Assessing Structural VARs
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Can the statistical technique macroeconomists use to isolate a shock's effects, fitting a handful of equations to the data, be trusted? This paper tests it on artificial data from models whose true answer is already known. It finds the technique works well once the shock studied explains at least about 1% of the variation in hours worked, under either of two common identification strategies, though one carries wider uncertainty bands. The authors also show a fix to one estimate removes most of the bias found in the hardest cases -- evidence the technique is more trustworthy than a contemporaneous critique claimed, which matters because it underpins applied macroeconomic policy evaluation.
What this paper finds — and why it matters
Christiano, Eichenbaum, and Vigfusson ask whether structural VAR (SVAR) methods reliably recover the dynamic response of hours worked to an identified shock, by generating artificial data from a series of estimated real-business-cycle (RBC) models and from the richer monetary DSGE model of Altig, Christiano, Eichenbaum, and Linde (2005) (ACEL), applying SVAR procedures to the artificial data, and checking the sampling properties (bias, confidence-interval coverage) of the resulting impulse-response estimates against the model’s true response. They find that, so long as the variance in hours explained by a given shock exceeds a “remarkably low” 1 percent, SVAR-based estimates of the response of hours to that shock have good sampling properties – confidence intervals accurately reflect true sampling uncertainty – regardless of whether identification uses short-run or long-run restrictions, though long-run-restriction confidence intervals are substantially wider. Short-run-restriction SVARs perform well even when technology shocks explain as little as 0.5% of the variance in hours. The authors trace the (occasional) bias in long-run-identified estimates to the difficulty of accurately estimating the sum of VAR coefficients with a finite-lag VAR when the true process is infinite-ordered, and propose and validate a modified estimator – based on a nonparametric estimate of the zero-frequency spectral density – that largely eliminates this bias in their examples. The paper’s conclusions about the overall reliability of long-run-identified SVARs differ sharply from the contemporaneous critique in Chari, Kehoe, and McGrattan (2008), which the authors attribute mainly to different parameter estimates of the relative importance of technology versus non-technology shocks, not to a disagreement about SVAR methodology itself.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. What two questions about VAR-based inference does the paper set out to answer?
The paper investigates (1) whether VAR-based confidence intervals for impulse response functions accurately reflect the true degree of sampling uncertainty, and (2) how large any bias is relative to that sampling uncertainty, and how the coverage rates of confidence intervals compare to their nominal size. The authors answer both questions using data simulated from estimated dynamic stochastic general equilibrium (DSGE) models – several real-business-cycle (RBC) parameterizations and the richer ACEL model with both real and nominal frictions – for which the true impulse responses are known by construction, organizing the analysis around how hours worked respond to an identified shock.
Q2. What is the paper’s central quantitative threshold result?
The authors find that, across all the data-generating processes they consider, as long as the variance in hours worked explained by the shock being studied is above roughly 1 percent, VAR-based estimators recover that shock’s impulse response on hours with good sampling properties. For specifications identified with short-run restrictions, this holds even when technology shocks account for as little as 0.5% of the variance in hours; for long-run-restriction specifications, good performance generally requires the technology share to be at least around 1%, below which bias can become large relative to sampling uncertainty (though the authors note this low-technology-share region does not correspond to empirically plausible parameterizations).
Q3. How do short-run- and long-run-identified SVARs differ in their performance?
Short-run-restriction SVARs perform well with small sampling uncertainty across all the specifications considered; long-run-restriction SVARs also perform well in the sense of accurately-sized confidence intervals, but those confidence intervals are substantially wider, and some bias can appear when the technology-shock share of hours variance is very small. The authors attribute the difference to the fact that long-run identification requires estimating the sum of the VAR’s coefficients (equivalently, the zero-frequency spectral density of the data), which a finite-lag VAR estimates poorly when the true, infinite-order VAR’s coefficients decay slowly – precisely when non-technology shocks are empirically important.
Q4. What alternative estimator does the paper propose, and does it work?
The authors propose replacing the standard long-run-restriction estimator’s use of the sum of estimated VAR coefficients with a nonparametric estimator of the zero-frequency spectral density of the data, and find that in the examples where the standard procedure shows bias, this modification “virtually eliminates” that bias.
Q5. What does the ACEL-model analysis add, and what does it say about the practical importance of technology shocks for hours?
Simulating data from the ACEL monetary DSGE model – which includes two types of technology shocks and a monetary-policy shock – the authors find technology shocks account for a much larger share of the variance in hours than in any of their estimated RBC parameterizations, so SVAR-based inference about the technology-shock response of hours is correspondingly much sharper (tighter confidence intervals) in that setting.
Q6. How does this paper’s assessment relate to, and differ from, Chari, Kehoe, and McGrattan’s (2008) critique of long-run-identified SVARs?
Although one of the RBC parameterizations the authors consider is identical to a specification used by Chari, Kehoe, and McGrattan (CKM), the two papers reach sharply different overall conclusions about the value of long-run-identified SVARs; the authors attribute this mainly to the fact that CKM’s maximum-likelihood parameter estimates imply substantially larger non-technology-shock variances (and in one specification a near-unit root in the nontechnology-shock process) than the authors’ own MLE estimates, which the paper discusses in its Section 5 comparison of the two sets of estimated parameters. The CKM parameterization is included in this paper “for pedagogical purposes only,” since the authors view it as overwhelmingly rejected by the data.
Q7. What is the paper’s overall assessment of structural VARs as a tool for macroeconomics?
The authors conclude that structural VARs, including long-run-identified ones, are a useful guide for constructing and evaluating DSGE models: when the data contain little information about a shock’s effect, the VAR’s wide confidence intervals correctly signal that, and when nontechnology shocks are not overwhelmingly dominant, both short- and long-run identified VARs recover the truth with accurately-sized uncertainty bands. They frame large confidence intervals as a feature, not a bug – reducible only by imposing more theoretical structure or obtaining better data, not evidence that the method itself is unreliable.
Key terms in this paper
Definitions below follow the paper's own usage.
- Lag-truncation / finite-order approximation error
- the unavoidable specification error that arises when the true data-generating VAR implied by a DSGE model is infinite-ordered but the econometrician must estimate a VAR with a small, finite number of lags because of limited sample length; identified by the authors as the source of bias in long-run-restriction estimators, particularly severe when the estimate of the sum of VAR coefficients (needed for long-run restrictions) is involved.
- 1-percent variance threshold
- the paper's empirical rule of thumb -- across RBC and ACEL data-generating processes, SVAR-based impulse-response estimators for hours worked have good sampling properties as long as the shock under study accounts for at least roughly 1 percent of the variance in hours (0.5 percent for short-run-identified specifications).
- Zero-frequency spectral density estimator
- the paper's proposed modification to the standard long-run-restriction SVAR procedure, replacing the usual estimate built from the sum of finite-lag VAR coefficients with a nonparametric estimate of the data's zero-frequency spectral density, shown to largely eliminate the bias that otherwise appears in some long-run-identified examples.
- ACEL model
- the estimated monetary DSGE model of Altig, Christiano, Eichenbaum, and Linde (2005), incorporating both real and nominal (firm-specific capital, price- and wage-setting) frictions and multiple shock types (two technology shocks plus a monetary-policy shock); used here as a richer, empirically-grounded data-generating process alongside the simpler RBC models.