Fiscal-Multipliers | Macro Paper Warehouse

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).

Disaggregated Economic Accounts

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

This paper develops and implements a system of disaggregated economic accounts that breaks down national accounting positions into bilateral flows between small groups of consumers, producers, the government, and the rest of the world. Standard national accounts document aggregate income and production plus input-output trade between producer industries; they contain no comprehensive data on which consumers buy from which producers or which producers pay income to which consumers. The paper fills this gap by measuring, for Denmark, all 36 positions in the UN System of National Accounts (SNA) — consumer spending, labor compensation, profit income, intermediates trade, government transfers and taxes, and foreign trade — as bilateral cell-to-cell flows, satisfying all national accounting identities at the level of individual cells and at the aggregate level. The data reveal systematic stylized facts about domestic spending shares, gravity of spending, urban bias, and assortative matching between consumer and producer characteristics. Combining the disaggregated accounts with a general equilibrium model with nominal wage rigidities, the paper shows that fiscal transfer multipliers vary substantially across consumer cells — from below 1 to above 2 — depending on the spending intensity of recipient cells on the slack (unemployed) portion of the economy. Applying the framework to a hypothetical U.S. tariff shock on Denmark (calibrated to July 2025 effective tariff levels on China), the paper demonstrates that the cells generating the highest multipliers are not those directly exposed to the shock or even those made slack, but those whose spending intensity on slack cells is high. The disaggregated accounts allow the government to select more effective fiscal policies: choosing transfers targeting high-spending-intensity cells saves approximately 0.4–0.7% of Danish GDP relative to programs targeting low-intensity cells, for the same GDP stimulus.

Measurement framework (Section II): The paper assigns every Danish adult to one of approximately 2,744 consumer cells, defined by the interaction of 98 municipalities (regions) and 28 industries (industry of main employment). Every production establishment is assigned to one of approximately 2,646 producer cells by region and industry. Median consumer cell contains 658 adults; median producer cell contains 47 establishments. The circular flow includes: (i) consumer spending on domestic and foreign producers; (ii) labor compensation paid by producer cells to consumer cells; (iii) profit income (dividends, mixed income, owner-occupied housing surplus) from producers to consumers; (iv) intermediates trade between domestic producers; (v) foreign trade; (vi) government taxes, transfers, and spending. A “bottom-up” approach uses microdata — geocoded transaction records from Danske Bank (largest Danish bank) and administrative government registers — to directly measure bilateral flows; a “top-down” approach distributes aggregate flows using assignment algorithms. Year: 2018. Data available at disaggregatedaccounts.com.

Stylized facts (Section IV):

1. Domestic spending shares (§IV.B): The share of a consumer cell’s spending going to domestic rather than foreign producers ranges from 75% to almost 100% (average 92%). Rural (small-population) cells, older cells, and less college-educated cells have higher domestic spending shares. Population size, average age, and college share jointly explain about half of the cross-cell variation in domestic shares; the patterns hold within industry and within region. The majority of foreign spending goes to travel-related and specialized retail categories (hotels, airlines, food away from home, clothing).

2. Gravity (§IV.C): Consumer spending declines with distance (log-log gradient = −1.33, column 1 of Table II). On average, roughly 50% of spending stays in the home region and an additional 10% goes to regions within 25 km. The distance gradient is steeper for groceries and fuel (local, in-person purchases) and shallower for telecommunications, insurance, and hotels. Rural, older, and less college-educated consumers spend more locally (stronger distance gradient, consistent with higher domestic shares).

3. Urban bias (§IV.E): Consumer spending flows disproportionately toward large cities. The 15 largest regions receive 34% of national consumer spending while accounting for only 27% of consumers. Urban bias is absent for everyday purchases (groceries) and strong for irregular or remote purchases (telecommunications, specialized retail). Rural consumers also visit urban regions in person, so urban bias is present in card payments too.

4. Assortative spending (§IV.D): Consumers tend to spend on producer cells employing workers with similar characteristics. Age of consumers and average age of workers in receiving cells are positively correlated (β = 0.178); college share similarly (β = 0.120); domestic spending share similarly (β = 0.203). The slopes are well below 1 (consumers purchase from many cells), but mild assortative spending reinforces first-order domestic spending patterns through higher-order connections.

5. Triangular flows (§IV.F): A distinctive cross-regional pattern: consumer spending and intermediates trade flow on net from rural to urban regions (urban regions run a net internal trade surplus); rural regions run a net external surplus (rural manufacturers export; e.g., Novo Nordisk in Kalundborg, Vestas in Nakskov); urban regions import relatively more from abroad. This triangular flow arises from urban consumption amenities and urban business service concentration.

