Seeing inside the black box: Using diffusion index methodology to construct factor proxies in largescale macroeconomic time series environments

In economics, common factors are often assumed to underlie the co-movements of a set of macroeconomic variables. For this reason, many authors have used estimated factors in the construction of prediction models. In this paper, we begin by surveying the extant literature on diffusion indexes. We then outline a number of approaches to the selection of factor proxies (observed variables that proxy unobserved estimated factors) using the statistics developed in Bai and Ng (2006a,b). Our approach to factor proxy selection is examined via a small Monte Carlo experiment, where evidence supporting our proposed methodology is presented, and via a large set of prediction experiments using the panel dataset of Stock and Watson (2005). One of our main empirical findings is that our smoothed approaches to factor proxy selection appear to yield predictions that are often superior not only to a benchmark factor model, but also to simple linear time series models which are generally difficult to beat in forecasting competitions. In some sense, by using our approach to predictive factor proxy selection, one is able to open up the black box often associated with factor analysis, and to identify actual variables that can serve as primitive building blocks for (prediction) models of a host of macroeconomic variables, and that can also serve are policy instruments, for example. Our findings suggest that important observable variables include: various S&P500 variables, including stock price indices and dividend series; a 1-year Treasury bond rate; various housing activity variables; industrial production; and exchange rates.