The observational equivalence of natural and unnatural rates of interest

The results of the study presented in this paper demonstrate that a structural model of the natural interest rate, which is consistent with the standard assumptions of the natural rate theory, admits an interpretable, observationally equivalent representation in which a redefined, ’unnatural’ equilibrium rate is different from the natural rate in the original model. The alternative representation was obtained by an invertible transformation implemented in the minimal state-space form of the natural-rate model. The identification theory for state-space models is used in the paper to prove the observational equivalence of these two representations. In the alternative representation, the equilibrium interest rate fails to meet the assumption of the natural rate theory, because it depends on past demand shocks. The alternative model, being observationally equivalent, has different implications for the conduct of monetary policy. The problem of observational equivalence arises in relation to natural-rate models because of the inherent unobservability of the natural interest rate; a potential solution to this problem could be the augmentation of the information set which is used to identify and estimate the natural rate.