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An Equilibrium Analysis of the Effects of Neighborhood-Based Interventions on Children

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

Overview

Research question. How should governments design neighborhood-based policies to improve long-run outcomes for children, once one accounts for general equilibrium (GE) forces—endogenous rents, neighborhood quality, wages, and distortionary taxation—that small-scale experimental studies cannot identify?

Model. The paper embeds neighborhood effects into a quantitative, heterogeneous-agent overlapping-generations (OLG) model with endogenous location choice and child skill development. The economy has three building blocks: (1) a dynastic life-cycle structure in which parents choose a neighborhood (from two options: a disadvantaged n=1 and an advantaged n=2) and allocate time to child development, with child skills produced by a nested CES aggregator combining parental time and neighborhood quality (proxied by per-capita income in the tract); (2) a GE Aiyagari incomplete-markets framework with endogenous labor supply, wage uncertainty, and progressive labor taxation; and (3) a government that finances housing vouchers or place-based wage subsidies by adjusting the labor income tax parameter, with all additional net expenses fully offset by tax revenue. Housing supply is upward-sloping (elasticity 1.75, from Saiz 2010), so rents are endogenous.

Data and calibration. The model is estimated by simulated method of moments to match U.S. data from the 2000s, drawing on the PSID, NLSY, ATUS, the 2012–2016 ACS, and the Opportunity Atlas (Chetty et al. 2018). Neighborhoods are mapped to Census tracts divided into bottom-10-percent and top-90-percent median household income groups within each commuting zone. Key targeted moments include the income gap between neighborhoods (108 percent higher mean individual income in n=2), the 30 percent higher incomes for children from low-income families raised in the better neighborhood, and a 32 percent gap in weekly parental time with children across neighborhoods.

Validation. Before policy counterfactuals, the calibrated model is validated against two bodies of reduced-form evidence. First, a simulated small-scale, single-generation, partial-equilibrium voucher experiment generates 23 percent higher income for children—close to the 31 percent MTO experimental estimate from Chetty et al. (2016), with the difference largely explained by a smaller poverty-rate contrast (18 vs. 22 percentage points) in the simulation. Second, a simulated 20 percent place-based wage subsidy generates 17–21 percent earnings gains for adult residents of n=1, consistent with Busso et al.’s (2013) quasi-experimental EZ estimates of 17–24 percent.

Main findings — housing vouchers. The welfare-maximizing voucher program features a 100 percent subsidy rate, targets households with children and wages below the 80th percentile (fourth quintile), and is financed by progressive labor taxes. In the long-run steady state this policy raises 12.5 percent more children in the advantaged neighborhood, increases labor productivity by 1.1 percent, reduces income inequality (variance of log after-tax lifetime earnings) by 6.3 percent—comparable in magnitude to the Sweden–U.S. after-tax inequality gap—and raises upward mobility by 27.7 percent (roughly half its standard deviation across U.S. Census tracts). The average marginal tax rate must increase by 15.7 percent to fund the program. Despite this, long-run welfare rises by 3.4 percent in consumption equivalence units. A decomposition shows that intergenerational dynamics add 11.5 percentage points to welfare (relative to a short-run, single-generation scenario), while taxation subtracts 10.2 percentage points, and rent plus neighborhood-quality effects together subtract only 1.4 percentage points—leaving the net long-run GE gain similar to the short-run partial-equilibrium gain of 3.5 percent. Crucially, non-targeting children generates welfare losses of 5.0 percent, confirming that restriction to households with children is essential.

Main findings — place-based wage subsidies. A 12 percent wage subsidy to workers in the disadvantaged neighborhood yields the highest steady-state welfare gain of 0.7 percent. This is approximately one-fifth of the gain achievable with the optimal voucher. The subsidy induces substantial resorting toward n=1, reducing the share of children in n=2 by 6.7 percent while raising neighborhood quality in n=1 by 19.7 percent. Income inequality falls by 8.7 percent and upward mobility rises by 20.4 percent. However, in a short-run partial-equilibrium setup, the wage subsidy has a negative welfare effect of −1.0 percent because it draws parents (and their children) into the disadvantaged area; the positive net effect only emerges through long-run intergenerational channels (+2.5 percentage points) and equilibrium neighborhood-quality adjustments.

Political economy. Because voucher gains are concentrated among young cohorts (those aged 16–43 at introduction), only 33 percent of incumbent adults would rationally vote for the housing voucher program. In contrast, the place-based wage subsidy provides positive average welfare gains for all age cohorts alive at introduction, yielding estimated majority support from over 63 percent of adults. This creates a fundamental political economy tradeoff: the policy with the larger long-run social gains lacks majority democratic support, while the policy with broader support delivers smaller long-run gains.

