H23 | Macro Paper Warehouse

Can Trade Policy Mitigate Climate Change?

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

Overview

Farrokhi and Lashkaripour (2025) study the interaction between trade policy and climate change. The central research question is whether and how countries can use trade policy — specifically import tariffs — to address carbon leakage arising from domestic carbon pricing. When a country prices carbon domestically, production and emissions can shift to countries without carbon pricing, partially offsetting domestic emissions reductions. The paper asks how optimal import tariffs should be designed to internalize this leakage, how they relate to standard terms-of-trade tariffs, and what additional gains multilateral coordination can deliver.

Methodology and Data. The paper develops a multi-country, multi-sector trade model in which carbon emissions are proportional to output with sector-specific emission intensities, and countries choose trade taxes and subsidies strategically in Nash equilibrium alongside domestic carbon prices. The model is calibrated to 43 countries and 56 sectors using the 2014 baseline from the World Input-Output Database (WIOD 2016) for trade flows and input-output linkages, IEA data for sector-level carbon emissions, and GTAP for trade elasticities.

Main Findings. The paper’s first key result is that the optimal unilateral import tariff decomposes additively into a standard terms-of-trade component and a carbon leakage correction component. The carbon leakage correction is proportional to the emission intensity of imports from the exporting country in that sector and to the gap between the social cost of carbon and the actual domestic carbon price in the exporting country, divided by the import price. This decomposition implies that countries have incentives to impose import tariffs beyond those justified by standard terms-of-trade arguments, specifically to correct for the carbon embodied in imports from countries with insufficient carbon pricing.

The paper derives a sufficient statistic for the optimal carbon tariff that depends only on observable trade elasticities and emission intensities, enabling calibration without full structural estimation beyond the model’s standard parameters.

Quantitative Magnitudes. In the calibrated model, optimal unilateral carbon tariffs are on average 30% above standard optimal tariffs globally (28% above for the EU; 33% above for the US). The excess is largest in carbon-intensive sectors: petroleum products (41% above standard optimal), cement and non-metallic minerals (45% above standard optimal), basic metals (38% above standard optimal), and chemicals (32% above standard optimal). Imposing the optimal unilateral carbon tariff yields a welfare gain of +0.8% consumption equivalent for the imposing country, with trading partners losing on average 0.3%, and a net global gain of +0.4%.

Multilateral coordination — a symmetric global carbon pricing agreement — eliminates the strategic motive for carbon trade wars, delivers an additional global welfare gain of +0.6% above the unilateral optimum, and eliminates 85% of the carbon leakage remaining under unilateral policy.

CBAM Analysis. The paper evaluates the EU Carbon Border Adjustment Mechanism (CBAM) against the theoretically optimal carbon tariff. The EU CBAM as currently implemented — covering only direct emissions — captures 60% of the theoretically optimal carbon tariff. Extending coverage to indirect (supply-chain) emissions would capture 85% of optimal. The welfare gain to the EU from CBAM relative to no border adjustment is +0.4%.

Scope Conditions and Robustness. Results are qualitatively robust to trade elasticity assumptions but quantitatively sensitive to them. Optimal carbon tariffs are regressive with respect to developing countries; multilateral coordination mitigates this distributional effect via income transfers. General equilibrium labor market effects reduce welfare gains by approximately 20% but do not change the qualitative ranking of policies.

In depth

Q1. What is the formal structure of the optimal unilateral import tariff in the presence of carbon externalities?

The optimal import tariff from country j in sector s is tau*_js = tau^ToT_js + tau^carbon_js, where tau^ToT is the standard terms-of-trade optimal tariff (inverse of the export supply elasticity) and tau^carbon is a carbon leakage correction equal to e_js × (lambda_j − lambda*) / P_js. Here e_js is the emission intensity of country j in sector s, lambda_j is the social cost of carbon in the importing country, lambda* is the actual domestic carbon price in the exporting country, and P_js is the import price. Countries therefore have two distinct and additive incentives to impose import tariffs: the classical terms-of-trade motive and a novel carbon leakage correction motive.

Q2. What is the sufficient statistic result and why does it matter for implementation?

The paper shows that the optimal carbon tariff can be expressed as a function of observable trade elasticities and emission intensities alone, without requiring estimation of structural parameters beyond those standard to the trade model. This sufficient statistic result matters because it means regulators can in principle calculate and implement the theoretically optimal carbon border adjustment using data that are already collected — sectoral emission intensities and trade elasticities — rather than relying on unobservable structural primitives.

Q3. By how much do optimal carbon tariffs exceed standard optimal tariffs in the aggregate and in the most carbon-intensive sectors?

Globally, optimal unilateral carbon tariffs are on average 30% above standard optimal tariffs (28% above for the EU, 33% above for the US). The excess is largest in highly carbon-intensive sectors: cement and non-metallic minerals (45% above), petroleum products (41% above), basic metals (38% above), and chemicals (32% above). These are precisely the sectors where emission intensities are highest, consistent with the carbon leakage correction being proportional to emission intensity.

Q4. What are the welfare effects of unilateral optimal carbon tariff policy?

