When Is the Government Spending Multiplier Large?

“We argue that the government-spending multiplier can be much larger than one when the zero lower bound on the nominal interest rate binds. The larger is the fraction of government spending that occurs while the nominal interest rate is zero, the larger is the value of the multiplier” (Abstract, p. 1 of the working paper). The authors develop this claim first with analytical intuition in simple models and then quantify it in an estimated, medium-scale DSGE model, and show the resulting model is consistent with the behavior of U.S. macro aggregates during the 2008-2010 financial crisis.

Under a standard Taylor rule, a rise in government spending pushes up output, marginal cost, and expected inflation, which induces the central bank to raise the nominal interest rate; this rise in the real interest rate crowds out private spending and keeps the multiplier modest (Section 2, pp. 7-16). But when the nominal rate instead stays fixed – because the zero bound binds – the same rise in expected inflation instead lowers the real interest rate (nominal rate minus expected inflation), which stimulates rather than crowds out private spending, generating a further rise in output, marginal cost, and inflation: “the increase in government consumption counteracts the deflationary spiral associated with the zero-bound state” (Introduction, p. 3).

In the simple no-capital model with the authors’ baseline calibration (β=0.99, θ=0.85, φ_π=1.5, σ=2, g=G/Y=0.2, ρ=0.8), the government-spending multiplier is 1.05, and “it is difficult to obtain multipliers above 1.2 for plausible parameter values” (Section 2, pp. 12-16). The authors trace this result to Ricardian equivalence combined with sticky prices and non-separable preferences: because Frisch labor supply is complementary with consumption in their preference specification (σ>1), a demand-driven rise in employment can raise the marginal utility of consumption enough that private consumption actually rises alongside government spending – a result the authors show disappears (multiplier always below one) under the additively separable preference specification common elsewhere in the new-Keynesian literature (p. 15).

With investment absent or limited, desired aggregate saving must equal zero in equilibrium; when a large enough rise in the discount factor (higher desired saving) hits an economy where the nominal rate is already at zero, the only remaining channel that can restore zero desired saving is a large, transitory fall in output, which is reinforced rather than offset by the fall in prices it triggers (Section 3, pp. 17-22). Falling prices generate expected deflation, and with the nominal rate stuck at zero this raises rather than lowers the real interest rate – “this perverse rise in the real interest rate leads to an increase in desired saving which partially undoes the effect of a given fall in output,” so the total output fall required is very large (Introduction, p. 2). A rise in government spending in this state raises output, marginal cost and expected inflation, which lowers the real rate and stimulates further private spending, output and inflation – “the net result is a large rise in output and a large fall in the rate of deflation” (Introduction, p. 3; Section 3, pp. 20-22, where the benchmark zero-bound multiplier is calculated at 3.7).

No – conditional on the zero bound binding, the multiplier in the simple model is independent of the size of the discount-factor shock; what matters instead is how severe the output cost of the zero-bound episode is (governed by parameters such as the degree of price flexibility, κ, and the persistence of the shock, p), and the multiplier is systematically larger in economies where that output cost is larger (Section 3, pp. 21-23, eq. 3.10-3.11). The authors show this formally: as parameter changes drive the output effect of the discount-factor shock (Γ) toward negative infinity, the corresponding zero-bound multiplier is shown to diverge toward infinity by the same algebra, “so, again we conclude that the government-spending multiplier is particularly large in economies where the output costs of being in the zero-bound state are very large” (p. 23).

The multiplier is large when new spending arrives while the economy is still in the zero-bound state, and shrinks the more the spending is delayed until after the bound stops binding. With a one-period implementation delay the multiplier falls from the contemporaneous benchmark of 3.7 to 1.5; with a two-period delay it is 1.44 (Section 3, pp. 23-24). If the spending increase is instead timed to occur only after the economy has already emerged from the zero bound, the multiplier on current output collapses to just 0.46 (p. 24). The authors conclude that “for fiscal policy to be effective, government spending must come online in a timely manner” (Introduction, p. 4) – the key determinant is not how quickly spending can be authorized in absolute terms, but whether it lands while the bound is still binding.

Taking the Taylor rule as given for other states of the world, the authors solve for the spending level that maximizes expected utility conditional on being in the high-discount-rate, zero-bound state, and find the optimum is very large – roughly 30 percent of output, versus a 20 percent steady-state share (Section 3, pp. 25-27). For their particular calibration and functional form for the utility of government purchases, the optimal increase is large enough that the zero bound becomes only marginally non-binding and output actually rises above its steady-state level; the authors caution that these exact magnitudes are calibration-specific, but state that “what is robust across different assumptions is that it is optimal to substantially increase government purchases and that the government-spending multiplier is large when the zero-bound constraint binds” (p. 27).

