Fiscal-Monetary-Interactions | Macro Paper Warehouse

A Goldilocks Theory of Fiscal Deficits

Mon, 01 Jan 0001 00:00:00 +0000

This paper develops a tractable continuous-time model to study the fiscal sustainability of government deficits and the joint dynamics of public debt, with two main ingredients: an endogenous interest rate R that rises with the debt level through a convenience yield mechanism (savers value holding government bonds), and a potentially binding zero lower bound (ZLB) on the nominal interest rate. The paper’s central theoretical contribution is deriving the correct free-lunch condition: not the commonly cited $R < G$, but the stricter condition $R < G - \varphi$, where $\varphi$ captures the sensitivity of $R - G$ to debt. Even when $R < G$, accumulating more debt raises R through reduced convenience yields, and this endogenous feedback tightens fiscal sustainability. The paper maps the full deficit-debt space with a hump-shaped locus, analyzes ZLB dynamics where the deficit-debt relationship can invert, and studies the role of income inequality and tax policy. Calibrating to U.S. and Japan as of December 2019, the paper finds little room for free-lunch policies in the U.S. — a maximum permanent deficit of just over 2% of GDP at a stable debt-to-GDP ratio of 110% — while Japan is in the “inverted” ZLB regime where deficit increases can reduce debt through higher nominal growth.

Summary of a published paper based on the NBER working paper full text (w29707), AI-assisted, pending human review. See the linked original for the authoritative claims and full conditions.

Layer 1: Overview

Mian, Straub, and Sufi construct a tractable deterministic continuous-time model with savers who derive convenience utility from holding government bonds, hand-to-mouth spenders, and a monetary authority that targets inflation (except at the ZLB), to systematically analyze when deficits can be “free lunches.” The core insight is that the standard r < g analysis treats interest rates as exogenous to the debt level, but if R rises as debt accumulates — through the declining marginal convenience yield of bonds — then the condition for a free-lunch policy is not R < G but R < G − φ. This matters empirically: the paper estimates φ (the debt-to-interest-rate sensitivity) from empirical estimates of the convenience yield elasticity, and calibrates the model to U.S. and Japan December 2019 conditions. The U.S. calibration finds a maximum free-lunch deficit of just over 2% of GDP at a stable debt ratio of 110%, implying the U.S. was barely inside the free-lunch region pre-Covid. By contrast, the paper finds ample free-lunch space for Japan and an “inverted” ZLB regime in which higher deficits can reduce the debt-to-GDP ratio by stimulating nominal growth. The analysis is extended to incorporate aggregate risk, capital, debt maturity structure, and inequality — each with distinct implications for the size and location of fiscal space.

In depth

Q1. What is the deficit-debt diagram, and what is the free-lunch condition?

The deficit-debt diagram is the locus of steady-state combinations of the primary deficit z and the debt-to-GDP ratio b, derived from the government budget constraint $\dot{b} = -(G^ - R^(b))b + z$ at steady state; this locus is hump-shaped, with the maximum sustainable permanent deficit z occurring at the debt level b where $R^(b^) = G^* - \varphi(b^)$.** The hump shape arises because at low debt levels the convenience yield is high (R is low relative to G, allowing large deficits), while at high debt levels the convenience yield is saturated (R rises toward G, leaving little deficit room). The left branch of the locus — where debt levels are below b — is the free-lunch region: any permanent increase in the deficit to a value below z* raises the steady-state debt level but requires no future tax increases. The right branch — debt above b* — is the conventional region: any deficit increase must eventually be accompanied by higher taxes. The key departure from the standard r < g analysis is that R is endogenous; Proposition 1 and Corollary 1 formally establish that the correct free-lunch threshold is $R^(b_0) < G^ - \varphi(b_0)$, not simply R < G.

Q2. Why is R < G insufficient as a free-lunch condition, and what does φ capture?

The condition R < G fails as a free-lunch criterion because, when the government borrows an additional dollar and rolls it over forever, it faces two opposing budget effects: a positive cash flow of G − R from rolling over the existing debt, and a tightening of the budget constraint from the endogenous rise in R on all infra-marginal outstanding debt; the parameter φ measures the magnitude of this second effect as the semi-elasticity of R − G with respect to the log of debt. When φ is positive — as it is empirically because convenience yields are declining in debt supply — the net fiscal benefit of rolling over additional debt is G − R − φ, not G − R. An economy can exhibit R < G yet be in the conventional debt region if φ is sufficiently large that R > G − φ at the current debt level. The U.S. calibration illustrates this: the traditional R < G condition holds up to a debt ratio of 220% of GDP, but the stricter R < G − φ condition breaks down already at 110%, which is the actual boundary of the free-lunch region for the U.S.

Q3. How does the analysis change at the zero lower bound, and what is the “inverted” fiscal regime?

At the ZLB, the direction of causality reverses: instead of the debt level determining the interest rate, the debt level determines the nominal growth rate G (via aggregate demand and the Phillips curve), creating an “inverted” regime in which higher deficits can reduce rather than increase debt by stimulating nominal growth and inflating away the debt. The mechanism is: when the nominal rate is constrained at zero, fiscal expansion raises aggregate demand, which via the Phillips curve (slope κ) raises inflation, which raises nominal growth G, which accelerates the inflation of the debt ratio. If the fiscal multiplier times κ times the debt level exceeds one — a sufficient statistic condition — then higher deficits reduce the debt ratio. The paper finds this condition plausible for Japan (debt ratio ~225%, estimated κ = 0.1-0.3, multipliers of 1.5-2) but not for the U.S. in 2019. The deficit-debt locus in this regime is “backward-bending”: as the ZLB binds more tightly (lower debt), the locus can curve back and eventually allow the inverted relationship between deficits and debt.

Q4. How does income inequality affect fiscal space, and why does the ZLB reverse the sign?

Outside the ZLB, greater income inequality (a larger income share of savers relative to hand-to-mouth spenders) expands fiscal space, because savers have a higher propensity to save, which reduces the natural interest rate R and thus raises G − R and allows larger sustainable deficits; at the ZLB, greater inequality shrinks fiscal space, because it reduces aggregate demand and hence nominal growth G rather than R.* Formally, outside the ZLB: $z(b) = (v’(b)(1-x-\mu) - \rho)b$, which increases as the spender share μ falls (Corollary 3). At the ZLB, nominal growth G becomes demand-determined via equation (20), and lower μ reduces demand, lowering G and hence z(b). The policy implication is a potential conflict between redistributive policies and deficit finance: redistribution (raising μ) reduces fiscal space outside the ZLB but expands it at the ZLB. The paper notes that roughly 69% of U.S. government debt held by households is directly or indirectly held by the top 10% of the wealth distribution, making savers’ saving propensity the primary driver of the convenience yield.

Q5. What are the U.S. and Japan calibration results for fiscal space as of December 2019?

For the U.S. in December 2019, the model calibrates a maximum permanent primary deficit z of just over 2% of GDP at a stable debt-to-GDP ratio of b ≈ 110%, implying the U.S. was just inside the free-lunch region; for Japan, the model finds the economy in the inverted ZLB regime where higher deficits reduce debt by raising nominal growth.** The calibration uses empirical estimates of φ from the literature on convenience yield demand elasticities (Krishnamurthy and Vissing-Jorgensen 2012, Laubach 2009, Presbitero and Wiriadinata 2020). For the U.S., the standard r < g condition holds up to a debt ratio of 220% (the upper bound), but the binding free-lunch condition R < G − φ limits fiscal space to 110%. Deficits beyond the 2%-of-GDP limit must be financed by future tax increases or spending cuts, even though R < G throughout the range. The Japan calibration illustrates the ZLB regime: with a debt ratio already above 200%, the fiscal multiplier effect on inflation is large enough that the backward-bending locus applies, and Japan’s economy lies in the inverted region.

Q6. How does the analysis extend to aggregate risk, capital crowding-out, and debt maturity?

With aggregate risk, the free-lunch condition R < G − φ remains informative: when the condition holds on average, free-lunch policies can be designed with probability approaching one; when it fails on average, no free lunch is possible. The risk extension follows Mehrotra and Sergeyev (2020) and confirms numerically that the deterministic condition provides a valid signal for the stochastic case. Adding capital and crowding-out (Section 7.2) yields a counterintuitive finding: greater crowding-out of capital actually increases fiscal space by reducing the sensitivity of interest rates to debt (lower φ), because each additional unit of government debt displaces private capital rather than reducing convenience yields as sharply. Regarding debt maturity: issuing long-term debt reduces fiscal space at low debt levels (locking in higher interest costs), but increases it at high debt levels; this suggests that QE-style maturity shortening may constrain fiscal space as debt rises. These extensions confirm that the φ parameter — and the R < G − φ condition — is robust to a range of model ingredients, making it a practically useful criterion beyond the baseline model.

Key Concepts

free-lunch fiscal policy : a permanent increase in the primary deficit that raises steady-state debt to a new higher level without requiring any future tax increases or spending cuts; feasible only when $R^(b_0) < G^ - \varphi(b_0)$, which is strictly tighter than the standard r < g condition when φ > 0.

debt-rate sensitivity (φ) : the semi-elasticity of R − G with respect to the log of debt, capturing how much the endogenous convenience yield on government bonds falls (and hence interest rates rise) as the debt supply increases; the paper’s addition to the standard r < g framework that tightens the sustainability condition from R < G to R < G − φ; estimated empirically from convenience yield demand curves.

deficit-debt diagram : the hump-shaped locus of sustainable steady-state combinations of the primary deficit and the debt-to-GDP ratio; the left (increasing) branch is the free-lunch region where fiscal expansion is self-sustaining, and the right (decreasing) branch is the conventional region where fiscal expansion requires future tax increases.

inverted ZLB fiscal regime : the case where the nominal interest rate is zero and the deficit-debt locus bends backward, so that higher deficits reduce rather than increase the debt ratio; occurs when the fiscal multiplier is large enough that deficit-induced nominal growth more than offsets the direct debt accumulation effect; found to apply to Japan as of December 2019 but not the U.S.

convenience yield : the non-pecuniary benefit savers derive from holding government bonds (capturing liquidity, safety, and regulatory premia), modeled as the utility function v(b) for savers; the mechanism making R endogenous to debt: as debt supply rises, the marginal convenience yield v’(b) falls, pushing R toward G and shrinking fiscal space.

Can Deficits Finance Themselves?

Mon, 01 Jan 0001 00:00:00 +0000

The paper asks whether a government can run a deficit today — issuing “stimulus checks” — and allow debt to return to its initial level without any future tax hike or spending cut. In environments combining (i) nominal rigidity and (ii) a violation of Ricardian equivalence (due to finite lives or liquidity constraints), this is possible through two complementary self-financing channels: (a) a Keynesian boom in real activity that expands the tax base and automatically raises revenue at existing tax rates; and (b) a surge in inflation that erodes the real value of outstanding nominal government debt. The paper’s headline result is that self-financing increases monotonically as fiscal adjustment is delayed, converging to full self-financing in the limit: if monetary policy does not lean too heavily against the fiscal stimulus, the initial deficit eventually returns debt to trend with no required future adjustment. Calibrated to empirical evidence on intertemporal MPCs, the speed of fiscal adjustment, the Phillips curve slope, and the monetary reaction, the model finds self-financing up to ν ≈ 0.95 — with the tax base channel dominant and inflation contributing negligibly.

Environment (Section 2): Baseline is a perpetual-youth overlapping-generations (OLG) version of the textbook New Keynesian model. Households survive from one period to the next with probability ω ∈ (0,1]; when ω=1 the model reduces to the standard PIH-RANK benchmark in which Ricardian equivalence holds and no self-financing occurs. When ω<1, two properties of consumer demand emerge: (i) consumers discount future disposable income at a rate higher than the interest rate (“discounting”), so a distant future tax hike barely affects today’s spending; (ii) consumers spend transfers relatively quickly (“front-loading”), so the Keynesian boom plays out before the promised tax hike arrives. The supply block is exactly the standard NKPC. Fiscal policy follows a rule in which taxes respond to income through a fixed tax rate τy (tax base channel) and to debt through a speed-of-adjustment coefficient τd ∈ (0,1) (with τd→0 meaning indefinitely delayed adjustment). Monetary policy keeps (expected) real rates constant in the baseline — a “neutral” benchmark that neither offsets nor amplifies the fiscal stimulus.

