The efficient side of progressive income taxation

This paper examines allocative properties of progressive income taxation when individuals care about their relative income. It shows that introducing a progressive income tax can yield a Pareto improvement if pre-tax income is evenly distributed. Implementing undistorted choices of working hours requires a progressive tax schedule, and the optimal degree of progressivity decreases with pre-tax income inequality.     

When is a tax neutral?

A proportional income tax is said to be neutral if variations in the tax rate do not affect the optimal composition of the consumption commodities of a utility maximizing consumer. It is shown that neutrality obtains if and only if the indirect utility function of the consumer is groupwise homothetic. If the income tax rates on labor and property incomes are allowed to differ, then neutrality obtains if and only if the indirect utility function of the consumer is homothetically separable. If, in addition, it is required that the proportional income tax be neutral with respect to not only consumption commodities but also to leisure, then 'the indirect utility function must have the form: $\text{V = V(f(w)+H}{}^1\text{(p))}$, where w and p are the normalized prices of leisure and consumption respectively, and H¹(p) is homogeneous of degree one in p.     

Inequality: The original economic sin of capitalism? An Evaluation of Thomas Piketty's "Capital in the twenty-first century"

This is a review article of Thomas Piketty's book “Capital in the twenty-first century”. Piketty promotes the old theme that, under capitalism, the rich tend to become richer and the poor become poorer, at least in relative terms. We consider whether the data really shows that wealth and income are becoming more concentrated; the role of income transfers (Piketty's data is for pre-tax and pre-transfer income) and other influences on inequality such as real estate prices; the implications of social and economic mobility; the role of the state in fostering inequality; and the determination of socially acceptable inequality. We conclude that Piketty has not succeeded in showing that the inequality r > g (the rate of return is greater than the rate of growth) is the principal determinant of inequality. Piketty offers neither an accompanying theory of social justice nor a theoretical framework to support his case. In particular, lacking is a revealed appreciation of the effects of high marginal tax rates on growth and efficiency.     

SEPARATING EFFICIENCY AND EQUALITY,AUTOMATION, AND PIKETTY'S THEORY OF INCREASING CAPITAL SHARE

Despite disincentive effects, it is more efficient to tackle inequality by general equality promotion policies, including tax/transfers, than by trying to pursue equality in specific issues or policies. The latter policy also has the same degree of disincentive effects as the general policy but has additional distortive effects. While Piketty' concern with inequality is well taken and his proposal to reduce inequality has merits, his argument on the inevitability of increasing capital share under capitalism and the condition of rate of returns to capital being larger than the rate of growth in incomes (r > g) is not correct. (JEL D3, D6, H)     

Bayesian estimation of social welfare and tax progressivity measures

This paper examines Bayesian methods of examining posterior distributions of inequality, concentration, tax progressivity and social welfare measures. Use is made of an explicit income distribution assumption and two alternative assumptions regarding the distribution of pre-tax mean incomes within each income group. The methods are applied to a simulated distribution of individual incomes and tax payments. It is possible to identify a minimum acceptable number of income classes to be used. The results suggest support for the use of group means in practical applications, particularly where large sample sizes are available. First version received: August 2000/Final version received: July 2001 RID="*" ID="*"  This research was supported by a Melbourne University Faculty of Economics and Commerce Research Grant. We should like to thank Bill Griffiths and two referees for comments on an earlier draft.     

Equity,efficiency, and the structure of indirect taxation

Optimal tax formulae are derived and optimal tax rates calculated for the case where there are many consumers, an income tax is impossible and the government has to trade off efficiency in order to improve the real distribution of income. Consistent aggregation assumptions are used to permit the derivation of simple tax rules depending only on the behaviour of the average consumer and of a socially representative consumer. Calculations for the U.K. in 1972 show how subsidies and taxes vary with the government's revenue requirement and with the degree of egalitarianism in the social welfare function.     