Spending intensity (§IV.G): The paper constructs a reduced-form measure capturing, for each consumer cell i, how much its spending contributes to the income of a target group of cells — accounting for all higher-order connections (the infinite sum over indirect spending chains). The domestic spending intensity of cell i is defined recursively as the sum over all domestic producer cells j of (spending share αji × domestic spending intensity of producer cell j). Values range from roughly 0.4 to 0.9. The measure is strictly greater than the direct domestic spending share because the recursive formula incorporates second- and higher-order domestic connections. Domestic spending intensity is higher for rural, older, and less college-educated cells (consistent with the stylized facts). A spending intensity on slack cells can be constructed in the same way by replacing the target group with cells experiencing demand-driven unemployment.

General equilibrium model (Sections V–VI): The model is a static small open economy with many consumer and producer cells. Consumer utility is Cobb-Douglas over goods from all producer cells and foreign goods. Each producer cell’s production function is Cobb-Douglas with decreasing returns to scale (equivalent to a fixed factor). The key friction is downward nominal wage rigidity: Wi ≥ (1−δ)W̄i. When demand for a cell’s labor falls sufficiently (more than fraction δ), the wage rigidity binds and some workers in that cell become slack (unemployed demand-determined). A fiscal transfer to consumer cell i raises its income, which stimulates spending, which flows through the disaggregated network to raise labor demand across cells. The multiplier is higher when recipient spending flows disproportionately to slack cells, generating additional employment. The model is calibrated using the measured disaggregated accounts: spending shares αji, profit shares κij, labor shares λij, intermediates shares ωjj′, and tax rates are all taken directly from the disaggregated data. Baseline elasticity of substitution = 1 (Cobb-Douglas); robustness checks use short-run elasticities (< 1) and long-run elasticities (> 1), with no material change in conclusions.

Analytical result (Proposition 1): In an economy-wide recession (all cells slack), the vector of transfer multipliers is µ = ϕ′ · (I − M)⁻¹ · M · D((1 − τ̄ᵢ)⁻¹), where M is a transformed Leontief-style spending matrix incorporating the disaggregated accounts and τ̄ᵢ are fiscal externalities. The key insight is that the multiplier of cell i’s transfer is closely linked to its spending intensity on all other domestic cells, with all higher-order connections captured by the (I − M)⁻¹ M term. A cell’s multiplier is high when: (i) it spends domestically rather than on imports; (ii) it spends on producers that in turn employ domestic workers in slack cells; and (iii) these higher-order effects amplify through the circular flow.

Economy-wide recession: quantitative multipliers (Table III):

Transfer policy	Multiplier	Cost to raise GDP by 5% (bn DKK)
Uniform (all adults)	1.04	96.08
Top 10% domestic spending intensity	1.21	81.99
2018 child tax credit	1.02	97.85
2022 inflation relief to elderly	1.13	88.11
2023 housing rent inflation support	1.03	96.45
Construction worker support	1.23	81.16
Consulting/IT worker support	0.95	105.22

High-multiplier policies (construction workers, 2022 elderly relief) target rural, older, less college-educated cells with high domestic spending intensity. Low-multiplier policies (consulting/IT workers, 2023 housing relief, 2018 child tax credit) target urban, young, or college-educated cells with lower domestic intensity. The gap between the best and worst policies amounts to savings of roughly 15 bn DKK (≈ 2.4 bn USD), or 0.4–0.7% of Danish GDP, for the same aggregate GDP impact.

U.S. tariff shock application (Section VII): The paper analyzes a hypothetical U.S. tariff increase to 41.4% (the July 2025 effective U.S. tariff on China) on Danish exports, motivated by Greenland tensions. The shock reduces export revenue by 41.4% for each producer cell, with direct exposure varying by region: Billund (Lego headquarters), Kalundborg (pharmaceuticals), and a Copenhagen manufacturing hinterland face the largest direct declines — up to 8% of total regional sales. The shock propagates through the disaggregated network; cells whose income falls by more than 4% become slack. Key findings:

Regional slackness follows direct exposure but is also shaped by proximity to other exposed regions (urban bias propagates the shock to cities) and isolation (Billund has high direct exposure but low slackness relative to exposure because it is geographically isolated from other high-exposure cells)
Transfer multipliers for this heterogeneous recession (Proposition 2) depend on spending intensity on slack cells, not on direct exposure or own slackness
Table IV (R² for multiplier): slack cell indicator alone explains R² = 0.015; direct spending share on slack raises R² to 0.366; spending intensity on slack cells raises R² to 0.769 (column 3); adding both spending share and spending intensity on slack reaches R² = 0.840 (column 4)
Billund, despite high exposure, has low multiplier because its spending (often local to a low-exposure vicinity) does not create labor demand for slack cells elsewhere
Some of the highest-multiplier regions are themselves non-slack but are surrounded by many slack cells, so their spending effectively employs slack workers

Dynamic model (Section VIII): The paper extends to a dynamic OLG (Blanchard-Yaari) model with heterogeneous marginal propensities to consume (MPCs) calibrated from a 2009 Danish fiscal policy. Key result: static and year-4 dynamic multipliers are closely correlated (slope ≈ 0.898). Long-run cumulative multipliers exactly equal static multipliers (formally proved in Appendix V.F): in the long run, all transfers are fully spent. MPCs and domestic spending intensity are complementary determinants of dynamic multipliers — targeting high-MPC cells amplifies short-horizon (year 0–2) multipliers, while targeting high-spending-intensity cells shapes both short- and long-run multipliers. The paper’s main mechanism (spending intensity on slack cells) is robust at all horizons.