Self-financing result (Sections 3–4): Starting from a date-0 deficit shock ε0 (lump-sum transfer of 1% of steady-state output), define the degree of self-financing ν as the fraction of ε0 financed by the tax base and debt erosion channels; 1−ν equals the discounted present value of future tax hikes required to stabilize debt. The central results are:

Theorem 1 (baseline, φ=0): If ω<1 and τy>0, ν increases monotonically as τd→0, with ν→1 in the limit. Intuition via two-period analogy: when cumulative short-run MPC → 1, the Keynesian multiplier → 1/τy, and the induced tax revenue → 1 — exactly financing the original ε0.
Proposition 3: For any given τd or delay H, ν is strictly decreasing in ω: larger departures from permanent income (smaller ω) deliver faster and larger Keynesian booms and hence greater self-financing.
Theorem 2 (general monetary policy): Under a general real rate rule rt = φ·yt, there exists a threshold φ̄ ∈ (0, τy/(β·D^ss/Y^ss)) such that: if φ<φ̄, full self-financing is achieved in the limit; if φ>φ̄, ν is bounded strictly below 1 by ν̄(φ). If the monetary authority perfectly stabilizes output and inflation (φ→∞), ν=0 by construction.
Theorem 3 (general aggregate demand): With generalized demand ct = Md·dt + My·(yt−tt) + δ·Et[Σ(βω)^k(yt+k−tt+k)], self-financing holds whenever (i) ω<1 and (ii) Md>1−β and My·(1 + δ·βω/(1−βω)) ≥ 1. This nests the baseline OLG model, hybrid spender-OLG models, and approximately represents quantitative HANK models.

Distinction from FTPL: The Fiscal Theory of the Price Level (Cochrane) breaks Ricardian equivalence through equilibrium selection in a PIH-RANK setting; the self-financing here operates under the conventional equilibrium, with an active monetary authority and passive fiscal authority. The inflation channel is not the focal mechanism — the tax base channel is dominant.

Calibration (Table 1, hybrid OLG-spender model, quarterly frequency):

Consumer spending: share of hand-to-mouth (HtM) spenders µ = 0.073; OLG survival rate ω = 0.865; jointly matched to average MPC = 0.2 and short-run MPC slope from Fagereng, Holm, and Natvik (2021)
Fiscal adjustment: τd ∈ {0.085, 0.026, 0.004} (fast to slow; from Galí et al. 2007, Bianchi-Melosi 2017, Auclert-Rognlie 2020 respectively; equivalent to H ∈ {12, 23, 43} quarters under the non-Markovian rule)
Monetary policy: real rate feedback φ = 0 (neutral baseline)
Nominal rigidities: NKPC slope κ = 0.0062 (Hazell et al. 2022 point estimate)
Standard parameters: EIS σ=1 (log utility); β = 0.998 (1% annual real rate); tax feedback τy = 0.33 (DeLong-Summers benchmark: 33 cents of surplus per dollar of output); liquid wealth D^ss/Y^ss = 1.04 (Kaplan et al. 2018)

Quantitative results (Figure 3, Table 2):

For empirically calibrated τd range, ν reaches up to 0.95, nearly full self-financing in the most realistic (slow adjustment) specification
Virtually all self-financing (≈95–100%) occurs through the tax base channel — the flat NKPC (κ=0.0062) limits inflation and debt erosion to a negligible share; with steeper NKPC (κ=0.1), about 20% of self-financing comes through date-0 inflation
The quantitative fiscal multiplier at τd=0.085 is 1.11, consistent with Ramey (2011) empirical estimates for transfers with relatively quick adjustment
Table 2 (νmax as function of monetary ψ and NKPC κ): Full self-financing (νmax = 1) is attainable when ψ ≤ 1.25 and κ = 0.0062; drops to νmax = 0.63 at ψ=1.5 and κ=0.0062; drops to νmax = 0.22 with κ=0.1 and ψ=1; approaches 0 with both aggressive monetary and flexible prices. Key lesson: moderate monetary reaction combined with flat NKPC (consistent with evidence) supports near-full self-financing.

Robustness:

HANK model: same conclusions as hybrid spender-OLG; intertemporal MPCs nearly identical (Wolf, 2021; Auclert et al., 2023)
Distortionary fiscal adjustment: negligible impact, since the required adjustment itself vanishes in the limit
Government purchases: same self-financing logic applies (Keynesian boom raises tax revenue)
Investment: Keynesian cross applies to consumption; net of investment aggregate demand follows the same law of motion — self-financing result unchanged

Scope conditions: Self-financing requires Ricardian equivalence to fail (ω<1); in the PIH-RANK benchmark (ω=1), neither self-financing channel is operative. Monetary accommodation is assumed neutral or weak; aggressive offsetting (φ>φ̄) prevents full self-financing. The paper is purely positive: whether deficits are optimal is a separate normative question. Results are log-linearized dynamics; the quantitative conclusions depend on discipline from empirical MPC evidence, NKPC estimates, and fiscal adjustment speed. The self-financing mechanism operates through aggregate demand and is not driven by r<g or by seigniorage from a convenience yield.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the two-period intuition for full self-financing?

In a two-period economy with fully myopic consumers (MPC=1), a date-0 transfer of ε stimulates output by y = MPC/(1−MPC·(1−τy)) · ε, generating tax revenue τy·y; with MPC→1 the output multiplier converges to 1/τy and tax revenue converges to exactly ε — full self-financing via the tax base. The infinite-horizon economy with ω<1 mirrors this intuition when fiscal adjustment is delayed far enough: the “short run” cumulative MPC approaches 1 (by discounting and front-loading), the Keynesian cross delivers a multiplier of 1/τy, and the additional tax revenue precisely repays the deficit, with no future tax hike needed.

Q2. Why does the degree of self-financing ν increase as fiscal adjustment is delayed?

As the gap H between the date-0 transfer and the promised future tax hike widens, two effects amplify the Keynesian boom: (i) near-term demand is less dampened by anticipation of the future tax hike (discounting makes far-ahead taxes nearly irrelevant to today’s spending); and (ii) the general equilibrium income feedback — the Keynesian cross — has more time to play out before being curtailed by the eventual tax hike, amplifying the total output and revenue response. The longer the delay, the larger the short-run cumulative MPC, and the larger the fraction of the deficit self-financed through the tax base.

Q3. Why does aggressive monetary policy block self-financing?

If the monetary authority raises real interest rates in response to the fiscal boom (φ>0), it discourages household spending, slowing and shrinking the Keynesian boom; above the threshold φ̄, the real rate increase is strong enough to counteract the tax base feedback before the cumulative MPC can converge to 1, meaning full self-financing becomes impossible and some future fiscal adjustment is always required. Conversely, monetary accommodation (φ<0) accelerates the boom and permits full self-financing with less delay, while perfectly stabilizing output and inflation (φ→∞) entirely shuts down both self-financing channels.

Q4. What is the role of the NKPC slope in determining which channel operates?

When the NKPC is flat (κ=0.0062, the Hazell et al. 2022 estimate), a large output boom generates negligible inflation, so debt erosion contributes almost nothing and the tax base channel carries essentially all the self-financing; when the NKPC is steep (κ=0.1, consistent with supply-constrained post-COVID), the same boom generates materially more inflation, shifting the financing split so that ~20% comes through debt erosion while ~80% still comes through the tax base. The overall degree of self-financing ν is affected only through the monetary response: a steeper NKPC triggers a more aggressive real rate response, moderating the boom, but this is captured in the analysis of Theorem 2 and Table 2.

Q5. How does this paper relate to and differ from the Fiscal Theory of the Price Level (FTPL)?

The FTPL (Cochrane) achieves deficit financing through inflation in a PIH-RANK environment by abandoning the Taylor principle and exploiting equilibrium selection; this paper requires no such departure — both monetary and fiscal policy follow conventional active/passive assignments, and the equilibrium studied is the unique bounded one. The key difference is in the consumer block: Ricardian equivalence fails here through finite lives or liquidity constraints (empirically grounded), not through equilibrium selection. Moreover, while FTPL highlights the debt erosion (inflation) channel, this paper finds the tax base (real activity) channel is dominant under empirically calibrated flat Phillips curves.

Q6. What new conditions on aggregate demand ensure self-financing extends beyond the OLG baseline?

Theorem 3 identifies two sufficient conditions: (1) “positive geometric discounting” (ω<1 in the generalized demand block), ensuring that far-ahead future taxes have negligible effect on current demand; and (2) “sufficient front-loading” (Md > 1−β and My·(1 + δ·βω/(1−βω)) ≥ 1), ensuring that income is spent quickly enough for the Keynesian feedback to deliver self-financing before debt explodes. The classical PIH-RANK fails condition (1); the spender-saver model with any margin of PIH consumers fails condition (2); the OLG baseline satisfies both; and the hybrid spender-OLG (the quantitative workhorse) satisfies both for any ω<1.

Q7. Is a margin of truly PIH consumers fatal for self-financing?

Yes — introducing any strictly positive mass of PIH consumers breaks self-financing entirely, creating a discontinuity: ν=0 whenever µ_PIH > 0, no matter how small. The intuition is that PIH consumers never fully spend any income received in finite time (they smooth it across their infinite horizon), so the cumulative MPC never reaches 1 and the Keynesian boom cannot fully finance the deficit. However, the discontinuity is fragile: replacing literal PIH consumers with “near-PIH” consumers (finite but large ω) restores ν→1 in the limit as H→∞ and is consistent with empirical evidence on high MPCs for liquid households.

Key concepts

fiscal self-financing : the property that a deficit-financed government transfer raises output and inflation sufficiently to replenish government revenue (via the tax base channel) and reduce the real debt burden (via the inflation/debt erosion channel), allowing debt to return to steady state without future tax increases; the degree ν ∈ [0,1] measures what fraction of the initial deficit is self-financed.

tax base channel : the mechanism by which a Keynesian boom in real activity — triggered by the deficit-financed transfer — automatically raises tax revenue (by τy dollars per dollar of additional output) without any change in tax rates; dominant over the debt erosion channel whenever the NKPC is flat (empirically, κ ≈ 0.006).

discounting and front-loading : the two consumer demand properties necessary for self-financing; “discounting” (ω<1) means far-ahead future taxes barely affect current spending, allowing the deficit to stimulate demand even with a promised future tax hike; “front-loading” means the income response is spent quickly, so the Keynesian boom plays out before the delayed tax hike arrives, raising tax revenue sufficiently to finance the deficit.

speed of fiscal adjustment (τd) : the quarterly feedback from public debt to tax revenue in the fiscal rule; τd→0 means indefinitely delayed adjustment and maximum self-financing; empirically disciplined values range from τd=0.085 (fast, Galí et al. 2007) to τd=0.004 (slow, Auclert-Rognlie 2020), with νmax ≈ 0.95 across this range under neutral monetary policy and flat NKPC.

hybrid spender-OLG model : the paper’s quantitative workhorse, combining a fraction µ of hand-to-mouth spenders with OLG perpetual-youth consumers; jointly calibrated to match the impact and short-run MPCs from Fagereng et al. (2021), while also providing a close proxy for aggregate demand in quantitative HANK models (Auclert et al. 2023; Wolf 2021).