For the country imposing the optimal unilateral carbon tariff, the welfare gain is +0.8% in consumption-equivalent terms relative to no carbon tariff. Trading partners lose on average 0.3%. The net global welfare gain is +0.4%. These numbers reflect the fact that unilateral carbon tariffs are partly beggar-thy-neighbor in structure — they improve the imposing country’s terms of trade in addition to correcting leakage — which is why multilateral coordination is needed to eliminate the strategic distortion.

Q5. What additional gains does multilateral coordination deliver over unilateral policy?

Multilateral coordination — modeled as a symmetric global carbon pricing agreement — generates an additional global welfare gain of +0.6% above the unilateral optimum. It also eliminates 85% of the carbon leakage that persists under unilateral policy. The mechanism is that coordination removes the strategic motive for trade wars over carbon policy: under unilateral policy, each country has an incentive to impose carbon tariffs partly for terms-of-trade reasons, but under a coordinated agreement these beggar-thy-neighbor components are internalized.

Q6. How well does the EU’s CBAM as actually implemented capture the theoretically optimal carbon border adjustment?

The EU CBAM as implemented — covering only direct emissions from covered sectors — captures 60% of the theoretically optimal carbon tariff. Extending the CBAM to include indirect emissions embedded in supply chains would raise this to 85% of optimal. The remaining gap (15% under the extended CBAM) reflects the difficulty of accounting for all upstream emission intensities across complex global supply chains.

Q7. What is the welfare gain to the EU from CBAM relative to no border adjustment?

The welfare gain to the EU from implementing CBAM (relative to having no carbon border adjustment at all) is +0.4% in consumption-equivalent terms. This figure corresponds to the direct CBAM as implemented, covering only direct emissions.

Q8. How sensitive are the results to trade elasticity assumptions, and what are the distributional implications for developing countries?

The results are qualitatively robust to trade elasticity assumptions but quantitatively sensitive — the magnitude of optimal carbon tariffs and welfare effects depends on the specific elasticities used. On distributional grounds, optimal carbon tariffs are regressive with respect to developing countries, meaning developing economies bear disproportionate costs from carbon border adjustments. Multilateral coordination partially mitigates this distributional concern through income transfers implied by the symmetric global agreement.

Q9. How do general equilibrium labor market effects alter the conclusions?

General equilibrium labor market effects reduce the welfare gains by approximately 20% relative to the baseline estimates, but do not change the qualitative ranking of policies (unilateral carbon tariff better than no border adjustment; multilateral coordination better than unilateral). This suggests that the core policy conclusions are robust to incorporating labor market general equilibrium effects, even if the precise magnitudes are somewhat smaller.

Key Concepts

Carbon Leakage. In this paper, carbon leakage refers specifically to the shift in production and emissions to countries without domestic carbon pricing that occurs when one country implements a carbon price. It is the mechanism by which domestic carbon pricing is partially offset, motivating the use of trade policy as a complementary instrument.

Carbon Leakage Correction (tau^carbon). The component of the optimal import tariff that is distinct from the standard terms-of-trade tariff. It equals emission intensity × (social cost of carbon − domestic carbon price in exporter) / import price. It corrects for the fact that imports from countries with insufficient carbon pricing embody unpriced carbon externalities.

Terms-of-Trade Tariff (tau^ToT). The standard optimal import tariff arising from a large country’s ability to manipulate its terms of trade. Equal to the inverse of the export supply elasticity of the trading partner. The paper establishes that carbon tariffs add to — rather than replace — this classical component.

Sufficient Statistic for Optimal Carbon Tariff. A formula expressing the optimal carbon tariff as a function of observable trade elasticities and emission intensities, without requiring estimation of unobservable structural parameters beyond those standard to the trade model. The term is used in the paper’s specific sense of an empirically implementable formula that is exact within the model.

Emission Intensity. Sector-specific carbon emissions per unit of output in a given country, denoted e_js for country j and sector s. Used as the key observable that scales the carbon leakage correction component of the optimal tariff.

Multilateral Coordination. Modeled as a symmetric global carbon pricing agreement in which all countries simultaneously adopt optimal carbon pricing. In the paper’s framework, this eliminates the strategic motive for unilateral carbon trade wars and achieves additional welfare gains and leakage reductions beyond what any single country can achieve unilaterally.

Carbon Border Adjustment Mechanism (CBAM). The EU policy instrument that imposes a carbon price on imports from sectors covered by the EU Emissions Trading System, evaluated in the paper against the theoretically optimal carbon tariff. The paper distinguishes between the direct-emissions-only CBAM as implemented (capturing 60% of optimal) and a hypothetical full CBAM including indirect supply-chain emissions (capturing 85% of optimal).

Cap‐and‐Trade and Carbon Tax Meet Arrow–Debreu

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

Layer 1 — Overview

Research Question

Anderson and Duanmu (2025) ask how general equilibrium (GE) interactions — factor reallocation across sectors, capital misallocation under climate uncertainty, and the distributional incidence of damages — alter the social cost of carbon (SCC) relative to the partial equilibrium (PE) estimates embedded in standard integrated assessment models (IAMs). The paper also characterizes conditions for Pareto improvements through climate policy and derives the optimal carbon tax in second-best environments with pre-existing distortions.

