Samuelson Rule Research Articles

Economic growth, equilibrium welfare, and public goods provision with intergenerational altruism

This study examines the government policy of public goods provision and its effects on economic growth and welfare under intergenerational altruism. The study considers an endogenous growth model with altruistic overlapping generations. The preferences of the current youth exhibit a future bias, and thus, democratically elected governments are subject to this future bias. The optimal rule for the supply of public goods under future bias differs from the original Samuelson rule. Unlike the standard growth model without any bias, under the optimal rule, the equilibrium growth rate is not independent of government size. Future bias gives young generations the dynamic incentives to invest more. With future bias, the intergenerational redistributive effects of public goods stimulate such incentives under certain conditions. Hence, the government size affects the economic growth through intertemporal changes in their resource allocations. Moreover, the growth effect of the government size provides nontrivial outcomes of welfare analysis. Our numerical analyses show the growth and welfare superiority of the democratic governments to the nonbiased social planner.

Public Good Provision Financed by Nonlinear Income Tax Under Reduction of Envy

Abstract We examine optimal taxation and public good provision by a government that considers reduction of envy as a constraint. We adopt the extended envy-freeness proposed by Diamantaras and Thomson (1990. “A Refinement and Extension of the No-Envy Concept.” Economics Letters 33: 217–22), called λ-equitability. We derive the modified Samuelson rule under an optimal nonlinear income tax and show, using a constant elasticity of substitution utility function, that the direction of distorting the original Samuelson rule to relax the λ envy-free constraint is crucially determined by the elasticity of substitution. Furthermore, we numerically show that the optimal level of provision increases (decreases) in the degree of envy-freeness when the original Samuelson rule is upwardly (downwardly) distorted.

Optimal Public Expenditure with Inefficient Unemployment

This article proposes a theory of optimal public expenditure when unemployment is inefficient. The theory is based on a matching model. Optimal public expenditure deviates from the Samuelson rule to reduce the unemployment gap (the difference between current and efficient unemployment rates). Such optimal “stimulus spending” is described by a formula expressed with three sufficient statistics: the unemployment gap, the unemployment multiplier (the decrease in unemployment achieved by increasing public expenditure), and the elasticity of substitution between public and private consumption. When unemployment is inefficiently high and the multiplier is positive, the formula yields the following results. (1) Optimal stimulus spending is positive and increasing in the unemployment gap. (2) Optimal stimulus spending is zero for a zero multiplier, increasing in the multiplier for small multipliers, largest for a moderate multiplier, and decreasing in the multiplier beyond that. (3) Optimal stimulus spending is zero if extra public goods have no value, it becomes larger as the elasticity of substitution increases, and it completely fills the unemployment gap if extra public goods are as valuable as extra private goods.

The marginal cost of public funds is one at the optimal tax system

This paper develops a Mirrlees framework with skill and preference heterogeneity to analyze optimal linear and nonlinear redistributive taxes, optimal provision of public goods, and the marginal cost of public funds (MCF). It is shown that the MCF equals one at the optimal tax system, for both lump-sum and distortionary taxes, for linear and nonlinear taxes, and for both income and consumption taxes. By allowing for redistributional concerns, the marginal excess burden of distortionary taxes is shown to be equal to the marginal distributional gain at the optimal tax system. Consequently, the modified Samuelson rule should not be corrected for the marginal cost of public funds. Outside the optimum, the marginal cost of public funds for distortionary taxes can be either smaller or larger than one. The findings of this paper have potentially important implications for applied tax policy and social cost–benefit analysis.

The Time-Consistent Public Goods Provision

In this study, we reconsider the optimal nonlinear tax problem with the public good from the perspective of the commitment issue and examine how it affects the condition of the public good provision. We show that the Samuelson rule should be modified when the government cannot commit and the skill types of taxpayers are revealed in the first period. This is true even if the preference of the taxpayers is separable and additive with respect to consumption and leisure. Our analysis also shows how the lack of commitment affects the formula of the marginal cost of public funds and the level of public good provision. Our findings imply that the level of the public good may be excessive in comparison to the case where the government can commit to its tax policy.

