Optimal labor income taxation

Last updated December 03, 2023

Optimal labour income tax is a sub-area of optimal tax theory which refers to the study of designing a tax on individual labour income such that a given economic criterion like social welfare is optimized.

Efficiency-equity tradeoff

The modern literature on optimal labour income taxation largely follows from James Mirrlees' "Exploration in the Theory of Optimum Income Taxation".^[1] The approach is based on asymmetric information, as the government is assumed to be unable to observe the number of hours people work or how productive they are, but can observe individuals' incomes. This imposes incentive compatibility constraints that limit the taxes which the government is able to levy, and prevents it from taxing high-productivity people at higher rates than low-productivity people. The government seeks to maximise a utilitarian social welfare function subject to these constraints. It faces a tradeoff between efficiency and equity:

Higher levels of taxation on the rich create revenue that can be used to redistribute to the poor, which raises social welfare because the marginal utility of income is (assumed to be) higher for the poor than the rich;
However, taxation reduces the incentive to work, and so leads to labour supply below the optimal level.

Mechanical, behavioral and welfare effects

Emmanuel Saez in his article titled "Using Elasticities to Derive Optimal Income Tax Rates" derives a formula for optimal level of income tax using both the compensated and uncompensated elasticities.^[2] Saez writes that the tradeoff between equity and efficiency is a central consideration of optimal taxation, and implementing a progressive tax allows the government to reallocate their resources where they are needed most. However, this deters those of higher income levels to work at their optimal level. Saez decomposes the marginal effects of a tax change into mechanical, behavioural and welfare effects, as follows:^[2]

The mechanical effect is the effect that the tax change would have on government revenue, if no individuals changed their behaviour in response. For a tax increase, this is positive.
The behavioural effect is the effect that the behavioural change induced by the tax change would have on government revenue, at the initial tax rates. Raising taxes will discourage labour supply, and this will lead to lower tax revenue as a result; so for a tax increase, this is negative.
The welfare effect is the effect that the tax change has on the social welfare function by changing individual's utilities. For a tax increase, this is negative.

The sum of these effects should be zero at the optimum. Stipulating this condition results in the following formula for the optimal top tax rate, if incomes are Pareto distributed:

\tau ={\frac {1-{\bar {g}}}{1-{\bar {g}}+{\bar {\zeta }}^{u}+{\bar {\zeta }}^{c}(\alpha -1)}}

where:

$\tau$ is the tax rate
${\bar {g}}$ is the ratio of social marginal utility for the top bracket taxpayers to the marginal value of public funds for the government, which depends on the social welfare function. The case ${\bar {g}}=0$ corresponds to one where the government does not care about the welfare of top bracket taxpayers, and wants to raise as much revenue as possible from them, so setting ${\bar {g}}=0$ gives a formula for the revenue-maximising top tax rate.
${\bar {\zeta }}^{u}$ and ${\bar {\zeta }}^{c}$ are respectively the uncompensated and compensated elasticity of labour supply; higher elasticities imply that labour supply will fall more in response to an increase in taxes.
$\alpha$ is the shape parameter in the Pareto distribution of income.

Empirical estimation of the parameters of this equation suggests that the revenue-maximising top tax rate is between approximately 50% and 80%,^[3] although this estimate neglects long-run behavioural responses, which would imply higher elasticities and a lower optimal tax rate. Saez's analysis can also be generalised to tax rates other than the top rate.

Arithmetic vs. economic effects

In the late 1970s, Arthur Laffer developed the Laffer curve, which demonstrates that there are two effects of changing tax rates:

An arithmetic effect — if tax rates are lowered, revenue will be decrease by the same amount;
An economic effect — which provides incentives for individuals to increase their work output through low tax rates.^[4]

These correspond to the mechanical and behavioural effects discussed by Saez. The Laffer curve illustrates that, for sufficiently high tax levels, the (negative) behavioural effect will outweigh the (positive) mechanical effect of a tax increase, and so increasing tax rates will reduce tax revenue. In fact, tax revenue with a tax rate of 100% is likely to be 0, since there is no remaining incentive to work at all. Therefore, the tax rate that maximises revenue collected will typically be below 100% - as estimated by Saez, the revenue-maximising top rate is between 50% and 80%.^[4]