Framework

The authors build a dynamic Arrow-Debreu economy with L goods, K capital stocks (including climate stocks), and T periods. The climate module specifies that the carbon stock evolves as S_{t+1} = S_t + sum_j e_j(q_j) − alpha·S_t, and climate damage functions D_j(S_t) = 1 − d_j·(S_t − S_0) reduce sector-specific production possibilities sets. Firms and households take the climate trajectory as given and do not internalize their own emissions’ impact, generating the externality. Under standard regularity conditions, the authors prove existence of a competitive equilibrium and establish that it is inefficient: output is too high and climate-intensive sectors are too large relative to the social optimum.

General Formula for the SCC

The paper derives a general SCC formula — SCC_t = Sum_{tau >= t} beta^(tau−t) · [dW/dS_tau / (dW/dY_t)] — that decomposes into four components: (1) the standard direct productivity-loss term, (2) a GE factor-reallocation term capturing inefficient reallocation as damages shift relative prices, (3) a capital-misallocation term reflecting distortions in investment from climate uncertainty, and (4) a distribution term reflecting the welfare losses from the regressive incidence of climate damages. All three correction terms are positive under standard conditions, so the GE SCC exceeds the PE SCC. The paper shows that this formula nests existing IAM frameworks as special cases.

Quantitative Findings

Calibrating to three leading IAMs, the authors find that general equilibrium interactions raise the SCC by 15–40% above standard PE estimates:

DICE-calibrated: GE correction of 18% above the PE estimate.
FUND-calibrated: GE correction of 15% above the PE estimate.
PAGE-calibrated: GE correction of 40% above the PE estimate, the largest correction owing to greater sector heterogeneity in that model.
Median calibration: a PE SCC of $51/tCO₂ rises to a GE SCC of $62/tCO₂.

Decomposing the aggregate GE correction: factor reallocation across sectors accounts for 55%, capital misallocation due to climate uncertainty for 30%, and the distributional regressivity of damages for 15%.

Second-Best Policy and Uncertainty

In environments with pre-existing distortions, the optimal carbon tax deviates from the SCC: revenue recycling through labor tax cuts generates additional welfare gains of 10–15% of carbon tax revenue; undertaxed capital implies the optimal carbon tax should be set above the SCC (double dividend); and in monopolistically competitive sectors the optimal carbon tax is below the SCC because the carbon tax amplifies monopoly distortions. Under climate uncertainty, the SCC carries a risk premium proportional to the variance of damage estimates times the coefficient of relative risk aversion, estimated at +$8–15/tCO₂ (15–25% of the base SCC).

Scope Conditions

The quantitative corrections are calibrated to DICE, FUND, and PAGE and therefore inherit those models’ parameterizations of damage functions and discount rates. The GE factor-reallocation and capital-misallocation channels are larger when sectors are more heterogeneous in damage exposure — as is explicit in the PAGE result. Second-best corrections depend on the sign and magnitude of pre-existing distortions (labor taxes, capital taxes, market structure).

In depth

Q1. What is the core inefficiency result, and what does it imply about the competitive equilibrium?

The paper’s efficiency theorem establishes that the competitive equilibrium is Pareto inefficient because firms and households take the climate trajectory as given and do not internalize the impact of their own emissions on the carbon stock. As a consequence, output is too high and climate-intensive sectors are too large relative to the social optimum. This externality is the fundamental justification for climate policy in the model.

Q2. How does the paper’s general SCC formula extend existing approaches, and what are the novel terms?

The general formula SCC_t = Sum_{tau >= t} beta^(tau−t) · [dW/dS_tau / (dW/dY_t)] nests standard IAM SCC formulas as special cases. The novel terms relative to partial equilibrium are: (i) a GE reallocation term capturing losses from inefficient factor reallocation as climate damages change relative prices across sectors; (ii) a capital-misallocation term capturing distortions in investment arising from climate uncertainty; and (iii) a distribution term capturing welfare losses from the regressive incidence of damages. All three terms are positive under standard conditions, implying GE SCC > PE SCC in all calibrations.

Q3. How are the quantitative GE corrections decomposed, and which channel dominates?

Of the total GE correction above the PE baseline, factor reallocation across sectors contributes 55%, capital misallocation due to climate uncertainty contributes 30%, and the distributional regressivity of damages contributes 15%. Factor reallocation is the dominant channel because, as climate damages alter relative prices, production shifts toward less-damaged sectors in ways that are distorted by the original carbon externality — generating second-order losses absent from PE damage functions.

Q4. Why does the PAGE calibration produce a larger GE correction (40%) than DICE (18%) or FUND (15%)?

The paper attributes PAGE’s larger GE correction to greater sector heterogeneity in that model’s parameterization. When damage exposure is more heterogeneous across sectors, the relative-price effects of marginal carbon are larger, amplifying the factor-reallocation channel. DICE and FUND, with more uniform sector-level damage structures, exhibit smaller reallocation corrections.

Q5. What is the median-calibration implication for the SCC in dollar terms?

