Simulation-based tests of forward-looking models under VAR learning dynamics

In this paper we propose a simulation-based technique to investigate the finite sample performance of likelihood ratio (LR) tests for the nonlinear restrictions that arise when a class of forward-looking (FL) models typically used in monetary policy analysis is evaluated with vector autoregressive (VAR) models. We consider ‘one-shot’ tests to evaluate the FL model under the rational expectations hypothesis and sequences of tests obtained under the adaptive learning hypothesis. The analysis is based on a comparison between the unrestricted and restricted VAR likelihoods, and the p-values associated with the LR test statistics are computed by Monte Carlo simulation. We also address the case where the variables of the FL model can be approximated as non-stationary cointegrated processes. Application to the ‘hybrid’ New Keynesian Phillips Curve (NKPC) in the euro area shows that (i) the forward-looking component of inflation dynamics is much larger than the backward-looking component and (ii) the sequence of restrictions implied by the cointegrated NKPC under learning dynamics is not rejected over the monitoring period 1984–2005.