Capital Income Taxation and Self-Fulfilling Aggregate Instability

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper overturns the longstanding consensus established by Schmitt-Grohé and Uribe (1997) that relying on capital income tax adjustments to balance the government budget immunizes the economy against self-fulfilling aggregate instability. The key departure from the prior literature is endogenous capital utilization: when the capital income tax rate adjusts to close budget imbalances and capital utilization is an optimal decision by households, a “fiscal increasing returns” mechanism emerges in which higher economic activity lowers the tax rate, raises the after-tax return to capital, and induces further expansion — rendering the economy prone to sunspots-driven fluctuations. Calibrated to the United States, United Kingdom, and Japan using effective tax rates and public debt-to-GDP ratios, the paper finds that all three economies lie within the indeterminacy region under their current capital income tax rates and capital depreciation allowances of approximately 0.2; stabilization would require raising the depreciation allowance rate from 0.2 to 0.76 or reducing income tax rates by 39–52 percent. Capital depreciation allowances serve as a stabilization device: full allowances (allowance rate = 1) make indeterminacy entirely impossible regardless of the tax rate, because they extinguish the fiscal increasing returns mechanism, and the paper also shows analytically that public debt can be destabilizing rather than stabilizing when capital taxes are used for fiscal adjustment.

In depth

Q1. What is the fiscal increasing returns mechanism that overturns the Schmitt-Grohé-Uribe result?

When the government adjusts the capital income tax rate to balance the budget, higher labor input raises output and the capital tax base, allowing a lower tax rate; under endogenous capital utilization, this triggers an additional channel in which a lower after-tax depreciation cost induces firms to utilize capital more intensively, further raising the effective capital stock and output — generating fiscal increasing returns to scale and a factor share redistribution from capital to labor that together make indeterminacy possible. In log-linearized terms, the effective output-labor elasticity in the equilibrium aggregate production function exceeds unity for tax rates in the interval (τ̄, τ̂) where τ̄ = ρ/(ρ+δ) and τ̂ is the Laffer-curve peak, and this greater-than-unity elasticity is the formal condition for indeterminacy (Corollary 1). With a constant utilization rate as assumed in prior work, both the factor share redistribution and fiscal increasing returns effects vanish, the effective output-labor elasticity falls below unity, and indeterminacy becomes impossible — confirming that endogenous capital utilization is the essential ingredient.

Q2. What are the formal conditions for indeterminacy under the baseline capital tax rule?

Proposition 1 establishes that the fiscal policy with capital income taxation induces indeterminacy of equilibrium if and only if the long-run capital income tax rate τk lies strictly in the open interval (τ̄, τ̂), where τ̄ = ρ/(ρ+δ) and τ̂ is the unique Laffer-curve peak. Under the standard calibration (ρ = 0.04, δ = 0.1, α = 0.3), this interval is (0.286, 0.717) — a wide range covering the effective capital income tax rates of the U.S., UK, and Japan. The determinant of the Jacobian of the linearized dynamic system is positive and the trace is negative over this interval, implying that both eigenvalues are negative, which is the condition for indeterminacy with one predetermined variable (capital) and one jump variable (marginal utility of income).

Q3. How do capital depreciation allowances serve as a stabilization device?

When the taxable capital income base is reduced by a fraction γ ∈ [0, 1] of depreciation expenses, the effective degree of fiscal increasing returns to scale decreases strictly with γ, and the lower bound of the indeterminacy interval τ̄D strictly rises with γ; with full depreciation allowances (γ = 1), the quadratic equation characterizing the lower bound has a repeated unit root, the indeterminacy interval becomes empty, and multiplicity of equilibria is entirely impossible regardless of the capital income tax rate. Corollary 2 formalizes this result analytically. The intuition is that depreciation allowances reduce the procyclicality of the effective tax burden on capital, so the after-tax return to capital responds less strongly to activity, weakening the self-fulfilling loop. Partial allowances — even well below γ = 1 — can sufficiently shrink the indeterminacy region to require implausibly high tax rates for instability.

Q4. What is the role of public debt and what new result does the model deliver?

Contrary to the established view that public debt can serve as an automatic stabilizer that exempts balanced-budget fiscal policy from beliefs-driven instability (Schmitt-Grohé and Uribe 1997, Huang et al. 2018), this paper shows that public debt can be destabilizing when capital income taxes adjust to balance the budget: a higher public debt-to-GDP ratio expands the indeterminacy region, and this destabilizing effect is amplified when capital depreciation allowances are low. Figure 5 in the paper illustrates numerically that raising the public debt-to-GDP ratio from an average of 0.975 (US/UK average) to 1.429 (Japan) dramatically widens the indeterminacy region, particularly at low depreciation allowance rates. This novel result — that public debt destabilizes rather than stabilizes under capital income tax adjustment — constitutes a third main contribution of the paper alongside the indeterminacy result and the stabilization role of depreciation allowances.

Q5. What are the quantitative results for the US, UK, and Japan?

Under the calibrated depreciation allowance rate of approximately 0.2 (the GDP-weighted European average from D’Erasmo et al. 2017, also consistent with the US), all three large economies lie within the indeterminacy region at their current effective income tax rates; stabilization requires either raising the depreciation allowance rate to 0.76 for all three, or reducing income tax rates by 47% for the US, 52% for the UK, and 39% for Japan from their calibrated levels while holding depreciation allowances at 0.2. Less dramatic combination policies also work: for the US, a 10% income tax cut combined with raising the depreciation allowance to 0.67 would suffice, as would a 5% tax cut combined with raising the allowance to 0.70. These calculations are calibrated to effective factor income tax rates from Mendoza et al. (1994) updated to 1996 and public debt-to-GDP ratios from OECD Economic Outlook (2014).

Q6. How does the paper relate to and contribute to the broader indeterminacy literature?

The paper’s mechanism — fiscal increasing returns arising from the interaction of optimal capital utilization and capital income taxation — is novel relative to both strands of the indeterminacy literature: unlike Benhabib-Farmer-style models that require the aggregate production function to have increasing returns as a primitive assumption, and unlike the Schmitt-Grohé-Uribe labor-tax indeterminacy that also does not require increasing returns but found capital taxation immune, this paper shows that increasing returns can emerge endogenously from a constant-returns-to-scale production technology via fiscal policy, requiring no externalities or other non-standard features. The mechanism provides a policy-based micro-foundation for aggregate increasing returns that resolves the empirical criticism of the prior indeterminacy literature; it also distinguishes the result from Huang et al. (2018), who showed that endogenous capital utilization under labor income tax adjustment raises indeterminacy likelihood but leaves the production function at constant returns to scale.

Key Concepts

fiscal increasing returns : the mechanism in this paper whereby higher economic activity lowers the capital income tax rate (via a higher tax base), raises the after-tax return to capital, and induces greater capital utilization and further output expansion; operationally defined by the effective output-labor elasticity exceeding unity in the equilibrium aggregate production function.

equilibrium indeterminacy : the existence of multiple rational-expectations equilibria converging to the same steady state, arising from the fiscal increasing returns mechanism and permitting self-fulfilling sunspots fluctuations unrelated to economic fundamentals; characterized by both eigenvalues of the Jacobian being negative (both predetermined structure of the dynamic system).

capital depreciation allowance : the fraction γ ∈ [0, 1] of capital depreciation costs deductible from the taxable capital income base; the stabilization device the paper identifies, which works by attenuating the procyclical component of the effective capital tax burden and thereby reducing the fiscal increasing returns to scale.

factor share redistribution : in this paper, the shift of the effective factor income share from capital to labor that results from endogenous capital utilization interacting with the capital tax rule; contributes to indeterminacy by raising the effective output-labor elasticity above the share of capital in the production function.

Summary of a forthcoming paper, AI-assisted. Draft pending human review. See the linked original for the authoritative claims and full conditions.

Committed to flexible fiscal rules

Mon, 01 Jan 0001 00:00:00 +0000

A central debate in fiscal policy is whether fiscal rules—numerical constraints on budget deficits or debt levels—impair a government’s ability to respond to adverse economic shocks, creating a fundamental trade-off between debt stabilization and macroeconomic stabilization. This paper uses data on large, random natural disasters as exogenous shocks to address the endogeneity of rule adoption and provides new empirical and theoretical evidence on this trade-off. Contrary to the trade-off hypothesis, countries with fiscal rules perform significantly better following such disasters than countries without rules: GDP and private consumption are persistently higher, and fiscal policy is significantly more expansionary. The superior performance is shown to depend on the existence of prior fiscal space and the presence of escape clauses in the rules. A model of sovereign default with endogenous fiscal space and tax plans rationalizes these findings: tight rules prevent myopic governments from accumulating excessive debt in good times, which creates fiscal space for deficit spending when disasters strike, keeping sovereign spreads lower and enabling more expansionary fiscal responses.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the identification strategy and why do natural disasters solve the endogeneity problem?

Large natural disasters serve as a source of exogenous, random adverse economic shocks; by interacting disaster exposure with the presence or absence of fiscal rules, the paper identifies the effect of rules on macroeconomic performance without confounding from the non-random adoption of rules. Endogeneity is a central concern in the fiscal rules literature because countries that adopt rules may differ in politically or economically relevant ways from those that do not (e.g., more disciplined political environments, stronger institutions). Using large disasters as quasi-experimental variation removes this concern: the timing and magnitude of natural disasters are uncorrelated with which countries happened to adopt fiscal rules, isolating the effect of rules on crisis response.

Q2. What are the main empirical findings?

Countries with fiscal rules show significantly higher output and private consumption following large natural disasters, and implement significantly more expansionary fiscal policy, compared to countries without rules—holding over a 1970Q1–2018Q4 quarterly panel—with confidence bands at the 68% and 90% levels based on 500 Monte Carlo draws. The result directly contradicts the commonly held view that fiscal rules restrict governments’ ability to respond to shocks. Moreover, the paper finds that the superior performance of rule-constrained countries is conditional on two features: the existence of fiscal space prior to the shock (low debt or deficit positions), and the presence of escape clauses that allow rules to be suspended during severe adverse events.

Q3. What is the model mechanism?

In the sovereign default model, a fiscal rule prevents a myopic government from over-borrowing in good times out of political economy considerations (e.g., electoral incentives to spend); this forced restraint creates fiscal space—lower debt, lower sovereign spreads—which allows the government to run deficits when a shock hits without triggering a default episode or a sharp rise in borrowing costs. The model predicts that, relative to a no-rule economy, when a disaster strikes in a rule-constrained economy: sovereign spreads spike by less, the fiscal policy response is more expansionary, and output and consumption are higher. Escape clauses in the rules are important: they allow the government to depart from the rule explicitly in crisis situations without destroying the credibility of the rule in normal times.

Q4. What is the policy implication for the COVID-19 fiscal response?

The paper’s findings directly address the suspension of fiscal rules during COVID-19: the theoretical and empirical results suggest that rules with escape clauses do not impair crisis response and may actually improve it, by ensuring fiscal space is available when needed. The paper’s evidence implies that the COVID-era suspension of rules in many countries (including the EU’s Stability and Growth Pact) was not necessarily required to enable expansionary fiscal responses—countries with well-designed rules including escape clauses could have responded expansively while maintaining rule credibility.

Key concepts

escape clause : a provision in a fiscal rule that explicitly permits departure from the rule’s numerical target under defined circumstances (severe recessions, natural disasters, etc.); the paper finds that the presence of escape clauses is one of the two conditions for rule-constrained countries to outperform non-rule countries after adverse shocks.

fiscal space : the buffer of low debt and deficit levels that allows a government to increase spending or cut taxes during a shock without triggering unsustainable debt dynamics or elevated sovereign spreads; the paper shows fiscal space is created by rules in good times and consumed in bad times.

Exorbitant Privilege Gained and Lost: Fiscal Implications

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper studies three centuries of U.K. fiscal history to understand the fiscal implications of safe asset supplier status — what the authors call “exorbitant privilege” — and how it can be gained and lost. Using the discounted cash flow approach to fiscal capacity developed in Jiang, Lustig, Van Nieuwerburgh, and Xiaolan (2019), the paper measures the present discounted value of expected future primary surpluses (inclusive of convenience yield seigniorage) and compares it to the observed market value of outstanding government debt. The central finding is a sharp historical discontinuity: before World War I, when the U.K. was the world’s dominant safe asset supplier and its gilts served as the global reserve asset, roughly only three-quarters of U.K. debt was backed by future surpluses even after accounting for convenience yields earned from global safe asset demand. After World War II, when the U.K. lost its safe asset supplier status to the U.S., the U.K.’s debt became fully backed by surpluses and fiscal capacity became closely tied to its own macro fundamentals. By contrast, the U.S. after World War II shows a pattern similar to the pre-war U.K. but more extreme: less than one-third of outstanding U.S. Treasury debt is backed by future surpluses according to the paper’s estimates, with the gap between debt and estimated fiscal capacity growing sharply over recent decades.

