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Efficiency Criteria, Income Taxation, and Heterogeneous Elasticities

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

Overview

Research Question. Can income tax schedules be justified as utilitarian-optimal without adopting extreme normative assumptions about how household welfare should be measured? The paper proposes a welfare criterion strictly stronger than Pareto efficiency—called rationalizability with bounded curvature—and asks whether observed US income taxes satisfy it.

Starting Point. Any Pareto-efficient nonlinear income tax schedule can, in principle, be rationalized as utilitarian-optimal under some cardinalization of household utilities (i.e., some choice of how to measure the cardinal scale of each household’s well-being). However, the paper shows that rationalizing Pareto-efficient taxes in this way often requires cardinalizations under which there is no population upper bound on the curvature of utility with respect to consumption. Equivalently, a utilitarian planner’s marginal willingness to transfer resources to households must fall arbitrarily quickly with the size of those transfers—an extreme form of status quo bias violated by virtually all quantitative optimal-tax exercises.

The Proposed Criterion. The authors restrict attention to cardinalizations with locally bounded curvature: there exists a finite (though potentially arbitrarily large) upper bound on the coefficient of relative risk aversion across the population. This admits two interpretations: (i) ex post, it requires that the social value of transfers not change arbitrarily quickly with transfer size; (ii) ex ante, it corresponds to a decision-maker behind a veil of ignorance with bounded risk aversion.

Main Theoretical Result. Within a standard Mirrlees model of nonlinear income taxation with arbitrary preference heterogeneity and intensive-margin labor supply, the paper proves that a tax schedule can be rationalized with bounded curvature if and only if government revenues are both decreasing and concave (not merely decreasing) with respect to a class of narrowly targeted “two-bracket” reforms—reforms that raise retention by $1 local to some income level $z$ and zero elsewhere. This contrasts with Pareto efficiency, which requires only that revenues be decreasing in these reforms (Bierbrauer, Boyer, and Hansen 2023). The additional requirement of revenue concavity is what distinguishes the bounded-curvature criterion from pure Pareto efficiency.

Sufficient Statistics. The paper derives explicit sufficient-statistics expressions for the first- and second-order derivatives of tax revenue with respect to these targeted reforms. The second derivative depends on higher moments of the elasticity distribution, specifically the income-conditional variance of compensated elasticities of taxable income (ETIs). Revenue convexity—which causes the second-order condition to fail—arises when income-conditional ETI variance is sufficiently high, even holding the mean ETI fixed. The economic mechanism is a “sort-and-extort” dynamic: a small tax reform sorts higher-elasticity households into income brackets where marginal taxes fall and lower-elasticity households into brackets where marginal taxes rise; repeating the reform then exploits this sorting by differentially taxing households by elasticity, as if applying group-specific tax schedules within a uniform income tax.

Empirical Findings. Using the NBER panel of US tax returns from 1979 to 1990, the paper estimates income-conditional mean ETIs of approximately 0.2–0.3 at most income levels. Crucially, it estimates a lower bound on income-conditional ETI variance by comparing elasticities of light versus heavy itemizers (defined by whether a household claims above or below the mean value of deductions in its income bracket). The low-elasticity group has an ETI of approximately zero and the high-elasticity group has an ETI of approximately one, implying a lower bound on ETI variance of roughly 0.2 at most incomes and approximately 0.25 at the top of the distribution. This lower bound is close to—and under plausible assumptions above—the threshold required for the second-order condition to fail. The authors conclude that the US income tax schedule in 1990 was likely Pareto efficient but likely not rationalizable with bounded curvature.

Quantitative Welfare Gains. In a calibrated model with a 50% top marginal tax rate, Pareto-tail shape of 2.5, mean ETI of 0.3, and ETI standard deviation of 0.75 (50% above the estimated lower bound), the planner gains significant welfare from either raising or lowering top marginal taxes. The welfare-maximizing top rate below the baseline is 13.3%, generating social value equivalent to a transfer of $1,966 per top earner. The welfare-maximizing top rate above the baseline is 71.2%, generating social value equivalent to a transfer of $972 per top earner. The revenue-maximizing rate is 80.9% under the baseline calibration, ranging from 74.6% to 86.8% as ETI standard deviation varies by ±25% of the lower bound.

Scope Conditions. The theoretical analysis is restricted to intensive-margin labor supply (abstracting from extensive-margin decisions); the empirical application focuses on top incomes where extensive-margin effects are likely small. The empirical period is 1979–1990, covering major federal and state tax reforms. Results concern local efficiency of the tax schedule, not global optimization.

Q&A

Q1: What exactly is “rationalizability with bounded curvature” and how does it differ from Pareto efficiency? A: Pareto efficiency requires that no small reform makes someone better off without making anyone worse off. Rationalizability (with any cardinalization) is equivalent to Pareto efficiency in this setting. Rationalizability with bounded curvature additionally restricts the cardinalization: there must exist a finite upper bound on the coefficient of relative risk aversion (or equivalently, on the curvature of utility with respect to consumption) across the population. This is a strictly stronger criterion than Pareto efficiency. A schedule can be Pareto efficient but not rationalizable with bounded curvature if the only cardinalizations that rationalize it require unbounded consumption utility curvature.

Q2: Why do “extreme” cardinalizations with unbounded curvature arise when rationalizing Pareto-efficient taxes? A: When a Pareto-efficient schedule is rationalized as utilitarian, the cardinalization must make the set of feasible, recardinalized utilities convex so it can be separated from the set of Pareto-improving allocations. The paper constructs such a cardinalization explicitly: it takes the form of a function whose second derivative approaches negative infinity as utility approaches its baseline value. This implies the planner’s marginal value of transfers to a household falls precipitously as the household is made even slightly better off—an extreme status quo bias. Theorem 2.b establishes that all cardinalizations rationalizing a schedule with convex revenues must share this pathology.

Q3: What is the “sort-and-extort” mechanism and how does it generate revenue convexity? A: When elasticities of taxable income (ETIs) are heterogeneous within an income level and the income density is declining steeply, a reform that lowers marginal taxes around income $z$ brings more households into the local bracket (because there are more households just below $z$ than above). Crucially, it disproportionately attracts households with higher ETIs, since they respond more strongly to the marginal tax cut and relocate from further away, where the density differs more. Repeating the reform therefore faces a higher-elasticity composition at $z$, generating larger positive behavioral effects—making revenues convex in the size of the reform. The second step (“extort”) involves raising taxes on the now-concentrated low-elasticity households at adjacent brackets, achieving as-if group-specific taxation within a single income tax schedule.