Tax progressivity, income distribution and tax non-compliance

This article examines the determinants of tax non-compliance when we recognise the existence of an imperfectly competitive “tax advice” industry supplying schemes which help taxpayers reduce their tax liability. We apply a traditional industrial organisation framework to model the behaviour of this industry. This tells us that an important factor determining the equilibrium price and hence, the level of non-compliance, is the convexity of the demand schedule. We show that in this context, this convexity is affected by the distribution of pre-tax income, the progressivity of the tax-schedule and the way in which monitoring and penalties vary with income. It is shown that lower pre-tax income inequality as well as a less progressive tax code may cause more tax minimisation activities. Therefore, the frequently advocated policy of reducing the highest tax rate may fail as a policy directed at improving tax discipline. One way of offsetting the possible harm to tax compliance from a less progressive tax could be an adjustment of the penalty and monitoring functions.     

Taxation and Tournaments

This paper analyzes the effects of progressive taxes on labor supply and income distribution in the context of the rank‐order tournament model originally developed by Lazear and Rosen (1981). We show conditions under which a more progressive tax schedule will cause so large general equilibrium effects that the inequality in disposable income will actually increase. We also show that a non‐zero redistributive tax is always optimal if society's welfare function displays inequality aversion; this result always holds, regardless of behavioral responses and general equilibrium effects.     

Capital income taxation,tax criteria,and intergenerational welfare

In a two-period overlapping-generations model, residence criteria are shown to be optimal with lump-sum transfers to the younger generation in a dynamically efficient open economy even if all wage income, corresponding to rent income under exogenous labor supply, is not taxed away. When tax revenues are also distributed to the older generation — which indeed may be desirable for short-term intergenerational welfare distribution reasons — a weighted average rule is derived for optimal international taxation. The taxation of domestic savings income follows the inverse elasticity rule in respect to savings and, surprisingly, higher investment elasticity increases the tax level. Finally, for a small open economy and for large identical economies, tax competition with a mixed scheme of residence-based taxes and source-based subsidies yields the same tax policy as tax cooperation with no restrictions on the domestic and international capital income tax instruments.     

Facilitating Consumer Learning in Insurance Markets: What Are the Welfare Effects?

We model a monopoly insurance market in which consumers can learn their accident risks at a cost c . We then examine the welfare effects of a policy that reduces c . If c is sufficiently small (c  < c ^*), the optimal contract is such that the consumer gathers information. For c  < c ^*, both the insurer and the consumer benefit from a policy that reduces c further. For c   >  c ^*, marginally reducing c hurts the insurer and weakly benefits the consumer. Finally, a reduction in c that is successful, meaning that the consumer gathers information after the reduction but not before it, can hurt both parties.     

Tax Havens,Growth, and Welfare

This paper develops an endogenous growth model featuring tax havens, and uses it to examine how the existence of tax havens affects the economic growth rate and social welfare in high‐tax countries. We show that the presence of tax havens generates two conflicting channels in determining the growth effect. First, the public investment effect states that tax havens may erode tax revenues and in turn decrease the government's infrastructure expenditure, thereby reducing growth. Second, the tax planning effect of tax havens reduces marginal cost of capital and hence encourages capital accumulation so as to spur economic growth. The overall growth effect is ambiguous and is determined by the extent of these two effects. The welfare analysis shows that tax havens are more likely to be welfare‐enhancing if the government expenditure share in production is low, or the initial income tax rate is high. Moreover, the welfare‐maximizing income tax rate is lower than the growth‐maximizing income tax rate if tax havens are present.     

The Optimal Linear Income Tax Model: Utility or Equivalent Income?

This paper compares the use of equivalent income with that of utility, in the social welfare function, in optimal income tax models. Equivalent income is a money metric welfare measure that, unlike utility, is not affected by monotonic transformations of utility. The use of equivalent income is found to produce an optimal tax rate that is more sensitive to the degree of inequality aversion, compared with the use of utility. With Cobb-Douglas and CES utility functions, the optimal tax rate is the same for utility and equivalent income where relative inequality aversion is unity. When using equivalent incomes, the case for high marginal rates does not depend on the assumption of a very low elasticity of substitution between consumption and leisure.     

Age‐related Optimal Income Taxation*

In most countries, average income varies with age. In this paper we investigate if and how it is possible to enhance the redistributive mechanism by relating tax payments to age. Using an OLG model where some individuals are low skilled all their life while others are low skilled when young but high skilled when old, we first show how an age dependent optimal income tax can Pareto improve upon an age independent income tax. We then characterize the optimal age dependent income tax. A tax on interest income is part of the optimal tax structure.     

