Place-Based Redistribution

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:

1. Skill-taste correlation: higher-skill households have stronger tastes for Elsewhere, independent of wages or rents.
2. Comparative advantage: higher-skill workers are relatively more productive in Elsewhere.
3. 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.