Q4: What is the precise relationship between revenue convexity and ETI variance? A: The paper shows (Theorem 4) that the second-order revenue derivative with respect to a narrow two-bracket reform around income $z$ equals a positive function of the income density times the expression $-[1-R’_0(z)]\varepsilon(z) + [1-R’_0(z)]\alpha(z)[\varepsilon^2(z) + \text{var}_h[\varepsilon^h | z^h_0=z]]$. The first term is always negative (pushing toward revenue concavity). The second term, which includes the income-conditional variance of ETIs, can dominate and create revenue convexity when ETI variance is sufficiently large. In the benchmark case with a single household type at each income (no within-income heterogeneity), the variance term vanishes and revenues are always concave whenever decreasing.

Q5: What is the sufficient statistics test for rationalizability at the top of the income distribution? A: At top incomes (assuming no income effects, no super-elasticities, and CES preferences), taxes are Pareto efficient if and only if $\tau_\text{top} < \frac{1}{1+\alpha_\text{top}\varepsilon_\text{top}}$, and they are rationalizable with bounded curvature if and only if additionally $\tau_\text{top} < \frac{2}{1+\alpha_\text{top}(\varepsilon_\text{top} + \sigma^2_\text{top}/\varepsilon_\text{top})}$, where $\tau_\text{top}$ is the top marginal tax rate, $\alpha_\text{top}$ is the Pareto tail shape, $\varepsilon_\text{top}$ is the mean ETI at the top, and $\sigma^2_\text{top}$ is the income-conditional ETI variance at the top.

Q6: How does the paper estimate a lower bound on income-conditional ETI variance? A: The authors divide households at each income level into “heavy” and “light” itemizers based on whether their total deductions exceed the local income-bracket mean. They then estimate group-specific ETIs using local polynomial regressions of log income changes on log marginal retention changes, interacting tax changes with heavy-itemizer indicators. The within-year difference in elasticities between groups provides a lower bound on within-income ETI variance, since the two-group decomposition captures only a fraction of true variance. The interaction coefficient is allowed to vary by year to isolate within-year, within-income variation in elasticities rather than between-year compositional changes.

Q7: What are the estimated magnitudes of mean and variance of ETIs? A: Income-conditional average ETIs are estimated at between 0.2 and 0.3 at most income levels, consistent with but somewhat below prior literature estimates. The low-elasticity group (light itemizers) has an ETI of approximately zero, while the high-elasticity group (heavy itemizers) has an ETI of approximately one. Given roughly equal group sizes, this implies a lower bound on ETI variance of approximately 0.2 at most incomes and approximately 0.25 at the ninety-fifth percentile. Subdividing the high-elasticity group into two, three, and four subgroups yields a lower bound of approximately 0.25 for variance at the top.

Q8: How does the back-of-the-envelope calculation work to assess whether the second-order test fails? A: With $\tau_\text{top} \approx 0.5$, $\alpha_\text{top} \approx 2.5$, and $\varepsilon_\text{top} \approx 0.3$ (from prior literature), the second-order condition fails if and only if ETI variance exceeds approximately 0.27. The authors’ lower bound estimate of ETI variance is already approximately 0.25 (standard deviation approximately 0.5), just below this threshold. The authors note that if the true standard deviation exceeds the lower bound by more than 4%, the second-order condition fails, making it empirically likely that the 1990 US tax schedule was not rationalizable with bounded curvature.

Q9: Why does the paper focus on the top of the income distribution for the empirical test? A: The second-order condition is most likely to fail at high incomes for three reasons simultaneously: (i) the marginal tax rate is highest, (ii) ETI means are somewhat higher there, and (iii) the Pareto parameter $\alpha(z)$ is largest (income density falls steeply), which amplifies the sort-and-extort mechanism. The authors also note that extensive-margin labor supply responses—which are abstracted away in the theory—are likely small at high incomes.

Q10: What does the calibrated quantitative application reveal about optimal top tax policy? A: Calibrated with a 50% initial top marginal tax rate, Pareto tail shape of 2.5, mean ETI of 0.3, and ETI standard deviation of 0.75 (50% above the estimated lower bound), the model finds welfare gains in both directions of reform. The welfare-maximizing rate below the baseline is 13.3%, yielding equivalent welfare gains of $1,966 per top earner. The welfare-maximizing rate above the baseline is 71.2%, yielding equivalent gains of $972 per top earner. The revenue-maximizing rate is 80.9%, ranging from 74.6% to 86.8% when ETI standard deviation varies by ±25% of the lower bound. This sensitivity highlights that the optimal direction and magnitude of reform depend substantially on the uncertain degree of ETI heterogeneity.

Q11: How does the paper relate to the “inverse optimum” literature? A: The inverse optimum approach (Bourguignon and Spadaro 2012; Hendren 2020) infers the first-order welfare trade-offs implicit in an observed tax schedule. This paper goes further by inferring from second-order empirical moments—specifically the income-conditional ETI variance—whether taxes are consistent with minimal requirements on how sensitive the planner’s trade-offs are to household welfare levels. Rather than assuming a welfare function, it tests whether any welfare function with bounded curvature can rationalize the observed schedule.

Q12: Is revenue convexity possible without within-income heterogeneity in preferences? A: Yes, but only under more specific conditions. The paper provides two supplemental examples. In the first, all households have constant-elasticity labor disutility but differ in both productivity and elasticity across income levels; when lower-income households have higher elasticities, a reform reducing marginal taxes at $z$ attracts higher-elasticity households and raises the average elasticity, leading to convex revenues. In the second, all households have the same initial elasticity but individual elasticities change in response to reforms. However, with the standard additively separable CES preferences and no within-income heterogeneity, revenues are always concave when decreasing—consistent with Werning’s (2007) observation that the Pareto planner’s problem is convex in this case.

Q13: What is the role of random tax reforms in the paper’s logic? A: Random tax reforms serve as an expository bridge. The paper shows that if the second-order revenue effect of a two-bracket reform is positive at some income $z$, then a “randomized” reform that applies the reform with equal probability in positive and negative directions generates an expected Pareto improvement—because the convexity of revenues implies expected revenues rise, while for any household with bounded risk aversion the reform’s second-order utility effect is also positive when the reform is sufficiently narrow. This establishes that revenue convexity implies random Pareto inefficiency under bounded risk aversion, and then the paper shows the analogous deterministic result for rationalizability.