Robustness (Section IX): (i) Counterfactual accounts with reversed stylized patterns (e.g., rural cells spending like urban cells) lead to substantially different multipliers — the specific measured patterns drive the results. (ii) Imposing standard simplifying assumptions (consumer spending flows only to local producers; spending flows across regions in proportion to intermediate trade) misses most of the multiplier variation. (iii) The mechanism is similarly important in less open economies. (iv) Low short-run and high long-run substitution elasticities (from the trade literature) produce similar multiplier rankings across cells.

Scope conditions: The implementation is a proof of concept for Denmark, using existing micro data from a single large bank and government registers; full coverage of all banks and complete data on within-firm flows would strengthen measurement. Capital-related transactions (saving, investment, financial assets) are aggregated into a single capital accumulation cell — disaggregating these would require different data. The model is intentionally static (with a dynamic extension), abstracting from price adjustment dynamics beyond the NK wage rigidity. The analysis is a partial equilibrium in the sense that monetary policy response is not modeled; the fixed exchange rate assumption is realistic for Denmark (pegged to the Euro) but may not transfer to economies with flexible rates. The proof of concept suggests that national statistical agencies could benefit substantially from measuring disaggregated flows through refined surveys.

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 missing from standard national accounts that this paper’s system provides?

Standard national accounts measure aggregate consumer spending, income, and output, plus intermediates trade among producer industries (input-output tables); what they do not measure is which specific consumer groups buy from which specific producer groups, or which specific producer groups pay labor and profit income to which specific consumer groups. This means that propagation of a shock through the circular flow — e.g., a tariff shock that reduces exports by rural manufacturers, which reduces income for rural workers, who then reduce spending on urban services, which reduces urban workers’ income — cannot be traced without simplifying assumptions (like “spending flows only to local producers”) that the disaggregated data shows to be empirically inaccurate. The paper provides a proof of concept demonstrating that measuring these bilateral consumer-to-producer and producer-to-consumer flows, while satisfying all national accounting identities, is feasible with existing micro data and yields policy-relevant variation in fiscal multipliers.

Q2. Why do rural, older, and less college-educated consumer cells have higher fiscal multipliers during an economy-wide recession?

These groups have higher domestic spending intensity — a higher fraction of their spending reaches domestic consumers rather than leaking abroad — because they spend less on international tourism, less on imported goods accessed through online retail or urban services, and more on local goods purchased in person. The gravity patterns (stronger distance gradient) and direct domestic spending shares document this directly: rural consumers allocate ~92–100% of spending to domestic producers versus ~75–80% for urban young college-educated consumers. When all cells are slack, a transfer to a high-domestic-intensity cell circulates more within the country, generating more rounds of domestic income and employment before leaking to imports. The mild assortative spending pattern further reinforces the first-order effect: spending by rural older consumers flows toward producer cells employing workers with similar characteristics, who also spend domestically, so higher-order connections amplify rather than dilute the domestic spending effect.

Q3. Why does targeting directly exposed or slack cells not guarantee a high transfer multiplier after the U.S. tariff shock?

A transfer raises GDP by increasing spending, which creates labor demand for other consumer cells; a transfer to a slack cell only generates a high multiplier if that cell’s spending flows toward other slack cells (directly or through indirect chains) — not if it flows toward non-slack cells or abroad. The tariff shock creates isolated pockets of slackness in rural manufacturing regions (e.g., Billund for Lego) that are geographically far from other slack regions; Billund consumers spend locally (gravity) and their locality is not itself a center of other slack cells. In contrast, regions near Copenhagen with moderate direct exposure may have high multipliers if they are close to many other slack manufacturing cells — their spending generates employment across the slack network. The R² decomposition confirms this: knowing a cell is slack explains only 1.5% of multiplier variation (R² = 0.015), while knowing its spending intensity on slack cells explains 76.9% (R² = 0.769).

Q4. How does the paper ensure that the disaggregated flows satisfy national accounting identities?