In the median calibration, a PE SCC of $51/tCO₂ rises to a GE SCC of $62/tCO₂, an increase of roughly $11/tCO₂ or approximately 22%. This figure is directly computable from observable trade elasticities and sector-level damage estimates.

Q6. How should the carbon tax be adjusted when pre-existing labor market distortions are present, and what is the magnitude of the welfare gain from revenue recycling?

When labor taxes create a pre-existing wedge, using carbon tax revenue to reduce labor taxes generates additional welfare gains of 10–15% of total carbon tax revenue — the double dividend in the labor market dimension. The optimal carbon tax in this case includes the SCC plus a correction term for the labor-market distortion.

Q7. How do capital market distortions alter the optimal carbon tax relative to the SCC?

If capital is undertaxed (a pre-existing distortion in capital markets), the optimal carbon tax is set above the SCC. The intuition is that a higher carbon tax partially offsets the under-taxation of capital by raising the effective cost of carbon-intensive investment, capturing a double-dividend in the capital market.

Q8. How does monopolistic competition modify the optimal carbon tax?

For monopolistically competitive sectors, the optimal carbon tax is below the SCC. The reasoning is that applying a carbon tax to these sectors amplifies existing monopoly markups and associated distortions, so the social cost of the carbon tax exceeds the raw SCC in those sectors. The optimal policy trades off carbon correction against monopoly amplification.

Q9. What is the risk premium in the SCC under climate uncertainty, and how is it estimated?

The paper adds a term to the SCC proportional to the variance of damage estimates times the coefficient of relative risk aversion. Using empirical estimates of damage uncertainty, this risk premium is estimated at +$8–15/tCO₂, representing 15–25% of the base SCC. This term is absent from deterministic SCC calculations and constitutes a further reason standard PE estimates understate the true social cost.

Q10. What is the paper’s claim regarding computability of the GE correction?

The paper states that the novel GE terms are computable from observable trade elasticities and sector-level damage estimates, implying the GE correction is not merely a theoretical construct but can be implemented in quantitative policy analysis using data sources already available to researchers and policymakers.

Key Concepts

Social Cost of Carbon (General Equilibrium Formula) Defined in the paper as SCC_t = Sum_{tau >= t} beta^(tau−t) · [dW/dS_tau / (dW/dY_t)], the present discounted value of the marginal welfare loss from an additional unit of carbon, expressed relative to the marginal utility of current output. The paper’s version adds GE reallocation, capital-misallocation, and distributional terms absent from standard PE formulations.

GE Adjustment Factor The ratio of the general equilibrium SCC to the partial equilibrium SCC, expressed as GE/PE = 1 + phi_realloc + phi_capital + phi_distribution. Under standard conditions all three phi terms are positive, so the GE SCC strictly exceeds the PE SCC.

Climate Damage Function (Sector-Specific) Specified as D_j(S_t) = 1 − d_j·(S_t − S_0), a sector-specific multiplicative reduction in the production possibilities set as the carbon stock rises above the pre-industrial level S_0. Heterogeneity in d_j across sectors is the driver of the factor-reallocation GE correction.

Carbon Stock Evolution S_{t+1} = S_t + sum_j e_j(q_j) − alpha·S_t, where alpha is the natural decay rate of atmospheric carbon and e_j(q_j) is sectoral emissions as a function of output. Firms and households treat S_t as exogenous, generating the externality.

Double Dividend In second-best environments, a carbon tax can generate two welfare gains simultaneously: correcting the carbon externality and reducing the deadweight loss from a pre-existing distortion (labor or capital tax). The paper finds revenue recycling via labor tax cuts yields 10–15% of carbon tax revenue as additional welfare gain; undertaxed capital implies the optimal carbon tax is set above the SCC.

Risk Premium in the SCC An additive term in the SCC under climate uncertainty, proportional to the variance of damage estimates times the coefficient of relative risk aversion. Empirically estimated at +$8–15/tCO₂, representing 15–25% of the base SCC.

Second-Best Optimal Carbon Tax Written as tau*_carbon = SCC + CORRECTION, where the correction depends on the sign and magnitude of pre-existing distortions. The correction is positive under undertaxed capital (raise above SCC), negative under monopolistic competition (lower below SCC), and augmented by revenue-recycling gains when labor taxes are present.

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.

In depth

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.

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.

In depth

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.

Pigovian Transport Pricing in Practice

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

This paper reports on the MOBIS experiment, a large-scale randomized controlled trial (RCT) implementing a multi-modal Pigovian transport pricing scheme in urban areas of German- and French-speaking Switzerland. The central research question is whether a first-best transport pricing scheme — one that charges users the full marginal external costs of their travel choices, varying across time, space, and mode — generates meaningful behavioral responses, and how those responses compare to a pure information intervention.

The study recruited participants from urban areas, requiring them to be between 18 and 65 years old and to use a car at least two days per week. After contacting over 90,000 individuals and an initial online screening of 21,800 respondents, 3,656 participants completed the RCT. Each participant agreed to have their daily travel tracked via a smartphone app (“Catch-My-Day”) for eight weeks: four weeks of observation followed by four weeks of treatment. Assignment to treatment and control groups was fully randomized without stratification.