Q14: What scope conditions attach to the sufficient conditions for rationalizability (Theorem 3)? A: Theorem 3 requires Assumptions 1 and 3 plus two boundary conditions: the ratio $\delta\text{Rev}(z)/(zg(z))$ must remain bounded away from zero as income approaches 0 or infinity, and at all incomes there must exist households with low enough compensated elasticities. Assumption 1 requires that average and marginal taxes have upper bounds below one, that marginal taxes have a lower bound, and that $zg(z)$ converges to zero at the boundaries. Assumption 3 is a regularity condition on how conditional moments of the elasticity distribution vary with income. These conditions ensure that the narrow, self-financing reforms considered in the necessity proof cannot generate welfare improvements once revenues are both decreasing and concave.

Key Concepts

Rationalizability with Bounded Curvature. The property that a tax schedule is utilitarian-optimal under some cardinalization of household utilities in which there exists a finite (though potentially arbitrarily large) upper bound on the curvature of utility with respect to consumption across the population. Formally, there exists a continuous function $\bar{\rho}$ such that, for all households, the absolute value of $[w_h \circ u_h]_{cc} / [w_h \circ u_h]_c$ is bounded by $\bar{\rho}$ evaluated at the household’s income. This criterion is strictly stronger than Pareto efficiency and strictly weaker than utilitarian optimality under a fixed cardinalization.

Two-Bracket Reform. A targeted tax reform that increases retention (post-tax income) by $1 at incomes local to some level $z$ over a small bracket of width $\ell$, and zero elsewhere (smoothed at the edges). As $\ell \to 0$, this becomes an infinitesimally narrow reform. The first- and second-order revenue effects of these reforms—denoted $\delta\text{Rev}(z)$ and $\delta^2\text{Rev}(z)$—are the paper’s key objects: Pareto efficiency requires $\delta\text{Rev}(z) < 0$ for all $z$, and rationalizability with bounded curvature additionally requires $\delta^2\text{Rev}(z) \leq 0$ for all $z$.

Income-Conditional ETI Variance. The variance of compensated elasticities of taxable income (ETIs) among households with the same income level, $\text{var}_h[\varepsilon^h | z^h_0 = z]$. This is the paper’s primary empirical object of interest and the key determinant of whether revenues are convex or concave in the size of targeted reforms. Unlike the literature’s focus on mean ETIs by income bracket, this within-income variance captures heterogeneity among households sharing the same pre-reform income.

Sort-and-Extort Mechanism. The two-step economic mechanism underlying revenue convexity from ETI heterogeneity. In the first step (“sort”), a marginal tax cut around income $z$ disproportionately attracts higher-ETI households from lower incomes (because they respond more strongly and relocate from further away), shifting the elasticity composition at $z$ upward. In the second step (“extort”), repeating the reform finds higher-elasticity households concentrated where marginal taxes fall and lower-elasticity households where taxes rise, effectively applying differential tax treatment by elasticity within a single income tax schedule.

Local Pareto Parameter $\alpha(z)$. Defined as $-d\log(zg(z))/d\log z$, where $g(z)$ is the income density. This captures the rate at which the income density is falling in income locally at $z$, and governs the strength of the sort-and-extort mechanism. High $\alpha(z)$ at top incomes (reflecting a steeply declining Pareto-type density) amplifies revenue convexity from ETI heterogeneity.

Super-Elasticity. A concept that captures how a household’s compensated ETI would change if its income were different, holding preferences fixed. Formally, it is the derivative of the household’s elasticity with respect to its log income, decomposing into effects from changes in preference curvature and changes in the local curvature of the tax schedule. Super-elasticities are zero in the benchmark case of additively CES preferences and locally CES retention schedules but contribute additional terms to the second-order revenue expression in the general case.

Cardinalizing Function. A strictly increasing function $w_h$ that maps household $h$’s indirect utility $V_h$ to a cardinalized utility level $w_h(V_h)$. The social planner maximizes the expectation of cardinalized utilities. Different choices of ${w_h}_h$ correspond to different stances on interpersonal comparisons, including unbounded curvature (rationalizing any Pareto-efficient schedule) or bounded curvature (the paper’s proposed restriction). Rawlsian social welfare is a limit of utilitarian welfare with increasingly concave cardinalizing functions.

Measuring and Mitigating Racial Disparities in Tax Audits

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

Overview

Research Question. Do Black taxpayers face higher IRS audit rates than non-Black taxpayers, despite race-blind audit selection? And if so, why — and what would mitigation look like?

Data and Methodology. The authors use comprehensive administrative microdata covering approximately 148 million individual income tax returns and 780,627 operational audits for tax year 2014, supplemented with 71,878 research audits from the IRS National Research Program (NRP) pooled over 2010-2014. Because neither the researchers nor the IRS observe taxpayer race, the authors employ Bayesian Improved First Name Surname Geocoding (BIFSG), which imputes the probability that a taxpayer is Black from first name, surname, and Census Block Group. They develop a novel partial identification strategy: two estimators (a probabilistic estimator and a linear estimator) that, under conditions verified using a matched North Carolina voter-registration dataset containing self-reported race, asymptotically bound the true racial audit disparity from below and above respectively. To address the selective labels problem — underreporting is observable only for audited returns — the authors combine operational audit data with NRP random-sample audits to simulate counterfactual audit selection algorithms.

Main Findings.

Magnitude of the disparity. The probabilistic estimator implies a racial audit disparity of 0.81 percentage points; the linear estimator implies 1.34 percentage points. Against a base audit rate of 0.54% for the overall U.S. population in 2014, these bounds imply that Black taxpayers are audited at between 2.9 and 4.7 times the rate of non-Black taxpayers.

Role of the EITC. The disparity is concentrated among EITC claimants. The estimated disparity within the EITC population is 1.96 to 2.90 percentage points, compared to only 0.10 to 0.18 percentage points among non-EITC claimants. In relative terms, Black EITC claimants are audited at 2.9 to 4.4 times the rate of non-Black EITC claimants. A formal decomposition attributes 70-73% of the overall disparity to higher audit rates among Black EITC claimants, 20-21% to racial differences in EITC claiming rates, and 7-8% to differential audit rates among non-EITC filers. Within EITC claimants, 78.5% of the observed audit disparity is attributable to the Dependent Database (DDb) program.

