Instrumental Variable Identification of Dynamic Variance Decompositions

TL;DR

This paper develops new methods for identifying the importance of macroeconomic shocks using external instruments, providing bounds and conditions for precise variance decompositions without requiring invertibility, and applies them to U.S. data.

Contribution

It introduces a novel approach for variance decomposition identification in macroeconomics using external instruments, allowing for interval and point identification under various restrictions.

Findings

Interval-identified variance decompositions with informative bounds.

Conditions for point identification of variance and historical decompositions.

Tight upper bound on monetary shocks' role in inflation dynamics in U.S. data.

Abstract

Macroeconomists increasingly use external sources of exogenous variation for causal inference. However, unless such external instruments (proxies) capture the underlying shock without measurement error, existing methods are silent on the importance of that shock for macroeconomic fluctuations. We show that, in a general moving average model with external instruments, variance decompositions for the instrumented shock are interval-identified, with informative bounds. Various additional restrictions guarantee point identification of both variance and historical decompositions. Unlike SVAR analysis, our methods do not require invertibility. Applied to U.S. data, they give a tight upper bound on the importance of monetary shocks for inflation dynamics.