Estimating DSGE Models with Stochastic Singularity using Likelihood-based Dimensionality Reduction

Abstract This paper demonstrates a method of estimating and testing stochastically singular state-space models using likelihood-based methods. The approach uses dimensionality reduction of the observed data and rotates the model into directions of maximum variance, using the (dynamic) principal component analysis. The model is estimated in the space determined by a range (input space) of principal componetns. The principal components are then used as observables for transformed model, without any change of its economic structure. The method endogenously determines the structure of measurement errors. The approach can be interpreted as implementing identical principal-component filter to both data and the model before estimation