Clustered Local Projections for Short and Ultra-Short Time Series -- A Hierarchical Bayesian Framework

2026-08-05

AI Summary

Estimating the dynamic effects of economic shocks in very short time series is challenged by severe degrees-of-freedom constraints. This study proposes a Bayesian hierarchical local projection framework that, for the first time, integrates Bayesian hierarchical modeling with sparse finite mixture models to cluster time series in unbalanced panels according to the similarity of their impulse response profiles. By allowing short series to borrow strength from longer ones, the approach enhances estimation precision while effectively accommodating heterogeneous dynamics and data imbalance. Simulation exercises demonstrate substantial improvements in estimation performance under short-sample conditions. Empirical analysis further reveals pronounced heterogeneity in the responses of various price indicators to supply chain and oil price shocks.

Abstract

Estimating the dynamic effects of economic shocks in short and very short samples is impeded by a lack of degrees of freedom. We offer a solution based on 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. Since series might exhibit heterogeneous dynamics, we develop a sparse finite mixture pool that clusters units by similarity of their impulse response profiles. 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 heterogeneous reactions of different price measures, with headline price indices responding more sharply than their core counterparts and goods prices changing more than services prices.

Problem

• short time series
• impulse response estimation
• heterogeneous dynamics
• unbalanced panel
• degrees of freedom

Innovation

• Bayesian hierarchical model
• local projections
• short time series
• sparse finite mixture
• impulse response functions