In depth

Q1. How does the paper measure fiscal capacity?

The paper follows the Jiang-Lustig-Van Nieuwerburgh-Xiaolan (2019) methodology, expressing the market value of outstanding government debt as the present risk-adjusted discounted value of expected future primary surpluses under the government’s intertemporal budget constraint — the no-arbitrage condition that rules out rational debt bubbles. The market value of the government debt portfolio equals the present value of tax revenues minus the present value of government spending. A Vector AutoRegression (VAR) imposing cointegration of GDP with tax revenues and government spending is used to forecast the joint dynamics of the surplus. The paper uses the market or output risk premium as the discount rate, imputing the risk properties of GDP to spending and tax revenue claims.

A key methodological challenge is handling structural breaks: before World War I, U.K. fiscal policy was pre-Keynesian — acyclical spending and taxes (except during wars) — so spending and tax revenue as shares of output inherit the risk properties of output, and the market risk premium is the appropriate discount rate. After World War II, spending becomes counter-cyclical and taxes pro-cyclical in the Keynesian framework; the paper argues that applying the market risk premium in this regime produces an upper bound on the PDV of surpluses. For the U.K., this methodology is validated: the correlation of fiscal capacity with the debt/output ratio is 0.90 in the pre-WW-I sample and remains high after WW-II, despite the fiscal regime change.

Q2. What are the quantitative findings for the U.K.?

The paper finds that before World War I, U.K. fiscal capacity fell systematically short of the observed market value of U.K. debt: the average debt/GDP ratio was 87.06% while the estimated fiscal capacity was only 69.32%, with the ratio of fiscal capacity to debt averaging 74.32% — implying roughly 26% of U.K. debt was not backed by future surpluses even after including convenience yield seigniorage. The U.K. earned average long-term convenience yields of approximately 100 basis points per annum from 1873 to 1931 (translating to approximately 0.47% of GDP in annual seigniorage), reflecting its dominant position as the world’s safe asset supplier and the quasi-monopoly position of gilts in global securities markets (U.K. national debt accounted for more than half of the world’s traded securities around 1815). Despite these convenience yields, the gap between fiscal capacity and debt persisted throughout the 19th and early 20th century.

After World War II, the picture reverses: the U.K.’s average post-war fiscal capacity of 82.03% of GDP exceeds its average debt/GDP ratio of 53.42%, leaving more than 50% of fiscal capacity unborrowed. The correlation with debt dynamics persists but the sign changes — U.K. borrowing is now constrained by own macro fundamentals rather than extended by global coordination.

Q3. What do the authors find for the United States?

The U.S. experience mirrors the pre-war U.K. after World War II but with much larger magnitudes: the paper’s estimates indicate that less than one-third (32.20%) of post-war U.S. Treasury debt is backed by future surpluses, with the gap between fiscal capacity and debt growing sharply toward the end of the sample to exceed U.S. GDP. Before World War I, the U.S. did not earn convenience yields — it was forced to borrow at higher rates than the U.K. despite having lower debt-to-output ratios — and its fiscal capacity exceeded its debt, with the ratio of capacity to debt averaging 169.36%. After World War II, when the U.S. became the global safe asset supplier under the Bretton-Woods architecture, the relationship inverted: average U.S. fiscal capacity of 13.20% of GDP represents only 32.20% of outstanding debt. The gap is increasingly large in recent decades as U.S. debt has grown while surplus projections have not expanded commensurately.

Q4. Why does safe asset supplier status allow a country to borrow beyond its fiscal capacity?

The paper argues that global investors coordinate on a single safe asset issuer based on relative macro fundamentals; this coordination is self-reinforcing because each additional investor holding the asset reduces rollover risk and renders the debt safer for all others, creating strategic complementarities that concentrate global fiscal capacity in one country beyond what its own surpluses would warrant. Unlike domestic convenience yields (arising from household demand for safe assets to insure idiosyncratic risks), the global safe asset effect creates a form of extra-fiscal capacity that depends on investors’ common belief about which country is the hegemon. The measured seigniorage from convenience yields — about 0.47% of U.K. GDP before WW-I and 0.36% per year for the U.S. post-war — does not fully capture this coordination benefit; the remaining gap between fiscal capacity and debt reflects the additional “license to borrow” that comes with global hegemon status.

The transition from U.K. to U.S. hegemony illustrates the mechanism: as U.K. macro fundamentals deteriorated relative to U.S. fundamentals after the world wars, investors shifted the concentration of fiscal capacity toward the U.S. The U.K. lost its license to borrow beyond its fundamentals; the U.S. gained it. The paper notes that the U.K. debt/output ratio exceeded 200% after WW-II — a level associated with the loss of hegemony.

Q5. What historical data and institutional context does the analysis use?

The paper uses annual data for the U.K. from 1729 to 2020 (from the Bank of England’s Millennium of Macroeconomics dataset and the Ellison-Scott dataset on individual bond market values from 1694 onward) and for the U.S. from 1791 to 2020 (from Hall-Sargent and CRSP), constructing primary surpluses, tax revenues, spending, GDP, and convenience yields consistently over nearly three centuries. U.K. convenience yields before WW-I are measured as the interest rate differential between U.K. government securities and otherwise comparable bonds from countries on the gold standard; the sample average is approximately 147 basis points at the short end and 110 basis points at the long end, with the spread declining at longer maturities (the opposite of what default risk would predict), providing evidence that convenience yield rather than residual default risk drives the differential. U.S. post-war convenience yields are constructed from the spread between the 3-month Treasury yield and the 3-month CD rate (or bankers’ acceptance rate before 1964), averaging 36 basis points per year from 1947 to 2020.

Q6. What are the implications for models of fiscal capacity and debt sustainability?

The results favor models in which the safe asset supplier’s fiscal capacity is determined partly by relative macro fundamentals (which country the global financial system coordinates on) rather than solely by absolute fundamentals (its own surpluses), and challenge models that treat the transversality condition as a binding constraint at all times for all countries. The finding that a large fraction of U.S. Treasury debt is not backed by future surpluses — even when the market risk premium is used to discount — has implications for debt sustainability analyses: standard present-value-of-surpluses calculations will understate the true fiscal capacity of the safe asset supplier, while overstating it for others. The paper’s framework suggests this extra capacity depends on maintaining relative macro fundamentals and global investor coordination, and can be lost — as the U.K. experience demonstrates — when relative fundamentals deteriorate.

Key Concepts

fiscal capacity: the present risk-adjusted discounted value of a government’s expected future primary surpluses, computed from the government’s intertemporal budget constraint under no-arbitrage; in this paper, inclusive of seigniorage revenue from convenience yields earned on government debt.
exorbitant privilege: the ability of the safe asset supplier country to borrow at below-market interest rates due to global demand for its government debt as a safe asset; quantified in this paper as the gap between the market value of debt and estimated fiscal capacity from surpluses alone, which exceeds fiscal capacity for the pre-WW-I U.K. and post-WW-II U.S.
convenience yield: the yield reduction (below comparable risky borrowing rates) that the safe asset supplier earns from global safe asset demand; measured as approximately 100 bps long-term for the pre-WW-I U.K. and approximately 36 bps on average for the post-WW-II U.S., contributing 0.47% and 0.36% of GDP annually in seigniorage revenue respectively.
transversality condition (TVC): the condition ruling out rational government debt bubbles, requiring the expected discounted value of outstanding debt to approach zero at long horizons; the paper imposes the TVC and finds that for the pre-WW-I U.K. and post-WW-II U.S., the observed debt level exceeds fiscal capacity even under this constraint, interpreted as evidence of the extra borrowing license conferred by safe asset supplier status.

International trade and macroeconomic dynamics with sanctions

Mon, 01 Jan 0001 00:00:00 +0000

Sanctions are increasingly used as an instrument of economic statecraft, yet their macroeconomic consequences—especially the transitional dynamics and their effects on business cycles—are poorly understood. This paper develops a micro-founded framework combining the intertemporal general-equilibrium structure of standard open-economy macro models with the rich trade-theoretic microfoundations of modern trade theory to study sanctions systematically. In a two-country, two-sector model where Home specializes in differentiated consumption goods (heterogeneous firms, endogenous entry, Melitz-style) and Foreign specializes in homogeneous intermediate goods (Cournot oligopoly in extraction), sanctions—modeled as trade bans and financial restrictions excluding particular Foreign agents—reallocate resources across and within countries, affect production, exchange rates, and welfare, and are shown to inflict larger welfare losses when they target sectors of comparative disadvantage. A central finding is that focusing only on long-run outcomes and overlooking initial transitional dynamics substantially misdirects welfare assessments; sanctions weaken international comovement and fragment markets but, contrary to some claims, leave the structure of business cycles largely intact.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the model structure and what types of sanctions does it capture?

The model is a two-country, two-sector economy: Home has a comparative advantage in differentiated consumption goods (produced by heterogeneous firms with endogenous entry under monopolistic competition, as in Melitz 2003), while Foreign specializes in homogeneous intermediate goods (produced via Cournot competition among a fixed number of upstream firms and processed by a representative distributor). This structure is motivated by the pattern in which Western economies specialize in high-value, firm-entry-intensive industries while sanctioned countries often specialize in commodity production (energy, natural gas). Sanctions are modeled as two distinct instruments: trade bans (restrictions on commerce in goods) and financial restrictions (excluding particular Foreign agents from capital markets). The model accommodates both Ricardian and Melitz-type comparative advantage.

Q2. What are the key results on welfare effects and the role of transitional dynamics?

Sanctions reallocate resources across and within countries, with welfare losses larger when sanctions target sectors of comparative disadvantage rather than sectors of comparative advantage; and focusing only on long-run welfare ignores significant transitional costs that substantially change the total welfare assessment. The model implies that initial transitional dynamics—disruptions to trade flows, entry and exit of firms, exchange rate movements, and adjustment of resource allocation—can be quantitatively important and even dominate long-run effects in welfare calculations. Assessments based solely on steady-state comparisons may therefore produce seriously misleading conclusions about whether and how severely sanctions harm the imposing or target economy.

Q3. How do sanctions affect international comovement and business cycles?

Sanctions weaken international business cycle comovement and fragment markets—reducing the degree to which shocks in one country transmit to the other—but leave the structural properties of business cycles within each country largely intact, in the sense that the cyclical dynamics of output, consumption, and investment retain their qualitative features. This result has policy implications: sanctions can reduce the interdependence of the sanctioned country’s business cycle from the rest of the world (which could be either beneficial or harmful depending on the source of shocks), but cannot fundamentally restructure the domestic cycle.

Q4. What is the baseline application and what general lessons emerge?

While the model’s comparative advantage structure is explicitly motivated by the 2022 Western sanctions against Russia—with intermediate goods interpretable as energy—the framework is designed to be more broadly applicable to other geopolitical conflicts involving sanctioned commodity producers facing differentiated-goods exporters, such as US-China trade tensions. The general lessons are: (1) the sector targeted by sanctions matters greatly for their welfare costs; (2) transitional dynamics are not second-order; (3) financial sanctions operate through different channels than trade bans and should be modeled separately.

Key concepts

comparative disadvantage in sanctions : the paper’s finding that sanctions are more costly when they target goods in which the targeted country has a comparative disadvantage—sectors the country cannot efficiently produce domestically—because those are the sectors where trade provides the highest value and substitution is hardest.

financial restrictions : one of the two types of sanctions modeled, in which particular Foreign agents (firms or sovereign entities) are excluded from international capital markets, distinct from trade bans that restrict commerce in goods.

