The Fiscal Multiplier

The authors identify two necessary ingredients: “output is demand determined… so that a fiscal stimulus increases aggregate demand,” which requires nominal rigidities, and “a significant deviation from the permanent income hypothesis, such that households have a high marginal propensity to consume,” which requires incomplete markets (Introduction, p. 2). They argue the literature has typically had only one: flexible-price models (e.g. Baxter and King 1993) capture realistic MPC heterogeneity but shut off the demand channel, while representative-agent New Keynesian (RANK) models capture the demand channel but assume households “behave exactly like permanent-income ones and respond little to a temporary income shock,” contradicting “a large empirical literature that has documented substantial MPC heterogeneity and large consumption responses to transitory income and transfer payments” (p. 3).

By keeping the government budget constraint “at least partially” in nominal terms, the model can exploit “the result in Hagedorn (2016, 2018) that incomplete market models with (partially) nominal fiscal policy imply price level determinacy,” which “allows us to measure the size of fiscal multiplier for arbitrary combinations of monetary and fiscal policies of interest, including a constant nominal interest rate, without having to impose restrictions on policy rules to ensure determinacy” (Introduction, p. 3; Sec. 3.1, p. 16). The authors are explicit that this sidesteps “the indeterminacy issues with the representative-agent New Keynesian model at the ZLB raised by Cochrane (2017),” giving them “a uniquely determined fiscal multiplier at the ZLB, one of the cases where we are most interested in knowing its size” (Sec. 3.1, p. 16-17).

The paper distinguishes an intertemporal substitution channel – how the stimulus moves real interest rates and how strongly consumption responds to that – from a redistribution channel – how the stimulus’s effects on prices, income, and taxes redistribute resources across households with different MPCs (Sec. 3.1, p. 16). In incomplete markets, “the effect of the real interest rate on consumption is smaller since some households are credit constrained and thus not on their Euler equation, breaking the tight link between consumption and real interest rates. In addition, the change in real interest rates is smaller” than in complete markets (Sec. 3.1.1, p. 17-18) – so both components of the classical intertemporal-substitution mechanism are dampened, leaving more of the multiplier’s size to be explained by redistribution.

With a fixed nominal interest rate, the impact multiplier is 0.61 under tax financing (cumulative 0.43) versus 1.34 under deficit financing (cumulative 0.55) (Sec. 3.4, Table I). Under tax financing, “the contemporaneous cut in transfers lowers aggregate consumption by −0.031% on impact… since the government spending increases household’s income proportional to their productivity and thus benefits high income households more whereas the transfer cut is uniform across all income groups and thus negatively affects high MPC households” – a negative distributional channel (Sec. 3.4.1, p. 33). Under deficit financing, there is no offsetting contemporaneous tax increase, so “the fiscal expansion increases employment and thus labor income but… there is no offsetting effect through higher taxes,” which “benefits high MPC households, who primarily rely on labor income,” making the distributional channel positive instead (Sec. 3.4.2, p. 35).

Under deficit financing, “total savings increase… by more than they would have increased if the real interest rate… were to remain constant,” but “capital still falls below its steady-state level since the increase in savings is smaller than the increase in additional government debt” – the government absorbs more new saving than households generate, crowding out capital (Sec. 3.4.2, p. 36). This is why the cumulative multiplier under deficit financing (0.55) is markedly below the impact multiplier (1.34): “the increase in government spending is ultimately financed through a future reduction in transfers, which results in a contraction in future output” (p. 35), so much of the initial boost is later reversed.

The paper attributes this to anticipation: “while the TANK and our HANK economies feature the same quarterly MPC, the large difference between them is due to dynamic anticipation effects arising in the HANK model that are absent in TANK. The hand-to-mouth agents in TANK respond only to the contemporaneous decrease in transfers, but not to the anticipated cut in future transfers… leading to a much smaller drop in private consumption demand” under tax financing (Sec. 3.4.1, p. 34). More generally, the Introduction states that “future income increases (as opposed to increases in current income) drive the contemporaneous consumption response, while only the latter effect is featured by the TANK model” (p. 4) – households in the full model save part of a stimulus-induced income gain today, which raises future demand and income and, through relaxed precautionary-saving motives, feeds back to raise current consumption further.