Family and gender effects

Since only economic actors who engage in market activity of "entering the labour market" have an income tax liability on their wages, people who are able to consume leisure or engage in household production outside the market, by, for example, providing housewife services in lieu of hiring a maid, are taxed more lightly. With the "married filing jointly" tax unit in U.S. income tax law, the second earner's income is added to the first wage earner's taxable income and thus gets the highest marginal rate. This type of tax creates a large distortion, disfavoring women from the labour force during years when the couple has the greatest child care needs.

Optimal linear income tax

Eytan Sheshinski has studied a simplified income-tax model, in which the tax is a linear function of the income:^[5] $t(y)=-a+(1-b)y$ , where y is the income, t(y) is the tax paid by an individual with an income of y, 1-b is the tax rate, and a is a lump sum tax. The goal is to find the values of a and b such that the social welfare (the sum of individual utilities) is maximized.

In his model, all agents have the same utility function, which depends on consumption and labour: $u=u(c,l)$ . The consumption c is determined by the after-income tax: $c(y)=y-t(y)=a+by$ . The before-tax income y is determined by the amount of labor l and an innate ability factor n, where the relation is assumed to be linear too: $y=y(n,l)=n\cdot l$ . Each individual decides on the amount of labour l which maximizes his utility: $u(a+bnl,l)$ . These decisions define the labor supply as a function of the tax parameters a and b.

Under certain natural assumptions, it is proved that the optimal linear tax has a>0, i.e., it provides a positive lump-sum to individuals with zero income. This coincides with the idea of negative income tax. Additionally, the optimal tax rate is bounded above by a fraction that decreases with the minimum elasticity of the labour supply.

Developments

The theory of optimal labour income taxation started with a simple model of optimal linear taxation. It then developed to consider optimal nonlinear income taxation. Then, it considered various extensions of the standard model: tax avoidance, income shifting, international migration, rent-seeking, relative income concerns, couples and children, and non-cash transfers.^[6]

Related Research Articles

Labour economics, or labor economics, seeks to understand the functioning and dynamics of the markets for wage labour. Labour is a commodity that is supplied by labourers, usually in exchange for a wage paid by demanding firms. Because these labourers exist as parts of a social, institutional, or political system, labour economics must also account for social, cultural and political variables.

A tax is a compulsory financial charge or some other type of levy imposed on a taxpayer by a governmental organization in order to collectively fund government spending, public expenditures, or as a way to regulate and reduce negative externalities. Tax compliance refers to policy actions and individual behaviour aimed at ensuring that taxpayers are paying the right amount of tax at the right time and securing the correct tax allowances and tax relief. The first known taxation took place in Ancient Egypt around 3000–2800 BC. Taxes consist of direct or indirect taxes and may be paid in money or as its labor equivalent.

In economics, utility is a measure of the satisfaction that a certain person has from a certain state of the world. Over time, the term has been used in two different meanings.

This aims to be a complete article list of economics topics:

Supply-side economics is a macroeconomic theory postulating that economic growth can be most effectively fostered by lowering taxes, decreasing regulation, and allowing free trade. According to supply-side economics, consumers will benefit from greater supplies of goods and services at lower prices, and employment will increase. Supply-side fiscal policies are designed to increase aggregate supply, as opposed to aggregate demand, thereby expanding output and employment while lowering prices. Such policies are of several general varieties:

Investments in human capital, such as education, healthcare, and encouraging the transfer of technologies and business processes, to improve productivity. Encouraging globalized free trade via containerization is a major recent example.
Tax reduction, to provide incentives to work, invest and take risks. Lowering income tax rates and eliminating or lowering tariffs are examples of such policies.
Investments in new capital equipment and research and development (R&D), to further improve productivity. Allowing businesses to depreciate capital equipment more rapidly gives them an immediate financial incentive to invest in such equipment.
Reduction in government regulations, to encourage business formation and expansion.

