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.