Identification and Estimation of Initial Conditions in Non-Minimal State-Space Models

Abstract

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