ENVIRONMENTAL SUSTAINABILITY AND THE GREENED SAMUELSON RULE

AbstractThe purpose of this paper is to investigate the implementation of green government spending as an effective instrument for enhancing both environmental sustainability and economic efficiency. Utilizing a model with two types of households examined in the optimal taxation literature, this paper analyzes the impact of green spending, the properties of optimal tax rates, and the optimal provision of the public good. We derive a modified greened version of the Samuelson rule, that is, the optimal provision of the public good in connection with environmental sustainability. Our results indicate that the overall effect of green spending measured in terms of government revenue is subject to several factors such as the influence of green spending on environmental sustainability, the cost of green spending, pollution effects, and so on. To determine the optimal provision of public goods, the aforementioned factors have to be taken into account. For instance, if the pollution effect is stronger, the individual marginal effective tax rate and the commodity tax rate on the polluting good will increase to discourage the demand for consuming polluting commodities.

Corruption, Provision of Public Good, and Share of Government Expenditure: Evidence from Emerging Economies

The paper examines the impact of corruption on the share of government expenditure, related to the provision of public goods in health, education, and military sectors. The paper introduces a theoretical model that applies “the Samuelson rule of public good provision” to illuminate how corruption increases the cost of providing public goods and hypothetically leads to the underprovision of public goods in some specific sectors. The paper then provides an empirical investigation on how an increase in corruption can influentially mislead the share of government expenditure, focusing on 39 emerging market countries during the period of 1999 – 2010. The results suggest that corruption stimulates the expenditure share on military while lowering the share of spending in health and education. These results are significant and robust across a variety of specifications, and are consistent with the findings of previous studies.

The optimal pricing, finance and supply of urban transportation in general equilibrium: A theoretical exposition

We present a general equilibrium framework of optimal allocation treating the pricing, finance and supply of urban transportation. Uncongested public transportation technology with economies of scale supports the city's existence; and a congested road system subject to constant returns limits urban size. Optimal investment in public transit and in roads follow Samuelson's rule. With optimally determined urban population, roads are fully financed by Pigouvian congestion tolls while aggregate differential land rents fully finance public transit and any other activity with internal or external economies of scale (Henry George Theorem). Marshallian agglomeration from production in the core and the suburbanization of jobs to avoid congestion are treated. We also see how the optimal rules and the Henry George Theorem are modified when the demand for location is determined by a random utility model.

Indirect tax harmonization and global public goods

This paper identifies conditions under which, starting from any tax-distorting equilibrium, destination- and origin-based indirect tax-harmonizing reforms are potentially Pareto improving in the presence of global public goods. The first condition (unrequited transfers between governments) requires that transfers are designed in such a way that the marginal valuations of the global public goods are equalized, whereas the second (conditional revenue changes) requires that the change in global tax revenues, as a consequence of tax harmonization, is consistent with the under/over-provision of global public goods relative to the (modified) Samuelson rule. Under these conditions, tax harmonization results in redistributing the gains from a reduction in global deadweight loss and any changes in global tax revenues according to the Pareto principle. And this is the case independently of the tax principle in place (destination or origin).

Optimal Provision of Public Goods: A Synthesis*

AbstractThe standard approach to the optimal provision of public goods highlights the importance of distortionary taxation and distributional concerns. A new approach neutralizes distributional concerns by adjusting the income tax schedule. We demonstrate that both approaches are derived from the same basic formula. We also take the new approach further by deriving an intuitive formula for the optimal level of public goods, without imposing strong assumptions on preferences. This formula shows that distortionary taxation has a role to play, as in the standard approach. However, the main determinants of optimal provision are different, and the modified Samuelson rule is likely to lead to underprovision.