Under a Taylor rule, the deficit-financed impact multiplier falls from 1.34 to 0.66 (cumulative from 0.55 to 0.29), and the tax-financed multiplier falls more modestly from 0.61 to 0.54 (Sec. 3.5.1, p. 38). The mechanism is that “a higher nominal interest rate contracts consumption demand and thus reduces income, which in turn reduces savings and investment,” with “a 25 base point increase in the real rate… lead[ing] on impact to a 1% drop in output” (p. 38). Because deficit-financed spending is more inflationary to begin with, it triggers a larger monetary tightening, so “while the impact multipliers are very different between financing schemes with fixed nominal interest rates, they become quite similar when a Taylor rule is used” – deficit financing’s larger stimulus and larger induced tightening roughly offset each other (p. 38).

A one percent deficit-financed increase in transfers produces an impact multiplier of 0.66 – larger than the corresponding tax-financed spending multiplier because “an increase in transfers benefits low income, high MPC households since their disposable income increases more… than that of high income, low MPC households” – but a cumulative multiplier of only about 0.1 (Sec. 3.5.2, p. 39-40). The gap arises “because the future decrease in transfers needed to return nominal government debt to its steady state level is sufficiently contractionary to almost offset the contemporaneous gains” (p. 40); the paper also reports the transfer stimulus slightly lowers welfare (−0.00067% in consumption equivalents), “because the welfare gain in the initial periods is eventually (slightly) outweighed by the later welfare losses” (p. 40).

No – the paper explicitly contrasts its result with Farhi and Werning (2016), who “show that in complete markets New Keynesian models the further the spending is in the future the larger is the impact,” whereas “our analysis implies that the multiplier becomes smaller if the spending is pre-announced to occur at a future date” (Sec. 3.5.3, p. 44). With incomplete markets, anticipated future spending raises the price level gradually and “makes households shift consumption to these earlier periods, which dampens the fall in consumption initially but at the same time lowers their demand at the time of the actual spending increase,” so “the increase in consumption as well as the multiplier at that time are smaller than the corresponding multiplier in the case when the stimulus occurs immediately” (p. 44).

Simulating a large demand shock that pushes output down roughly 7% and binds the zero lower bound (following Cochrane 2017’s calibration), the paper finds “both the spending and the transfer multipliers in a liquidity trap are not very different from their counterparts in the benchmark experiments outside the liquidity trap” (Sec. 3.5.7, p. 47) – a notable contrast with some complete-markets ZLB models where multipliers become extreme. The paper also shows the multiplier declines with the scale of the stimulus (larger transfers/spending imply lower marginal propensities to consume, consistent with the model’s partial-equilibrium MPC schedule, Sec. 3.5.4), rises with the persistence of the spending increase (Sec. 3.5.5), and is sensitive to the degree of price and wage rigidity assumed (Sec. 3.5.8).

The conclusion lists five interacting features as essential (Sec. 4, p. 50-51): (1) market incompleteness generates realistic, heterogeneous MPCs and breaks Ricardian equivalence, so financing has real distributional consequences and transfer multipliers become meaningful to analyze; (2) empirically realistic price rigidity ensures the model captures the aggregate-demand channel as observed in the data; (3) the fully dynamic (not one-shot) structure lets households’ current spending respond to anticipated future income and financing changes, which the paper shows is central to why HANK multipliers exceed TANK multipliers; (4) nominal government bonds deliver price-level determinacy, letting the model evaluate arbitrary monetary-fiscal policy combinations including an interest-rate peg; and (5) capital accumulation adds an investment channel that interacts with – and can be crowded out by – the consumption channel, particularly under deficit financing.