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Abstract: We propose a Bayesian hierarchical framework for estimating local projection (LP) impulse response functions across a panel of related time series. The framework explicitly accommodates unbalanced panels in which some series are substantially shorter than others, allowing the short series to borrow information from longer ones at horizons where the short series carry little or no own data. The basic specification pools coefficients across units via a Gaussian hierarchical prior. We then generalize to a sparse finite mixture pool that clusters units by similarity of their impulse response profiles, with a further pooling prior on the cluster means. We show in simulations that our approach substantially improves LP estimation accuracy relative to the standard approach if the time series are short while producing similar LPs for longer time series. Using a US price dataset, augmented with survey responses, we find that supply chain and oil shocks trigger heterogenous reactions of different price measures and expectations.

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