R10 | Macro Paper Warehouse

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.

Place-Based Redistribution

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

Place-Based Redistribution: Overview

Research Question

Should national governments redistribute income to residents of poor areas through place-based transfers, or should redistribution rely solely on place-blind (income-only) taxes? The longstanding view in urban economics—“help poor people, not poor places”—holds that place-based aid is inefficient because it channels activity to less productive locations. This paper challenges that view by formalizing the conditions under which place-based redistribution improves on purely income-based transfers, using tools from optimal tax theory embedded in a spatial equilibrium model.

Model and Methodology

The paper develops a two-location model (“Distressed” and “Elsewhere”) with a unit mass of heterogeneous households who differ in skill level (θ) and idiosyncratic preference for living in Distressed (φ). Households choose where to live and how much to earn, facing competitive labor and housing markets in each location. Locations may differ in amenity levels, wage schedules (which may embody skill-specific comparative advantage), and housing costs. A utilitarian planner sets location-specific income tax schedules—observed earnings and location are the only signals of unobserved skill—maximizing a weighted average of household utilities and landlord profits subject to a budget constraint.

The paper proceeds in three steps. First, it derives closed-form conditions for the optimality of a lump-sum place-based transfer under a fixed income tax. Second, it characterizes fully general optimal nonlinear, location-specific marginal tax rate (MTR) schedules (Proposition 2). Third, it calibrates the model numerically, anchoring to the U.S. Empowerment Zone (EZ) program.

Three Sorting Mechanisms and Their Policy Implications

The paper identifies three polar mechanisms that generate sorting of lower-skill households into Distressed:

Skill-taste correlation: higher-skill households have stronger tastes for Elsewhere, independent of wages or rents.
Comparative advantage: higher-skill workers are relatively more productive in Elsewhere.
Income-based sorting: because Elsewhere is more expensive, lower-income households are priced into Distressed.

Under skill-taste correlation, place-based transfers to Distressed are unambiguously welfare-improving even when income taxes are already optimal, because high-skill households prefer Elsewhere for reasons that are orthogonal to income. Under comparative advantage, the direction of the optimal transfer depends on migration elasticities: low migration elasticities favor transfers to Distressed, while high migration elasticities can reverse the sign. Under pure income-based sorting (with homogeneous locational preferences), the conditions for superfluous commodity taxation (Atkinson-Stiglitz 1976) are satisfied, and optimal place-based transfers are zero—though idiosyncratic preference heterogeneity restores non-zero optimal transfers even in this case.

Quantitative Findings

Numerical simulations use Census data and ACS moments calibrated to EZ areas. With high migration responsiveness (κ = 0.5, approximating urban EZs) and skill-taste correlation as the sole sorting driver, the optimal average place-based transfer to Distressed is $4,805, with about 40% ($1,943) arising from lower MTRs rather than a higher demogrant. With low migration responsiveness (κ = 4, approximating rural EZs), the optimal transfer more than doubles to $10,918.

When comparative advantage alone drives sorting and migration is low (κ = 4), the optimal transfer to Distressed is $7,091, with a $3,740 larger demogrant. With high migration and comparative advantage, the transfer reverses to −$2,763 (i.e., Elsewhere receives the subsidy). For intermediate migration under comparative advantage (e.g., κ ≈ 1), the optimal policy is nonlinear: the poorest Distressed residents receive a place-based transfer of $1,254, while high-skill Distressed residents face a place-based tax of $12,398 at the 99th percentile.

In the empirically calibrated urban EZ baseline (migration elasticity 0.82, rent ratio 0.86, sorting driven by skill-taste correlation and income effects), the optimal average place-based transfer is $3,143, roughly matching the magnitude of actual EZ wage tax credits (~$3,000 for full-time eligible workers). The demogrant advantage for Distressed is $1,462, with just over half of the transfer arising from lower MTRs.

In the rural EZ baseline (migration elasticity 0.20, rent ratio 0.54, comparative advantage and income effects), the optimal average transfer rises to $4,329, concentrated in lower MTRs rather than a larger demogrant. Halving the migration elasticity from the rural baseline raises the optimal transfer to $6,906, while doubling it reduces the transfer to near zero ($573).