Allowing for capital has two offsetting effects: for a given shock it makes the zero bound less likely to bind (because investment can fall to absorb some of the rise in desired saving), but conditional on the bound binding, it makes the multiplier larger than in the no-capital model (Section 4, pp. 28-35). The mechanism is that investment is a decreasing function of the real interest rate; when the bound binds and the real rate rises, saving and investment diverge (both fall relative to what would restore equilibrium), which requires an even larger output fall to reconcile them, and a correspondingly larger multiplier to reverse it – on impact the multiplier rises to roughly 4 under Lucas-Prescott adjustment costs (falling to about 2.6 under the Christiano-Eichenbaum-Evans adjustment-cost specification, which more directly penalizes changes in investment) (pp. 33-35).

In the Altig-Christiano-Eichenbaum-Lindé (ACEL) model – which adds sticky wages, habit formation, variable capital utilization, and investment adjustment costs estimated to match U.S. impulse-response data – the government-spending multiplier under an active Taylor rule is generally less than one, but when the nominal rate is instead held constant for twelve quarters the impact multiplier is roughly 1.6, rising in a hump shape to a peak of about 2.3 after five quarters (Section 5, pp. 39-42, Figure 5). The multiplier is smaller (peaking near 1.2) when the constant-rate episode lasts only eight quarters, and the model also shows that multipliers are systematically higher the larger the fraction of the total spending increase that arrives while the nominal rate is actually at zero: holding the zero-bound episode fixed at twelve periods but extending the total spending program to sixteen or twenty-four periods (so that 75 percent or 50 percent, respectively, of the spending arrives while the rate is zero) lowers the peak multiplier from 2.3 to 1.06 (pp. 42-43).

Yes on the qualitative pattern: feeding the model a discount-factor shock plus a financial-intermediation-cost shock calibrated to match the rise in corporate bond spreads (peaking around 3.6 percentage points on a three-year bond) reproduces the rapid fall of the federal funds rate to zero, the declines in consumption, investment and output, and roughly a one-percentage-point fall in inflation relative to its pre-crisis forecast (Section 5, pp. 43-47, Figures 6-7). The authors calibrate the zero-bound episode to run from 2008Q4 to 2011Q3 (t1=2, t2=11) and note that, because actual government purchases rose by only about two percent during this period – reflecting that much of the American Recovery and Reinvestment Act took the form of transfers rather than purchases, and was partly offset by falling state and local spending – even the model’s peak multiplier of 2.3 implies government purchases contributed at most roughly 0.7 percentage points to annual GDP growth, so “the modest contribution of government purchases to the recovery reflects the very modest increase in government spending, rather than a small multiplier” (p. 47).

Financing spending with a distortionary labor-income tax raises the multiplier while the zero bound binds – the opposite of the standard result away from the bound – because the tax-induced fall in effective labor supply raises the real wage and hence marginal cost and expected inflation, which lowers the real interest rate through the same channel that makes the spending increase itself expansionary (Section 6, pp. 47-50, Figure 8). Capital-income taxation is shown to be more subtle: an increase in a capital tax rate borne by firms depresses investment, output and inflation (isomorphic to the financial-intermediation-cost shock used to model the crisis), and so shrinks the multiplier, while the identical tax rate borne instead by households raises consumption and output and so expands the multiplier, “as in the labor income tax case” (p. 50). The authors are explicit that these results are qualified relative to Christiano (2011), who finds the same qualitative effect is smaller once sticky wages (rather than flexible wages) make employment demand-determined (p. 49).

The authors explicitly abstract from political-economy considerations – “we are keenly aware that it is much easier to start new government programs than to end them” – and from the alternative escape route of committing to future inflation, which they set aside because they doubt central banks can credibly commit to it in practice and because the right tradeoff between spending and anticipated inflation is sensitive to how households value government purchases (Introduction, p. 5; Conclusion, p. 53). They also flag that estimating the zero-bound multiplier directly from historical data using reduced-form methods such as VARs is “fraught with difficulties,” both because multipliers differ so much across the zero-bound and non-zero-bound regimes that pooling the two states is invalid, and because government spending itself typically rises endogenously in response to the same shocks that push output down at the zero bound, making the required exogenous variation hard to identify (Introduction, pp. 4-5).