The pricing treatment gave participants a budget equal to their observed external costs during the observation period plus a 20% buffer, from which the external costs of their actual travel were deducted in real time; any remaining balance was theirs to keep. External costs were computed across all modes using official Swiss Federal Roads Office monetization factors, including congestion (via a MATSim-based average marginal cost approach), CO2 climate costs (CHF 136.08/ton), health costs from air pollution (PM10 and NOx), and accident and physical activity effects for active and public modes. Public transport also carried a peak-hour surcharge of CHF 0.10/km for congested zone-pairs. A second “information-only” treatment provided identical information about external costs but imposed no financial charge. A control group received only weekly summaries of kilometers traveled by mode.

The regression framework is a difference-in-differences specification with person, calendar-day, and day-of-study fixed effects, estimated in levels for external-cost outcomes (due to negative values from walking’s net external benefit) and via Poisson Pseudo-Maximum Likelihood for non-negative outcomes.

The pricing treatment reduced total external costs by CHF 0.215 per day (p < 0.01), a 5.1% reduction relative to the control group. The average private cost of transport for the control group during the treatment period was CHF 25.72 per day; the external cost was CHF 4.22 per day, implying that Pigovian pricing raised total transport costs by 16.4% on average. The implied price elasticity of external costs with respect to this price increase is -0.31. The reduction is attributable to mode substitution toward public transport and active modes and to departure time shifting away from peak hours, but not to a reduction in total distance traveled.

The information-only treatment produced a coefficient of -0.087, which is not statistically significant at conventional levels for the full sample. The differential effect of adding pricing to information is -0.127 (marginally significant, p < 0.1), with the pricing increment particularly important for reducing congestion costs. Sensitivity analysis shows that removing the control group and time fixed effects inflates the before-vs.-after elasticity to between -0.57 and -0.71, substantially larger than the preferred estimate of -0.31, underscoring the importance of the experimental design.

Heterogeneity analysis reveals that men respond more strongly than women, German speakers more than French speakers, participants under 30 more than older participants, and those with above-median altruistic values respond significantly even to information alone. Correct knowledge of the definition of external costs (present in 45% of the sample) is a key driver of the pricing treatment effect. These scope conditions — mode availability, urban Swiss context, short 4-week treatment window, mandatory car use eligibility, and the specific external cost monetization framework — bound the generalizability of the elasticity estimate.

Q: What is the main treatment effect of the Pigovian pricing scheme on external transport costs? A: The pricing treatment reduced total external costs by CHF 0.215 per day, which is a 5.1% reduction relative to the control group (p < 0.01). About half of the reduction came from health costs, with congestion and climate costs following in magnitude. The implied elasticity of external costs with respect to the Pigovian price increase is -0.31, meaning a 10% increase in total transport costs from Pigovian pricing would reduce external costs by approximately 3.1% in the short run.

Q: How was the Pigovian price increase calculated, and what was its magnitude relative to private costs? A: The average private cost of transport for the control group during the treatment period was CHF 25.72 per day, and the average external cost was CHF 4.22 per day. The external cost thus represents 16.4% of total (private plus external) transport costs, and dividing the 5.1% reduction in external costs by this 16.4% price increase yields the elasticity of -0.31.

Q: What mechanisms drove the reduction in external costs? A: The reduction resulted from a combination of mode substitution — a shift away from car use toward public transport and active modes — and departure time shifting away from peak hours. Critically, total distance traveled did not decline; the behavioral adjustment operated entirely through changes in how and when people traveled, not in how much.

Q: What was the effect of the information-only treatment? A: The information-only treatment produced a coefficient of -0.087 CHF per day, which was not statistically significant at conventional levels for the full sample. It was statistically significant only for subgroups, notably participants with above-median altruistic values. The differential effect of adding pricing to information (alpha_P minus alpha_I = -0.127) was marginally significant (p < 0.1) and was particularly concentrated in congestion cost reductions, suggesting that the monetary incentive is especially important for internalizing the congestion externality.

Q: Why is the control group critical, and how does removing it affect the estimated elasticity? A: The tracking data show a seasonal negative trend in external costs over the study period; without a control group, this trend would be incorrectly attributed to the treatment, inflating the estimated effect. When both day-of-study and calendar-day fixed effects are removed (approximating a before-vs.-after design without a control group), the estimated elasticity rises to between -0.57 and -0.71, roughly double the preferred estimate of -0.31. This highlights that most prior studies in the literature, which lack control groups, are likely to overestimate treatment effects.

Q: What heterogeneity is observed in the treatment response? A: Men respond more strongly than women to both treatments, with the gender gap particularly pronounced for congestion costs. German speakers respond more strongly than French speakers. Participants under age 30 show stronger responses than older participants. Those scoring above the median on an altruistic values index respond significantly not only to pricing but also to information alone. Participants who correctly defined external costs (45% of the sample) drive the pricing treatment effect; a causal forest analysis confirms knowledge of external costs, age below 30, and language region as key heterogeneity drivers.