In depth

Q1. What are the two market frictions that justify government intervention in the model?

A1: The first friction is the absence of intergenerational borrowing markets: parents cannot borrow against their child’s future income, which limits the parent’s willingness to pay the higher rent in n=2 to give their child a developmental advantage. Housing vouchers act as a tax-financed substitute for this missing contract by paying the rent premium and recovering the cost through taxes on the high-earning adults the children become. The second friction is a neighborhood externality: individuals do not internalize the effect of their own income on the neighborhood quality experienced by neighbors’ children. Place-based wage subsidies partially correct this externality by subsidizing work in the disadvantaged area, raising local income per capita and thereby improving the neighborhood quality index for all children resident there.

Q2. How is neighborhood quality defined and modeled, and why is this specification chosen?

A2: Neighborhood quality sn is defined as total income per capita (the sum of labor and capital income) for all residents of neighborhood n, including non-workers. This specification is intended to capture multiple mechanisms: school quality (which depends on local tax bases), role-model effects from productive adults, and social organization effects through adult supervision of children. The formulation includes retired and non-working residents, which means the arrival of children mechanically reduces neighborhood quality per capita in the model, partially capturing a crowding channel. Formally, the neighborhood spillover function takes the power form f(sn) = A * sn^ζ, where ζ governs the elasticity of child development to neighborhood quality.

Q3. How does the paper validate the model’s key mechanism — the neighborhood effect on children?

A3: The validation mimics the MTO RCT within the calibrated model: the government provides a 100 percent rent voucher usable only in n=2 to households in n=1 with incomes below the 10th percentile, holding prices and neighborhood qualities fixed (as in a small-scale experiment). The model generates 25 percent voucher take-up and a 23 percent increase in children’s income in their late 20s. This compares to the experimental MTO estimate of approximately 31 percent. The paper attributes most of the gap to the smaller poverty-rate contrast in the simulation (18 percentage points) relative to MTO (22 percentage points), and shows that plotting the simulated result against the site-specific MTO estimates in a scatterplot of child income gains against neighborhood poverty reductions places the model prediction on the fitted line through the experimental data.

Q4. What is the quantitative role of long-run intergenerational dynamics in the voucher program, relative to other GE channels?

A4: The decomposition in Table 5 isolates four GE channels. Starting from a short-run partial-equilibrium welfare gain of 3.5 percent (for the children of a single treated generation), allowing the economy to operate for the long run while holding prices and taxes fixed raises welfare to 15.0 percent — an increase of 11.5 percentage points — because improved skills in one generation create higher-skilled, higher-income parents who invest more in the next generation. Introducing housing market price adjustments (rents rise by 3.9 percent in n=2) reduces welfare by only 0.6 percentage points. Allowing neighborhood quality to adjust (quality in n=2 falls by 4 percent as lower-income families move in) reduces welfare by an additional 0.8 percentage points. Adding full taxation to balance the government budget reduces welfare by 10.2 percentage points, from 13.6 to 3.4 percent. The four channels nearly cancel, leaving the long-run GE steady-state gain close to the short-run single-generation gain.

Q5. Why does the optimal voucher program require targeting to families with children, and what happens without this restriction?

A5: When the voucher is extended to all households regardless of children (Column 6 of Table 4), nearly 82.6 percent of the population receives a subsidy, pushing almost everyone to n=2. Rents in n=2 rise by 5.3 percent. To finance this much broader program, the average marginal tax rate must increase by 44 percent, far exceeding the 15.7 percent required for the children-targeted program. The large tax increase suppresses labor supply and income, which reduces neighborhood quality in n=2 by 11.6 percent. The net effect is a welfare loss of 5.0 percent. The intuition is that the benefit of the voucher program flows primarily through child skill development, so subsidizing adults without children is fiscally expensive without producing the intergenerational gains that justify the cost.

Q6. What drives the difference in long-run welfare gains between vouchers (3.4 percent) and place-based wage subsidies (0.7 percent)?

