A new index of financial conditions

The paper builds a single unified model addressing three limitations of typical financial conditions indices at once: it allows the weights on individual financial variables to change over time, allows the actual set of financial variables entering the index to change over time, and estimates the index and its relationship to the macroeconomy jointly rather than in a two-step procedure. It does so via a time-varying-parameter factor-augmented VAR (TVP-FAVAR) enriched with dynamic model averaging and selection (DMA/DMS), evaluated by comparing its resulting financial conditions index (FCI) to a set of four existing indices and testing its usefulness for forecasting inflation, unemployment, and output growth.

The model has two linked blocks estimated jointly: a “financial block” in which n financial variables x_t load on both a latent factor f_t (the FCI) and the contemporaneous macro variables y_t (GDP deflator inflation, unemployment, real GDP growth), and a “macro-FCI VAR block” in which y_t and f_t jointly follow a VAR with p lags. Both the factor loadings in the financial block and the VAR coefficients in the macro-FCI block are allowed to evolve as multivariate random walks, so the loadings and dynamics driving the FCI’s construction and its relationship with the macroeconomy are both permitted to change every period rather than being fixed once and for all.

Identification rests on two restrictions: the covariance matrix of the financial block’s idiosyncratic errors is restricted to be diagonal, and the contemporaneous macro variables y_t are included on the right-hand side of the financial block for the specific purpose of stripping out their effect before the residual co-movement in financial variables is summarized by f_t. The authors describe this macro-variable term as “intended solely to ensure the FCI reflects only financial conditions” (p. 103) — without it, the estimated factor could simply reflect current output and price dynamics rather than distinctly financial conditions. As a robustness check, the authors note the same y_t term could instead be replaced with professional forecasts of the macro variables, which would capture expected rather than current conditions — an issue they describe as “common to all FCIs.”

Estimation uses a simulation-free, two-step “dual Kalman filter” algorithm that avoids Markov Chain Monte Carlo entirely: at each iteration, the time-varying parameters are estimated conditional on a principal-components estimate of the factor, and then the factor itself is re-estimated conditional on those parameters via the Kalman filter and smoother, with the two steps iterated to convergence. The error covariance matrices governing shock volatility and coefficient drift are not estimated by full likelihood maximization but by exponentially weighted moving averages (EWMA), using a decay factor of 0.96 for the observation-equation covariances and a forgetting factor of 0.99 for the state-equation covariances — fixed choices the authors defend in an appendix as approximately non-informative, chosen specifically to avoid computationally intensive likelihood maximization.

Of the 18 financial variables, the S&P 500 is always included and the remaining 17 are subject to dynamic model averaging (DMA) or dynamic model selection (DMS), which searches over all 2^17 = 131,072 possible subsets of those 17 variables and updates each subset-specific model’s probability every period using a forgetting-factor recursion (following Raftery, Karny, and Ettler 2010) based on how well that subset has predicted recently. The forgetting factor alpha controls how much past predictive performance is discounted: alpha = 0.99 gives genuine dynamic model averaging (weights adapt over time), while alpha = 1 nests static Bayesian model averaging with fixed weights; DMS instead picks the single highest-probability subset at each date rather than averaging across subsets.

The TVP-FAVAR-DMA index begins declining before the onset of the 2007-2009 recession and bottoms out in early 2009, a pattern the authors note is shared by their alternative model specifications (“all of them bottoming out in early 2009”). Among the four existing indices used for comparison, the authors’ FCI is “most comparable” to the Chicago Fed National Financial Conditions Index, but started dropping earlier in 2008 and reached a lower trough during the recession, and after the 2001 recession “grew faster and peaked at a higher level” than the Chicago Fed measure; financial stress indices such as the Cleveland Fed’s differ more substantially, which the authors attribute to FSIs measuring financial stress specifically rather than broad financial conditions.

DMA selects on average between about 5 and 8 of the 17 optional financial variables at any point in time, with a slow decline toward roughly 5 variables through the late 1990s, an abrupt increase to roughly 8 in the run-up to the 2007-2009 recession, and a subsequent drop that stabilizes by the end of the recession. The identities of the selected variables also switch substantially over the sample — the authors note there are “a few variables which enter then leave (or vice versa) the FCI” — while the S&P 500 has selection probability 1 throughout by construction, since it is never subject to exclusion.

Yes: over the 1990Q1-2013Q3 evaluation window, the TVP-FAVAR-DMA specification (with decay/forgetting factors 0.96 and 0.99) produces lower mean squared forecast error (MSFE) and higher average predictive likelihood than a VAR benchmark at every forecast horizon h = 0 through 4 for inflation, unemployment, and output growth. Selected relative-MSFE values from Table 2 illustrate the magnitude: for unemployment, relative MSFE is 0.63 at h=0 and 0.55 at h=2 (i.e., 37-45% lower forecast-error variance than the VAR); for output, 0.74 at h=0 and 0.67 at h=2; for inflation, more modest gains of 0.94 at h=0 and 0.82 at h=2 — all marked in the paper as statistically significant improvements.

Against VARs augmented with existing financial conditions indices (evaluated 2000Q1-2013Q3), a TVP-VAR that includes the Chicago Fed’s index (FCI4) performs about as well as the authors’ full TVP-FAVAR, but the authors report that “TVP-FAVAR-DMA and TVP-FAVAR-DMS almost always forecast better than the TVP-VAR-FCI4” (p. 114) — the DMA/DMS step still adds value even against the single best existing-index-augmented model. Comparing nested model variants, the authors attribute “the largest improvements” to allowing for stochastic volatility (time-varying error covariances) in the model’s parameters; allowing the VAR coefficients themselves to be time-varying provides a further increment, the FAVAR factor structure adds more, and DMA/DMS “are either the best or among the best forecasting models for all the macroeconomic variables at all forecasting horizons,” adding a final layer of improvement beyond the full-variable TVP-FAVAR.