Monetary–Fiscal Policy Interactions When Price Stability Occasionally Takes a Back Seat

Mon, 01 Jan 0001 00:00:00 +0000

The paper builds a discrete-time DSGE model with Calvo sticky prices in which the public sector has two feedback rules that can hit corners, generating endogenous shifts between an “orthodox” regime and a “fiscally-dominant” regime. Fiscal policy sets the primary surplus as s̃_t = min(ϕb̃_{t−1}, s̄): the surplus tracks real debt with coefficient ϕ = 0.1 until the limit s̄ = 0.01 (1% of output in deviation from steady state; approximately 3% in level) binds. Monetary policy follows R̂_t = min(αp̂_t, R̄): a standard Taylor rule with coefficient α = 2.5 until the nominal interest rate cap R̄ ≈ 5% (annualized) is hit. When the surplus limit is slack — the orthodox regime — fiscal policy is locally passive and monetary policy is active in the sense of Leeper (1991). When the surplus limit binds — the fiscally-dominant regime — the central bank caps its policy rate to avoid aggravating fiscal stress, and price stability takes a back seat.

Calibration (Table 1): β = 0.995 (annual steady-state real rate ≈ 2%), σ = 1 (log utility), κ = 0.0093 (Calvo Phillips curve slope), η = 1 (inverse labor supply elasticity), θ = 10 (price elasticity of demand), ω = 0.8 (Calvo price-stickiness), α = 2.5, ϕ = 0.1, b/(4y) = 1 (100% debt-to-GDP), s̄ = 0.01, R̄ = 0.0074 in deviation from steady state (≈ 5% annualized), AR(1) coefficient ρ = 0.6, shock standard deviation σ_μ = 0.0016. The model is solved globally using a projection method to handle the kinks from the min operators.

In the fiscally-dominant regime, monetary policy is asymmetric: the central bank always lowers the rate for deflationary shocks but cannot raise it fully for large inflationary shocks (rate hits R̄). This stabilizes real debt in both shock directions while creating an asymmetric inflation response — inflation rises more in response to a positive cost-push shock than it falls for a negative shock of equal magnitude. This asymmetric profile is baked into agents’ expectations in all states of the world, including the orthodox regime, generating a systematic inflation bias that is increasing in the real value of government debt.

Simulation results (Table 2, based on 3,000 simulations of 1,000 quarters): the fiscally-dominant regime (surplus limit binding) occurs in 20% of periods, with an average duration of 3.6 quarters; the rate cap additionally binds in 10% of periods, with an average duration of 1.8 quarters.

Risky steady state (Table 3): The point to which the economy converges when transitory shocks have receded but agents fully internalize future regime-shift risk differs from the deterministic steady state: inflation is 27bp higher, output is 0.26pp lower, the real interest rate is 41bp higher, and the government debt-to-GDP ratio is 1.07pp higher. At the risky steady state the economy remains in the orthodox regime; all four effects stem from the inflation expectations channel.

Vicious-cycle mechanism: Higher debt raises the probability of fiscal dominance → larger inflation bias → higher real interest rate (the Taylor rule raises the nominal rate more than one-for-one with the inflation bias) → upward pressure on debt. The fiscal dominance risk is state-dependent: it increases with the cost-push shock and with the debt level (Figure 4).

Policy finding (Section 3.3 and Table 4): Because regime switches are endogenous, the central bank can reduce fiscal dominance risk by responding more moderately to inflation — lowering α from 2.5 to 1.5 — while still satisfying the Taylor principle (α > 1/β). A lower α attenuates the increase in debt servicing costs after an inflationary shock, requiring larger shocks to push the surplus limit to bind. Under α = 1.5: the fiscal dominance regime frequency falls to 0%; the risky steady-state inflation bias falls to essentially zero (0.01bp); inflation volatility falls from 1.93% to 1.89% — the volatility-reducing effect of avoiding fiscal dominance dominates the direct volatility-raising effect of a weaker response. At α ≈ 1.5, welfare (measured as the linear-quadratic loss −E[π̂² + λŷ²] with λ = κ/θ) is higher than at α = 2.5 (Figure 6). By contrast, under the benchmark configuration (no fiscal dominance risk), welfare falls monotonically as α declines.

Extension 1 — Distortionary taxation (Section 4.1): Replacing lump-sum taxes with a labor income tax (τL = 24%, cap = 25%) amplifies the mechanism. The risky steady-state inflation bias rises to 0.59pp; fiscal dominance occurs in 29% of periods; the rate cap binds in 16% of periods. The amplification reflects that the tax rate enters the Phillips curve, creating an additional cost-push channel when the tax cap binds.

Extension 2 — Passive monetary policy in the fiscally-dominant regime (Section 4.2): When the central bank switches to a passive rule with αF = 0.95 (rather than imposing a hard rate cap), the inflation bias is 0.23pp and fiscal dominance occurs in 15% of periods.

Scope conditions: The model features a representative household, a single cost-push shock, and lump-sum taxes in the baseline. All quantitative results are specific to the parameterization in Table 1, targeting 100% debt-to-GDP. Agents are assumed to have perfect knowledge of the central bank’s policy rule; in practice, a moderate α could be misinterpreted as abandoning the Taylor principle. The analysis is primarily conceptual; the paper notes that extending to a full-fledged multi-shock quantitative model is left for future work.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What are the two regimes in the model, and how do transitions occur?

The orthodox regime is characterized by an active central bank (α > 1/β, Taylor principle satisfied) and a passive fiscal authority (surplus responds to debt, ϕ ∈ (1−β, 1)); the fiscally-dominant regime arises when the fiscal surplus hits its upper limit s̄ = 0.01 and the central bank caps its nominal rate at R̄ ≈ 5% annualized to avoid deepening the fiscal stress. Transitions are driven entirely by the state of the economy: when real debt b̃_{t-1} crosses the threshold b̄ = s̄/ϕ from below following a sufficiently large inflationary cost-push shock, the surplus limit binds and the economy enters the fiscally-dominant regime. Exit occurs when a sequence of disinflationary shocks, together with the central bank’s rate cuts, lowers debt below the threshold. Both the entry and exit thresholds are determined by the structural parameters of the model, not set exogenously.

Q2. Why does fiscal dominance risk generate an inflation bias in the orthodox regime?

The key transmission channel runs through expectations: in the fiscally-dominant regime the central bank responds asymmetrically to shocks (always cutting for deflation, capped on the upside for large inflation), creating an asymmetric inflation distribution; agents rationally incorporate this skewness into their inflation expectations in all states — including the orthodox regime — pushing expected inflation above target; the Taylor rule then allows actual inflation to be persistently elevated because the response coefficient α = 2.5, while large, does not fully offset the expectations-induced inflation pressure. The upward inflation expectations shift appears in the forward-looking Phillips curve (equation 2): higher Etπ_{t+1} raises current inflation πt, and the Taylor rule’s response is insufficient to fully counteract the expectations-driven component of the inflation bias.

Q3. Why does the inflation bias increase with the debt level?

Higher beginning-of-period government debt reduces the buffer between current debt and the threshold b̄, so that any given realization of the cost-push shock has a higher probability of pushing debt over the threshold and triggering a shift to the fiscally-dominant regime next period; the larger this probability, the larger the expectations-driven inflation bias in the current period. This mechanism is illustrated in Figure 4, which shows the probability of fiscal dominance next period as an increasing function of the current cost-push shock (given debt near the risky steady state), and Figure 2, which plots the monotone increasing relationship between current debt and the inflation rate in both regimes.

Q4. How does the vicious cycle between inflation, interest rates, and debt operate?

The cycle works as follows: a larger inflation bias induced by higher debt triggers a stronger nominal interest rate response from the Taylor rule; in the orthodox regime this raises the real interest rate, which increases debt servicing costs and pushes real debt upward; higher debt in turn raises the probability of fiscal dominance, which amplifies the inflation bias in the next period. The cycle is self-reinforcing but not necessarily explosive in the baseline calibration — the model has a unique risky steady state at which these forces balance — but it does shift equilibrium outcomes permanently upward relative to the deterministic steady state: the real rate is 41bp higher, debt 1.07pp higher, and inflation 27bp higher at the risky steady state (Table 3).

Q5. Can the central bank break the cycle without abandoning price stability?

Yes: by lowering the Taylor rule coefficient from α = 2.5 to α = 1.5, the central bank reduces the increase in debt servicing costs after an inflationary shock, thereby making it less likely that the surplus limit binds; when the probability of fiscal dominance approaches zero, inflation expectations are anchored at the deterministic steady state and the inflation bias disappears. This works without violating the Taylor principle (α = 1.5 > 1/β ≈ 1.005) because the objective is not to tolerate more inflation at each point in time, but to reduce the regime-switch risk that is the source of the bias. Crucially, the central bank does not need to commit to any specific regime-change-contingent rule — modifying the response coefficient of the standard Taylor rule is sufficient.

Q6. Why does lower α also reduce inflation volatility, not just the bias?

In the regime-switching model there are two competing effects on inflation volatility when α falls: (i) a direct volatility-raising effect because a weaker rate response gives more room for cost-push shocks to move inflation, and (ii) a volatility-reducing effect because the fiscally-dominant regime — where inflation is amplified by asymmetric monetary policy — is less frequently visited. At α = 1.5, effect (ii) dominates: the standard deviation of annualized inflation falls from 1.93% (α = 2.5) to 1.89% (α = 1.5). This contrasts with the benchmark configuration (no fiscal dominance possible), where effect (i) always dominates and welfare falls monotonically with α.

Q7. What does distortionary taxation add to the baseline result?

When the government adjusts a labor income tax rate (τL capped at 25%, baseline 24%) instead of lump-sum taxes, the inflation bias is amplified to 0.59pp (versus 0.27bp in the baseline) and the fiscally-dominant regime occurs 29% of the time (versus 20%). The amplification comes from two sources: the labor tax rate appears directly in the New Keynesian Phillips curve (equation 9), so a binding tax cap generates an additional cost-push effect that raises inflation independently of the interest rate channel; and output is increasing in the debt level in the fiscally-dominant regime (because a higher debt level makes the rate cap more likely, raising output through the demand channel), which further increases the primary surplus through the tax base, partly offsetting the tax cap but complicating the fiscal dynamics.

Q8. How does the passive monetary policy extension compare to the baseline?

When the central bank switches to a passive rule αF = 0.95 in the fiscally-dominant regime (rather than imposing a hard nominal interest rate cap), the inflation bias at the risky steady state falls to 0.23pp and the fiscally-dominant regime occurs in 15% of periods — both improvements over the baseline (0.27bp, 20%), but the mechanism is somewhat different. Under the passive rule, there is no hard constraint on the interest rate, so the central bank can still raise rates to some extent in response to inflationary shocks in the fiscally-dominant regime, reducing the asymmetry in the inflation response. The rate cap extension (baseline) is the more extreme case in which the constraint is fully binding.

Q9. How does this paper differ from exogenous regime-switching models?

The key difference is that in this model the probability of a regime shift is not exogenous — it is a function of the current state (debt level, cost-push shock) and of the policy parameters (α, ϕ, s̄, R̄); this means the central bank can influence regime-change risk by changing its policy rule, which is not possible in models like Davig and Leeper (2006), Bianchi and Melosi (2017, 2019), or Bianchi and Ilut (2017) where switching probabilities are fixed Markov parameters. The ability of the central bank to manage regime-switch risk is the novel channel through which monetary policy can attenuate the inflation bias without abandoning price stability — a result that has no counterpart in models where the fiscal authority’s behavior is exogenous.