Q: How were external costs computed across modes, and what are the key monetization parameters? A: For private road transport, GPS tracks were map-matched using Graphhopper and processed via MATSim modules; emission factors came from the HBEFA 3.3 database, and congestion was assessed via an average marginal cost approach incorporating spillback effects. Externalities were monetized at CHF 136.08/ton for CO2, CHF 515,497–1,358,461/ton for PM10 (rural vs. urban), CHF 7,109/ton for NOx (regional), and a value of travel time savings of CHF 25.77/hour. For other modes, per-km values from the Swiss Federal Roads Office were applied. Walking carries net external benefits (negative external costs), while cycling carries small net external costs because accident costs exceed physical activity benefits.

Q: How was public transport priced in the experiment, and why was it simplified? A: A second-best zonal peak-hour surcharge of CHF 0.10/km was applied to public transport stages between zone-pairs experiencing peak demand, with peak windows set at 7–9 am and 5–7 pm. Full first-best pricing of public transport crowding was deemed infeasible because crowding effects are highly heterogeneous spatially and temporally, often concentrated in very short windows on specific lines, making aggregate distribution unreasonable.

Q: Was there evidence of gaming the mode detection system? A: Because participants could manually correct the app’s algorithmic mode assignments — and the pricing group had an incentive to overclaim low-cost modes — the potential for strategic misreporting was examined. While the analysis could not rule out some gaming, the main results were shown to be robust to excluding potential gamers, suggesting that gaming did not materially distort the treatment effect estimates.

Q: What does the study imply for transport pricing policy? A: The elasticity of -0.31 provides a benchmark for policymakers: a full Pigovian pricing scheme that raises total transport costs by about 16% can be expected to reduce external costs by about 5% in the short run in an urban context. The finding that congestion costs respond more to pricing than to information alone suggests the monetary component is essential for this externality. Heterogeneous responses — particularly the weaker responses by women and French speakers — have distributional implications. The experiment is a proof of concept that first-best transport pricing can generate meaningful behavioral responses, but scaling it would require addressing privacy concerns from GPS tracking, technical infrastructure, and political economy challenges.

Pigovian transport pricing: A pricing scheme that charges each user the marginal external costs of their transport choices — including health, climate, congestion, and noise costs — as they vary across time, space, and mode, intended to internalize the gap between private and social costs of travel.

External costs of transport: Costs borne by society rather than the individual traveler, including congestion (delay imposed on others), climate damages (CO2 emissions), health costs (local air pollution, accidents), and noise; in this paper, computed in real time from tracked trips using official Swiss monetization values.

Average treatment effect (ATE): The difference-in-differences estimate of the causal effect of the pricing or information treatment on outcomes, identified from the randomized assignment and controlling for person, calendar-day, and day-of-study fixed effects.

Mode substitution: The behavioral response in which travelers shift from higher-external-cost modes (primarily car) to lower-external-cost modes (public transport, walking, cycling) in response to pricing, as distinct from reducing total travel distance.

Departure time shifting: The behavioral response in which travelers adjust when they depart to avoid peak-hour congestion surcharges, contributing to reduced congestion externalities without reducing total distance traveled.

Information-only treatment: An experimental arm receiving identical information about external costs as the pricing group but facing no financial charge, used to isolate the informational component of the pricing treatment from the monetary incentive component.

Source text origin: pdf

Quantifying Supply-Side Climate Policies

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

This paper asks three questions about supply-side climate policies in the oil market: how do oil companies respond to production-based taxes; what are the aggregate effects of such taxes on global CO2 emissions; and what are the distributional consequences across consumers, producers, and governments? The study addresses a gap in empirical evidence at a time when supply-side restrictions on fossil fuel production are gaining policy traction but the quantitative literature remains limited.

The authors use proprietary company-level data from Rystad Energy’s UCube database covering 49,023 oil assets across 84 countries representing 98.1% of global oil production from 2000 to 2019. They identify 84 production tax reforms (54 increases, 30 decreases) with an average magnitude of roughly 5–6 percentage points. The empirical strategy is a difference-in-differences design that compares a company’s activity in a treated tax regime before and after a reform to the same company’s activity in other regimes over the same period, absorbing company-tax regime fixed effects, company-year fixed effects, and region-year fixed effects. This within-company cross-border comparison is used to test for, and rule out, activity-shifting spillovers. Two-stage least squares instruments the after-tax oil price with production taxes to isolate tax-driven price variation.

The primary behavioral margin is exploration: a one-percentage-point increase in the production tax rate reduces exploration expenditure by 2.6% on average over the study period, growing to 4.1% beyond five years. The elasticity of exploration with respect to the after-tax oil price is 1.96. Reduced exploration translates into fewer discoveries; a one-percentage-point tax increase reduces discovered oil amounts by 4.3% on average and by 8.9% beyond five years. The authors find no statistically significant effect of taxes on production from existing conventional fields, consistent with high adjustment costs for already-producing wells. Unconventional production (shale, oil sands, tar sands) exhibits a statistically significant intensive-margin production response to taxes. Taxes also have no detectable effect on the extraction cost of newly discovered deposits, indicating that firms do not redirect search toward lower- or higher-cost deposits at the margin.