The theory of consumer choice is the branch of microeconomics that relates preferences to consumption expenditures and to consumer demand curves. It analyzes how consumers maximize the desirability of their consumption, by maximizing utility subject to a consumer budget constraint. Factors influencing consumers' evaluation of the utility of goods include: income level, cultural factors, product information and physio-psychological factors.

A progressive tax is a tax in which the tax rate increases as the taxable amount increases. The term progressive refers to the way the tax rate progresses from low to high, with the result that a taxpayer's average tax rate is less than the person's marginal tax rate. The term can be applied to individual taxes or to a tax system as a whole. Progressive taxes are imposed in an attempt to reduce the tax incidence of people with a lower ability to pay, as such taxes shift the incidence increasingly to those with a higher ability-to-pay. The opposite of a progressive tax is a regressive tax, such as a sales tax, where the poor pay a larger proportion of their income compared to the rich.

Utility maximization was first developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill. In microeconomics, the utility maximization problem is the problem consumers face: "How should I spend my money in order to maximize my utility?" It is a type of optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending (income), the prices of the goods and their preferences.

Mental accounting is a model of consumer behaviour developed by Richard Thaler that attempts to describe the process whereby people code, categorize and evaluate economic outcomes. Mental accounting incorporates the economic concepts of prospect theory and transactional utility theory to evaluate how people create distinctions between their financial resources in the form of mental accounts, which in turn impacts the buyer decision process and reaction to economic outcomes. People are presumed to make mental accounts as a self control strategy to manage and keep track of their spending and resources. People budget money into mental accounts for savings or expense categories. People also are assumed to make mental accounts to facilitate savings for larger purposes. Mental accounting can result in people demonstrating greater loss aversion for certain mental accounts, resulting in cognitive bias that incentivizes systematic departures from consumer rationality. Through increased understanding of mental accounting differences in decision making based on different resources, and different reactions based on similar outcomes can be greater understood.

The Ramsey problem, or Ramsey pricing, or Ramsey–Boiteux pricing, is a second-best policy problem concerning what prices a public monopoly should charge for the various products it sells in order to maximize social welfare while earning enough revenue to cover its fixed costs.

<span class="mw-page-title-main">Tax revenue</span> Income collected by governments via tax

Tax revenue is the income that is collected by governments through taxation. Taxation is the primary source of government revenue. Revenue may be extracted from sources such as individuals, public enterprises, trade, royalties on natural resources and/or foreign aid. An inefficient collection of taxes is greater in countries characterized by poverty, a large agricultural sector and large amounts of foreign aid.

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In economics, tax incidence or tax burden is the effect of a particular tax on the distribution of economic welfare. Economists distinguish between the entities who ultimately bear the tax burden and those on whom the tax is initially imposed. The tax burden measures the true economic effect of the tax, measured by the difference between real incomes or utilities before and after imposing the tax, and taking into account how the tax causes prices to change. For example, if a 10% tax is imposed on sellers of butter, but the market price rises 8% as a result, most of the tax burden is on buyers, not sellers. The concept of tax incidence was initially brought to economists' attention by the French Physiocrats, in particular François Quesnay, who argued that the incidence of all taxation falls ultimately on landowners and is at the expense of land rent. Tax incidence is said to "fall" upon the group that ultimately bears the burden of, or ultimately suffers a loss from, the tax. The key concept of tax incidence is that the tax incidence or tax burden does not depend on where the revenue is collected, but on the price elasticity of demand and price elasticity of supply. As a general policy matter, the tax incidence should not violate the principles of a desirable tax system, especially fairness and transparency. The concept of tax incidence is used in political science and sociology to analyze the level of resources extracted from each income social stratum in order to describe how the tax burden is distributed among social classes. That allows one to derive some inferences about the progressive nature of the tax system, according to principles of vertical equity.