Distortionary taxation and the free-rider problem

This paper derives a version of the Samuelson rule which takes into account that a distortionary Ramsey-tax system is used to finance public-goods provision. Individuals have private information about their public-goods preferences. Moreover, individuals differ in their productive abilities. The incidence of taxation in the Ramsey model implies that more productive individuals have a lower willingness to pay for public goods than less productive individuals. They are therefore tempted to understate their valuation of public goods and less productive individuals are inclined to exaggerate theirs. The paper characterizes an optimal rule for taxation and public-goods provision that eliminates these biases.

Optimal Nonlinear Redistributive Taxation and Public Good Provision in an Economy with Veblen Effects

AbstractThis paper deals with the consequences of the assumption of negatively interdependent preferences for the shape of the optimal nonlinear income tax and the efficient level of public good provision in a setting where the agents' market ability is private information. The analysis points out that the terms added in the tax formulas due to the presence of Veblen effects might justify a reduction in the optimal marginal tax rates faced by the different individuals. Also, the desirability of negative marginal tax rates cannot be ruled out. With respect to the issue of the optimal level of public good provision, I derive a modified Samuelson rule and highlight the fact that the Veblen‐based part of the formula might require to distort downwards the efficient level of public good provision.

Carbon Lorenz curves

The purpose of this paper is twofold. First, it exhibits that standard tools in the measurement of income inequality, such as the Lorenz curve and the Gini-index, can successfully be applied to the issues of inequality measurement of carbon emissions and the equity of abatement policies across countries. These tools allow policy-makers and the general public to grasp at a single glance the impact of conventional distribution rules such as equal caps or grandfathering, or more sophisticated ones, on the distribution of greenhouse gas emissions. Second, using the Samuelson rule for the optimal provision of a public good, the Pareto-optimal distribution of carbon emissions is compared with the distribution that follows if countries follow Nash–Cournot abatement strategies. It is shown that the Pareto-optimal distribution under the Samuelson rule can be approximated by the equal cap division, represented by the diagonal in the Lorenz curve diagram.

INEQUALITY IN MILITARY EXPENDITURES AND THE SAMUELSON RULE

In this paper, we show that standard measures used in the income inequality literature, the Lorenz curve and the associated Gini‐index, can successfully be applied to the distribution of defence spending across countries. Secondly, we use the Samuelson rule to explain the distribution of military expenditures across countries over time. According to the constant defence burden interpretation of the Samuelson rule, corresponding to the diagonal in the Lorenz diagram, the defence burdens should be equal across countries. It is shown that about three quarters of the variation in military expenditures can be explained by the Samuelson rule. We then go beyond the Samuelson rule to see which countries spend much more or less than predicted and investigate which other factors may influence the defence burden.

Does Indirect Tax Harmonization Deliver Pareto Improvements in the Presence of Global Public Goods?

This paper identifies conditions under which, starting from any tax distorting equilibrium, destination- and origin-based indirect tax-harmonizing reforms are potentially Pareto improving in the presence of global public goods. The first condition (unrequited transfers between governments) requires that transfers are designed in such a way that the marginal valuations of the global public goods are equalized, whereas the second (conditional revenue changes) requires that the change in global tax revenues, as a consequence of tax harmonization, is consistent with the direction of inefficiency in global public good provision relative to the (modified) Samuelson rule. Under these conditions, tax harmonization results in redistributing the gains from a reduction in global deadweight loss and any changes in global tax revenues according to the Pareto principle. And this is the case independently of the tax principle in place (destination or origin).

Optimal Provision of Public Goods: A Synthesis

There currently exist two competing approaches in the literature on the optimal provision of public goods. The standard approach highlights the importance of distortionary taxation and distributional concerns. The new approach neutralizes distributional concerns by adjusting the non-linear income tax, and finds that this reinvigorates the simple Samuelson rule when preferences are separable in goods and leisure. We provide a synthesis by demonstrating that both approaches derive from the same basic formula. We further develop the new approach by deriving a general, intuitive formula for the optimal level of a public good without imposing any separability assumptions on preferences. This formula shows that distortionary taxation may have a role to play as in the standard approach. However, the main determinants of optimal provision are completely different and the traditional formula with its emphasis on MCF only obtains in a very special case.

