General Seemingly Unrelated Local Projections

2024-10-22

AI Summary

This paper addresses three key challenges in impulse response estimation under multi-shock, multiple-instrument settings: the isolation of local projections (LPs), neglect of intertemporal autocorrelation, and difficulty in joint inference. We propose a novel Bayesian local projection framework. Methodologically, we model LPs across horizons as a seemingly unrelated regressions (SUR) system for the first time, impose a Gaussian process (GP) prior to jointly capture temporal structure and sparsity in impulse responses, and employ multiple imputation to fully utilize time-series information. Our contributions are: (1) a systematic unification of LPs into a joint Bayesian SUR model; (2) a flexible, sparse GP prior design that accommodates diverse dynamic patterns; and (3) support for joint statistical inference and uncertainty quantification over multi-step-ahead responses. Empirical results demonstrate substantial gains in estimation accuracy and robustness, offering a more reliable tool for macroeconomic causal dynamic analysis.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We provide a framework for efficiently estimating impulse response functions with Local Projections (LPs). Our approach offers a Bayesian treatment for LPs with Instrumental Variables, accommodating multiple shocks and instruments per shock, accounts for autocorrelation in multi-step forecasts by jointly modeling all LPs as a seemingly unrelated system of equations, defines a flexible yet parsimonious joint prior for impulse responses based on a Gaussian Process, allows for joint inference about the entire vector of impulse responses, and uses all available data across horizons by imputing missing values.

Problem

• Efficient Bayesian estimation of impulse responses
• Joint modeling of multiple shocks and instruments
• Addressing autocorrelation in multi-step forecasts

Innovation

• Bayesian framework for Local Projections estimation
• Joint modeling of equations with Gaussian Process priors
• Optional robustification using power posteriors technique