Scope Conditions

All results are derived under the assumption of no market failures; the model deliberately excludes agglomeration spillovers or other Pigouvian motives, attributing the case for place-based redistribution purely to redistributive goals.
The planner observes only earnings and location, not skill type directly.
Household Pareto weights are set equal to one across types in the simulations, so redistribution is driven solely by diminishing marginal utility of consumption.
The model abstracts from interactions with subnational governments, local public services, and endogenous amenities.
Results on the desirability of transfers to Distressed hinge critically on the motive for sorting, not simply on the existence of spatial income inequality.

Q&A

Q1: What is the equity-efficiency tradeoff formula for a lump-sum place-based transfer, and what does it reveal?

Lemma 1 shows that the first-order welfare effect of a small per-capita transfer from Elsewhere to Distressed starting from a place-blind tax system is dSWF/dt = (λ̄₁ − λ̄₀) + Eθ{m(0)·[T(z₁*) − T(z₀*)]}. The equity gain (λ̄₁ − λ̄₀) is positive when Distressed households have higher average social marginal welfare weights, which holds when their skill distribution is first-order stochastically dominated by Elsewhere’s. The fiscal cost equals the earnings-tax-revenue loss from movers: households induced to migrate to Distressed who earn less there generate lower tax payments. This formula identifies the earnings response to migration as a sufficient statistic for the efficiency cost of place-based policy.

Q2: What characterizes the optimal lump-sum transfer t in Proposition 1?*

Proposition 1 shows t* = [λ̄₁(t*) − λ̄₀(t*) + Eθ{m(t*)·[T(z₁*) − T(z₀*)]}] / (Eθ[m(t*)] / [L₀(t*)L₁(t*)]). The optimal transfer is larger when (i) the average social marginal welfare weight gap between Distressed and Elsewhere is greater, (ii) migration responses m(t*) are small, and (iii) the earnings difference between locations for marginal movers is small. This formula holds regardless of whether the income tax schedule T(·) is itself set optimally.

Q3: Under skill-taste correlation, why are place-based transfers always welfare-improving even under an optimal income tax?

When sorting is driven by skill-taste correlation (high-skill households have stronger preferences for Elsewhere despite identical wages and rents), the equity gain λ̄₁ − λ̄₀ is positive because low-skill households concentrate in Distressed. A small positive transfer starting from t = 0 also incurs zero fiscal cost because movers between locations face identical wages and do not change their earnings. Thus, welfare unambiguously increases. The key insight is that skill-taste correlation violates the Atkinson-Stiglitz condition: high earners would still prefer Elsewhere even if forced to earn less, so location serves as a proxy for skill not captured by income taxes alone.

Q4: Under comparative advantage, why can the sign of the optimal transfer reverse with migration elasticity?

When higher-skill workers are more productive in Elsewhere, movers to Distressed experience wage and earnings reductions, generating a fiscal externality. When migration elasticities are high (low κ), this fiscal cost is large and can dominate the equity gain, making transfers to Elsewhere optimal (simulated optimal transfer of −$2,763 at κ = 0.5). When migration elasticities are low (high κ), the fiscal cost is small and equity considerations dominate, yielding transfers to Distressed ($7,091 at κ = 4). At intermediate elasticities, the optimal policy is nonlinear, redistributing to poor Distressed residents while taxing rich Distressed residents more.

Q5: Why are place-based transfers superfluous under pure income-based sorting with homogeneous locational preferences?

Example 6 (and its formal proof in Appendix B.3.5) demonstrates that when sorting arises solely from higher rents in Elsewhere and preferences over location are homogeneous (no idiosyncratic φ heterogeneity), the Atkinson-Stiglitz sufficient condition for commodity tax superfluousness is met: hypothetically forcing high earners to earn less would not change their preferred consumption bundle relative to low earners. Hence a place-blind income tax implements optimal redistribution without spatial supplements. As the variance of idiosyncratic location preferences κ shrinks toward zero, Figure 3 confirms that optimal place-based transfers tend toward zero across all three sorting motives.

Q6: What new terms appear in the optimal location-specific MTR formulas (Proposition 2) relative to a standalone-economy optimum?

The optimal MTR schedules in Proposition 2 contain two new terms beyond the standard Mirrlees (1971)/Saez (2001) formula. The term Δτ+(θ) captures the fiscal externality from migration: raising Elsewhere’s MTR at skill level θ and above induces movers to Distressed who change their tax revenue by T₁(z₁*(s)) − T₀(z₀*(s)). The term (λ_L − 1)Δr+(θ) captures the equilibrium rent effect: MTR changes shift households between locations, altering rents in both communities and redistributing between renters and landlords. When λ_L < 1 (landlords are weighted less than average households), the rent term creates additional motives for spatial redistribution depending on the ratio of rents to housing supply elasticities across locations.