Source of the disparity — algorithmic objective. Using counterfactual audit selection algorithms estimated on NRP data, the authors find that allocating EITC audits to maximize detected total underreporting (from any source) would produce audit rates of 0.74% for Black EITC claimants versus 1.63% for non-Black EITC claimants — reversing the disparity. In contrast, the status quo, which prioritizes detecting overclaimed refundable credits, yields 3.00% for Black claimants versus 1.04% for non-Black claimants. The primary driver is a difference in the types of noncompliance that are more prevalent by race: dependent-claiming errors are more common among Black EITC claimants (dependent error rate of 26.6% vs. 16.3% for non-Black), while the highest underreporting via business income underreporting is disproportionately concentrated among non-Black EITC claimants. An algorithm focused on refundable credit overclaims implicitly targets dependent errors and therefore selects Black taxpayers at higher rates.

Prediction model bias. Even conditional on the refundable-credit objective, the status quo disparity (1.96 p.p.) exceeds the disparity that would arise under an oracle that uses actual rather than predicted refundable credit overclaims (1.08 p.p.), suggesting that prediction errors are unevenly distributed by race. The refundable credit prediction algorithm generates a disparity of 1.75 p.p., approximately 60% larger than the oracle. The authors find suggestive evidence of missingness in birth certificate data (paternal information is disproportionately missing for children claimed on Black taxpayers’ returns) and differential predictive accuracy in the DDb risk score across race.

Operational consequences. Switching the objective from refundable credit overclaims to total underreporting would shift the composition of audited returns from predominantly dependent-eligibility issues (80% of refundable credit oracle-selected returns contain a dependent error) toward business income (86% of total-underreporting oracle-selected returns have business income underreporting). EITC returns with substantial business income (gross receipts above $25,000) cost on average $369.70 to audit versus $23.09 for other EITC returns. Holding the audit rate fixed, the switch would raise average examination costs by nearly an order of magnitude, while also increasing detected underreporting (mean adjustment of $22,578 per return under the total underreporting oracle versus $9,595 under the refundable credit oracle).

Scope Conditions. Results pertain primarily to tax year 2014. The paper finds similar patterns for tax years 2010, 2012, 2016, and 2018. The analysis covers Black versus non-Black taxpayers; disparities for other racial and ethnic groups are not the focus. The selective labels identification strategy relies on the NRP random-audit sample and the bounding conditions verified in the North Carolina matched data.

Q&A

Q1. Why can’t the disparity be attributed simply to Black taxpayers being more likely to claim the EITC, combined with EITC claimants facing higher audit rates generally?

The authors test this directly by estimating racial audit disparities separately within EITC claimants and non-claimants. If differential EITC claiming rates were the full explanation, the within-EITC disparity would be close to zero. Instead, the disparity among EITC claimants (1.96-2.90 p.p.) is larger in absolute terms than the overall disparity (0.81-1.34 p.p.), indicating that Black EITC claimants face substantially higher audit rates than non-Black EITC claimants even holding EITC claimant status fixed. The formal decomposition attributes 70-73% of the overall disparity to differential audit rates within the EITC claimant population, not to differential claiming rates across the population.

Q2. How does the partial identification strategy work, and what are its key identifying assumptions?

The authors derive two estimators of the racial audit disparity that use BIFSG-imputed race probabilities rather than observed race. The probabilistic estimator weights each taxpayer’s contribution by their estimated probability of being Black; it is downward-biased when there is a positive residual covariance between audits and true race after conditioning on imputed race (E[Cov(Y,B|b)] > 0). The linear estimator regresses audit status on imputed race probability; it is upward-biased when there is a positive residual covariance between audits and imputed race after conditioning on true race (E[Cov(Y,b|B)] > 0). When both covariance terms are positive, the probabilistic and linear estimates bound the true disparity from below and above. The authors verify both conditions are positive and statistically significant (p < 0.01) in the matched North Carolina dataset, for the full population and the EITC population specifically.

Q3. Does the racial audit disparity within EITC claimants disappear when comparing taxpayers with similar levels of underreporting?

No. The authors use NRP data to estimate audit rates by race within each underreporting decile among EITC claimants. Within every decile of the underreporting distribution, the estimated audit rate for Black taxpayers exceeds that for non-Black taxpayers. An oracle algorithm that selects returns in descending order of actual underreporting produces an audit rate of 0.74% for Black EITC claimants and 1.63% for non-Black EITC claimants — the opposite of the status quo pattern (3.00% for Black, 1.04% for non-Black). This rules out total-dollar underreporting as the primary driver of the observed disparity.

Q4. Why does focusing audit selection on refundable credit overclaims specifically lead to higher audit rates for Black taxpayers?

Two mechanisms operate simultaneously. First, EITC eligibility is linked to children, so detecting erroneously claimed dependents generates large refundable credit adjustments. The dependent error rate is higher among Black EITC claimants than non-Black EITC claimants (26.6% vs. 16.3% in the probabilistic estimate, or 30.8% vs. 15.4% in the linear estimate). Second, the highest-dollar noncompliance via underreported business income is disproportionately concentrated among non-Black EITC claimants: among EITC claimants in the top 1% of business income underreporting, the probabilistic estimate shows 0.05% are Black compared to 0.21% non-Black. An algorithm aimed at refundable credit overclaims implicitly targets dependent errors and therefore selects Black taxpayers at higher rates; one aimed at total underreporting would prioritize business income underreporting instead and therefore select non-Black taxpayers at higher rates.

Q5. How do the simulated algorithms compare to the actual IRS algorithms?

The authors cannot directly replicate the IRS’s confidential DDb algorithm, but they provide three pieces of evidence that their refundable credit prediction algorithm is a reasonable proxy. First, public governmental documents describe DDb’s stated goal as identifying taxpayers who do not meet refundable credit eligibility requirements. Second, when selecting audits based on predicted refundable credit overclaims using largely the same features available to IRS, the authors generate a disparity (1.75 p.p.) close to the status quo disparity (1.96 p.p.). Third, operational audits of EITC returns are strongly associated with their predicted refundable credit overclaims measure but show a much weaker association with predicted total underreporting.

Q6. What does the status quo disparity exceeding the refundable credit oracle disparity reveal about prediction model design?