A6: The primary channel is labor productivity. The optimal voucher program raises labor productivity by 1.1 percent by increasing the average neighborhood quality to which children are exposed by 1.2 percent. The wage subsidy raises productivity by only 0.2 percent because it induces resorting toward the disadvantaged neighborhood, meaning children’s average neighborhood quality actually decreases by 0.2 percent despite large improvements in n=1’s quality (up 19.7 percent), since fewer children reside in n=1 after the subsidy draws their parents there. Inequality reduction is not the source of the gap: the wage subsidy actually reduces inequality more (8.7–8.9 percent) than the voucher (6.3 percent), but this inequality effect does not translate into larger aggregate welfare because productivity effects dominate.

Q7. How does the wage subsidy produce positive long-run welfare when it generates negative welfare in the short run?

A7: In the short run, the wage subsidy draws parents into the disadvantaged neighborhood to exploit higher wages, which reduces the share of children in the advantaged neighborhood n=2 and lowers children’s late-life productivity (welfare of −1.0 percent for treated children in the single-generation scenario). Two long-run channels flip the sign. First, the subsidy is permanent, so children themselves receive it as adults, providing a direct wage income benefit. Second, the sustained presence of higher-income workers in n=1 raises neighborhood quality there durably (by 19.7 percent at the steady state), which benefits the children who reside in n=1. Together these intergenerational effects add 2.5 percentage points to welfare, while taxation costs reduce it by only 1.4 percentage points, yielding a net gain of 0.7 percent.

Q8. What determines the political economy divide between the two policies?

A8: For the housing voucher, welfare gains are concentrated among younger incumbent adults (ages 16–43), particularly those who are about to have or already have children, while older adults tend to lose because they face higher taxes without benefiting from improved neighborhood quality for their (now independent) children. This concentration implies only 33 percent of incumbent adults would support the voucher under the model’s welfare metric. For the place-based wage subsidy, average welfare gains are positive for every age cohort alive at introduction (though larger for younger cohorts), because the wage subsidy raises incomes for workers in n=1 immediately and benefits from equilibrium rent declines in n=1 that allow all residents to benefit. Over 63 percent of adults would support the wage subsidy. The paper notes that if the government could borrow to initially finance the voucher program and pay for it later (as in Daruich 2020 for early childhood programs), majority support for the voucher could potentially be achieved.

Q9. How sensitive are the welfare results to the key calibrated parameters?

A9: The sensitivity analysis (Table 9, following Andrews et al. 2017) shows that individual parameters would need to change substantially to overturn the conclusion that vouchers generate larger steady-state welfare gains than wage subsidies. For example, the altruism parameter β̃ would need to increase by 22 percent to eliminate the voucher welfare gain, which would require average parental transfers to rise to 198 percent of income — far from the empirical target of 125.4 percent. Using the more conservative tract-level housing supply elasticity from Baum-Snow and Han (2021) of 0.3–0.4 (about 80 percent below the baseline Saiz 2010 estimate of 1.75) would reduce the voucher welfare gain from 3.37 to approximately 2.57 percent, not reversing the qualitative conclusion. The parameters with the largest influence on welfare gains are the labor disutility parameter µ and the altruism parameter β̃; the housing supply elasticity matters more for the voucher than the wage subsidy because easier housing supply accommodates growth in n=2 without displacement under the voucher.

Q10. What does the transition path of the voucher program look like, and why do welfare gains initially dip before recovering?

A10: When the voucher is unexpectedly introduced, the first newborn cohort gains approximately 4 percent welfare, but gains for subsequent cohorts initially dip to around 3 percent before stabilizing at 3.4 percent by the 20th post-introduction cohort. The dip occurs because moving costs slow resorting: immediately after introduction, rents in n=2 begin rising and neighborhood quality there begins falling as low-income families move in, but the capital stock adjustment (which would counteract these effects by raising GDP) lags the resorting. The rebound comes as capital accumulates in n=2 over time and as intergenerational productivity gains build through successive cohorts of better-skilled parents. Labor productivity jumps noticeably for the first cohort born to parents who received the voucher (approximately 28 years after introduction) and again for the first cohort born to grandparents who received it, visibly demonstrating the intergenerational mechanism. In contrast, the wage subsidy’s welfare gains are approximately constant at 0.7 percent across all cohorts because the key channels (neighborhood quality improvement in n=1 and wage gains) materialize rapidly and remain stable throughout the transition.

Key Concepts

Neighborhood quality (sn): In this paper, neighborhood quality is not school quality or amenities in a generic sense but is explicitly defined as total income per capita — the sum of labor income and capital income — for all residents of neighborhood n, including non-workers. This endogenous measure rises when higher-income or more productive residents move in and falls when lower-income residents or additional children arrive.

