from there, identify which individuals best represent the factor space by using a new clustering mechanism. Asymptotically, the developed procedure correctly identifies the factor when N and T jointly approach infinity. The procedure is shown to be quite effective in the finite sample by means of Monte Carlo simulation. The procedure is then applied to an empirical example, demonstrating that the newly developed method identifies the unknown common factors accurately.