The status quo disparity (1.96 p.p.) is approximately 80% larger than the disparity that would arise if the IRS were perfectly informed about actual refundable credit overclaims and selected accordingly (oracle disparity: 1.08 p.p.). The refundable credit prediction algorithm generates a disparity of 1.75 p.p., approximately 60% larger than the oracle. This gap between the oracle and prediction disparity is consistent with prediction errors being distributed unevenly by race. The authors find that birth certificates of children claimed on Black taxpayers’ returns are substantially more likely to be missing paternal identity information, which may reduce the predictive accuracy of the DDb model for this population. They provide suggestive evidence that modifying the predictive features used could reduce the disparity without substantially degrading credit overclaim detection.

Q7. What are the downstream operational consequences of switching the algorithmic objective?

Switching from refundable credit overclaims to total underreporting would shift audited issues from dependent eligibility (80% of refundable credit oracle-selected returns have a dependent error) toward business income (86% of total underreporting oracle-selected returns have business income underreporting). Auditing business income returns is substantially more resource-intensive: $369.70 per return on average for returns with gross receipts above $25,000, versus $23.09 for other EITC returns. Holding the current EITC audit rate fixed, the share of audited returns with substantial business income would rise from 3% to 93%, raising total examination costs by nearly an order of magnitude. However, because total detected underreporting per audited return would also rise substantially (mean of $22,578 vs. $9,595), the increase in detected noncompliance would exceed the increase in audit costs, and the qualitative pattern persists even when accounting for higher per-return costs.

Q8. Is the disparity consistent across years, and is it driven by a particular audit type?

The authors find comparable audit disparities for tax years 2010, 2012, 2016, and 2018, confirming the 2014 results are not year-specific. The disparity is concentrated in correspondence audits: the estimated disparity in correspondence audit rates is 0.804-1.328 p.p. for the full population, while the disparity in field/office audit rates is only 0.010-0.016 p.p. The disparity is present in both pre-refund and post-refund audits, though pre-refund audits show a larger disparity even among correspondence audits alone. Among EITC claimants, the correspondence audit channel is nearly entirely responsible for the group-level disparity.

Q9. What heterogeneity exists within EITC claimants?

The disparity is especially pronounced among unmarried male EITC claimants with dependents: among this subgroup, the audit rate for Black men exceeds the audit rate for non-Black men by more than 4 percentage points, and both are an order of magnitude above the overall U.S. population audit rate. Disparities are smaller among joint filers, unmarried women, and unmarried men without dependents, though the ratio of Black to non-Black audit rates remains substantial across all subgroups. The concentration of the disparity among unmarried men with dependents is consistent with the role of dependent-claiming errors, which are more likely to arise in family structures characterized by nonmarital cohabitation — a pattern more prevalent among Black Americans due to lower marriage rates.

Q10. Can the disparity be attributed to disparate treatment — i.e., race-conscious selection?

The authors rule out disparate treatment for the EITC population. The DDb audit selection process for EITC returns is automated (no manual review), and IRS does not use race or geography as an input into audit selection. The disparity is therefore the product of disparate impact: race-neutral selection criteria interact with racially correlated patterns of tax return characteristics to produce differential audit rates. For higher-income non-EITC taxpayers, where audit selection may involve human classifiers, the authors cannot rule out disparate treatment.

Key Concepts

Audit Disparity (D). Defined in the paper as D = E[Y|B=1] - E[Y|B=0], the difference in audit rates between Black taxpayers (B=1) and non-Black taxpayers (B=0). This is a group-level difference in selection rates, not conditional on any other characteristic, and is the primary estimand throughout.

Probabilistic Disparity Estimator. An estimator that calculates group-specific audit rates by weighting each taxpayer’s contribution by their BIFSG-imputed probability of being Black (or non-Black). It is shown to be downward-biased when E[Cov(Y,B|b)] > 0, i.e., when there is residual positive association between true race and audits after conditioning on imputed race.

Linear Disparity Estimator. An estimator based on regressing audit status (Y) on BIFSG-imputed race probability (b). It is shown to be upward-biased when E[Cov(Y,b|B)] > 0, i.e., when imputed race probability predicts audits even after conditioning on true race. Together, the probabilistic and linear estimators form bounds on the true disparity under conditions verified empirically.

BIFSG (Bayesian Improved First Name Surname Geocoding). A probabilistic race imputation method that uses Bayes rule under a conditional independence assumption (first name, surname, and geography are independent given race) to compute Pr[Black | first name, surname, Census Block Group]. Applied here to all 148 million tax returns; calibrated and validated against matched North Carolina voter registration data with self-reported race.

Selective Labels Problem. The problem that noncompliance (underreporting) is observed only for returns selected for audit, not for the full filing population. In this paper it means the IRS cannot directly observe the underreporting distribution for unaudited returns. The authors address this using NRP random-audit data, which allows estimation of the unaudited underreporting distribution and construction of counterfactual selection algorithms.

Algorithmic Objective. The paper distinguishes between (1) the prediction component of audit selection — which model to use to forecast noncompliance — and (2) the objective component — what type of noncompliance to predict and pursue (overclaimed refundable credits versus total underreporting from any source). The paper finds that the objective, not just prediction error, is an independent driver of the racial audit disparity.

Dependent Database (DDb) Program. The IRS’s primary EITC audit selection program, responsible for approximately 75% of audited EITC returns in 2014. DDb flags returns based on rules, heuristics, and proprietary risk scores, with the stated goal of identifying taxpayers who do not meet refundable credit eligibility requirements. Selection through DDb is fully automated, without human classifier review.

National Research Program (NRP). A stratified random sample audit program through which the IRS conducts near-line-by-line examinations of a small fraction of the filing population each year (approximately 2% of audited returns in 2014). The paper pools 71,878 NRP audits from 2010-2014 to identify the distribution of underreporting in the full EITC filing population and to estimate counterfactual selection algorithms.

Optimal Taxation and Market Power

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

Overview

This paper asks whether and how optimal income taxation should change when firms have market power. The question is motivated by the documented rise in economy-wide markups since 1980, which has compressed the labor share, widened the gap between worker and entrepreneurial income, and generated allocative inefficiency through excessive pricing.

The authors develop a Mirrleesian optimal taxation framework augmented with three features absent from the canonical literature: (i) oligopolistic intermediate goods markets with endogenous, variable markups, (ii) heterogeneous firm productivities, and (iii) two occupational groups—wage-earning workers and profit-earning entrepreneurs—whose abilities are private information. Entrepreneurs strategically set prices under Cournot competition, which means that the tax system affects profits both through a firm’s own behavior and through the responses of its competitors. This strategic interaction is the critical novelty relative to prior work that assumes monopolistic competition.