Key concepts

orthodox regime : the policy configuration in which the fiscal surplus limit is slack (s̃_t < s̄) and the central bank follows a standard Taylor rule (R̂_t = αp̂_t with α > 1/β); fiscal policy is passive and monetary policy is active in Leeper’s (1991) sense.

fiscally-dominant regime : the policy configuration in which the fiscal surplus limit binds (s̃_t = s̄) because the real value of government debt is sufficiently high, and the central bank caps its nominal interest rate at R̄ to prevent fiscal stability from deteriorating further; monetary policy becomes fiscally accommodative.

risky steady state : the point to which the economy converges when transitory shocks have receded but agents fully incorporate future regime-shift risk into their expectations; it differs from the deterministic steady state by an inflation bias of 27bp, a real interest rate premium of 41bp, an output shortfall of 0.26pp, and an additional 1.07pp of government debt (all in the baseline calibration).

inflation bias : the systematic elevation of equilibrium inflation above the price stability target that arises from the risk of future fiscal dominance episodes; it is increasing in the real value of government debt and is present even in periods when the economy is in the orthodox regime, because agents rationally incorporate fiscal dominance risk into their expectations.

endogenous regime switching : the feature of the model that distinguishes it from earlier regime-switching frameworks — the probability of a shift to the fiscally-dominant regime is a function of the current state of the economy (debt, cost-push shock) and of the policy parameters, so the central bank can influence regime-change risk through its choice of the Taylor rule coefficient.

vicious cycle : the self-reinforcing dynamic between debt, fiscal dominance risk, the inflation bias, and the real interest rate: higher debt raises fiscal dominance risk → larger inflation bias → higher real rate (via Taylor rule) → higher debt servicing costs → further upward pressure on debt.

Optimal Fiscal Policy with Heterogeneous Agents and Capital: Overturning Chamley-Judd

Mon, 01 Jan 0001 00:00:00 +0000

The Chamley-Judd result (1986) states that the optimal long-run capital income tax rate is zero in representative-agent models. This paper shows that introducing heterogeneous agents — specifically, agents with uninsurable idiosyncratic income risk who use precautionary saving — overturns this result. When agents differ in their wealth and income realizations, a capital income tax serves as a form of insurance that representative-agent models cannot provide. The paper derives a tractable analytical characterization of the optimal capital tax in an Aiyagari-type heterogeneous-agent model and finds that the optimal rate lies in the range of 10–30 percent at the steady state — strictly positive, in direct contradiction to Chamley-Judd. The magnitude of the optimal tax depends on the degree of idiosyncratic risk and the availability of alternative redistribution instruments: when other redistributive tools are limited, the optimal capital tax is higher.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. Why does heterogeneity overturn Chamley-Judd?

In representative-agent models, all agents hold the same capital stock, so a capital tax distorts intertemporal decisions identically and the Ramsey planner finds it optimal to zero out the distortion in the long run. With heterogeneous agents and uninsurable risk, the capital tax has an additional insurance role: taxing capital income and redistributing it reduces consumption variance across agents, generating welfare gains that outweigh the intertemporal distortion costs. The insurance benefit makes the optimal tax positive at the steady state because the tax-and-redistribute mechanism provides risk-sharing that incomplete markets cannot.

Q2. How tractable is the analytical result?

The paper derives closed-form expressions for the optimal tax rate as a function of the degree of idiosyncratic risk, the wealth distribution’s spread, and the available redistribution instruments, enabling comparative statics that go beyond what purely computational approaches provide. This tractability distinguishes the result from earlier numerical work that demonstrated positive optimal capital taxes without clear analytical structure.

Q3. What is the quantitative magnitude?

The optimal steady-state capital income tax is in the range of 10–30 percent, substantially above zero but well below confiscatory rates, in the paper’s benchmark calibration matched to U.S. income and wealth inequality. The range reflects the sensitivity to available redistribution instruments: the lower bound applies when the government has a rich set of redistribution tools, the upper bound when capital taxation is the only available instrument.

Key concepts

Chamley-Judd result : the proposition that the optimal long-run capital income tax is zero in representative-agent Ramsey taxation models; overturned in this paper once heterogeneous agents with uninsurable risk are introduced.

insurance role of capital taxation : the mechanism by which a capital income tax reduces consumption inequality in a heterogeneous-agent economy, generating welfare gains that outweigh the intertemporal distortion costs and making the optimal capital tax positive.

Passive Quantitative Easing: Bond Supply Effects through Lower Debt Issuance

Mon, 01 Jan 0001 00:00:00 +0000

The paper introduces the concept of “passive quantitative easing” (passive QE): a deliberate reduction in government debt issuance that lowers anticipated future bond supply and reduces long-term yields through the same supply channel as central bank asset purchases, without involving asset purchases or reserves creation. The authors develop a unified classification scheme for central bank balance sheet policies organized by their net effect on anticipated future bond supply, and show that the Danish government’s unexpected January 2015 debt halt — which removed approximately 29.9 billion DKK from the outstanding bond stock over roughly nine months — was followed by a two-day yield decline of approximately 25 basis points across the entire yield curve. Regression estimates controlling for concurrent ECB and SNB actions imply that the halt raised the safety premium on Danish bonds by 17–22 basis points and reduced the ten-year term premium by 37–70 basis points, with combined effects pointing to 54–92 basis points in lower yields relative to the counterfactual. The Danish episode ranks approximately on par with the Federal Reserve’s QE3 in the classification scheme, and the paper argues that passive QT — unexpectedly higher debt issuance — is contractionary through two additional portfolio balance channels not present in active QT and should be treated as an active policy tool rather than a neutral background condition.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is “passive QE” and what distinguishes it from conventional QE?

The paper defines passive QE as a reduction in government debt issuance that lowers anticipated future bond supply, arguing this is functionally equivalent to central bank asset purchases in its effects on long-term yields, even though it involves neither asset purchases nor reserves creation. The supply-side equivalence holds because what matters for term premia and safe-asset premia is the anticipated future stock of bonds available to private investors: whether the central bank withdraws bonds via outright purchases or the government simply issues fewer new ones, the anticipated future supply declines, requiring downward adjustment in the compensation investors demand for duration risk and scarcity. The distinction from active QE is therefore operational rather than economic: passive QE leaves the central bank’s balance sheet unchanged, makes no reserve injection, and requires no fiscal–monetary coordination beyond the government’s own debt management decisions.

Q2. How do the authors classify central bank balance sheet policies?

The paper proposes a unified classification scheme that maps central bank balance sheet policies by their net effect on anticipated future bond supply, placing passive QE in the same stimulative category as active QE programs and ranking the Danish halt at approximately −0.0104 on this measure — nearly on par with the Federal Reserve’s QE3 at −0.0120. The scheme allows cross-country and cross-program comparisons of unconventional monetary policy actions by reducing them to a common currency of anticipated supply change. The classification also distinguishes passive QT from active QT: the paper argues that passive QT (higher-than-anticipated issuance) is more contractionary than active QT of equal magnitude because higher issuance also reduces safe-asset scarcity value and shifts duration risk back to the market through two additional portfolio balance channels.

Q3. What does the Danish debt halt episode show?

The January 30, 2015 announcement by Denmark’s debt management office that it would halt new government bond issuance for the remainder of the year was unexpected and was followed within two trading days by a yield decline of approximately 25 basis points across the entire yield curve. The halt lasted roughly nine months and reduced the outstanding Danish government bond stock by approximately 29.9 billion DKK. The reaction is interpreted as evidence that market participants immediately revised down their expectations of future bond supply, compressing the compensation required for holding duration risk and raising the relative value of the now-scarcer safe assets.

Q4. What do the regression estimates imply?

Controlling for the concurrent SNB and ECB announcements in January 2015, the authors’ regression estimates imply that the Danish halt raised the safety premium on Danish bonds by 17–22 basis points and reduced the ten-year term premium by 37–70 basis points, pointing to a combined reduction in bond yields of 54–92 basis points relative to the counterfactual without the halt, measured over the halt period. The term-premium decline is interpreted as consistent with supply-induced portfolio balance effects: fewer bonds requiring lower duration-risk compensation. The safety-premium increase is consistent with safe-asset scarcity effects: a tighter supply of high-quality government bonds raising their relative scarcity value. These two channels are identified separately in the yield decomposition and estimated to be independently significant.

Q5. How does the paper treat passive QT?

The paper argues that passive QT — a higher-than-anticipated level of government debt issuance — is not a neutral background condition but an active contractionary force, and potentially more contractionary than active QT of equal magnitude through two additional portfolio balance channels. The argument is that higher issuance reduces safe-asset scarcity value and directly shifts duration risk from the central bank to the market, while active QT (central bank balance sheet reduction) lacks these two additional channels. This implies that fiscal authorities’ debt issuance decisions carry monetary policy implications that are not captured in frameworks treating issuance as a non-monetary decision.

Key concepts

passive QE : a deliberate reduction in government debt issuance that lowers anticipated future bond supply and reduces long-term yields through supply effects; the paper treats it as functionally equivalent to central bank asset purchase programs despite involving no asset purchases or reserves creation.

passive QT : higher-than-anticipated government debt issuance; the paper treats it as an active contractionary tool, potentially more contractionary than active QT of equal magnitude, because it triggers two additional portfolio balance channels.

safety premium : the premium on high-quality safe assets such as government bonds reflecting their scarcity value; in the Danish halt episode this rose as supply tightened.

term premium : the component of a long-term bond yield compensating investors for bearing duration risk; in the Danish halt episode this fell as anticipated future bond supply declined.

classification scheme : the paper’s taxonomy of central bank balance sheet policies organized by their net effect on anticipated future bond supply, allowing cross-program comparisons including passive QE and passive QT.

Danish debt halt : the January 30, 2015 announcement by Denmark’s debt management office of a halt to new government bond issuance for the remainder of the year, used as the natural experiment to test the passive QE hypothesis.

Self-Fulfilling Debt Crises with Long Stagnations

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper asks whether sovereign debt crises can be self-fulfilling — triggered by lenders’ expectations of default rather than by weak fiscal fundamentals alone — and whether such crises are empirically plausible. Following the mechanism of Calvo (1988), high expected default probabilities require high interest rates to compensate lenders, but high interest rates in turn raise the cost of debt service and the probability of default, making the pessimistic expectations self-confirming. The key theoretical contribution is to show that this multiplicity of equilibria is state-dependent: it arises only in periods of stagnation, when the endowment process is in a persistent low-growth regime. The paper modifies a standard infinite-horizon sovereign default model (in the spirit of Eaton-Gersovitz and Arellano 2008) by introducing a two-state Markov regime-switching process for trend growth and by having the borrower choose current debt rather than debt at maturity — a timing assumption that is essential for multiplicity. Calibrating the output process to Argentina, Brazil, Italy, Portugal, and Spain using 1980–2017 data, the paper finds that for intermediate levels of debt and in low-growth states, interest rates can be either low (around 4%) or high (around 46%) depending on the coordination of lenders’ beliefs — a self-fulfilling crisis range that reproduces the qualitative features of the European sovereign debt crisis of 2010–2012 and the Argentine crisis of 1998–2002. In high-growth states, the multiplicity region is negligibly small or absent entirely.

In depth

Q1. What is the Calvo (1988) mechanism, and why does it require a bimodal endowment process?

The Calvo mechanism generates multiple equilibrium interest rates for a given level of debt: lenders’ expectation that the borrower will default in the low-output state forces them to charge a high interest rate to break even, but the high rate raises the debt service burden and makes default more likely, validating the pessimistic expectation. For this self-confirming loop to sustain multiple stable equilibria, the interest rate correspondence — mapping debt levels to possible interest rates — must have an upward-sloping region at both the low and high rate. A unimodal endowment distribution generates a correspondence with a downward-sloping high-rate segment (higher debt → lower high interest rate), which is inadmissible and eliminates multiplicity. A bimodal distribution with well-separated high and low growth states, as observed empirically in crisis-prone countries, generates an upward-sloping correspondence at both rates, creating a region of intermediate debt levels where either rate is an equilibrium.

The second key model feature is the timing of moves: the borrower chooses current debt (amount borrowed today) rather than debt at maturity (the repayment obligation). When the borrower chooses debt at maturity, it implicitly pins down the default probability and therefore the interest rate, eliminating multiplicity. When the borrower chooses current debt, the interest rate is determined by lenders and can take either the high or the low value consistent with break-even pricing, given the chosen debt level.

Q2. How does the paper calibrate the endowment process and what does the estimation reveal?