Intergenerational borrowing constraint: The inability of parents to borrow against their child’s future income, modeled as a non-negativity constraint on the monetary transfer from parent to child (transfer ≥ 0). This is the paper’s first key market friction: without it, a poor parent who moved to a better neighborhood would smooth consumption across generations by having the high-earning child compensate the parent. The constraint prevents this, reducing parental investment below the socially efficient level.

Consumption equivalence (veil of ignorance): The welfare metric used throughout the policy analysis. It is defined as the percentage change in consumption that would make a newborn individual indifferent between the pre-policy and post-policy steady states, computed before knowing their position in the skill or income distribution. This is the paper’s measure of long-run steady-state welfare.

Parental investment aggregator (CES): A nested constant-elasticity-of-substitution function that determines how parental time τ and neighborhood quality sn combine to form the effective investment input I into child skill development: I = Ā[αI f(sn)^γ + (1 − αI)τ^γ]^(1/γ). The elasticity parameter 1/(1 − γ), estimated at 0.41, governs the degree of complementarity between time and neighborhood quality; a lower elasticity (γ = −1.43) implies the two inputs are complements, so parents with children in better neighborhoods also spend more time with them.

Place-based wage subsidy: A neighborhood-specific wage premium (denoted w̃s) paid to all workers who both live and work in the disadvantaged neighborhood n=1, raising their effective wage to w1 = (1 + w̃s)w2. This policy targets the neighborhood externality by increasing the income of residents in n=1, which raises neighborhood quality and provides an incentive for higher-skilled workers to relocate to (or remain in) the disadvantaged area.

Upward mobility: Measured in this paper as the probability that a child born to parents in the bottom 20 percent of the income distribution reaches the top 20 percent of the income distribution during the working stage of their own life. This is distinct from mean income rank measures; it specifically tracks cross-quintile transitions in the model’s stationary distribution.

Equilibrium decomposition: A simulation-based method in which GE channels are progressively activated. Starting from a short-run, partial-equilibrium, single-generation baseline (analogous to an RCT), the authors sequentially allow: (i) long-run intergenerational dynamics while holding prices fixed; (ii) housing market price adjustments; (iii) neighborhood quality adjustments; (iv) tax and production-price adjustments. Each step’s change in outcomes identifies the quantitative contribution of that specific channel.

What Do Policies Value?

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

This paper asks a fundamental question about policy design: when a program prioritizes one group over another, is that because the group benefits more from the intervention, or because the policy assigns them higher intrinsic welfare weight? Björkegren, Blumenstock, and Knight develop a two-stage method to decompose observed allocation decisions into their underlying components: (i) welfare weights assigned to different types of people, (ii) heterogeneous treatment effects of the intervention, and (iii) relative weights on different outcomes. The key insight is that the same allocation rule can be consistent with very different value systems depending on how much each group actually benefits.

The method works as follows. In a first stage, the analyst estimates heterogeneous treatment effects — how much each individual benefits on each outcome dimension — using OLS or machine learning methods (e.g., causal forests). In a second stage, the analyst reconciles the observed ranking of beneficiaries with an implicit welfare function using an exploded logit likelihood, recovering welfare weights (who is valued), impact weights (how different outcomes are valued), and a base value for treatment independent of measured outcomes. Identification requires an exclusion restriction: the covariates used to estimate treatment effect heterogeneity must include variables excluded from the welfare weight specification, allowing the analyst to compare households with similar welfare weights but differential treatment effects. Variants of the method that impose known welfare weights or known impact weights can be used without the exclusion restriction.

The paper demonstrates the method using PROGRESA, Mexico’s large conditional cash transfer program launched in 1997. PROGRESA ranked households by a proxy means test poverty score and transferred approximately 197 pesos per month (roughly $20 USD) to eligible poor households, conditional on school attendance and doctor visits. The analysis uses endline survey data on 7,767 households and focuses on three outcomes emphasized in program documents: log per-capita consumption, child sick days (ages 0-5), and school days missed (ages 6-16).

The program’s average treatment effects were: a 0.149 log point increase in monthly consumption (SE=0.015), a 0.165 reduction in sick days per child (SE=0.051), and a near-zero effect on school days missed (-0.0053, SE=0.028). These effects were heterogeneous: indigenous households, for instance, benefited substantially more from the program.

The paper’s central empirical finding inverts the naive interpretation of PROGRESA’s targeting. Indigenous households were ranked 60.6 log points higher in the program’s priority order. A simple regression suggests the program favored them. But after accounting for the fact that indigenous households benefit substantially more from treatment, the method finds that the program’s implied welfare weight on indigenous households is, if anything, lower by 17.4% relative to non-indigenous households — not higher. The program’s prioritization of indigenous households is thus explained by efficiency, not by preferential welfare weighting.

