Precision-Based Sampling with Missing Observations: A Factor Model Application

Abstract

We propose a new approach to sample unobserved states conditional on available data in (conditionally) linear unobserved component models when some of the observations are missing. The approach is based on the precision matrix of the states and model variables, which is sparse and banded in many economic applications and allows for efficient sampling. The existing literature on precision-based sampling is focused on complete-data applications, whereas the proposed samplers in this paper provide draws for states and missing observations by using permutations of the precision matrix. The approaches can be easily integrated into Bayesian estimation procedures like the Gibbs sampler. By allowing for incomplete data sets, the proposed sampler expands the range of potential applications for precision-based samplers in practice. We derive the sampler for a factor model, although it can be applied to a wider range of empirical macroeconomic models. In an empirical application, we estimate international factors in GDP growth in a large unbalanced data set of about 180 countries.