Social Protection & Choice

Key economic models and papers about social protection policies and choice

Sufficient Statistic

A summary measure of data that contains all the information needed to evaluate a specific policy or estimate a parameter, without needing to know the complex underlying structural details

Mirrlees (1971) - “An Exploration in the Theory of Optimum Income Taxation”

The social planner maximizes v(c(theta),l(theta)), which is an agent’s utility conditional on their after-tax income and labor supply (which are functions of their ability). The elasticity of labor supply with respect to post-tax income captures how much people work when taxes change. The optimal tax rate balances the gain from increasing taxes against the loss from distorting labor supply, Smaller elasticities mean that higher taxes are ok.

Saez (2002) - '“Optimal Income Transfer Programs: Intensive versus Extensive Labor Supply Responses”

Empirically tests the Mirrlees model and concludes that the elasticity of labor supply (with respect to taxes) is a sufficient statistic for assessing welfare programs. When the elasticity is close to 0, you can phase out welfare programs as the gain from giving to the poor is outweighed by the loss from taxing the employed.

Challenges with targeting in developing countries

1. Elasticities of labor supply are small

2. Income is unobservable

3. Inclusion and exclusion errors

Akerlof (1978) - “The Economics of ‘Tagging’ as Applied to the Optimal Income Tax, Welfare Programs, and Manpower Planning”

Target transfers based on tags (individual characteristics)

Forms the basis of proxy-means-tests

BHO Model - Individual problem

An individual’s problem is to choose the self-reported income that maximizes their utility. Their utility is given by their true income, a lump sum, the amount transferred (based on the difference between the poverty line and predicted income (based on the government’s weights between self-reported and audit-based income) minus the cost of mis-reporting (the difference between audited income and self-reported income).

The solution is that self-reported income is real income minus the government’s weightage on self-reported incomes * transfer rate / mis-reporting parameter

BHO Model - Government’s problem

The government maximizes the utility across all individuals under the poverty line (based on weights and density of incomes) subject to a budget constraint (total budget minus the transfers given minus the budget drain from misreporting)

BHO Model - Homogenous misreporting

If all individuals have the same cost of misreporting incomes, the government can predict how much they distort income, and can therefore target properly. They set T = 0 (no universal lump-sum) and alpha = 1 (rely fully on self-reports instead of audits)

The government can back-out true-income based on the weightage on self-reported income, transfer rate, and cost-of-misreporting

A known,, biased estimator is as good as an unbiased one. The audit estimate adds new noise. The bias introduced by self-reports is predictable and uniform.

Jensen (2022) - “Employment Structure and the Rise of the Modern Tax System”

Uses historical cross-country panel data to show that the share of employment in non-ag, non-self-employment sectors drives tax capacity. Countries that industrialized saw increases in tax revenues. Targeting is challenging in countries that are informal where governments don’t know incomes

Banerjee et al. (2017) - “Debunking the Stereotype of the Lazy Welfare Recipient: Evidnece from Cash Transfer Programs”

No evidence that cash transfers reduce work. Analyzed conditional cash transfers (not linked to income so they could isolate the income effect). The income effect (richer means less work) and substitution effect (transfers tax earnings so work less) are both 0

Dispute the Mirrlees paper; labor supply distortions aren’t as relevant in developing countries

Baird et al. (2018) - “The Effects of Cash Transfers on Adult Labor Market Outcomes”

Confirms that labor supply is unaffected by redistribution (lit review of cash transfer programs)

Compensated wage elasticity

Horizontal inequity

People with the same true income get different transfers depending on the realized audit noise.

There is a tradeoff in BHO. If alpha = 1, full self-reports eliminates noise but allows for misreporting, while alpha = 0, full audits eliminates misreporting budget drain, but exposes everyone to audit noise.

