Sims (1980) questioned the way classical simultaneous equations models were specified and identified. He argued in particular that the exogeneity assumptions for some of the variables are often problematic. As an alternative he advocated the use of vector autoregressive (VAR) models for macroeconometric analysis. These models have the form where y t = (y1t,…,y Kt )′(the prime denotes the transpose) is a vector of K observed variables of interest, the A i are (K × K) parameter matrices, p is the lag order and u t is an error process which is assumed to be white noise with zero mean, that is, E(u t = 0, the covariance matrix, E(u t u ′ ) =∑ u , is time invariant and the m/s are serially uncorrelated or independent. There are usually also deterministic terms such as constants, seasonal dummies or polynomial trends. These terms are neglected here because they are not of interest in what follows. The relations between the variables in a VAR model are difficult to see directly from the parameter matrices. Therefore, impulse response functions have been proposed as tools for interpreting VAR models.
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