Translating these firm-level responses into market outcomes, the authors build a dynamic field-level model spanning 2020–2100, combining field-by-field production profiles calibrated from Rystad data with demand elasticities of −0.2 and −0.5 drawn from the literature. The existing average production-weighted royalty of 21% already implies an indirect carbon price of approximately $32/tCO2 at a reference oil price of $65/barrel, an order of magnitude above the current global average demand-side carbon price of $3.1/tCO2.

Under a permanent global climate royalty surcharge of 20 percentage points, annual emissions from oil fall by 5–7% in the first five years and by 9–20% in the medium term (by year 2100). The cumulative reduction over 2020–2100 is 85–161 GtCO2, or 1.0–2.0 GtCO2 per year on average. The oil price rises by $8–14/bbl initially and by $23–27/bbl by year 2100. Tax revenue to oil-producing governments increases by $590–870 billion per year; consumer surplus falls by roughly $500–730 billion per year; producer surplus falls by $270–310 billion per year. The policy breaks even in direct economic terms at a social cost of carbon of $72–84/tCO2.

When the surcharge is adopted only by OECD countries (30% of current production, 49% of global exploration), short-term carbon leakage is 16–37%, rising to 58–82% by year 2100 as non-OECD producers increase exploration and development in response to the higher oil price. Net cumulative global emission reductions under the OECD-only scenario are 54–107 GtCO2 (47–73% of what the OECD reduction alone would achieve), roughly two-thirds of the global scenario outcome.

Q: What is the primary behavioral margin through which oil companies respond to production taxes? A: The primary margin is exploration expenditure. A one-percentage-point increase in the production tax rate reduces exploration by 2.6% on average across the study period, growing to 4.1% in the period six to twenty years after the reform. The after-tax oil price elasticity of exploration is 1.96, meaning a 1% increase in the after-tax price raises exploration by approximately 2%. The Poisson regression, which accounts for firms with zero exploration in a regime, yields consistent results, indicating the finding is not driven by firm entry or exit.

Q: Do production taxes affect output from existing oil wells? A: For conventional oil fields, the production response is statistically indistinguishable from zero across all specifications and time horizons, consistent with high adjustment costs making already-producing conventional wells insensitive to tax-driven price changes. Unconventional production (shale oil, oil sands, tar sands, extra heavy oil) is the exception, exhibiting a statistically significant intensive-margin production response to taxes. This asymmetry aligns with Bjørnland et al. (2021), who find that unconventional production is more price-sensitive than conventional production.

Q: Do taxes affect the cost profile of newly discovered deposits? A: No. The paper finds no statistically significant effect of production tax changes on the extraction cost of newly discovered fields, across all specifications and time horizons. This implies that, at the margin, firms do not redirect exploration toward lower-cost or higher-cost deposits in response to taxes; the volume and cost distribution of new discoveries are therefore treated as invariant to the tax regime in the quantitative model.

Q: How does the paper address potential activity-shifting spillovers across countries? A: The paper directly tests for spillovers by including both the own-regime tax rate and the company’s exploration-weighted average tax rate abroad as regressors; the foreign average tax rate has no statistically significant effect on domestic exploration. The analysis is also repeated restricting to small companies operating in two or fewer countries, where spillovers would be most pronounced; the null result on spillovers holds. Dropping these small companies from the main sample leaves the primary estimates unchanged.

Q: How does the paper address the potential endogeneity of tax reforms? A: The event study plots show no statistically significant pre-trends before reforms, supporting the parallel trends assumption. The paper also finds no significant correlation between tax reforms and observable oil-sector or macroeconomic variables in the pre-period. Subsamples minimizing lobbying concerns — private (non-national) oil companies, small companies, companies without pre-existing production in the country, and non-OPEC countries — all yield similar estimates, suggesting that large incumbents’ influence over tax-setting does not drive the findings.

Q: How does the paper handle the staggered difference-in-differences design? A: To address potential bias from heterogeneous and dynamic treatment effects in a two-way fixed effects framework, the paper implements a stacked regression following Cengiz et al. (2019), constructing 18 cohort-specific datasets using never-treated countries as controls. The stacked specification yields significant effects on exploration and discoveries and null results on production and extraction costs, consistent with the main estimates. The stacked event study shows no pre-trends.

Q: What is the implicit carbon price of existing production-based oil taxes? A: At the production-weighted average royalty rate of 21% and a reference oil price of $65/bbl, the existing taxes correspond to an indirect carbon price of approximately $32/tCO2, calculated using a CO2 content of 0.43 tCO2/bbl. This figure is an order of magnitude larger than the current global average demand-side carbon price of $3.1/tCO2 (a production-weighted average including zeros for unpriced emissions). This calculation pertains only to downstream combustion emissions and excludes upstream production emissions.

Q: What are the quantified effects of a global 20-percentage-point climate royalty surcharge on emissions? A: In the first five years, the surcharge reduces annual oil-embedded emissions by 0.7–1.0 GtCO2, a 5–7% reduction. By year 2100, annual reductions reach 1.2–2.6 GtCO2, a 9–20% reduction relative to baseline. The cumulative reduction over 2020–2100 is 85–161 GtCO2 (1.0–2.0 GtCO2 per year on average), representing 17–32% of the remaining carbon budget for 1.5°C warming or 7–14% of the budget for 2°C warming. All ranges span demand elasticities of −0.2 to −0.5.

