In this paper the identification problem is considered for initial conditionsin a non-minimal state-space model that includes interpretable state variablesgenerated by non-stationary stochastic processes. In order to solve theidentification problem, structural restrictions are imposed on initial conditionsin a state-space model with redundant state variables. The correspondingrestricted maximum likelihood estimator of initial conditions is derived.The restricted estimator of initial conditions can be used in order tocompute uniquely identified realizations of interpretable latent variables. Theidentification problem is illustrated analytically using a simple structuraleconomic model.

In this paper a semi-structural econometric model is implemented in order to estimate the natural rates of interest in two large economies of the Euro Area: Germany an Italy. The estimates suggest that after the financial crisis of 2007–2008 a decrease of the growth rate of potential output and the corresponding natural rate of interest was greater in Italy than in Germany which could have had important implications for the effectiveness of a common monetary policy. Unlike in other studies, it is found that the monetary policy stance was less expansionary in Italy as compared to Germany for the whole after-crisis period.