Are Structural VARs with Long-Run Restrictions Useful in Developing Business Cycle Theory?
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
A popular statistical technique concluded that a boost in technology makes workers' hours fall, which researchers used to argue that classic business-cycle models are wrong. This paper runs that same technique on made-up data from a model where the true answer -- hours rise after a technology boost -- is already known, and shows the technique gets the sign backwards whenever other (non-technology) shocks matter much, simply because realistic sample sizes force too few lags into the statistical model. The authors conclude the technique is trustworthy only in the implausible case where technology shocks explain nearly all economic fluctuations.
What this paper finds — and why it matters
Chari, Kehoe, and McGrattan subject the popular structural-VAR (SVAR) procedure – used by Gali (1999), Francis and Ramey (2005), and others to argue that technology shocks make hours fall, and therefore that real-business-cycle (RBC) models are “unpromising” – to a direct internal test: they generate artificial data from a multiple-shock RBC model whose true technology-shock response of hours is known to be positive, then apply the standard SVAR procedure to that artificial data and see whether it recovers the right answer. They find that when non-technology (“demand”) shocks account for a nontrivial share of output fluctuations, the differenced-hours SVAR (DSVAR) specification confidently but incorrectly infers a negative hours response even though the data-generating model’s true response is positive; at a 50% demand-shock share, the SVAR’s estimated impact response matches Gali’s own negative estimate, with confidence bands that would reject the true RBC model that actually generated the data. An alternative specification that uses the level rather than the difference of hours (LSVAR) avoids false confidence but instead produces confidence intervals so wide that it cannot distinguish an RBC model from a sticky-price model. The authors trace both failures to the fact that the model’s true vector autoregression is infinite-ordered, so the small number of lags that limited sample lengths force researchers to use makes the estimated VAR a poor approximation whenever non-technology shocks matter – a “lag-truncation bias” problem, not a flaw specific to any one data-generating model. They conclude the common long-run-restriction SVAR approach is a reliable guide to model development only in the implausible case that technology shocks explain virtually all output fluctuations.
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 specific claim in the SVAR literature does this paper test, and how?
The paper tests the claim, advanced using long-run-restriction SVARs by Gali (1999), Francis and Ramey (2005), and Gali and Rabanal (2005), that a technology shock causes hours to fall, and that this finding can be used to judge whole classes of business-cycle models as promising or not, regardless of the details of non-technology shocks. The authors’ test is a “natural economic test”: they take a real-business-cycle model with technology shocks and labor-wedge (“nontechnology”) shocks as the known data-generating process, simulate many artificial data sets of about the length of actual postwar U.S. data, apply the standard SVAR procedure (with the typical small number of lags, usually four) to each simulated data set, and compare the estimated SVAR impulse responses to the model’s true theoretical impulse responses.
Q2. What are the two SVAR specifications evaluated, and how do their failure modes differ?
The paper evaluates the differenced-hours specification (DSVAR), which uses the growth rate of labor productivity and the first difference of hours, and the level-hours specification (LSVAR), which instead uses the level of hours. For the DSVAR, when nontechnology shocks play a nontrivial role, the mean of the estimated impulse responses is biased toward showing hours fall after a technology shock, even though the data-generating model’s true response is a rise – a confident but wrong inference. For the LSVAR, the authors find that nontrivial nontechnology shocks instead produce confidence bands so wide that the procedure cannot tell whether the data came from the RBC model or from a sticky-price model, so it fails to discriminate even though it is not confidently wrong.
Q3. At what point does the SVAR procedure actually work well, according to the paper?
The authors find the DSVAR claim – that the procedure does not require specifying the details of nontechnology shocks – is correct only when nontechnology shocks account for a trivial share of output fluctuations, or when extremely long time series are available; with realistic (postwar U.S.-length) samples and a nontrivial nontechnology-shock share, the procedure fails. Specifically, when nontechnology shocks account for 50% of output fluctuations, the DSVAR’s estimated impact effect of a technology shock on hours matches Gali’s own negative point estimate, with confidence bands that exclude the true RBC model that generated the data.
