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

In this paper we propose simulation-based techniques 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 both `one-shot' tests and sequences of tests under a particular form of adaptive learning dynamics, where `boundedly rational' agents use VARs recursively to update their beliefs. The analysis is based on the comparison of the likelihood of the unrestricted and restricted VAR, and the p-values associated with the LR statistics are computed by Monte Carlo simulation. We also address the case where the variables of the FL model are approximated as non-stationary cointegrated processes. Application to the New Keynesian Phillips Curve in the euro area shows that the FL model of inflation dynamics is not rejected once the suggested simulation-based tests are applied. The result is robust to specification of the VAR as a stationary (albeit highly persistent) or cointegrated system. However, in the second case the imposition of cointegration restrictions changes the estimated degree of price stickiness.