The main theoretical contribution is the derivation of optimal tax formulas for both labor income and profit income that decompose into four named components: (i) the Mirrleesian incentive component, which reflects the standard trade-off between redistribution and labor supply distortions; (ii) the Pigouvian component, which corrects for the externality from market power by subsidizing labor and entrepreneurial effort to offset the output shortfall from high markups; (iii) the Reallocation Effect (RE), which shifts the profit tax to redirect labor inputs from low-markup firms to high-markup firms where labor is inefficiently scarce, and which emerges only under heterogeneous markups; and (iv) the Indirect Redistribution Effect (IRE), which uses changes in competitors’ product prices—a channel present only under oligopolistic (not monopolistic) competition—to redistribute income between entrepreneurs.

For the labor income tax, the dominant force is the Pigouvian component. As average markups rise, the Pigouvian subsidy to labor supply grows, mechanically reducing optimal labor income tax rates. The profit tax is shaped by all four components in opposing directions; the net quantitative effect is resolved empirically.

The model is calibrated to match distributions of labor income (from the Current Population Survey), profits (from Compustat-based data in De Loecker, Eeckhout, and Unger 2020), and firm-level markups (also from De Loecker, Eeckhout, and Unger 2020, using the cost-minimization approach) for the US in 1980 and 2019. The cost-weighted average markup rose from 1.25 in 1980 to 1.33 in 2019, with the increase concentrated at the top of the markup distribution.

The central quantitative prescription is that the optimal labor income tax rate should decline by 7.7 percentage points between 1980 and 2019 (average optimal rate falls from 22.0 percent to 14.3 percent), while the optimal profit tax rate should rise by 2.2 percentage points on average (from 58.4 percent to 60.5 percent) and by 29.1 percentage points at the top. The decline in the labor income tax is driven primarily by the rise in average markups reducing the Pigouvian component. The increase in the profit tax, especially at the top, is driven primarily by the Mirrleesian component operating through the skill gap, which rises because higher markups reduce profit elasticity. The Pigouvian and reallocation components push in the opposite direction on the profit tax, but the Mirrleesian effect dominates.

The optimal profit tax structure is regressive for large, high-markup firms—reflecting the RE, which requires lower tax rates for high-markup firms to incentivize labor reallocation toward them—but less regressive in 2019 than in 1980, reflecting the distributional tightening from rising markup inequality.

Robustness checks across parameter values for the social welfare curvature k, the span of control ξ, and the elasticity of substitution σ confirm that the directional results hold: labor income tax rates decrease and profit tax rates increase from 1980 to 2019 across all parameter configurations. Extensions to nonlinear sales taxes and conditioning on markups confirm that even when the planner can observe markups directly, the first-best is not achievable because markups are endogenous to entrepreneurs’ unobservable decisions.

Q&A

Q1: What is the fundamental difference between this paper’s model and prior work on optimal taxation with market power?

Prior work using monopolistic competition (e.g., Gürer 2021; Boar and Midrigan 2019) assumes each entrepreneur holds monopoly power in its own market, so no strategic interaction exists between firms. Under monopolistic competition, entrepreneurs price to maximize utility given competitors’ choices, and the envelope theorem implies that tax changes have no first-order effect on prices or utility through the pricing channel—the Indirect Redistribution Effect (IRE) disappears. In this paper, entrepreneurs compete in Cournot oligopolistic markets with a finite number of firms I, so each firm’s pricing depends on competitors’ output. A change in one firm’s output (induced by taxation) shifts competitors’ prices, opening a redistribution channel through product markets that is entirely absent in monopolistic competition. Additionally, the Reallocation Effect (RE) emerges only when firm-level markups are heterogeneous, which requires oligopolistic (not perfectly competitive) markets.

Q2: What are the four components of the optimal tax formula and how does each relate to market power?

The optimal tax wedge for both labor and profit income decomposes into four components. First, the Mirrleesian component reflects the standard trade-off between redistribution and the efficiency cost of taxation; in the presence of market power, it is modified because the skill gap for entrepreneurs depends on markups through the profit elasticity. Second, the Pigouvian component corrects the externality from market power, which causes prices to exceed marginal cost and output to be inefficiently low; it implies a subsidy to both worker and entrepreneurial effort, scaled by the reciprocal of the average markup (for the labor tax) or firm-level markup (for the profit tax). Third, the Reallocation Effect (RE) applies only to the profit tax and reflects that labor should be shifted toward high-markup firms where it is inefficiently underemployed; it reduces the tax rate for firms whose markup exceeds the average. Fourth, the Indirect Redistribution Effect (IRE) captures redistribution through competitor price changes under oligopolistic interaction; it can either raise or lower the profit tax rate depending on the distribution of social welfare weights and the cross-inverse demand elasticity.

Q3: What happens to the labor income tax formula as average markups rise?

The labor income tax formula contains a Pigouvian component equal to the reciprocal of the employment-weighted average markup. As average markups rise, this reciprocal falls, reducing the optimal labor income tax rate. Quantitatively, the optimal average labor income tax rate declines from 22.0 percent in 1980 to 14.3 percent in 2019, a decrease of 7.7 percentage points. In a purely competitive benchmark economy, the top labor income tax rate would be around 60 percent (consistent with Saez 2001); in the calibrated model with market power, it is 34.2 percent in 1980 and 28.7 percent in 2019. The Pigouvian component accounts for essentially the entire difference because the Mirrleesian component, when calibrated to the same labor income distribution, is unchanged.

Q4: How does the Mirrleesian component cause the top profit tax rate to rise with market power?

The Mirrleesian component of the profit tax is driven by the skill gap, defined as the proportional rate of change in the composite entrepreneur ability measure. The skill gap depends on markups through the profit elasticity: as markups rise, profit elasticity falls (since profit elasticity is approximately the reciprocal of markup minus the span-of-control parameter minus the inverse of the labor supply elasticity term), which increases the skill gap. A higher skill gap amplifies the income divergence across entrepreneur types, increasing the Mirrleesian incentive to redistribute at the top. Quantitatively, Figure 5 shows that the rise in the skill gap from 1980 to 2019 tracks almost exactly the change in the inverse of profit elasticity, confirming that markup changes—not changes in the ability distribution—are the primary driver of increased Mirrleesian pressure on top profit taxes.

Q5: How does the Reallocation Effect influence the structure (progressivity) of the profit tax?

