Some Fiscal Calculus

Questions & answers

Q1. What question does the paper ask, and what is its headline finding?

“What is the impact of fiscal policy on the economy? How large are the ‘multipliers’ of government spending and tax cuts?” (p. 30). The paper’s central finding is that short-run fiscal multipliers computed from a standard neoclassical growth model “can be dramatically misleading”: government spending initially “stimulates output,” generating net-present-value multipliers “well in excess of unity,” but “this turns into a prolonged below trend performance of output, as the tax increases necessary to repay the increased debt impact on the economy,” so that “the net present fiscal multiplier for government spending turns negative too, as the horizon increases” (p. 30).

Q2. What kind of model produces this result, and what are its key ingredients?

A baseline neoclassical growth model with endogenous labor supply and a full fiscal sector: government spending, lump-sum transfers, government debt, and distortionary taxes on labor and capital income (Section I, pp. 31-32). The representative household maximizes expected discounted utility over consumption and leisure subject to a budget constraint that includes capital income, government bond holdings, and taxes on consumption, wage income, and capital income; production is Cobb-Douglas; and the government budget constraint links spending, transfers, bond issuance, and tax revenue, with “excess deficits…repaid at speed ψ” (calibrated to 0.05) entirely through adjustments to the distortionary labor tax rate, holding all other tax rates and transfers fixed (p. 31). The author calibrates the model’s parameters – including a labor share of 62 percent and a Frisch elasticity of 1 – following Trabandt and Uhlig (2009) and log-linearizes the model around its deterministic steady state (p. 32).

Q3. How is the ARRA-like government spending shock calibrated?

Government spending is assumed to follow an AR(2) process calibrated to match the path documented in Cogan et al. (forthcoming) for the actual ARRA, with the fiscal surprise dated to 2009Q2 and spending rising to a peak of about 1.78 percent of steady-state output in 2010Q2 (six quarters after the shock) (Section II, p. 33, Figure 1). The author notes that spending in his simulation “falls off more slowly…than in Cogan et al.,” reflecting both the simple AR(2) process used and “a skepticism that stimulus spending will truly return back to normal as quickly as envisioned by the ARRA,” which he says it is appropriate to build into a rational-expectations model of this kind (p. 33).

Q4. What is the “net present value fiscal multiplier,” and how does it behave over the first three years?

The multiplier at date t is defined as the sum of output responses through t, discounted at the steady-state interest rate, divided by the correspondingly discounted sum of government spending (or forgone tax revenue) through t (Section II, p. 33, eq. for φ_t). Computed this way, the government-spending multiplier “starts at infinity” (because spending is initially near zero while output has already begun responding to anticipated future spending) and then “remains initially higher” than the tax multiplier before “gradually declining to 0.15 at the beginning of 2012,” while the comparable tax-cut multiplier “start[s] at about one and reach[es] 1.3 at the beginning of 2012” (Section II, pp. 33-34, Figure 2). Over this three-year window, output initially rises above trend on impact in response to both experiments (Figure 3).

Q5. Why does output rise on impact, given that this model has no price stickiness or demand-side frictions at all?

The initial output boost operates entirely through a real-business-cycle wealth effect on labor supply: the anticipation of future government spending and the taxes needed to finance it “leads the representative agent to consume less leisure, i.e., supply more labor, thereby boosting output initially” (Section II, p. 34). The author explicitly warns against reading this as evidence that “government spending is successful in stimulating the economy” in the sense usually intended by fiscal-stimulus advocates – he notes the resulting short-run multiplier magnitudes are “somewhat similar” to those in the Romer-Bernstein (2009) White House analysis of the ARRA, but calls that comparison “a misleading interpretation” once the financing side of the model is taken into account (p. 34).

Q6. What happens to output and the multiplier over a longer, 40-year horizon?

Because the spending increase “needs to be financed” – initially by debt, and “eventually” by higher labor taxes – the model generates “a very persistent and prolonged below trend performance for output” over the following decades, and the net-present-value government-spending multiplier “converges to a value of -3.4 eventually,” meaning $3.40 of output is ultimately lost, in present-value terms discounted to the beginning of 2009, for every dollar of increased government spending (Section II, pp. 34, Figures 4-5). The mechanism is that the slow, 0.05-speed debt-repayment rule requires a persistent rise in the distortionary labor tax rate, and “the increased tax burden in later years leads to disincentives on the labor market,” which is what converts the model’s short-run output gain into a multi-decade drag (p. 34).

Q7. How does the tax-cut experiment compare to the spending experiment in the long run?

The comparable tax-cut experiment converges to a net-present-value multiplier of roughly +2.4, so that “for a tax cut and each discounted dollar given up in terms of taxing labor, one obtains an increase of $2.40 in discounted output eventually” (Abstract, p. 30; Conclusion, p. 34). Because both experiments share the same debt-and-repayment financing structure in the model, the contrast between a positive long-run multiplier for the tax cut and a negative one for the spending increase reflects the fact that the tax cut directly removes a labor-supply distortion, whereas the spending increase must eventually be paid for by adding one.

Q8. What caveats does the author attach to interpreting these results, and how does the paper relate to follow-up work?

The author is explicit that the paper is “a positive, not a normative analysis”: it reports only output paths for a representative agent, and “one therefore should not draw welfare conclusions from the consumption and leisure path for the representative agent,” since a heterogeneous-agent version of the same model – in which agents hold different amounts of capital and value government goods differently – would generally produce heterogeneous welfare effects across the population that the representative-agent output path cannot capture (Section III, “Conclusions,” p. 34). He also flags that the model is deliberately stylized and omits Keynesian features such as sticky prices and rule-of-thumb consumers; a companion paper, Drautzburg and Uhlig (2010), studies the same experiment in a New Keynesian model and finds the initial output impact is “actually more muted,” because the wealth effect on labor supply “is diluted in a Keynesian environment of sticky wages and demand-driven labor markets,” while the model’s long-run behavior remains neoclassical – so, in the author’s words, “the long run issues raised here are surely not a matter of principle, but a matter of degree” (p. 31).