Because PROGRESA cash transfers relax household budget constraints and outcomes like consumption reflect household choices, the impact weights capture the difference between how the policy values outcomes and how households value them. The estimates strongly reject non-paternalism: the policy implicitly values consumption and potentially health differently from household decision-makers. Of the total welfare impact, approximately 55% is attributed to the base value of the transfer itself (independent of measured outcomes), approximately 45% to consumption impacts, and less than 1% to health and schooling impacts combined. The implied value of providing the transfer independent of outcomes corresponds to 0.16 log points of consumption, or about 23.1 pesos per person per month — slightly below the average transfer of 33.9 pesos per person per month.

The paper also runs counterfactual exercises showing how alternative preference structures would have changed the allocation. A policy maximizing only educational impacts would have prioritized richer, smaller households; one maximizing only consumption impacts would have further prioritized indigenous households. These counterfactuals are mapped onto a Pareto frontier across the three outcomes. The estimated welfare weights from the implemented policy align closely with preferences elicited in a 2023 survey of 429 Mexican residents, though residents placed higher value on child health relative to what the policy implied.

Q: What is the core identification challenge the paper addresses? A: When a policy prioritizes a group, it could be because the group benefits more (efficiency) or because the policy assigns them intrinsically higher value (preference). These two explanations are observationally equivalent from the allocation alone. The paper separates them by first estimating heterogeneous treatment effects and then inverting the allocation to recover residual welfare weights.

Q: What is the exclusion restriction required for full identification? A: The covariates used to estimate treatment effect heterogeneity (x-tilde) must include at least some variables excluded from the welfare weight specification (x). This allows the analyst to compare households with similar welfare weights but different predicted treatment effects, pinning down how much of the ranking reflects efficiency versus preference. Without this restriction, one can still recover conditional preferences by imposing known values for either welfare weights or impact weights.

Q: How does the exploded logit likelihood work in this setting? A: The analyst observes a single full ranking of all households, rather than partial orderings from multiple decision-makers. The welfare impact of treating household i is modeled as a linear function of predicted treatment effects scaled by welfare and impact weights, plus an extreme-value-distributed shock. The likelihood of observing household i ranked above household i-prime is the ratio of their exponentiated welfare scores, summed over all households ranked below i. Maximum likelihood recovers the welfare weights, impact weights, and base value simultaneously.

Q: What were PROGRESA’s average treatment effects on the three focal outcomes? A: Average treatment increased log monthly consumption by 0.149 (SE=0.015), reduced child sick days by 0.165 (SE=0.051), and had a near-zero effect on school days missed (-0.0053, SE=0.028). The consumption and health effects are statistically significant; the schooling effect is not distinguishable from zero.

Q: What does the analysis find about the welfare weight assigned to indigenous households? A: In the raw ranking regression, indigenous households are ranked 60.6 log points higher, suggesting the program favored them. After accounting for the fact that indigenous households benefit substantially more from treatment, the method finds the implied welfare weight on indigenous households is lower, not higher — specifically, about 17.4% lower than non-indigenous households. The program’s higher ranking of indigenous households is explained entirely by their larger treatment effects, not by preferential weighting.

Q: How are the impact weights on consumption, health, and schooling interpreted given that outcomes reflect household choices? A: Because PROGRESA relaxes household budget constraints and outcomes like consumption result from household optimization, the estimated impact weights capture the difference between how the policy values outcomes relative to how households value them (internalities), rather than the absolute policy valuation. A nonzero weight implies the policy disagrees with household preferences — paternalism. The positive coefficient on log consumption implies the policy values this outcome more than households do.

Q: How much of PROGRESA’s welfare impact comes from the base transfer value versus measured outcomes? A: The base value of the transfer (independent of measured impacts on consumption, health, and schooling) accounts for approximately 55% of total implied welfare impact. The impact on consumption accounts for approximately 45%. Impacts on health and schooling together account for less than 1%. The implied value of the base transfer corresponds to 0.16 log points of consumption per capita, or about 23.1 pesos per person per month — somewhat below the average transfer amount of 33.9 pesos per person per month.

Q: Does the analysis reject egalitarian welfare weights and non-paternalism? A: Yes, using Wald tests with bootstrapped covariance matrices. The hypothesis of egalitarian weights (all gamma equal to one) is rejected. Non-paternalism (all beta equal to zero) is strongly rejected. The joint hypothesis of egalitarianism and non-paternalism is also rejected across all specifications tested.