The RE term equals the ratio of the average markup to the firm-level markup minus one: RE(θe) = μ/μ(θe) − 1. For firms with markups above the average, RE is negative, reducing their optimal tax rate; for firms below the average, RE is positive, increasing it. This implies that the optimal profit tax should be regressive relative to markup (i.e., high-markup firms face lower marginal tax rates), even though the overall profit tax rises on average. This provides a novel rationale for why the profit tax schedule in practice is less progressive—or even regressive—for large firms. As markups rise across the distribution, the reallocation effect pushes down the top profit tax but does not offset the larger increase from the Mirrleesian component in the quantitative exercise.

Q6: What is the Indirect Redistribution Effect and why does it disappear under monopolistic competition?

The IRE captures the change in entrepreneurial utility that arises because a tax reduction for one entrepreneur increases their output, which reduces the prices of substitute goods produced by competitors, thereby lowering competitors’ incomes. Under oligopolistic competition with I > 1 firms per market, the cross-inverse demand elasticity is nonzero, so competitor prices are sensitive to any one firm’s output decision, and this redistribution channel is open. Under monopolistic competition (I = 1), each entrepreneur is the sole producer in its market; competitors’ prices do not depend on the firm’s output, the cross-inverse demand elasticity is zero, and the IRE vanishes by the envelope theorem. The IRE is also absent in perfectly competitive economies. Empirical evidence for the US suggests the hazard ratio of profits is sufficiently high that the IRE generally pushes toward a lower top profit tax rate, but the Mirrleesian effect dominates in the quantitative results.

Q7: What is the quantitative effect of rising markups on the optimal tax rates, and what drives the net change in the profit tax?

The model calibrated to 1980 and 2019 US data prescribes a decline in the optimal average labor income tax rate of 7.7 percentage points (from 22.0 to 14.3 percent) and an increase in the optimal average profit tax rate of 2.2 percentage points (from 58.4 to 60.5 percent). At the top of the profit distribution, the increase is 29.1 percentage points. The net profit tax increase results from four opposing forces: the Pigouvian component falls (pushing toward lower taxes) and the RE decreases for high-markup firms (also pushing down the top rate), while the IRE and especially the Mirrleesian component rise (pushing up top rates). The Mirrleesian effect is the dominant force, driven by rising markup inequality reducing profit elasticity and widening the skill gap for top entrepreneurs.

Q8: How does the counterfactual analysis isolate the role of markups from productivity changes?

The counterfactual fixes the markup distribution at its 1980 level while holding the 2019 productivity distribution constant, then solves for optimal taxes. The result is that high-profit entrepreneurs would face lower optimal tax rates under 1980 markups than under 2019 markups, while low-profit entrepreneurs would face higher rates. Decomposing the difference, the Pigouvian component and the RE are larger for high incomes under 1980 (lower) markups, making the profit tax more regressive, while the IRE and the Mirrleesian component are smaller under 1980 markups, producing a lower top rate. The increase in the Mirrleesian component due to the markup increase from 1980 to 2019 is identified as the primary reason top profit taxes rise. This isolates the markup channel from the productivity channel in accounting for changes in optimal taxes.

Q9: What does the robustness analysis reveal about parameter sensitivity?

The main qualitative result—labor income taxes decline and profit taxes rise from 1980 to 2019—holds across a broad parameter space. The optimal profit tax rate is largely insensitive to the social welfare curvature parameter k: across k ∈ {0.77, 1, 3}, the average optimal profit tax rate is approximately 58 percent in 1980 and 61 percent in 2019. The optimal average labor income tax rate is more sensitive to k: for k = 0.7, 1, and 3, the 1980 rates are 20.3, 26.7, and 44.6 percent, and the 2019 rates are 12.5, 19.4, and 39.1 percent, respectively. Changes in the span-of-control parameter ξ and the substitution elasticity σ do not affect the labor income tax wedge schedule directly but do influence it indirectly through the markup distribution. The directional results are confirmed for all tested parameter configurations.

Q10: What is the role of the “additivity property” from prior externality literature, and why does it fail here?

The additivity property from the Pigouvian externality literature (see Kopczuk 2003; Sandmo 1975) states that the Pigouvian correction is separable from other components of the optimal tax formula, implying that rising markups would simply decrease the optimal tax rate (since 1/μ falls). This property holds under simplifying assumptions that abstract from the general equilibrium and incentive effects of market power. In the present model, the additivity property does not hold because markups enter all four components of the optimal tax formula—not just the Pigouvian term—through the skill gap (Mirrleesian component), the RE, and the IRE. As a result, rising markups can increase the optimal profit tax rate even though the Pigouvian component falls, because the skill gap and Mirrleesian force dominate.

Q11: Can the government attain the first-best by conditioning taxes on markups?

No. The paper demonstrates that even if the planner can observe and condition taxes on firm-level markups, the first-best is not achievable. The reason is that markups are endogenous to the entrepreneurs’ unobservable decisions: an entrepreneur’s markup depends on their privately known type and chosen output. When the planner designs a mechanism that conditions on markup, the incentive constraint facing entrepreneurs remains the same as in the benchmark model, because the promise-keeping constraints are independent of the entrepreneur’s true type when markups are observable. The optimal allocation with markup-conditioned taxes is shown to be equivalent to the second-best with nonlinear sales taxes, which still falls short of the first-best.

Q12: What are the policy implications for the design of the profit tax schedule?

The model yields three concrete prescriptions for the joint design of labor and profit income taxes in the context of rising market power. First, labor income taxes should be reduced and top profit taxes should be increased as market power rises. Second, for large, high-productivity firms the profit tax should be designed to be appropriately regressive to enhance allocative efficiency through the Reallocation Effect—this provides a new normative justification for why profit tax schedules observed in practice are often less progressive than labor income taxes. Third, while profit taxes should be regressive for large firms, the degree of regressivity should decrease as market power rises, reflecting the trade-off between efficiency and equality: higher markups increase the Mirrleesian pressure for redistribution at the top, reducing the optimal regressivity.

Key Concepts

Mirrleesian component (of the optimal tax formula): The standard incentive component of the optimal tax, capturing the trade-off between direct redistribution and the efficiency cost of taxation. In the presence of market power, this component is modified because the skill gap for entrepreneurs depends on markups through the profit elasticity: higher markups reduce profit elasticity, widen the skill gap, and amplify the Mirrleesian force toward higher top profit taxes.

