[Paper Review] Instrumental Variable Identification of Dynamic Variance Decompositions

Mikkel Plagborg‐Møller, Christian K. Wolf|arXiv (Cornell University)|Nov 2, 2020

Monetary Policy and Economic Impact35 references62 citations

TL;DR

This paper develops instrumental variable (IV) methods for identifying variance decompositions in dynamic macroeconomic models with measurement error in external instruments. It shows that, without additional assumptions, the variance contribution of an instrumented shock is interval-identified with sharp bounds; under recoverability, point identification is achieved. Applied to U.S. inflation, the method finds monetary shocks contribute at most 8% to inflation variance after 1990, challenging conventional SVAR findings.

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.

Motivation & Objective

• To address the lack of identification for variance decompositions when external instruments are contaminated by measurement error.
• To provide sharp bounds on the variance contribution of instrumented shocks in moving average models without requiring invertibility.
• To establish conditions under which point identification of variance and historical decompositions is possible.
• To develop a practical, implementable inference framework with confidence intervals for applied researchers.

Proposed method

• Models the instrumented shock as a dynamic measurement error model, using second-order moments of macro variables and instruments.
• Derives sharp lower and upper bounds on the signal-to-noise ratio of the instrument using observed autocovariances.
• Imposes the recoverability assumption—i.e., the shock is spanned by all lags and leads of observed variables—to achieve point identification.
• Uses a reduced-form VAR in macro variables and instruments to estimate second moments.
• Applies the Imbens-Manski (2004) confidence procedure to construct asymptotically valid confidence intervals for bounds and point estimates.
• Develops a code suite for inference, including a pre-test for invertibility based on Granger causality.

Experimental results

Research questions

• RQ1 To what extent can external instruments with measurement error identify the true variance contribution of a structural shock in a dynamic model?
• RQ2 What are the sharp bounds on the variance decomposition of an instrumented shock when measurement error is present?
• RQ3 Under what conditions is point identification of variance and historical decompositions possible in the presence of measurement error?
• RQ4 Can a pre-test for invertibility be constructed that exploits the strongest testable implication of the model?
• RQ5 How do the bounds and point estimates compare to standard SVAR-based estimates in empirical applications?

Key findings

• In the absence of additional restrictions, the variance contribution of the instrumented shock is interval-identified with informative, sharp bounds.
• The lower bound corresponds to treating the instrument as a perfect proxy (zero measurement error), while the upper bound reflects the maximum plausible signal-to-noise ratio consistent with observed data co-movement.
• Under the recoverability assumption—i.e., the shock is spanned by all lags and leads of observed variables—both variance and historical decompositions are point-identified.
• The method produces a 90% confidence interval for the forecast variance contribution of monetary shocks in U.S. inflation dynamics that rules out values above 8% at all horizons after 1990.
• The data are consistent with substantial non-invertibility in the post-1990 period, undermining standard SVAR-IV estimates.
• The proposed pre-test for invertibility is shown to exploit the strongest possible testable implication of the model.