VARs, Common Factors and the Empirical Validation of Equilibrium Business Cycle Models

Equilibrium business cycle models have typically less shocks than variables.
As pointed out by Altug, 1989 and Sargent, 1989, if variables are measured with
error, this characteristic implies that the model solution for measured variables has
a factor structure. This paper compares estimation performance for the impulse
response coefficients based on a VAR approximation to this class of models and
an estimation method that explicitly takes into account the restrictions implied
by the factor structure. Bias and mean squared error for both factor based and
VAR based estimates of impulse response functions are quantified using, as data
generating process, a calibrated standard equilibrium business cycle model. We
show that, at short horizons, VAR estimates of impulse response functions are less
accurate than factor estimates while the two methods perform similarly at medium
and long run horizons.