Director's Law of Public Income

The University of ChicagoThe Booth School of Business of the University of ChicagoThe University of Chicago Law School

Director's Law of Public Income RedistributionAuthor(s): George J. StiglerSource: Journal of Law and Economics, Vol. 13, No. 1 (Apr., 1970), pp. 1-10Published by: The University of Chicago Press for The Booth School of Business of the University ofChicago and The University of Chicago Law SchoolStable URL: http://www.jstor.org/stable/724835 .

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DIRECTOR'S LAW OF PUBLIC INCOME REDISTRIBUTION

GEORGE J. STIGLER

University of Chicago

ALMOST a decade ago Aaron Director proposed a law of public expenditures: Public expenditures are made for the primary benefit of the middle classes, and financed with taxes which are borne in considerable part by the poor and rich. The law was empirical, and the present essay seeks not only to present and illustrate the law (which its inventor refuses to do) but to offer an explanation for it.

The philosophy of Director's law is as follows. Government has coercive power, which allows it to engage in acts (above all, the taking of resources) which could not be performed by voluntary agreement of the members of a society. Any portion of the society which can secure control of the state's machinery will employ the machinery to improve its own position. Under a set of conditions to be discussed below, this dominant group will be the middle income classes.

I. DIRECTOR'S LAW ILLUSTRATED

A reasonably rigorous demonstration that the state redistributed income in favor of the middle income classes would require vast empirical studies of the distribution of public revenues, non-revenue burdens, and benefits, by income class. We are content here to defend the plausibility of Director's Law.

The distribution of incomes of parents of students in California institutions of higher education is highly skewed toward larger incomes (see Table 1). California is a relatively wealthy state so somewhat lower incomes would be received by parents in other states, but no defensible adjustments of the data would qualify the assertion that the colleges of America are populated by the children of the middle and upper classes. The rough estimates of the distribution of state and local taxation by income classes are persuasive: public provision of higher education redistributes income from the poorer to the higher income classes.

The same redistributive effect, one may conjecture, was achieved in equal degree by the public provision of high school education thirty years ago, and

1



2 THE JOURNAL OF LAW AND ECONOMICS

TABLE 1 DISTRIBUTION OF PARENTS OF STUDENTS IN CALIFORNIA COLLEGES AND UNIVERSITIES

BY INCOME, 1964, AND RELATED DATA

1964 Percentage of Parents 1965 State 1961 Share

1964 and Local of Total University Percentage Taxes as State

State of of all U.S. Per cent and Local Income Class Colleges California Families of Income Taxes Paid

Under $4,000 4 5 26 11 17 $ 4,000-$ 8,000 27 19 38 10 46 $ 8,000-$14,000 48 38 27 9 27 $14,000 and over 21 39 9 8 9

Sources: Parents income: J. Edward Sanders and Hans C. Palmer, The Financial Barrier to Higher Education In California; A Study Prepared for the California State Scholarship Commission (1965). Family income: U.S. Bureau of the Census, Statistical Abstract of the United States, Table 472, at 324 (1968) [approximate]. Taxes as Per cent of Income and Share of Total Taxes: Tax Burdens & Benefits of Gov. Expenditures by Income Class, 1961 and 1965, Tables 7, B-9 (Tax Foundation, 1967) [approximate].

even today the parents of high school graduates are primarily in middle and upper income classes. In the nineteenth century the same analysis would apply to elementary public schools; the graduates of elementary schools in 1900 were probably largely from middle income class families.

The main beneficiaries of several other traditional governmental functions appears to be much the same. Fire and police activities, for example, are clearly middle-income oriented to the extent that they protect property, and it would be interesting to investigate the extent to which such activities are provided more liberally in middle than in lower income areas of cities. But the major examples of the use of the state by the middle classes lie elsewhere:

1. Farm policy. The basic method of assisting farmers has been to raise prices by restricting output, and the restriction of output has been based upon the use of land. The beneficiaries of the policy have therefore been the farm land owners, not the poorer farm laborers and tenants. The burden of the system has been placed upon the consumers of farm products-a regressive excise tax, in effect-as well as on the public treasury. The redistribution of income has therefore much exceeded direct governmental expenditures.'