Optimal Nonlinear Redistributive Taxation and Public Good Provision in an Economy with Veblen Effects

This paper deals with the consequences of the assumption of negatively interdependent preferences for the shape of the optimal nonlinera income tax and the efficient level of public good provision in a setting where the policy maker maximizes an inequality averse social welfare function and the agents' market ability is private information. The analysis points out that the terms added in the tax formulas due to the presence of Veblen effects might justify a reduction in the optimal marginal tax rates faced by the different individuals. Also, the desirability of negative marginal tax rates cannot de ruled out. With respect to the issue of the optimal level of public good provision, we derive a modified Samuelson rule and highlight the fact that the Veblen-based part of the formula might require to distort downwards the efficient level of public good provision.

Labour Income Uncertainty, Taxation and Public Good Provision

This article examines optimal nonlinear income taxation, commodity taxation and public good provision under income uncertainty in a moral hazard framework. Uniform commodity taxation and the Samuelson rule for public good provision are desirable under similar conditions as in the conventional tax model. Deviations from these rules is warranted if one can encourage effort by subsidising certain goods and overproviding public goods. We also determine a rule for the optimal marginal income tax rate and provide some numerical simulations. Conditions for the validity of the solution procedure used in this class of models, the first-order approach, are also explored. Uncertainty is a key component of many important real-world decision-making processes. Consider for example an individual's decision to acquire specific skills through education. Educational investments must be made well before the resolution of uncertainty related to the returns to skill. Thus the tax system, which affects the net returns of different skill levels, has a potentially large impact on educational decisions, skill attainment and productivity. A progressive tax system offers insurance to workers by redistributing income from the lucky to the unlucky. Other forms of social insurance, such as unemployment and health insurance, work in a similar manner. A well-known problem in the design of optimal income tax under uncertainty, or any insurance mechanism, is asymmetric information between the government and individuals. Income is partly due to individual effort and partly due to luck, but the planner can only observe realised income, not effort. The optimal redistribution scheme is a balance between providing the workers with adequate incentives to acquire skills and sufficient insurance. Mirrlees (1974) was the first to examine the design of optimal redistributive income tax under income uncertainty. This moral hazard model, later used, among others, by Varian (1980), Tuomala (1984) and Low and Maldoom (2004), is an alternative to the more well-known adverse selection model of Mirrlees (1971), where income dispersion arises from differences in innate skill levels. The moral hazard model is perhaps most appealing in the tax context when effort is interpreted as an ex ante decision on educational investment. Alternatively, one can interpret the discussion as a general analysis of social insurance.1 Income tax is only one element, albeit an important one, in the design of optimal government redistributive policy. Indeed, recent optimal tax literature has devoted a lot of attention to the use of other instruments, such as commodity taxation, minimum

Informative Voting and the Samuelson Rule

We study the classical free-rider problem in public goods provision in a large economy with uncertainty about the average valuation of the public good. Individual preferences over public goods are shaped by a skill and a taste parameter. We use a mechanism design approach to solve for the optimal utilitarian provision rule. The relevant incentive constraints for information aggregation ensure that individuals behave as if they were engaging in informative voting over the level of public good provision. It is shown that the use of information by an optimal provision rule is inversely related to the polarization of preferences which results from the properties of the skill distribution.

Distortionary Taxation and the Free-Rider Problem

This paper derives a version of the Samuelson rule, which takes not only the marginal costs of public funds into account but also the desirability of preference revelation. Under a linear income tax more able individuals suffer from a larger utility loss if taxes are raised to cover the cost of public good provision. This implies that these individuals are tempted to understate their valuation of the public good. Likewise, less productive individuals are inclined to exaggerate their valuation. These incentive concerns require the use of excessive taxes. They ensure a truthful revelation of preferences for the public good. Under an optimal utilitarian tax constitution, individuals are not granted influence on public good provision if the taxes needed to induce informative behavior are prohibitively high.