Federal Reserve Bank of Dallas paper details weak instrument bias in impulse response estimators, favoring VARs over local projections
A new working paper from the Federal Reserve Bank of Dallas, authored by Daniel J. Lewis and Karel Mertens, details weak instrument bias in impulse response function (IRF) estimators. Published in January 2026, the research suggests favoring vector autoregressions (VARs) over local projections (LPs) and introduces a novel test for weak identification.
VARs preferred for robustness
Impulse response function (IRF) analysis, crucial in empirical macroeconomics, often relies on ratio-based estimators that face significant statistical challenges in finite samples.
This can lead to severe bias and non-normal distributions, particularly in macro applications with short samples.
The paper develops new tools using a local-to-zero asymptotic framework to analyze weak instrument bias in just-identified IRF estimators.
Measuring bias by the major mode, the research concludes that when weak instrument bias is a primary concern, researchers should prefer vector autoregressions (VARs) over local projections (LPs).
This preference holds because the modal IRF bias in VARs never exceeds that in LPs, and is often smaller, especially when the number of horizons equals or exceeds the number of variables in the VAR.
A novel test for weak identification
Existing testing procedures for weak instrument bias in single-equation models are often ill-suited for most IRF applications.
The authors propose a novel, simple test based on the first-stage F-statistic, with critical values easily obtained.
This test can be extended for heteroskedasticity and serial correlation.
Applying it to various IRF applications from the literature, the proposed test frequently yields results diverging from existing procedures, indicating that weak identification remains an important concern.
The paper also demonstrates that adding restrictions on structural parameters leads to a more powerful constrained weak instrument test, quantifying the restrictiveness needed to rule out meaningful bias.
Robustness demands a new approach
This working paper delivers a crucial methodological warning for empirical macroeconomists, highlighting the pervasive and often underestimated issue of weak instrument bias.
Its finding that VARs offer superior robustness compared to LPs challenges common practice and demands a re-evaluation of identification strategies.
Ultimately, the proposed novel test provides a much-needed tool to enhance the credibility of dynamic causal effect estimates in macroeconomic research.