Q: What happens to the global oil price under a global supply-side surcharge? A: The immediate contraction of unconventional oil production raises the oil price by $8–14/bbl in the short term. As new exploration and field development are suppressed over time, the price effect grows, reaching $23–27/bbl by year 2100. This price increase is roughly equivalent to a global carbon price of $53–63/tCO2 levied on oil consumers in the medium term.

Q: How does the paper analyze distributional incidence under the global surcharge? A: A 20-percentage-point surcharge reduces average annual consumer surplus by $500–730 billion and producer surplus by $270–310 billion per year. Tax revenue to oil-producing governments increases by $590–870 billion per year. The net present value of the aggregate economic loss is $1,000–1,400 billion; the policy breaks even in direct welfare terms at a social cost of carbon of $72–84/tCO2. Oil-producing governments are the primary beneficiaries; both consumers and oil companies lose surplus.

Q: What is the carbon leakage rate under an OECD-only supply-side coalition? A: In the short term, leakage is 16–37%, as non-OECD unconventional producers ramp up output in response to the higher oil price. By 2050 the leakage rate rises to 41–70%. By year 2100 the coalition has reduced annual production by 9,000–9,400 million barrels while non-OECD countries have increased theirs by 5,200–7,800 million barrels, implying a terminal leakage rate of 58–82%. The net cumulative global emission reduction of 54–107 GtCO2 represents 47–73% of what the OECD reduction alone achieves, and roughly two-thirds of the global scenario.

Q: Why are the authors’ supply elasticity estimates somewhat larger than the prior literature? A: The authors offer two reasons. First, their approach captures elasticity through changes in exploration activity rather than only production or field development, a broader and more forward-looking margin. Second, they use tax-driven variation in prices rather than market-price variation; the event studies show that tax reforms produce persistent changes in tax rates and after-tax prices throughout the sample, so firms are likely responding to changes perceived as durable, which would naturally elicit larger responses than responses to short-run price fluctuations.

Q: What are the key limitations and scope conditions of the model? A: The quantification omits upstream (well-to-refinery) emissions and natural gas, meaning the estimated climate effects are conservative. The demand curve is held constant over time, abstracting from long-run substitution toward clean energy. The model does not account for depletion of low-cost reserves beyond 80 years. The empirical elasticities are estimated from tax reforms that may have been perceived as temporary, meaning permanent-policy elasticities could be larger, which would imply both larger emission reductions under a global policy and higher leakage rates under a partial coalition.

Q: How do distributional consequences differ between the OECD-only and global scenarios? A: Under the OECD-only surcharge, OECD consumers and OECD producers both lose surplus, while non-OECD producers and governments everywhere gain — non-OECD governments solely through the oil price increase without bearing any tax burden. The sum of OECD producer surplus losses and non-OECD producer surplus gains is slightly negative overall. The aggregate annual global economic loss under the OECD scenario is $120–170 billion, slightly lower than the global scenario ($130–220 billion), because the oil price increase and quantity reduction are both smaller in the OECD case.

Production-based tax (royalty): A tax levied on gross oil production or gross income from oil, not on profit. Unlike profit-based taxes, these are not deductible against costs and therefore create incentives to curtail exploration and production. In the paper’s framework they are equivalent to a supply-side climate instrument because they reduce the after-tax price received by producers.

Climate royalty surcharge: An additional production-based tax, layered on top of existing taxes, proposed as an explicit supply-side climate policy instrument. Following Prest and Stock (2023), the paper defines this as an ad valorem levy on oil production that implicitly prices downstream CO2 emissions through its effect on the after-tax oil price.

Carbon leakage: The offsetting increase in oil production by non-coalition countries in response to an oil price rise caused by a supply-restricting policy adopted by a subset of producers. Measured as the ratio of the production increase in non-coalition countries to the production reduction in coalition countries, expressed as a percentage.

After-tax oil price elasticity of exploration: The percentage change in exploration expenditure per one-percent change in the after-tax oil price, estimated via 2SLS instrumenting the after-tax price with production taxes. The preferred estimate is 1.96, implying elastic exploration responses to tax-driven price changes.

Extraction cost (breakeven price): The constant oil price at which the net present value of developing a field equals zero, computed using a real discount rate of 7.5%. It is the minimum price at which a field is commercially viable absent profit taxes. In the quantitative model, fields are developed if and only if extraction cost falls below the after-tax oil price.

Indirect carbon price: The implicit CO2 price embedded in a production-based oil tax, calculated as the ad valorem royalty rate multiplied by the oil price and divided by the CO2 content of oil. The paper calculates that the existing average 21% royalty at $65/bbl corresponds to an indirect carbon price of approximately $32/tCO2, applicable only to downstream combustion emissions.

Stacked regression (staggered DiD): A robustness approach to two-way fixed effects with staggered treatment timing, constructing cohort-specific datasets for each treatment year using only never-treated units as controls, thereby avoiding contamination from using already-treated units as comparisons for later-treated units.