Q4. What is the paper’s diagnosis of why the SVAR procedure fails in these cases?
The paper’s diagnosis is “lag-truncation bias”: the model’s true VAR representation for the observable variables is infinite-ordered, and when nontechnology shocks are not a trivial share of fluctuations, the true VAR’s coefficients decay very slowly, so a VAR estimated with the small number of lags that limited data availability requires (typically four) is a poor approximation to the true infinite-order process. One proposition in the paper formally shows the observables’ VAR is infinite-ordered with slowly-decaying coefficients; a second shows that a short-lag VAR is in fact a good approximation when nontechnology shocks play only a minor role, which is why the SVAR procedure performs well in that special case.
Q5. What broader inference about the importance of technology shocks does the paper challenge?
The authors challenge Gali’s (1999) inference that, because SVARs show hours falling after a technology shock while hours are procyclical in the data, technology shocks can account for only a minor fraction of business-cycle fluctuations – noting the irony that their results show SVAR-based inference is likely to be wrong precisely when technology shocks are a minor fraction of fluctuations, and right only when technology shocks explain essentially all of them.
Q6. Does the paper argue that the SVAR procedure is never useful, or that it should never be used?
No – the authors are explicit that not all SVAR approaches share this problem; they identify the “Sims-Cogley-Nason approach,” which compares the data’s empirical impulse responses to impulse responses from identical, short-sample SVARs run on model-simulated data of the same length, as logically superior because it treats actual and model data symmetrically and so avoids the asymmetric comparison (short-sample empirical responses versus an infinite-horizon theoretical response) that creates the bias they document. Their critique targets the specific “common approach” of comparing empirical SVAR responses to full theoretical model responses, not structural VAR methods in general.
Q7. What alternative tool do the authors point to for guiding business-cycle model development?
The authors point to “business cycle accounting,” developed in their companion work (Chari, Kehoe, and McGrattan 2007b), as an approach that shares the SVAR literature’s goal of quickly identifying which class of models is promising but, they argue, avoids the specification problems documented in this paper.
Key terms in this paper
Definitions below follow the paper's own usage.
- Lag-truncation bias
- the paper's diagnosis for why standard SVARs misstate the response of hours to a technology shock -- the data-generating model's true vector autoregression on observables is infinite-ordered, with slowly decaying coefficients whenever nontechnology shocks are nontrivial, so the small number of lags that realistic sample lengths force on an estimated VAR cannot adequately approximate it.
- DSVAR (differenced-hours specification)
- the structural VAR specification -- used by Gali (1999) and others -- built on the growth rate of labor productivity and the first difference of the log of hours, identified by the long-run restriction that only technology shocks affect the level of labor productivity in the long run; the paper's central finding is that this specification is confidently wrong about the sign of the technology-shock response to hours once nontechnology shocks are nontrivial.
- LSVAR (level-hours specification)
- an alternative structural VAR that uses the level (rather than the first difference) of hours; the paper finds it avoids the DSVAR's confident bias but instead produces such wide confidence intervals, once nontechnology shocks matter, that it cannot distinguish an RBC model's data from a sticky-price model's data.
- Natural economic test
- the paper's method of evaluating an empirical procedure by applying it to data simulated from a model whose true structure and true impulse responses are known by construction, so that any divergence between the procedure's estimates and the known truth can be attributed to the procedure itself rather than to uncertainty about the real economy's structure.
- Sims-Cogley-Nason approach
- the alternative SVAR practice, attributed to Sims (1989) and applied by Cogley and Nason (1995), of comparing empirical impulse responses to impulse responses from SVARs of the same specification and sample length run on model-simulated data, rather than to the model's full theoretical (infinite-sample) impulse responses; judged by the authors to be a logically superior comparison because it treats the data and the model symmetrically.