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Optimal tax theory or the theory of optimal taxation is the study of designing and implementing a tax that maximises a social welfare function subject to economic constraints. The social welfare function used is typically a function of individuals' utilities, most commonly some form of utilitarian function, so the tax system is chosen to maximise the aggregate of individual utilities. Tax revenue is required to fund the provision of public goods and other government services, as well as for redistribution from rich to poor individuals. However, most taxes distort individual behavior, because the activity that is taxed becomes relatively less desirable; for instance, taxes on labour income reduce the incentive to work. The optimization problem involves minimizing the distortions caused by taxation, while achieving desired levels of redistribution and revenue. Some taxes are thought to be less distorting, such as lump-sum taxes and Pigouvian taxes, where the market consumption of a good is inefficient, and a tax brings consumption closer to the efficient level.

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In economics, the Laffer curve illustrates a theoretical relationship between rates of taxation and the resulting levels of the government's tax revenue. The Laffer curve assumes that no tax revenue is raised at the extreme tax rates of 0% and 100%, meaning that there is a tax rate between 0% and 100% that maximizes government tax revenue.

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Optimal capital income taxation is a subarea of optimal tax theory which studies the design of taxes on capital income such that a given economic criterion like utility is optimized.

This glossary of economics is a list of definitions of terms and concepts used in economics, its sub-disciplines, and related fields.

References

↑ Mirrlees, J. A. (1971). "An Exploration in the Theory of Optimum Income Taxation". The Review of Economic Studies . 38 (2): 175–208. doi:10.2307/2296779. JSTOR 2296779.
1 2 Saez, Emmanuel (2001). "Using Elasticities to Derive Optimal Income Tax Rates" (PDF). Review of Economic Studies. 68: 105–229. doi:10.1111/1467-937x.00166.
↑ Diamond, Peter; Saez, Emmanuel (November 2011). "The Case for a Progressive Tax: From Basic Research to Policy Recommendation". Journal of Economic Perspectives . 25 (4): 165–190. doi: 10.1257/jep.25.4.165 . ISSN 0895-3309.
1 2 Laffer, Arthur (2004). "The Laffer Curve: Past, Present and Future". The Heritage Foundation (1765): 1–18.
↑ Sheshinski, Eytan (1972). "The Optimal Linear Income-tax". The Review of Economic Studies. 39 (3): 297–302. doi:10.2307/2296360. ISSN 0034-6527. JSTOR 2296360.
↑ Thomas Piketty and Emmanuel Saez (2013). "Optimal Labor Income Taxation". Handbook of public economics, vol. 5. Vol. 5. pp. 391–474. doi:10.1016/B978-0-444-53759-1.00007-8. ISBN 9780444537591. S2CID 3472836.{{cite book}}: |website= ignored (help)

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[1] Mirrlees, J. A. (1971). "An Exploration in the Theory of Optimum Income Taxation". The Review of Economic Studies . 38 (2): 175–208. doi:10.2307/2296779. JSTOR 2296779.

[Saez_2001_105–229-2] 1 2 Saez, Emmanuel (2001). "Using Elasticities to Derive Optimal Income Tax Rates" (PDF). Review of Economic Studies. 68: 105–229. doi:10.1111/1467-937x.00166.

[3] Diamond, Peter; Saez, Emmanuel (November 2011). "The Case for a Progressive Tax: From Basic Research to Policy Recommendation". Journal of Economic Perspectives . 25 (4): 165–190. doi: 10.1257/jep.25.4.165 . ISSN 0895-3309.

[Laffer_2004_1–18-4] 1 2 Laffer, Arthur (2004). "The Laffer Curve: Past, Present and Future". The Heritage Foundation (1765): 1–18.

[5] Sheshinski, Eytan (1972). "The Optimal Linear Income-tax". The Review of Economic Studies. 39 (3): 297–302. doi:10.2307/2296360. ISSN 0034-6527. JSTOR 2296360.

[6] Thomas Piketty and Emmanuel Saez (2013). "Optimal Labor Income Taxation". Handbook of public economics, vol. 5. Vol. 5. pp. 391–474. doi:10.1016/B978-0-444-53759-1.00007-8. ISBN 9780444537591. S2CID 3472836.{{cite book}}: |website= ignored (help)

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