Pigouvian component: The correction in the optimal tax formula for the externality from market power. Because oligopolistic pricing causes output to be inefficiently low, the optimal tax subsidizes both worker and entrepreneurial labor supply. In the labor income tax formula, the Pigouvian component is the reciprocal of the employment-weighted average markup; in the profit tax formula, it is the reciprocal of the firm-level markup. As average markups rise, the Pigouvian component reduces the optimal labor income tax rate.

Reallocation Effect (RE): A component of the optimal profit tax formula that captures the efficiency gain from reallocating labor inputs from low-markup firms (where labor’s marginal product is high relative to value) to high-markup firms (where labor demand is inefficiently low). It equals the ratio of the average markup to the firm-level markup minus one. It implies a lower optimal marginal tax rate for firms with markups above the average, producing a regressive structure in the profit tax for large firms. This effect is absent under monopolistic competition (uniform markups) and in competitive markets.

Indirect Redistribution Effect (IRE): A component of the optimal profit tax formula specific to oligopolistic competition, capturing redistribution through competitor prices. Lowering the marginal tax rate of a high-productivity entrepreneur raises their output, which reduces the prices of substitutable goods produced by their competitors, thereby lowering competitors’ incomes and redistributing toward workers who benefit from lower prices. This effect is present only when the cross-inverse demand elasticity is nonzero—i.e., only under oligopolistic (Cournot) competition with multiple firms per market—and vanishes under monopolistic competition and in the limit as the number of firms grows to infinity.

Skill gap (for entrepreneurs): The proportional rate of change in the composite entrepreneur ability measure with respect to entrepreneur type, analogous to the Mirrleesian skill gap for workers. Under market power, the entrepreneur skill gap depends on the markup through the profit elasticity: as firm-level markups rise, profit elasticity falls, the skill gap increases, and the income dispersion across entrepreneurs widens, which amplifies the Mirrleesian incentive to redistribute at the top and raises the optimal top profit tax rate.

Symmetric Cournot Competitive Tax Equilibrium (SCCTE): The equilibrium concept used in the paper. It is a combination of a tax system, symmetric allocation, and symmetric price system such that all agents (final goods producer, entrepreneurs of each type, workers) are optimizing, strategic interaction in the intermediate goods market is a Cournot Nash equilibrium within each granular market, and all commodity and labor markets clear. Strategic interaction is restricted to within each granular market (firms in the same market compete), so decisions across markets are taken as given.

Composite ability: A combined measure of entrepreneur productivity that determines equilibrium allocations and optimal taxation in the nested-CES economy. It aggregates the entrepreneur’s raw ability (affecting output capacity) and the demand parameter (affecting the market-level markup). The markup-relevant component and the quantity-relevant component are not perfect substitutes in the composite, since equilibrium prices depend on their specific composition while equilibrium quantities depend only on their combined value.

The Impact of EITC on Education, Labour Market Trajectories, and Inequalities

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

This paper studies the effect of the Earned Income Tax Credit (EITC) on educational attainment and labor market trajectories through two complementary approaches. Using policy discontinuities at U.S. state borders—exploiting variation in state EITC generosity set as a percentage of the federal EITC—the paper finds that an increase in the state EITC leads to a statistically significant increase in the high school dropout rate. The mechanism is that a tax credit targeted at low-wage (low-skilled) workers increases the value of low-skilled employment and reduces the relative return to schooling, generating a powerful disincentive to pursue long-term studies. A structural life-cycle matching model with directed search and endogenous educational choices, search intensities, hirings, hours worked, and separations is developed to quantify the long-run general equilibrium effects: in the long run, EITC reduces the proportion of high-skilled workers, with ambiguous effects on income inequality that depend on the competing channels through which EITC affects both the supply and demand sides of the labor market.

Summary based on a working paper version, AI-assisted and human-reviewed. See the linked published article for the authoritative version.

In depth

Q1. What is the empirical strategy for identifying the effect of EITC on education?

The paper identifies the causal effect of state EITC on education by exploiting policy discontinuities at U.S. state borders, comparing contiguous PUMA pairs on opposite sides of state borders that differ in state EITC generosity. State EITC rates are set as a percentage of the federal EITC and have varied considerably since the mid-1980s. Borrowing from the minimum wage literature (Dube et al., 2010; Hagedorn et al., 2015), the border-discontinuity design controls for local labor market conditions that vary continuously across state borders while isolating the effect of the discrete EITC policy difference.

Q2. What is the labor market mechanism linking EITC to education?

EITC raises the value of low-skilled employment by directly increasing the earnings of low-wage workers, which in turn reduces the relative return to investing in education, generating a powerful disincentive to pursue long-term studies. When directed search is present—as supported by recent empirical studies—educational decisions affect both job-finding probabilities and labor incomes over the life cycle. EITC’s subsidization of low-skilled work contracts the education premium in this framework, making the forgone earnings cost of staying in school larger relative to the low-skilled employment option supported by the EITC.

Q3. What does the life-cycle matching model contribute?

The structural life-cycle matching model with directed search and endogenous educational choices, search intensities, hirings, hours worked, and separations quantifies the general equilibrium and long-run effects of EITC that purely reduced-form studies cannot capture—including the feedback of an expanded low-skilled labor force on equilibrium wages and job creation. The model endogenizes labor demand, capturing both household responses (education, hours, search intensity) and firms’ responses (job creation and destruction). It is solved and estimated to replicate the life-cycle profile of labor market variables.

Q4. What are the long-run implications for inequality?

In the long run, EITC reduces the proportion of high-skilled workers in the economy, with ambiguous effects on income inequality because of offsetting channels: EITC directly increases earnings of low-skilled workers, but by expanding the supply of low-skilled labor it may also depress low-skilled wages; additional channels through unemployed workers’ search effort and employed workers’ hours further complicate the net effect. The model is used to determine the optimal design of the EITC that balances the income-support objective against these unintended long-run effects.

Key concepts

state EITC : a supplement to the federal Earned Income Tax Credit set as a fixed percentage of the federal credit; varies across states; used in this paper as the identification source for the effect of EITC generosity on education via border discontinuities. directed search : a labor market framework in which workers and firms direct their search to specific submarkets with posted wages; in this setting, educational choice affects both job-finding probabilities and wages over the life cycle, amplifying the disincentive effects of EITC on education relative to random-search models. education-EITC disincentive : the mechanism by which EITC targeted at low-wage workers raises the relative value of low-skilled employment and reduces the return to schooling, generating an increase in high school dropout rates as a side effect of the anti-poverty policy.