The system is designed so that every cell’s total inflows equal total outflows (a cell-level balance sheet constraint), and the sum of all cell-level flows equals the corresponding national aggregate from the SNA — both conditions are imposed by construction, not just approximated. For most positions, a bottom-up approach uses observed bilateral microdata (e.g., card payments from Danske Bank directly measure consumer spending by consumer cell i at producer cell j); for positions without direct microdata, a top-down algorithm distributes an aggregate total across cells using assignment rules grounded in the microdata. This dual approach ensures national comprehensiveness (the sum of disaggregated flows equals aggregate national accounts) and individual consistency (cell-level identities hold), unlike existing regional accounts or social accounting matrices that satisfy only one of these constraints.

Q5. What is the relationship between spending intensity and the standard fiscal multiplier formula?

The cell-level multiplier (dGDP/dTi) in Proposition 1 equals approximately the cell’s spending intensity on domestic cells, corrected for fiscal externalities and price effects of the fixed factor. The formal difference is that the model multiplier involves the matrix (I − M)⁻¹M where M incorporates both spending and production shares (through which price changes for the fixed factor enter), while the reduced-form spending intensity uses only the spending matrix. Despite this difference, the two measures are highly correlated empirically: the regression of cell-level multipliers on domestic spending intensity has a slope of approximately 1.66 for static multipliers. The spending intensity can thus be calculated directly from the disaggregated accounts without solving the full general equilibrium model, making it a practical statistic for policy guidance.

Q6. How does the dynamic model reconcile the fact that rural, older, and less college-educated cells have high spending intensities but typically lower MPCs?

MPCs and spending intensities are complementary but distinct determinants of dynamic multipliers at short horizons: high-MPC cells spend the transfer quickly (year 0–1), generating a large immediate impact, while high-spending-intensity cells ensure that spending, whenever it occurs, circulates domestically and reaches slack labor markets. At long horizons (year 4+) the two effects converge because all cells eventually spend their full transfer (long-run MPC = 1) and the multiplier converges to the static model’s value, which depends only on spending intensity. The practical implication is that policies targeting rural/older/less-educated cells (high intensity, lower MPC) may have lower immediate multipliers than policies targeting high-MPC urban consumers, but converge to higher long-run multipliers. The year-4 cumulative multipliers from the dynamic model closely resemble the static model, suggesting a 3–5 year business cycle horizon is well captured by the static analysis.

Q7. What does the triangular flow pattern imply for understanding regional inequality and fiscal redistribution?

The triangular flow — rural regions receive net income from foreign exports; rural consumers spend net inflows toward urban regions; urban consumers spend net toward abroad — means that rural regions’ incomes depend on export competitiveness while urban regions’ incomes depend on domestic consumption demand; fiscal transfers to rural consumers thus have high domestic multipliers because their spending boosts urban income (via the rural-to-urban spending flow), which then circulates domestically before leaking abroad. This pattern is also consistent with the political economy finding that high-multiplier cells (rural, older, less educated) are more likely to vote for right-wing populists and feel politically disenfranchised — they are the “left behind” groups that economic research associates with exposure to globalization and automation, but whose spending patterns happen to generate large domestic multipliers during recessions.

Key concepts

disaggregated economic accounts : a system that breaks down all national accounting positions — consumer spending, labor and profit income, intermediates trade, government transactions, foreign trade — into bilateral flows between consistently defined region-by-industry consumer cells and producer cells, satisfying national accounting identities both at the cell level and in aggregate; the paper’s proof of concept is implemented for Denmark using 2,744 consumer cells and 2,646 producer cells in 2018.

spending intensity : a cell-level, reduced-form statistic capturing how much a consumer cell’s spending contributes to the income of a target group of cells (e.g., all domestic cells or all slack cells), accounting for all indirect higher-order connections through the circular flow; formally defined as a recursive sum that incorporates the full disaggregated network structure; ranges from 0.4 to 0.9 for domestic spending intensity and is systematically higher for rural, older, and less college-educated cells.

slack cell : in the paper’s NK model, a consumer cell for which demand-driven unemployment occurs because the nominal wage rigidity binds — labor supply exceeds demand when the cell’s income declines by more than a threshold δ due to a negative demand shock; fiscal transfers with high multipliers are those whose spending reaches slack cells (directly or through higher-order network connections).

triangular flows : the cross-regional spending pattern documented for Denmark in which net consumption spending flows from rural regions to urban regions (urban bias), net foreign export revenue flows to rural regions (rural manufacturing), and net foreign import spending flows from urban regions; implies that rural-to-urban spending flows act as an important transmission channel for fiscal stimulus targeted at rural consumers.

bottom-up vs top-down disaggregation : the two methodological approaches for constructing bilateral cell-to-cell flows; the bottom-up approach uses individual-level microdata (e.g., bank transaction records) to directly observe cell-to-cell payment flows; the top-down approach allocates an aggregate national accounting position across cells using assignment algorithms informed by microdata; both approaches are designed so that the resulting disaggregated flows sum to the corresponding SNA aggregate.