The paper estimates a two-state Markov regime-switching model for annual GDP per capita growth for Argentina, Brazil, Italy, Portugal, and Spain using data from 1980 to 2017, and finds clear evidence of a bimodal distribution with persistent high- and low-growth regimes across all five countries. Estimated using a Bayesian MCMC algorithm with the Kim (1994) filter, the posterior means for the benchmark cross-country calibration are: low-growth rate gL = −1.0% per year, high-growth rate gH = 3.0% per year, persistence of low-growth state pL = 0.60, persistence of high-growth state pH = 0.80, and standard deviation of transitory shocks σ = 0.015. The average gap between gL and gH across countries is approximately 6 percentage points, more than three times the standard deviation of the transitory shock — confirming the bimodal structure that is essential for multiplicity. Both growth regimes are persistent, with the low-growth state having 60–80% persistence across countries.

The quantitative model uses these estimates together with standard parameters: risk-free rate R* = 3.5%, recovery rate κ = 75%, discount factor β = 0.75, and risk aversion γ = 3. The sunspot process governing equilibrium selection is i.i.d. with a 5% probability of the bad (high-rate) sunspot in each period.

Q3. What does the calibrated model predict for interest rates and when do self-fulfilling crises occur?

In the calibrated quantitative model, the multiplicity region is present only in the low-growth state and for intermediate debt levels; in the high-growth state, the multiplicity region is either empty or negligibly small. In the low-growth state with intermediate debt, the interest rate schedule features two admissible equilibria: a low-rate equilibrium consistent with a low probability of default (1.7% in the benchmark simulation) and a high-rate equilibrium consistent with a high probability of default (60.1%). Both are sustained by self-confirming expectations. The scenario simulation illustrates this starkly: two economies starting from identical wealth and facing identical growth-shock sequences but different sunspot realizations in period t=2 (when they are in the low-growth state) face interest rates of 4.0% versus 46.4% and next-period default probabilities of 1.7% versus 60.1%, respectively, with no difference in fundamentals.

The model also generates endogenous austerity: borrowers optimally refrain from increasing debt to avoid discrete jumps in interest rates, both at the fundamental threshold (driven by the growth regime) and at the expectations-driven threshold (driven by the sunspot). In low-growth states facing the bad sunspot, the borrower either bunches at a low debt level below the multiplicity region or makes a discrete jump above it, echoing the binary fiscal-adjustment dynamics observed in crisis episodes.

Q4. How does the model interpret the European debt crisis and the role of the ECB?

The model provides a direct interpretation of the European sovereign debt crisis: the southern European economies (Italy, Spain, Portugal) entered a low-growth state around 2009–2010, which created conditions for the Calvo mechanism to operate; spreads jumped to high-rate equilibria driven by expectations rather than by fundamentals alone. The ECB’s announcement of the Outright Monetary Transactions (OMT) program in September 2012 — the commitment to purchase sovereign bonds in secondary markets — shifted lenders’ beliefs from the bad-sunspot equilibrium to the good-sunspot equilibrium, collapsing spreads substantially even without actual intervention. In the model’s language, a credible lender of last resort can eliminate the bad equilibrium by committing to lend at the low-rate schedule, rendering the high-rate self-fulfilling expectations non-viable. The Argentine crisis of 1998–2002 fits the model as an alternative trajectory: Argentina entered the low-growth state with a 7% spread on 35% debt-to-GDP and, without a lender of last resort intervention, eventually defaulted in 2002 — consistent with the bad-sunspot equilibrium path.

Q5. What role does persistence of the low-growth state play?

The persistence of the low-growth state (pL) is the key parameter governing the severity of self-fulfilling crises: higher pL generates higher equilibrium interest rates in the bad-sunspot equilibrium and a larger multiplicity region. Intuitively, if the economy is likely to remain in the low-growth state for a long time, the probability of default conditional on entry into the bad equilibrium is very high, requiring lenders to charge very high interest rates to break even. The higher the interest rate, the more debt service costs compress fiscal space, making default even more likely and potentially sustainable at even lower debt levels. The paper shows in robustness exercises that the multiplicity result is robust to reasonable perturbations in pL, κ (recovery rate), σ (transitory shock standard deviation), gL, and gH, with the key ingredient being the bimodal structure of the endowment process rather than any single parameter value.

Q6. What are the policy implications for lenders of last resort?

The central policy implication is that a lender of last resort — such as the ECB or the IMF — is justified precisely when fundamentals are weak, not because fundamentals alone cause the crisis but because weak fundamentals create conditions in which expectations can trigger a self-fulfilling crisis. Intervening in the bad-sunspot equilibrium by committing to supply funds at low-rate terms makes the high-rate equilibrium infeasible: lenders cannot expect default because the lender of last resort ensures the borrower can always roll over at low rates. The model thus rationalizes the design of the OMT: a credible commitment with no limit on size is sufficient to rule out the bad equilibrium without necessarily requiring actual asset purchases. The paper notes that such interventions will also have effects on the economy outside the period of crisis, since the availability of backstop financing may affect the equilibrium path more broadly.

Key Concepts

Calvo (1988) mechanism: the self-fulfilling loop in sovereign debt markets in which high lender expectations of default require high interest rates for break-even pricing, which raise the actual default probability and thereby confirm the initial pessimistic expectations; generates multiple equilibrium interest rates for a given debt level.
state-dependent multiplicity: the feature of the model in which multiple interest rate equilibria arise only in periods of low and persistent growth (stagnation), not in high-growth regimes; the central quantitative finding that self-fulfilling crises are empirically plausible only when growth fundamentals are weak.
endogenous austerity: the borrower’s optimal choice to hold debt below the multiplicity region to avoid discrete jumps in interest rates triggered by either fundamentals or expectations; reflected in the flat portions of the debt policy function and consistent with fiscal consolidation patterns observed in crisis episodes.
sunspot variable: the exogenous coordination device that selects among the multiple equilibrium interest rate schedules; takes a bad or good realization each period according to an i.i.d. process, with the bad sunspot selecting the high-rate schedule and the good sunspot selecting the low-rate schedule in the low-growth state.

The Welfare and Distributional Consequences of Corporate Tax Cuts in Open Economies

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper uses an open-economy heterogeneous-household model with incomplete markets to evaluate the welfare and distributional consequences of the U.S. Tax Cuts and Jobs Act (TCJA) of 2017 — which reduced the U.S. corporate tax rate from 35 to 21 percent — both within the U.S. and in affected trading partners. The model features three economies (the U.S., a small open economy calibrated to Canada, and the rest of the world), free capital flows, progressive income taxes, and idiosyncratic uninsurable labor income shocks generating empirically realistic wealth Gini coefficients (0.80 for the U.S., 0.70 for Canada). Three main results are established. First, the TCJA is regressive in the U.S. — under a permanent cut, the bottom 5 percent of U.S. households by wealth experience welfare losses of 0.10–0.26 percent of lifetime consumption, while the top 1 percent gain 0.92 percent — and generates an even more regressive outcome in trading partners, where approximately the bottom 80 percent of the small open economy’s wealth distribution experience welfare losses averaging 1.28 percent at the bottom decile against gains of 2.57 percent at the top. Second, whether U.S. wealth-poor households benefit depends critically on the persistence of the tax cut: under a permanent cut, households above approximately the bottom 5 percent of the U.S. wealth distribution gain (driven by wage increases from capital inflows), but under an anticipated partial reversal from 21 to 28 percent after 7 years, approximately the bottom 75 percent of U.S. households experience welfare losses because the temporary wage gain is dominated by a persistent increase in the public debt burden. Third, when the small open economy reciprocates by matching the U.S. corporate tax reduction to 21 percent, the domestic distributional consequence reverses: all wealth quintiles in the small open economy gain (Table 5, Panel B shows gains of 0.52–1.19 percent across all groups), with the gain being roughly progressive within the SOE — a result driven by the wage increase from capital inflows exceeding the financing cost, which falls primarily on the wealth-rich through higher top marginal tax rates.

In depth

Q1. What is the model structure and how are the three economies connected?

The paper extends the Aiyagari (1994) incomplete-markets heterogeneous-household model to an open-economy setting with three countries — the U.S., a small open economy (SOE) modeled as Canada, and the rest of the world (ROW) modeled with Canadian parameters — linked by free capital flows that equalize after-tax returns to capital across countries: (1 − τc^US)r^US = (1 − τc^SOE)r^SOE = (1 − τc^ROW)r^ROW = r^b. Households in each economy face idiosyncratic uninsurable productivity shocks (three states: low s₁ = 0.167, medium s₂ = 0.839, high s₃ = 5.087, with a persistent Markov transition matrix following Domeij and Heathcote 2004) and save in internationally traded capital and government bonds, subject to borrowing constraints calibrated to match wealth Gini coefficients. The fiscal rule follows Bohn (1998) with the residence-based tax revenue responding to the debt-to-GDP ratio to ensure stationarity, and the top marginal tax rate τ₁ adjusts endogenously when corporate tax revenues change (consistent with Mertens and Montiel Olea 2018’s evidence on tax instrument choice). The SOE size is 10 percent of the U.S., enabling the paper to capture the asymmetric spillover mechanism by which U.S. corporate tax policy creates large distributional consequences abroad without generating offsetting fiscal adjustments in the SOE.

Q2. What are the distributional effects of the permanent TCJA in the U.S. and SOE?

Under a permanent reduction from 35 to 21 percent in the U.S. corporate tax rate, the average U.S. welfare gain is +0.146 percent of lifetime consumption, but this masks a strongly regressive distribution: households in the bottom 5 percent of the U.S. wealth distribution experience welfare losses of −0.045 to −0.101 percent, while those in the top 1 percent gain +0.920 percent, with gains monotonically increasing through the wealth distribution above the 5th percentile; in the SOE, the average welfare effect is −0.392 percent, and the losses are far larger and more broadly distributed, with approximately the bottom 80 percent (up to the 75th–95th percentile boundary) experiencing losses ranging from −0.582 to −1.282 percent while the top 1 percent gains +2.566 percent (Table 3). The mechanism for the U.S. involves capital inflows that raise wages (benefiting labor-income-reliant poor households at least partially) offset by increased tax burden from debt accumulation; in the SOE, capital outflows depress wages more severely, and wealth-rich households in the SOE gain even more than their U.S. counterparts because SOE households face no increase in their domestic tax burden to finance the U.S. corporate tax cut, making the SOE spillover a “free lunch” for SOE capital owners.

Q3. Why does the permanence of the tax cut matter for lower-wealth U.S. households?

When the TCJA is anticipated to be partially reversed — from 21 percent back to 28 percent after 7 years — households in approximately the bottom 75 percent of the U.S. wealth distribution experience welfare losses averaging from −0.091 to −0.259 percent; under a permanent cut only approximately the bottom 5 percent suffer losses, so the reversal shifts the crossover point from the 5th to the 75th percentile of the wealth distribution (Table 4, Panel A). The mechanism is that under a temporary tax cut the capital inflow is short-lived and so the wage increase is limited in duration, while the increase in U.S. government debt is persistent — because the government finances the cut through debt issuance and the debt level remains elevated even after the reversal from 21 to 28 percent, the resulting higher tax burden on labor income persists and dominates the temporary wage benefit for wealth-poor households who primarily earn labor income. This result has a direct policy implication: the distributional case for extending or making permanent the TCJA’s corporate rate reduction is much stronger than for a time-limited cut, because the wage-raising channel — the main argument for the cut’s benefits to workers — operates only persistently.

Q4. What happens when the small open economy reciprocates with its own corporate tax cut?

When the SOE reduces its corporate tax rate to match the U.S. at 21 percent (from 38 percent) simultaneously with the TCJA, all wealth groups in the SOE experience welfare gains (Table 5, Panel B shows average gains of +0.524 to +1.190 percent across wealth groups), with the distributional effect being progressive within the SOE: the incremental gain from reciprocation compared to not reciprocating is +1.807 percent for the bottom 1 percent of the SOE wealth distribution and −1.376 percent for the top 1 percent (Table 5, Panel C). The reason the SOE reciprocation is progressive is that the capital inflow triggered by the SOE’s cut raises wages across the SOE (benefiting labor-income-reliant poor households), while the financing cost of the cut — through debt accumulation and the eventual increase in top marginal tax rates — falls disproportionately on wealthy households. The paper notes this result depends on the SOE’s small size: because the SOE is only 10 percent of the U.S., its corporate tax cut creates a better investment opportunity for all global capital owners but the financing cost falls entirely on SOE residents, creating a distributional asymmetry between who benefits (all capital owners globally) and who pays (SOE income-rich households domestically).

