As we saw in the post on vector autoregressive (VAR) models, traditional VAR models suffer from a so-called curse of dimensionality. Each additional variable adds a further equation and a further lag polynomial to every other equation, so the number of coefficients grows with the square of the number of variables. With the few decades of quarterly data that are usually available this limits a VAR to a handful of variables. Policy makers, however, base their decisions on a much larger set of indicators than a VAR can accommodate, and leaving that information out of the model can distort the results.
A financial conditions index (FCI) compresses a large number of financial market series – spreads, prices, volatilities, survey measures – into a single series that is meant to say whether financial conditions are tight or loose. The obvious tool for that job is a factor model. The harder question is which series should count towards the index, and by how much, given that the answer plainly changes over time: the TED spread said something quite different about the state of the financial system in 2008 than it did in 1995.
Koop and Korobilis (2014) answer it by letting the factor loadings drift. Their index comes out of a factor augmented VAR (FAVAR) in which both the loadings and the transition coefficients follow random walks, so a series can enter and leave the index as the sample proceeds. What makes the paper more than a large state space model is how it is estimated: the priors on the innovation variances are replaced by forgetting factors, which reduces the whole estimation to two passes of a Kalman filter and smoother. No posterior simulation is involved, and the entire index over 175 quarters and 18 financial series is obtained in a hundredth of a second.
This post reproduces the two exercises the paper is built around – the index itself and its real-time counterpart – using the fincond package.