Evaluating latent and observed factors in macroeconomics and finance

Common factors play an important role in many disciplines of social science. In economics, the factors are the common shocks that underlie the co-movements of the large number of economic time series. The question of interest is whether some observable economic variables are in fact the underlying unobserved factors. We consider statistics to determine if the observed and the latent factors are exactly the same. We also provide simple to construct statistics that indicate the extent to which the two sets of factors differ. The key to the analysis is that the space spanned by the latent factors can be consistently estimated when the sample size is large in both the cross-section and the time series dimensions. The tests are used to assess how well the so-called Fama and French factors as well as several business cycle indicators approximate the factors in portfolio and individual stock returns. Data from a large panel of macroeconomic are also analyzed.