Q7: How do housing supply elasticities affect the optimal spatial transfer, and why does the sign differ between urban and rural settings?

The rent redistribution term Δr+(θ) has sign determined by r₁/ϱ₁ − r₀/ϱ₀. For urban EZs, where Distressed has lower rents but also lower housing supply elasticity than Elsewhere (ϱ₁ = 0.24, ϱ₀ = 0.34 in the baseline), this ratio is positive, meaning transfers to Distressed shift households into relatively inelastic markets, raising rents there and generating landlord income. When λ_L < 1, this reduces the desirability of transfers to Distressed. For rural EZs, Distressed has higher housing supply elasticity (ϱ₁ = 0.60), so the ratio is negative: transfers shift households to more elastic markets where rents rise minimally. When λ_L < 1, this actually motivates more transfers to rural Distressed areas. In the 75%-landlord-weight sensitivity, optimal urban transfers fall by ~$1,000 while rural transfers rise by ~$1,000, illustrating this asymmetry.

Q8: What does the urban EZ baseline calibration find about optimal transfers and how does it compare to actual EZ policy?

The urban baseline targets a migration elasticity of 0.82 (from Busso et al. 2013), a Distressed-to-Elsewhere rent ratio of 0.86, and 56% of Distressed residents earning under $50,000. The calibrated κ is 0.44. At the optimum, Distressed residents receive an average place-based transfer of $3,143, with $1,462 as a higher demogrant and the remainder from lower MTRs. By comparison, actual EZs provide a wage tax credit of approximately $3,000 per eligible full-time worker. The paper concludes that the magnitude—but not the capped, flat structure—of EZ transfers approximates the optimal level.

Q9: What does the rural EZ calibration find, and how sensitive are results to migration assumptions?

The rural baseline targets a migration elasticity of 0.20 (from Sprung-Keyser et al. 2022), a rent ratio of 0.54, and 60% of Distressed residents earning under $50,000, with sorting attributed to comparative advantage and income effects. The calibrated κ is 4.06. The optimal average transfer is $4,329, primarily arising from lower MTRs rather than a higher demogrant ($532). Doubling the migration elasticity reduces the optimal transfer to near zero ($573); halving it raises it to $6,906. The direction and magnitude of optimal transfers are therefore highly sensitive to the assumed level of migration responsiveness, highlighting the empirical importance of estimating migration elasticities—particularly heterogeneity in migration by income level and earnings changes for marginal movers.

Q10: Do within-income transfers arising from differences in marital and parental status across communities effectively constitute place-based redistribution?

Online Appendix A investigates this by estimating the implicit place-based transfer induced by marital and parental status differences between EZ communities and the rest of the country. Using ACS tract-level data merged with Piketty-Saez-Zucman distributional national accounts (DINA), the authors find that marital status and parental status have offsetting effects: marital status raises taxes on single households (common in Distressed), while parental status increases transfers to households with children (also common in Distressed). Across all preferred CPS-adjusted estimates, net within-earnings transfers are below $1,000 in magnitude, and the two factors essentially cancel. The authors conclude that marital and parental status differences do not yield substantial de facto place-based redistribution within income levels.

Q11: What does the MTR decomposition (Table 3) reveal about why sorting motives generate different MTR patterns?

The decomposition separates the optimal MTR into a within-community component (standard equity-efficiency tradeoff) and a between-community component (fiscal externality from migration). Under skill-taste correlation with high migration (κ = 0.5), both components contribute positively to the Distressed MTR (0.246 within + 0.234 between = 0.479), yielding lower MTRs in Distressed (0.479) than in Elsewhere (0.510). Under comparative advantage with high migration, the within-community component is negative (−0.111) because high MTRs at the optimum reduce the concentration of high-skill types in Distressed, depressing the standard revenue-raising benefit of MTRs. The large positive between-community component (0.655) reflects the large fiscal externality from movers and overcomes this, yielding higher Distressed MTRs (0.544 vs. 0.509 in Elsewhere). With low migration (κ = 4), between-community components shrink substantially, and MTRs in Distressed fall below Elsewhere in all sorting scenarios.

