Latent Variables Analysis in Structural Models: A New Decomposition of the Kalman Smoother

Abstract Standard latent variable analysis in structural state space models decomposes latent variables into contributions of structural shocks (shock decomposition), or into contributions of the observable variables (data decomposition). We propose to link the shock decomposition of the latent variables and the data decomposition of the structural shocks in what we call the double decomposition. This decomposition allows us to better gauge the influence of data on latent variables by taking into account the transmission mechanism of each type of shock. We show the usefulness of the double decomposition by analyzing the role of observable variables in estimating the output gap in two models and by studying the role of news in revisions of the output gap.