Caldara-Kamps (2017) The Analytics of SVARs: A Unified Framework to Measure Fiscal Multipliers

Summary

This paper explains why structural VAR estimates of fiscal multipliers disagree so much, and offers a unified framework to reconcile them. Caldara and Kamps derive analytical relationships between the output elasticities of fiscal variables and the implied fiscal multipliers, and show that the leading SVAR identification schemes — Blanchard-Perotti recursive, sign restrictions, narrative/proxy, and others — are observationally equivalent except that each implicitly imposes a different value (prior) on the fiscal elasticities. The wide dispersion in published multipliers is therefore mostly a disagreement about elasticities, not about the data. Using extra-model (institutional) information to pin down a plausible range of elasticities, they sharpen inference: for the U.S. 1947–2006, the probability that the tax multiplier exceeds the spending multiplier is below 0.5 at all horizons.

Key Claims

• Multipliers are a function of elasticities. In the fiscal SVAR the contemporaneous response of taxes and spending to output (their output elasticities) is exactly the identifying quantity; the paper derives closed-form maps from those elasticities to the spending and tax multipliers.
• Identification schemes = priors on elasticities. Blanchard-Perotti (2002) recursiveness, sign restrictions (Mountford-Uhlig 2009), and narrative/proxy approaches differ, at bottom, only in the elasticity values they assume; plugged into the same analytics they reproduce the literature's scattered multiplier estimates.
• Dispersion is about assumptions, not data. Because the schemes are near-observationally-equivalent, the large cross-study variation in multipliers reflects the different implicit elasticity priors rather than genuinely different evidence — a diagnosis in the spirit of treating identification as a prior (Bayesian SVAR identification).
• Discipline elasticities with outside information. Institutional and micro estimates of tax and spending elasticities narrow the empirically plausible set, which in turn narrows the multiplier posterior — sharper and more defensible than picking one identification scheme.
• U.S. result. Over 1947–2006, spending multipliers are, if anything, larger than tax multipliers: $\Pr(\text{tax multiplier} > \text{spending multiplier}) < 0.5$ at every horizon.

Concepts Introduced or Extended

• Fiscal Policy Shocks
• Bayesian SVAR Identification

Entities Mentioned

• Dario Caldara
• Christophe Kamps

Quotes

"We show that standard identification schemes imply different priors on elasticities, generating a large dispersion in multiplier estimates. We then use extra-model information to narrow the set of empirically plausible elasticities, allowing for sharper inference on multipliers."

My Take

The paper's contribution is clarifying rather than empirical: by writing the multiplier as an explicit function of the fiscal elasticities, it shows that the decade-long fight over "which identification scheme is right" for fiscal SVARs was really a fight over an elasticity number that each scheme buries in its assumptions. That reframing is the same move as Baumeister-Hamilton make for SVARs generally — identification is a prior on an economically interpretable parameter — applied to the fiscal case and made analytically transparent. For the wiki it is the natural bridge between the fiscal-multiplier page and the prior-based identification concept. The honest limits are that "extra-model information" on elasticities is itself contested, and that the analytics assume the linear SVAR mapping, so state-dependent or nonlinear multipliers sit outside the framework.