Variance Decomposition

Abstract

Variance decomposition is a classical statistical method in multivariate analysis for uncovering simplifying structures in a large set of variables (for example, Anderson, 2003). For example, factor analysis or principal components are tools that are in widespread use. Factor analytic methods have, for instance, been used extensively in economic forecasting (see for example, Forni et al. 2000; Stock and Watson, 2002). In macroeconomic analysis the term ‘variance decomposition’ or, more precisely, ‘forecast error variance decomposition’ is used more narrowly for a specific tool for interpreting the relations between variables described by vector autoregressive (VAR) models. These models were advocated by Sims (1980) and used since then by many economists and econometricians as alternatives to classical simultaneous equations models. Sims criticized the way the latter models were specified, and questioned in particular the exogeneity assumptions common in simultaneous equations modelling.