Q12: What does the crosswalk from urban to rural baseline reveal about which assumptions drive the change in optimal transfers?

Table 5 traces the urban-to-rural transition step by step. Starting from the urban baseline ($3,143 average transfer), replacing the migration elasticity target with the rural value of 0.20 triples the optimal transfer to $9,870. Subsequently replacing skill-taste correlation with comparative advantage as the sorting mechanism reduces the transfer by roughly half ($6,402). Adjusting rent to match the rural ratio (0.54) reduces it further to $2,780, as lower Distressed rent reduces the marginal utility of consumption at the bottom and increases income-based sorting. Targeting the rural income share (60% below $50K) raises it back to $4,140, and incorporating rural housing supply elasticities yields the rural baseline result of $4,329. This decomposition reveals that lower migration responsiveness is the single largest driver of higher optimal transfers in rural settings.

Key Concepts

Place-based redistribution: Transfer schemes in which economic benefits or tax burdens are conditioned on the geographic location of residence, as distinct from place-blind income taxes that condition only on earned income. In this paper, modeled as location-specific tax schedules T_j(z) that may differ across communities j.

Skill-taste correlation: A source of spatial sorting in which households with higher skill levels (θ) have systematically stronger preferences for the “Elsewhere” location, independently of wage or rent differences. Formally, the conditional distribution G_θ(φ) of locational tastes given skill is weakly increasing in θ. This correlation breaks the Atkinson-Stiglitz sufficient condition for commodity tax superfluousness and generates unambiguously positive optimal transfers to Distressed.

Comparative advantage (spatial): A sorting mechanism in which higher-skill workers are disproportionately more productive in Elsewhere than in Distressed, captured by the wage elasticity with respect to skill being higher in Elsewhere (γ₀(θ) > γ₁(θ)). Households with skill above a threshold sort into Elsewhere even with homogeneous locational preferences. The existence of spatial comparative advantage means that migrants to Distressed earn less, creating a fiscal externality for place-based transfers.

Income-based sorting: Sorting of lower-income, lower-skill households into Distressed arising purely from the higher cost of living in Elsewhere, without any systematic skill-taste correlation or comparative advantage. Because high-skill households are less sensitive to rent differences, they sort into Elsewhere when rents there are higher. When this is the sole sorting mechanism and locational preferences are homogeneous, the Atkinson-Stiglitz commodity tax superfluousness conditions are satisfied and optimal place-based transfers are zero.

Fiscal externality (migration): The change in income tax revenue caused by migration responses to place-based policy changes, not by changes in incentives for stayers. When movers from Elsewhere to Distressed earn less in their new location, they generate lower tax payments, imposing a first-order cost on the government budget. This externality is measured by Δτ+(θ) in the optimal MTR formulas and equals the earnings-tax-revenue loss from movers across all skill levels above θ. This term is a “sufficient statistic” for the efficiency cost of place-based transfers in the sense of Chetty (2009).

Demogrant (∆₀): The difference in lump-sum transfers provided to zero-earners across the two locations (−T₀(0) − (−T₁(0)) = T₀(0) − T₁(0)). A positive ∆₀ means Distressed provides a larger transfer to non-earners. It represents the place-based redistribution that occurs at the bottom of the earnings distribution, independently of MTR differences. In the paper’s decomposition, total optimal place-based redistribution (∆_z) exceeds ∆₀ when Distressed also has lower MTRs, meaning redistribution grows with income.

Income-constant average tax difference (∆_z): The paper’s preferred summary measure of the average place-based transfer, defined as an equally weighted average of two tax-difference indices: the tax difference evaluated at Elsewhere earnings levels and the tax difference evaluated at Distressed earnings levels. This measure isolates tax schedule differences from productivity differences across locations, avoiding conflation of tax policy and wage effects on measured income.

Landlord welfare weight (λ_L): The social marginal welfare weight assigned to landlords relative to the multiplier on the government budget constraint. When λ_L < 1, the planner values a marginal dollar of public funds more than a marginal dollar to landlords, creating a motive to use place-based taxes to shift rent incidence. The rent redistribution effect on optimal MTRs operates through the term (λ_L − 1)Δr+(θ), which has opposite signs in urban (positive) and rural (negative) distressed areas because of their different housing supply elasticities.