Does it add up? Reconciling forecasts and impulse responses for hierarchical macroeconomic data

Boris Blagov and Clara Krause

No 1224, Ruhr Economic Papers from RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen

Abstract: This paper introduces a mixed-frequency Gaussian state-space framework that embeds forecast reconciliation into Bayesian VAR modeling for hierarchical macroeconomic data. Using precision-based sampling to generate high-frequency latent estimates, we construct a consistent proxy for the forecast-error covariance matrix, enabling optimal reconciliation with short datasets. We prove the symptotic convergence of this estimator and show that forecast reconciliation can be formally derived as a special case of conditional forecasting, allowing straightforward implementation with standard state-space algorithms. We derive reconciled impulse response functions that ensure bottom-level structural responses aggregate exactly to the top-level impulse response. Applying the framework to UK and German regional economic data, we demonstrate improvements in the forecast accuracy alongside structurally consistent impulse responses.

Keywords: forecast reconciliation; regional forecasts; mixed-frequency; hierarchical impulse responses (search for similar items in EconPapers)
JEL-codes: C32 C53 R11 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:rwirep:343573

DOI: 10.4419/96973409

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