Notwithstanding the increased use of estimated dynamic stochastic general equilibrium (DSGE) models over the last decade, structural vector autoregressive (VAR) models continue to be the workhorse of empirical macroeconomics and finance. Structural VAR models have four main applications. First, they are used to study the expected response of the model variables to a given one- time structural shock. Second, they allow the construction of forecast error variance decompositions that quantify the average contribution of a given structural shock to the variability of the data. Third, they can be used to provide historical decompositions that measure the cumulative contribution of each structural shock to the evolution of each variable over time. Historical decompositions are essential, for example, in understanding the genesis of recessions or of surges in energy prices (see, for example, Edelstein and Kilian, 2009; Kilian and Murphy, 2013). Finally, structural VAR models allow the construction of forecast scenarios conditional on hypothetical sequences of future structural shocks (see, for example, Waggoner and Zha, 1999; Baumeister and Kilian, 2012). VAR models were first proposed by Sims (1980a) as an alternative to traditional large- scale dynamic simultaneous equation models. Sims’ research program stressed the need to dispense with ad hoc dynamic exclusion restrictions in regression models and to discard empirically implausible exogeneity assumptions.
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