Abstract

We introduce a time-series model for a large set of variables in which the structural shocks identified are employed to simultaneously explain the evolution of both the level (conditional mean) and the volatility (conditional variance) of the variables. Specifically, the total volatility of macroeconomic variables is first decomposed into two separate components: an idiosyncratic component, and a component common to all of the variables. Then, the common volatility component, often interpreted as a measure of uncertainty, is further decomposed into three parts, respectively driven by the volatilities of the demand, supply and monetary/financial shocks. From a methodological point of view, the model is an extension of the homoscedastic Multivariate Autoregressive Index (MAI) model (Reinsel, 1983) to the case of time-varying volatility. We derive the conditional posterior distribution of the coefficients needed to perform estimations via Gibbs sampling. By estimating the model with US data, we find that the common component of volatility is substantial, and it explains at least 50 per cent of the overall volatility for most variables. The relative contribution of the demand, supply and financial volatilities to the common volatility component is variable specific and often time-varying, and some interesting patterns emerge.

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