Alternative specification, estimation and identification of vector autoregressions

The article focuses on various aspects of specifi cation, estimation and identifi cation of vector autoregression (VAR) models. Key VAR-specifi c topics of verifi cation of an estimated model are also covered, as well as the differences between a standard (unrestricted) and structural VAR model. Subsequently, we address theoretical properties and practical aspects of impulse response functions (IRFs) as calculated upon estimated VAR models. Topics such as Cholesky decomposition (CHD), orthogonalised and generalised IRFs are discussed. Properties of VAR models are compared against alternative econometric modelling tools, such as simultaneous equation models and dynamic stochastic general equilibrium (DSGE) models. The article is supplemented with an illustrative example: on an aggregated EMU-wide level, we estimate a VAR (2) model for real GDP, CPI and PPI infl ation. IRFs are calculated using two different CHD orderings and compared to generalised IRFs. We fi nd the IRFs from our illustrative model to be very robust against the chosen IRF calculation method and against equation ordering changes.