In this article we investigate the theoretical behaviour of finite lag VAR(n) models fitted to
time series that in truth come from an infinite order VAR(∞) data generating mechanism. We
show that the overall error can be broken down into two basic components, an estimation error
that stems from the difference between the parameter estimates and their population ensemble
VAR(n) counterparts, and an approximation error that stems from the difference between the
VAR(n) and the true VAR(∞). The two sources of error are shown to be present in other performance
indicators previously employed in the literature to characterize, so called, truncation
effects. Our theoretical analysis indicates that the magnitude of the estimation error exceeds
that of the approximation error, but experimental results based upon a prototypical real business
cycle model and a practical example indicate that the approximation error approaches its
asymptotic position far more slowly than does the estimation error, their relative orders of magnitude
notwithstanding. The experimental results suggest that with sample sizes and lag lengths
like those commonly employed in practice VAR(n) models are likely to exhibit serious errors
of both types when attempting to replicate the dynamics of the true underlying process and that
inferences based on VAR(n) models can be very untrustworthy.
approximation error; estimation error; bias; structural VAR; order of magnitude.