Fuel for inequality: Distributional effects of environmental reforms on private transport

This paper provides the first empirical evidence of the distributional effects of subsidies for the purchase of alternative vehicles based on an extended version of Hausman's exact consumer surplus. In consistence with economic theory, we estimate changes in household welfare, inequality, and social welfare resulting from different reforms. First, we find that an additional tax on conventional fuel is regressive. However, returning the additional tax revenue via lump-sum transfers can alleviate this effect. Second, when the additional revenue is also used to finance subsidies for electrical and compressed natural gas (CNG) vehicles, households that own such vehicles experience welfare gains. However, this policy also increases income inequality and decreases social welfare.     

The limitations of decentralized world redistribution: An optimal taxation approach

A centralized scheme of world redistribution that maximizes a border-neutral social welfare function, subject to the disincentive effects it would create, generates a drastic reduction in world consumption inequality, dropping the Gini coefficient from 0.69 to 0.25. In contrast, an optimal decentralized (i.e., with no cross-country transfers) redistribution has a miniscule effect on world income inequality. Thus, the traditional public finance concern about the excess burden of redistribution cannot explain why there is so little world redistribution.Actual foreign aid is vastly lower than the transfers under the simulated world income tax, suggesting that voluntary world transfers - subject to a free-rider problem - produces an outcome that is consistent with rich countries such as the United States either placing a much lower value on the welfare of foreigners, or else expecting that a very significant fraction of cross-border transfers is wasted. The product of the welfare weight and one minus the share of transfers that are wasted constitutes the implicit weight that the United States assigns to foreigners. We calculate that value to be as low as 1/2000 of the value put on the welfare of an American, suggesting that U.S. policy is consistent with social preferences that place essentially no value on the welfare of the citizens of the poorest countries, or that implicitly assumes that essentially all transfers are wasted.     

Externalities and optimal taxation

This paper reexamines the optimal tax design problem (income and commodities) in the presence of externalities. The nature of the second–best, and the choice of the tax instruments, are motivated by the informational structure in the economy. The main results are: (i) environmental levies (linear or nonlinear) differ in formula from Pigouvian taxes by the expressions for the optimal tax on private goods; (ii) externalities do not affect commodity tax formulas (linear and nonlinear) for private goods; (iii) externalities do not affect the income tax structure if commodity taxes are nonlinear and affect it if commodity taxes are linear; and (iv) a general income tax plus strictly Pigouvian taxes are sufficient for efficient taxation if individuals of different types have identical marginal rates of substitution (at any given consumption bundle).     

How and why transition made income inequality increase in urban Russia: A local study

Using sample surveys from the city of Taganrog in 1989 and 2000, we investigate household income, its composition, and its distribution in urban Russia. Income inequality increased greatly as real income at the lowest part of the distribution decreased considerably. Earnings are more concentrated in the upper part of the income distribution in 2000 than in 1989. For many households, public transfers, allowances, private transfers, or subsidiary earned income prevented income from falling further. However, Russia did not inherit from its Soviet past an efficient progressive tax system or programs to protect jobless workers and households facing severe drops in income. Journal of Comparative Economics 33 (4) (2005) 772–787.     

