Stock-Watson (2018) Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments

Summary

Stock's 2017 Sargan Lecture unifies the rapidly growing macroeconometric literature that identifies dynamic causal effects (structural impulse responses) using external instruments — as-if-random variation correlated with the shock of interest but not with other shocks. This imports the microeconometric quasi-experimental instrumental-variables (IV) strategy into macro, in contrast to the Sims-tradition SVAR that identifies through internal restrictions. Two estimators are compared: a one-step direct local-projections IV (LP-IV) regression and a more efficient two-step SVAR-IV method. The central theoretical result is a sharp trade-off: LP-IV is valid without invertibility but requires a strong lead–lag exogeneity condition, while SVAR-IV is asymptotically more efficient and needs no lead–lag exogeneity but requires invertibility — and comparing the two yields a Hausman-type test of invertibility. The methods are illustrated with the Gertler-Karadi (2015) high-frequency monetary-policy instrument.

Key Claims

• External vs. internal instruments. SVARs since Sims (1980) identify structural shocks through internal instruments (exclusion/timing restrictions internal to the system, à la three-stage least squares); the external-instruments programme instead uses variation external to the system — e.g. oil kept off-market by political disruption, tax changes orthogonal to the cycle, or the surprise revealed in an FOMC announcement window. Constructed shock measures have measurement error (biasing them as shocks) that need not compromise their validity as instruments.
• LP-IV without invertibility. The one-step direct regression (an IV version of a direct multistep/local-projection forecast) estimates the structural impulse response without assuming invertibility, provided the instrument satisfies lead–lag exogeneity: it must be uncorrelated with past and future shocks (after conditioning on controls), plus contemporaneous relevance/exogeneity. This condition gives concrete guidance for constructing instruments and choosing controls.
• SVAR-IV requires invertibility. The two-step method (recover VAR innovations, then use the instrument to identify the structural rotation) is asymptotically more efficient under strong-instrument asymptotics and does not need lead–lag exogeneity, but is consistent only under invertibility — the assumption that structural shocks are recoverable from current and lagged observables, equivalently that a VAR forecaster would gain nothing from also observing the true shocks (an omitted-variables interpretation).
• A Hausman test for invertibility. Because SVAR-IV is efficient-but-invertibility-dependent and LP-IV is inefficient-but-invertibility-free, their difference forms a Hausman (1978)-type test whose estimand is the impulse response function itself. Under the null it is asymptotically $\chi^2_n$; the paper introduces local non-invertibility and derives the test's local asymptotic power. This differs from omitted-variables invertibility tests (e.g. Forni-Gambetti 2014) that add variables.
• "No free lunch" theorem. If the instrument violates lead–lag exogeneity by depending on past shocks, the natural fix is to add lagged macro variables as controls — but the condition for those controls to deliver valid LP-IV inference is in general equivalent to assuming invertibility of the corresponding VAR, in which case SVAR-IV is more efficient. LP-IV's freedom from invertibility is not free once lagged controls are needed.
• Econometric odds and ends. Long-horizon impulse responses generally need heteroscedasticity- and autocorrelation-robust (HAR) standard errors (except when controls are lagged $Y$ and the instrument is serially uncorrelated); weak-instrument inference can use HAR versions of Moreira's (2003) conditional likelihood ratio or Montiel Olea-Pflueger (2013)/Andrews (2018); the framework also covers cumulative-effect ratios (fiscal multipliers), historical and forecast-error variance decompositions, and factor-augmented LP-IV (the local-projection counterpart of a FAVAR).
• Identification as external information. Every invertible Gaussian model has observationally equivalent non-invertible representations, so distinguishing them requires outside information. The literature's three routes are non-Gaussian/independent-shock higher-moment restrictions, informative priors, and — the paper's subject — an external instrument.

Concepts Introduced or Extended

• External Instruments — the paper's central object; formalises LP-IV vs. SVAR-IV, lead–lag exogeneity, and the proxy-SVAR identification of structural impulse responses
• Local Projections — Jordà (2005) direct multistep impulse-response estimation and its IV extension (LP-IV)
• Invertibility Problem — omitted-variables interpretation of invertibility; the Hausman-type test and local non-invertibility
• Impulse Response Function — the estimand; direct vs. iterated (VAR-based) estimation
• Structural Identification — internal vs. external instruments; connection to Sargan/three-stage least squares
• Monetary Policy Shocks — Gertler-Karadi (2015) high-frequency FOMC-announcement instrument illustration
• Vector Autoregression — SVAR-IV as an iterated multistep forecast
• Variance Decomposition — historical and forecast-error variance decompositions under external-instrument identification

Entities Mentioned

• James H. Stock
• Mark W. Watson
• Christopher Sims

Quotes

"In referring to these instruments as external, we also connect with the original term for instruments, external factors (Wright, 1928)."

"Invertibility is a very strong, albeit commonly made, assumption: under invertibility, a forecaster using a VAR would find no value in augmenting her system with data on the true macroeconomic shocks, were they magically to become available."

"Lest one think that LP-IV is too good to be true, we provide a 'no free lunch' result."

"In our view, the most exciting work to be done in this area is empirical. We look forward to the development of new external instruments that provide plausibly exogenous variation to provide more credible identification of dynamic causal effects."

My Take

This is now the canonical reference tying together the proxy-SVAR / external-instruments programme (Stock 2008; Stock-Watson 2012; Mertens-Ravn 2013; Gertler-Karadi 2015) and the local-projections-IV strand (Jordà 2005; Ramey 2016). Its lasting contribution is conceptual clarity: framing constructed shock series as instruments (measurement error and all), and pinning down exactly what each method buys you. The LP-IV-vs-SVAR-IV dichotomy — invertibility-free but lead–lag-exogeneity-hungry versus efficient but invertibility-bound — plus the "no free lunch" theorem is the sharpest available statement of why the popular "local projections are robust, VARs are fragile" intuition is only half true: once you need lagged controls, LP-IV quietly re-imposes invertibility. The Hausman-type invertibility test is the practical deliverable, though the authors flag that robustifying it to weak instruments is open. The paper deliberately restricts to linear, homogeneous-treatment-effect models, so the frequently-invoked non-linearity advantage of local projections is set aside and, they suspect, would face a non-linear analogue of the no-free-lunch result. Complements the wiki's existing structural-VAR and invertibility material and the ABCD (Fernández-Villaverde et al. 2007) treatment of when VARs recover structural shocks.