Another look into the factor model black box: factors interpretation and structural (in)stability

Dynamic factor models have become extensively used for macroeconomic forecasting and for structural analysis. In these models, a small number of latent variables (the factors) are supposed to drive the bulk of the comovements of a generally large number of macroeconomic series. However, these models suffer from two weaknesses. First, it is generally very difficult – or impossible – to give an economic interpretation to the estimated factors, and these models are often considered as black boxes, useful for forecasting. Second, there is recent and mounting evidence that the model parameters can suffer from structural instability, potentially leading to an inconsistent estimation of the factors. In this paper, we address both issues of factors uninterpretability and structural instability, which we examine on a large dataset of US macroeconomic and financial variables, the well-known FRED-MD database. We tackle the interpretability issue using two different approaches: first, we apply different rotation techniques to the factors initially estimated by standard PCA and second, we estimate the factors using sparse PCA. These methods lead to very similar results, and allow a clear economic interpretation of the factors. We use this framework to study the issue of structural instability. Using different tests recently proposed in the literature, we find evidence of instability for some parameters, which can generally be economically interpretable.
Joint work with Thomas Despois.