Q5. How does the model fit the pre-TCJA data and what are the calibration targets?

The model closely matches its calibration targets: capital-to-output ratios of 2.50–2.52 (target 2.50), debt-to-GDP ratios of 0.827–0.882 (targets from Jordà-Schularick-Taylor 2017), and wealth Gini coefficients of 0.82 for the U.S. (target 0.80, from Budría-Rodríguez et al. 2002) and 0.71 for the SOE (target 0.70, from Brzozowski et al. 2010); and generates an untargeted prediction that the U.S. is a net borrower and Canada a net lender, consistent with data (Table 2, Panel B). The discount factors are calibrated to β^US = 0.968 and β^SOE = 0.969 to match the capital-output ratio, and the borrowing constraints are set at ψ = −1.65 for the U.S. and ψ = −0.88 for the SOE/ROW to match their respective wealth Gini coefficients. The model abstracts from terms-of-trade effects (consistent with Hanson et al. 2021’s evidence that US-Canada terms of trade are unaffected by US corporate tax changes) and aggregate uncertainty beyond corporate tax changes, and the SOE is set at 10 percent of the U.S. economy by population size.

Q6. How do the results change under alternative fiscal financing assumptions?

The key qualitative results — regressivity of the TCJA in the U.S. and its greater regressivity in the SOE — are robust across alternative fiscal financing assumptions: when the corporate tax cut is financed by immediately increasing the residence-based tax (χ = 1) rather than by debt (χ = 0 in the baseline), the losses at the bottom of the U.S. distribution become larger (approximately the bottom 70 percent lose rather than the bottom 5 percent), and when progressivity of the income tax (τ₃) rather than the top marginal rate (τ₁) adjusts, the additional tax burden falls more on wealth-poor households, making the cut even more regressive. The SOE reciprocation result is also robust: Appendix C.3 shows that financing the SOE corporate tax cut through increases in the residence-based tax (χ^SOE = 1) reduces the welfare gains for all SOE households but preserves the progressive distributional pattern within the SOE, while appendices C.1–C.2 show that the results are linear in the size of the SOE’s tax cut (at 30 and 18 percent, the distributional pattern is similar in direction).

Key Concepts

open-economy Aiyagari model : the paper’s framework — an extension of the Aiyagari (1994) incomplete-markets model with heterogeneous households and idiosyncratic uninsurable labor shocks to an international setting with free capital flows — used to capture how corporate tax changes distribute welfare across the wealth distribution in multiple countries simultaneously.

consumption equivalent variation : the proportional change in lifetime consumption required to make a household in the counterfactual no-TCJA economy as well off as in the economy with the TCJA; the welfare metric used in Tables 3–5, measured in percent of lifetime consumption, conditional on wealth and productivity state at the time of implementation.

TCJA persistence channel : the mechanism by which the distributional effect of the corporate tax cut for lower-wealth U.S. households depends on whether the cut is permanent: a permanent cut sustains capital inflows and wage gains long enough to dominate the increased tax burden, while a temporary cut leaves only a persistent debt overhang with limited wage benefits, turning even the bottom 75 percent of U.S. households into net losers.

SOE reciprocation progressivity : the finding that a small open economy that matches the U.S. corporate tax reduction achieves a progressive domestic distributional outcome because the wage increase from capital inflows benefits all households but the financing cost (through higher top marginal tax rates) falls mainly on the wealthy; this mechanism is size-dependent and reverses the regressivity that the U.S. cut generates domestically.

Summary of a forthcoming paper, AI-assisted. Draft pending human review. See the linked original for the authoritative claims and full conditions.

US Public Debt and Safe Asset Market Power

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper asks whether the U.S. government exploits its market power as the dominant global supplier of safe assets when setting the quantity of public debt, and quantifies the macroeconomic consequences of this strategic behavior. The paper develops a two-country general equilibrium model in which U.S. public debt provides a non-pecuniary benefit to foreign holders (capturing liquidity, collateral, and safety value) and the U.S. is the monopoly provider of this asset — facing a downward-sloping demand curve for Treasuries, so that issuing more debt reduces the convenience yield. The paper then tests empirically whether the data favor this monopoly model over a price-taking benchmark, exploiting the industrial organization insight that rotations in the demand curve (changes in elasticities during high- versus low-volatility regimes) can distinguish strategic from competitive behavior. Using quarterly data from 1935 to 2020, the paper finds that the data reject price-taking behavior in favor of the monopoly model across a wide range of specifications. Quantitatively, the monopoly calibration implies that U.S. market power generates approximately 45% of the observed convenience yield as a markup (about 30 basis points out of 68 basis points on average), causes safe asset supply to be roughly half what it would be under price-taking, and generates welfare gains to the U.S. of 0.21% in permanent consumption equivalents — almost half of which is attributable to market power rather than to the non-pecuniary value itself.

In depth

Q1. What is the theoretical framework for U.S. market power in safe assets?

The paper develops a deterministic, infinite-horizon, two-country model in which the U.S. is the sole provider of an asset with a non-pecuniary benefit to foreign (Rest of World) households, so the U.S. faces a downward-sloping demand curve for its public debt and acts as a monopolist in equilibrium. In the model, purchasing U.S. public debt yields a non-pecuniary flow benefit captured by an increasing, concave function f(b*). Because of this benefit, the equilibrium return on U.S. debt is lower than the return on capital — the gap being the convenience yield, defined as the spread between the U.S. capital return and the return on U.S. public debt. The U.S. Ramsey government internalizes the inverse demand function for its debt when solving its optimal fiscal problem, creating a standard monopoly markup: the equilibrium markup equals the inverse of the demand elasticity, µ = 1/ε_D, where ε_D is the price elasticity of foreign demand for U.S. Treasuries. Under price-taking, the markup is zero and the convenience yield reflects only the non-pecuniary value; under the monopoly model, the convenience yield is inflated by the markup, reducing debt supply below the competitive level.

Q2. How does the paper test monopoly versus price-taking behavior empirically?

The paper applies the conduct-testing approach of Bresnahan (1982) and the model selection test of Rivers and Vuong (2002): since rotations in the demand curve (changes in the elasticity, holding the level fixed) shift prices only if the firm exploits market power, a finding that convenience yields increase in high-elasticity regimes while quantities decrease is evidence of strategic behavior. The paper uses a regime indicator for periods of high global volatility (measured by the rolling standard deviation of MSCI UK Index returns over 1935–2020) as the demand rotator: during high-volatility periods, investors’ demand for safe assets is more inelastic (flight-to-safety), causing the demand curve to both shift outward and rotate (become steeper). The monopoly model predicts that the U.S. responds to the more inelastic demand by raising the convenience yield through higher markups and restricting supply, whereas the price-taking model attributes any convenience yield increase purely to shifts in marginal cost.

Empirically, the data show that convenience yields are higher and debt-to-GDP ratios lower during high-volatility periods — inconsistent with the price-taking model’s prediction that both prices and quantities should rise in a demand shift, and consistent with the monopoly model’s prediction of reduced supply. The estimated demand semi-elasticities are −0.20% per log-point in low volatility and −0.59% per log-point in high volatility (OLS), implying demand elasticities of 1.07 in low volatility and 3.18 in high volatility. The Rivers-Vuong test statistics reject price-taking in favor of the monopoly model at the 1% significance level under both OLS and IV specifications and across a wide range of assumed cost elasticities.

Q3. What is the quantitative magnitude of safe asset underprovision?

Using a demand elasticity of 2.2 (the average of the OLS and IV estimates from specifications without the demand rotator, consistent with the prior literature), the paper’s calibrated monopoly model implies that the U.S. safe asset supply is approximately half as large as it would be if the U.S. acted as a price taker: the steady-state total safe assets-to-GDP ratio is 0.39 in the monopoly equilibrium versus 0.59 in the competitive equilibrium. The markup accounts for approximately 45% of the average convenience yield of 68 basis points, implying a markup of about 30 basis points. The interest rate on U.S. public debt is 0.97% in the monopoly equilibrium versus 1.09% in the competitive equilibrium — a difference of 12 basis points — reflecting both the lower debt level and the higher convenience yield that the monopoly generates. These results hold across alternative parameterizations of the cost and demand elasticities.

Q4. What are the welfare implications of safe asset market power?

Market power generates significant welfare gains to the U.S. and welfare losses to the Rest of World: transitioning from the monopoly steady state to an economy with no special role for U.S. assets costs the U.S. 0.21% in permanent consumption equivalents and benefits the Rest of World by 0.34%; transitioning to a competitive equilibrium (price-taking but maintaining the special role) costs the U.S. 0.08% and benefits the Rest of World by 0.10%. This decomposition implies that roughly 60% of the U.S. welfare gain from its safe asset status is attributable to the non-pecuniary value (the benefit function f), and approximately 40% is attributable to market power per se. The interpretation is that the U.S. captures surplus from global safe asset demand through both the intrinsic value of its debt and through monopoly rents from restricting supply. The paper interprets these welfare gains as a quantification of “exorbitant privilege” arising from the supply side rather than from risk premium considerations.

Q5. What happens when safe asset competition increases?

The paper analyzes the effects of introducing Cournot competition among multiple sovereign safe asset suppliers, finding that while the aggregate supply of global safe assets increases substantially with more competitors, the U.S. public debt level itself is fairly stable, borrowing costs for the U.S. increase, and the Rest of World welfare improves. With N=2 symmetric Cournot competitors, the aggregate safe asset supply approximately doubles relative to the monopoly baseline, but each supplier’s equilibrium quantity is roughly unchanged. As N increases further, aggregate supply continues to grow, convenience yields fall, and interest rates on U.S. debt rise. A domestic financial fringe competing with U.S. government debt is modeled differently: because the U.S. government internalizes domestic fringe profits, domestic competition results in less competitive pressure, higher markups, and smaller welfare losses for the U.S. than the same amount of competition from foreign suppliers. These results quantify the macroeconomic stakes of initiatives to create alternative safe assets, such as euro area supranational safe bonds or Chinese reserve currency aspirations.

Q6. What identifies strategic versus competitive behavior using debt holder composition?

As a complementary identification strategy, the paper exploits time variation in the composition of U.S. Treasury holders: foreign investors (primarily official sector) have more inelastic demand than domestic investors (primarily financial institutions and mutual funds), and the increasing share of foreign investors since the 1970s implies a secular decline in the average demand elasticity. The paper estimates demand elasticities separately for the two groups, finds the foreign investor curve is more inelastic, and uses the implied time-varying average elasticity as a second demand rotator. The conduct test under this alternative approach also rejects price-taking in favor of the monopoly model. The monopoly model explains the observed increase in long-term convenience yields since the 1970s through rising markups driven by the shift toward less elastic foreign investors, rather than through rising marginal costs of debt issuance.

Key Concepts

safe asset market power: the U.S. government’s ability to internalize the downward-sloping foreign demand curve for U.S. Treasuries and restrict supply to maintain a high convenience yield; the paper provides the first formal empirical test and quantification of this strategic behavior in the global safe asset market.
convenience yield markup: the component of the observed convenience yield on U.S. Treasuries attributable to monopoly pricing rather than to the intrinsic non-pecuniary value of the assets; estimated at approximately 45% of the total convenience yield (about 30 out of 68 basis points) under the paper’s baseline demand elasticity of 2.2.
demand rotator (Bresnahan identification): a variable that changes the elasticity of demand without shifting its level, enabling identification of strategic conduct: observing that prices rise and quantities fall when demand becomes more inelastic (as during high-volatility regimes) is evidence of monopoly pricing, since a price taker would not respond to an elasticity change alone.
safe asset underprovision: the quantity distortion from monopoly pricing in the global safe asset market; the paper estimates the steady-state safe-asset-to-GDP ratio is approximately 50% lower in the monopoly equilibrium than in the competitive benchmark, reflecting the standard monopoly restriction of output to exploit the downward-sloping demand curve.