Unequal inequalities. II

This paper analyzes properties of measures of inequality, applied to income inequalities but meaningful for practically any measure of dispersion in economics. We call n the number of persons, i the person's index, x_i person i's income, $\text{x}\text{= Σ(}\text{x}{}_{\mathrm{i}}\text{n}\text{)}$ the average income, x the vector of the x_i's or income distribution, I(x) a real-valued function of x which is the measure (or index) of inequality.Part I (Sects. I–V), which appeared in the last issue of this journal, analyzed several structures or properties, and specific forms, of I. We distinguished several I's: the measures of inequality per person (or “absolute”) I^a, per pound (or “relative”) $\text{I}{}^{\mathrm{r}}\text{=}\text{I}{}^{\mathrm{a}}\text{x}$, and total nI^a. We presented several possible properties of inequality measures, such as: I = 0 if all x_i's are equal (“zero at equality”), I > 0 otherwise (“positivity out of equality”), symmetry of I for x (“impartiality”), $\text{((}\text{?I}\text{?x}{}_{\mathrm{i}}\text{) ? (}\text{?I}\text{?x}{}_{\mathrm{i}}\text{))(x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{) > 0}$ for x_i ≠ x_j (“rectifiance” of the function I, or “transfers principle,” this being the strict form whereas the weak one is with sign ?), the fact that $\text{(}\text{?(}\text{x}\text{? I}{}^{\mathrm{a}}\text{)}\text{?}{}_{\mathrm{i}}\text{)}\text{(}\text{?(}\text{x}\text{? I}{}^{\mathrm{a}}\text{)}\text{?}{}_{\mathrm{j}}\text{)}$ does not depend upon x_k for k ≠ i,j (“welfare independence,” or, for short, “independence”). Rectifiance plus symmetry is Schur-convexity. Independence plus symmetry plus zero at equality implies that $\text{x}\text{≡}\text{x}\text{? I}{}^{\mathrm{a}}\text{= ?}{}^{\mathrm{?1}}\text{[(}\text{1}\text{n}\text{) Σ ?(x}{}_{\mathrm{i}}\text{)]}$ where $\text{x}$ is the “equal equivalent income”; and we will show that, these three properties being satisfied, the following ones are equivalent to each other: positivity out of equality, rectifiance, quasi-convexity, ?'s concavity.Part I largely focused on the study of six related specific measures of inequality, which in particular possess all the above properties: ?, α, and Ξ being positive parameters, they are $\text{I}{}_{\mathrm{c}}{}^{\mathrm{a}}\text{=}\text{x}\text{+ξ ? [(}\text{1}\text{n}\text{∑ (x}{}_{\mathrm{i}}\text{+ ξ)}{}^{\mathrm{1?epsi;}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>1</mtext><mtext>??</mtext>}}$, $\text{I}{}_{\mathrm{c}}{}^{\mathrm{a}}\text{=}\text{x}\text{+ξ ? ∏ (x}{}_{\mathrm{i}}\text{+ ξ)}{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}$, $\text{I}{}_{\mathrm{c}}{}^{\mathrm{r}}\text{=}\text{I}{}_{\mathrm{c}}{}^{\mathrm{a}}\text{x}$, I_r=I_c^r for ξ=O, $\text{I}{}_{\mathrm{r}}{}^{\mathrm{a}}\text{=}\text{x}\text{I}{}_{\mathrm{r}}\text{=I}{}_{\mathrm{c}}{}^{\mathrm{a}}$ for ξ=, $\text{I}{}_{\mathrm{l}}\text{=(}\text{1}\text{α}\text{)}\text{log}\text{[(}\text{1}\text{n}\text{) ∑ eα·(x?x}{}_{\mathrm{i}}\text{)]}$ and $\text{I}{}_{\mathrm{l}}{}^{\mathrm{r}}\text{=}\text{I}{}_{\mathrm{l}}\text{x}$. Lower indices c, r, l respectively stand for “centrist,” “rightist,” and “leftist” measures of inequality. I_r and I_l are invariant under respectively equiproportional variation in, or equal addition to, all incomes; measures which have the first of these two properties are said to be “intensive.”We now consider different and more general measures, and other properties. We first reconcile the last two properties by dropping the “indepencence” one (Section VI.). Then, we analyze another mildly equalitarian property, the “principle of diminishing transfers” (Section VII). Section VIII turns to the relations between inequality measures and Lorenz and concentration curves. We then consider the effect on inequality of additions of incomes, and we analyze the properties of “diminishing equality” (Section IX). The effect of unions of populations is the topic of Section X. Finally, the last section (XI) presents the more general relations between the various structural properties of inequality measures.¹     

Some results on “an income fluctuation problem”

A consumer at each period, given the income available, y, has to decide how much to consume and save. If he consumes c ? 0 units he gets u(c) units of satisfaction or utility, and if x = y ? c ? 0 is the amount saved then the available income in the next period is rx + ω^k, where ω^k is a random variable, and r is an interest factor that is assumed to be known with certainty. Infinite time horizon problems are considered, and it is shown that if 0 < δr < 1, where 0 < δ < 1 is a discount factor, then the limiting policy is optimal. Questions about the behavior of the stock level, such as boundness, are considered, and an example is given that shows that the stock level might converge almost surely to infinity. Finally an economic explanation is given.