If the cost of misreporting is homogenous, audit noise is a worse problem

BHO Model - Heterogeneous mis-reporting

People might differ in how costly it is for them to misreport income, meaning the government can’t “back-out” true incomes from self-reports. If the government only uses self-reported income, transfers go more towards dishonest people who lied more than honest people who lied a little. Then the government tradeoff is to rely more on self-reports to avoid audit noice (which rewards liars) or rely more on a noisy audit (leading to horizontal inequity)

The optimal result is for governments to balance both self-reported and audit-based income, but also to introduce a universal component that isn’t entirely income based

The weight placed on self-reported income decreases when there is more heterogeneity in misreporting; and it increases when there is a higher variance of audit noise

What impacts dishonesty and the cost of misreporting (a)

a is the individual-cost of misreporting income

• fear of punishment

• access to corrupt officials

• cognitive capacity and knowing how to “game” a PMT

• social norms and stigma

• asset visibility

Geographic targeting

Targeting programs to poorer regions, without differentiating individuals within those regions

Pros: simple, can be chosen in a data-driven way; cost-effective

Cons: less accurate than individual targeting (high inclusion and exclusion errors); can lead to migration responses

Proxy-Means-Tests

Training data with measures of what a government wants to target (ex: consumption) and the characteristics used (demographics, assets). Use a regression to predict consumption/income based on observable, non-income characteristics. Predict who is poor and use that to determine eligibility

Pros: works well; accurate at the individual level; scalable; limits self-reporting

Cons: inclusion/exclusion errors; reporting distortions exist; data updated infrequently; subject to reporting manipulation when the formula is known; heterogeneity in household preferences

Types of targeting

• Geographic

• Proxy-Means-Testing

• Self-Selection (workfare, application ordeals)

• Community-Based

Hanna and Olken (2018) - “Universal Basic Income versus Targeted Transfers: Anti-Poverty Programs in Developing Countries”

Evaluates targeting performance to see how good PMTs are at predicting consumption

PMT outperforms universal transfers

McBride and Nichols (2018) - “Retooling Poverty Targeting Using Out-of-Sample Validation and Machine Learning”

Baez, Kshirsagar and Skouflas (2019)

Areias and Wai-Poi

Use ML methods (LASSO, random forests, gradient boosting) to PMT prediction and find little improvement

The reason ML doesn’t help is not model complexity, but data limitations - the individual variables don’t have enough information about true consumption

Banerjee et al. (2020b) - “The (Lack of) Distortionary Effects of Proxy-Means Tests: Results from a Nationwide Experiment in Indonesia

Camacho and Conover (2011) - “Manipulation of Social Program Eligibility”

Returns to manipulation are low when the PMT formula is secret

Banerjee et al — RCT that varied whether TV asset ownership was on the questionnaire or not

Cmacho and Conover - making SISBEN score PMT formula public led to bunching

Alatas et al. (2016)

Self-targeting reduced inclusion and exclusion errors by enabling only people who are extremely poor to actually apply (richer people the PMT might have found eligible might be less likely to apply)

Self Selection

Introducing large ordeals (workfare) or small ordeals (applications) such that only the needy apply makes the poor self-select and the non-poor opt out

Pros: can be effective for screening and leverages a beneficiaries’ own private information; reduces a government’s data collection burden

Cons: imposes real costs; can still have high exclusion errors for the most marginalized

Community-based-targeting

Allow community members to identify and rank the poor

Pros: captures local information PMTs miss; reduces exclusion errors; pretty effective at identifying people who experienced recent shocks

Cons: Worse than PMT; elite capture is possible; depends on network structure; community fatigue degrades accuracy

Bhattacharya and Dupas (2012) - “Inferring Welfare Maximizing Treatment Assignment under Budget Constraints”

The authors study subsidies for anti-malarial bednets where the relevant treatment effect is use of the net. Accounting for heterogeneity in the probability of use improves the cost-effectiveness of the program

Wagner and Athey (2018) - “Estimation and Inference of Heterogeneous Treatment Effects Using Random Forests”

Causal forests target the treatment effect rather than the conditional mean of Y

Caria et al (2023) - “An Adaptive Targeted FIeld Experiment: Job Search Assistance for Refugees in Jordan”

Update an algorithm and assignment probabilities to find the treatment arm (intensity of job search assistance) that dominates

Finklestein, Hendren, Shepard (2019) - “Subsidizing Health Insurance for Low-Income Adults: Evidence from Massachusetts”

Track which households opt into coverage of health insurance at different price points to estimate the demand for government health insurance