The Fiscal Multiplier — a Blanchard–Perotti SVAR

Python · R · Part 13 of the VAR arc — identification from fiscal institutions

Overview

Part 13 of the VAR arc: the fiscal multiplier. Every structural VAR so far studied monetary (Part 2) or oil (Part 8) shocks. Fiscal policy raises the same question in sharper form: if the government spends an extra dollar, how much does GDP rise — and does raising taxes contract output? The obstacle is simultaneity — spending, taxes and output are jointly determined. Blanchard & Perotti (2002) solve it not with a statistical assumption but with an institutional one: the decision and implementation lags of fiscal policy mean that within a quarter government spending is essentially predetermined, and the only automatic response of taxes to output is the automatic stabiliser, whose size can be calibrated from the tax code rather than estimated. That is a genuinely different route to identification from the recursive zeros, sign restrictions, elasticity bounds and heteroskedasticity of earlier parts.

spending shock=ug,tax shock=ut−a uy,dYdG=∂log⁡Y∂log⁡G⋅YG\text{spending shock} = u_g, \quad \text{tax shock} = u_t - a\,u_y, \qquad \frac{\text{d}Y}{\text{d}G} = \frac{\partial\log Y}{\partial\log G}\cdot\frac{Y}{G}

Identification from institutional timing and a calibrated elasticity

A quarterly VAR(4) in log real government spending gg, net taxes tt, and GDP yy (US, 1960–2019). The structural shocks are recovered from three institutional facts about the reduced-form residuals ug,ut,uyu_g, u_t, u_y: (1) spending is predetermined — discretionary spending takes longer than a quarter to legislate and implement, so the spending shock is just ugu_g; (2) taxes move with output automatically — Blanchard–Perotti calibrate the output-elasticity of taxes (a≈2.08a\approx 2.08) from institutional data and strip it out, so the discretionary tax shock is ut−a uyu_t - a\,u_y; (3) output responds to both fiscal shocks contemporaneously — estimated by instrumental variables, using the now-known structural fiscal shocks as instruments. Solving this triangular-with-calibration system gives the impact matrix B0B_0 and the impulse responses; the multiplier converts the estimated elasticity to dollars, dY/dG=(∂log⁡Y/∂log⁡G)×(Y/G)\text{d}Y/\text{d}G = (\partial\log Y/\partial\log G)\times(Y/G). The reduced-form VAR / moving-average / posterior machinery is reused unaltered from Part 8 (oilsvar.py); the Blanchard–Perotti identification and the dollar multipliers are a small dedicated module (fiscal.py) layered on top, with bands from the Normal-inverse-Wishart posterior.

Results

A dollar of government spending raises output by about a dollar. The spending multiplier is ~0.9 on impact and at its peak (68% band [0.68, 1.09] on impact) — just below one, the canonical Blanchard–Perotti result: fiscal spending has a real, roughly one-for-one effect on output, with mild crowding-out keeping it under unity. Because spending is predetermined within the quarter, this is a clean causal read, not the government spending because the economy is weak. Tax hikes contract output, increasingly over time: a dollar of higher taxes lowers GDP ~0.4 on impact, reaching about −1.3 by two years and deepening to about −1.5 over the five-year horizon as the drag on private demand accumulates — taxes bite with a lag, spending more immediately. Both multipliers are economically large — the empirical backbone of the stimulus-vs-austerity debate — and the asymmetry (spending fast, taxes slow) matters for the timing of fiscal packages. A new kind of identification: Blanchard–Perotti buy it with institutional timing and a calibrated elasticity, not a statistical restriction — the most economics-driven identification in the series, and a clean complement to the Part 8b debate: where the elasticity is genuinely known from institutions rather than assumed, the structural shock is credible. Fiscal joins monetary and oil as a third structural domain, identified its own way. (Caveat kept in view: the tax series is federal current receipts, not the broader net-tax aggregate, and a=2.08a=2.08 is the standard calibration — so the tax multiplier is the more approximate of the two; the spending multiplier, which does not lean on the calibration, is the robust headline.) Cross-checked in R (vars + the Blanchard–Perotti identification).

Notebooks

Python The fiscal multiplier from scratch — a Blanchard–Perotti SVAR: institutional timing + calibrated tax elasticity, spending and tax multipliers with posterior bands (Python) Open → R R cross-check — vars with the Blanchard–Perotti identification (R) Open →

Downloads

fiscal.py The from-scratch Blanchard–Perotti identification — structural spending & tax shocks from institutional timing and the calibrated tax elasticity, and the dollar multipliers with Normal-inverse-Wishart posterior bands (imports oilsvar.py) oilsvar.py The shared reduced-form SVAR engine — VAR, moving-average / impulse responses, and posterior draws — reused unaltered from the oil-market SVAR (Part 8) fiscal_data.csv Log real US government spending, federal current receipts, and GDP, quarterly 1960–2019

References