Philipp Hauber (University of Würzburg, Kiel Institute)
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. In an application, I apply the proposed sampler to conditional forecasts. Using a large real-time dataset of the German economy and focusing on a broad cross-section of variables such as activity series including components of the gross domestic product and gross value added, deflators and other price measures as well as several labor market indicators, I investigate to what extent the forecast accuracy improves when we condition on professional forecasters’ view on GDP growth and CPI inflation. Over the period from 2006 to 2017, I find that conditioning on external information tends to improve the forecast accuracy in some instances but typically only for those series - such as real activity indicators and some price measures - where the unconditional forecasts are already quite accurate. For around a third of the variables under consideration, the differences in forecast accuracy between conditional and unconditional forecasts are statistically significant for density forecasts; for point forecasts on the other hand we find no significant differences..
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