Q: How do the estimated welfare weights compare to stated preferences of Mexican residents? A: The 2023 survey of 429 Mexican residents elicited preferences using multiple price lists over how to prioritize different household types. The welfare weights implied by the implemented policy are broadly similar to resident preferences, but the policy places relatively higher welfare weight on indigenous households than the median survey respondent does. Survey respondents value child health impacts more than household decision-makers and more than the implemented policy does, consistent with support for paternalism.

Q: What do counterfactual allocations reveal about the relationship between policy goals and targeting priorities? A: A policy maximizing only consumption impacts would further prioritize indigenous households with lower income. A policy maximizing only educational impacts would instead prioritize richer, smaller households. A policy maximizing only health impacts would largely preserve indigenous household prioritization while placing less emphasis on lower-education households. These three extreme policies map to the corners of a Pareto frontier, and the implemented PROGRESA policy lies close to the allocation consistent with surveyed resident preferences.

Q: What changed when Mexico reformed PROGRESA’s poverty score in 2003? A: The 2003 reform increased the priority of older and smaller households. Applying the method to the new poverty score reveals that it implicitly switched to assigning a positive welfare weight to indigenous households (compared to the negative implied weight under the original score), and placed less welfare weight on lower-income and younger households relative to the original design.

Q: What are the main limitations and scope conditions of the method? A: Full identification requires an exclusion restriction (some treatment effect heterogeneity predictors excluded from welfare weights) and sufficient variation in treatment effects across household types. If treatment effects are homogeneous, welfare weights and impact weights cannot be separately identified. If correlated unobservables drive the ranking but are not modeled, the method recovers preferences consistent with included variables only, analogous to omitted variable bias in OLS. The method also requires a way to estimate treatment effect heterogeneity, which is most credible with a randomized pilot, though non-experimental methods are in principle applicable.

Q: How does this paper relate to the inverse optimum public finance literature? A: The inverse optimum literature (Bourguignon and Spadaro 2012; Saez and Stantcheva 2016; Hendren 2020) recovers the redistribution preferences consistent with income tax schedules, conditioning on a single covariate (pre-tax income) affecting a single outcome (net-of-tax consumption). This paper generalizes that framework to arbitrary allocation policies conditioning on a vector of covariates and affecting a vector of outcomes, and extends it to settings beyond income taxation where heterogeneous treatment effects can be estimated.

Q: Can the method be applied when only a binary allocation is observed rather than a full ranking? A: Yes. A binary allocation corresponds to a ranking with only two levels, and the same exploded logit procedure applies, though with reduced statistical power. The paper provides an empirical illustration of this setting in Section 5.2.1.

Welfare weights (w(x_i)): The policy’s differential valuation of one household’s utility relative to another, expressed as a multiplicative function of household characteristics. Distinct from how much a household benefits — two households may be ranked identically despite different benefits if their welfare weights differ proportionally.

Impact weights (beta_j): The policy’s relative valuation of different outcome components (consumption, health, schooling). For outcomes that are household choices, impact weights capture the difference between how the policy values the outcome and how the household values it — an internality or paternalistic preference.

Base value (alpha): The value a policy assigns to providing a treatment independent of its measured impact on any specific outcome. Captures either a direct utility benefit of treatment or the value of relaxing household budget constraints when outcomes are choices.

Exclusion restriction: The requirement that the set of covariates used to estimate treatment effect heterogeneity includes at least some variables excluded from the welfare weight specification. Enables separate identification of efficiency-based and preference-based components of a ranking by comparing households similar in welfare weight but different in predicted treatment effects.

Exploded logit likelihood: The econometric procedure used in the second stage, adapted for a single complete ranking of all alternatives rather than partial orderings. Treats the observed ranking of household i as a choice from the set of all households ranked below it, with likelihood given by the softmax of welfare scores.

Value audit: A retrospective application of the method that reads the implicit values encoded in an implemented policy’s allocation decisions, enabling comparison against stated policy objectives, constituent preferences, or normative benchmarks.

Paternalism (in this paper’s sense): A policy is paternalistic if it assigns nonzero impact weight (beta_j ≠ 0) to outcomes that are household choices — meaning the policy values those outcomes differently from the households making the choices. The envelope theorem implies a non-paternalistic policy would place zero weight on choice outcomes beyond the general constraint relaxation.