2. Minimum wage laws. The main beneficiaries of minimum wage legislation have been two types of workers. The first is the higher paid Northern worker (in textiles, for example) who received some measure of protection from the Southern, low-wage branch of the industry. The second class of beneficiaries has been the better-paid workers, for whom the lower-paid workers are an

1 See John E. Floyd, The Effects of Farm Price Supports on the Returns to Land and Labor in Agriculture, 73 J. of Pol. Econ. 148 (1965).



DIRECTOR'S LAW OF PUBLIC INCOME REDISTRIBUTION 3

important substitute. The income redistribution, which is not part of the public budget, is financed by the workers who are displaced by the minimum wage statute and the consumers who purchase the products of low-wage industries.

3. Social security. The social security system taxes most heavily, relative to the benefits they will receive,

i. Those who begin work early, as compared with those who continue in school.

ii. Those who die early, as compared with those who live longer. iii. Those families in which the wife works, relative to those in which she

does not. iv. Those who were young, as compared to those who were old, when first

covered by the law.

All of these effects are in favor of the middle classes. There are other effects which run in favor of lower income classes (for example, benefits are a lower fraction of average wages as wages rise), but it is quite possible that the system on balance redistributes income to the middle classes.2

4. Public housing. The public housing program has had for its primary pur- poses the reduction in the density of population and improvement in the quality of structure, with the implicit rise in housing costs offset to some extent by public subsidies. Even when the new housing is made available to those displaced, many of the displaced cannot be rehoused in the area, and of course the more attractive housing attracts the competition of those who are better off. The public housing has therefore at a minimum injured many of the poor, and in good measure benefited the non-poor.3

5. Tax exempt institutions. One form of subsidy is tax exemption, and if we examine the classes of institutions which were given tax exemption, we find that they were primarily those which served the middle classes. Churches are the largest of the tax exempt institutions, but educational and medical institutions are equally directed to the middle classes.

6. Welfare expenditures. Public charitable expenditures in the nineteenth century could be viewed as the transfer to the state of burdens otherwise necessarily borne by the well-to-do. The great modern programs presumably involve net transfers to the poor and are therefore apparently contradictory to Director's Law. We shall return to this category of state expenditures.

2 This argument implicitly assumes that workers bear the tax; if consumers bear a portion, the conclusion is even more likely.

3 See Martin Anderson, The Federal Bulldozer, A Critical Analysis of Urban Renewal, 1949-1962 (1964).




There remains that enormously expensive social activity, war. Have the middle classes been the special beneficiaries of war? Possibly some wars, such as the American Revolution, could be viewed as levying a highly progressive tax on the wealthy loyalists. Modern wars, however, are not easily viewed as profitable to any income class (although by devices such as conscription the middle classes reduce the costs to them). Simply to put aside a large subject which should not be dismissed simply as pathological, wars will be adduced neither as support nor counter-evidence on Director's Law.

II. THE BASES FOR VOTER COALITIONS

A majority coalition of voters may be formed upon any of a variety of bases: religion, nationality, region, industry, or income, to mention only a few historically important bases. If the coalition of voters is to make effective use of the political machinery of the state to redistribute income, it must find a state activity (expenditure) whose benefits flow to the coalition in greater proportion than the taxes which will finance the activity.

In the nineteenth century there were relatively few available tax bases or functions (expenditure categories) which were closely related to income. The federal governmental revenues (the Civil War period aside) were either custom duties or excises upon liquor and tobacco, and of course the burden of commodity taxes is only loosely related to income. The overwhelming pre- ponderance of state and local governmental revenues came from the general property tax, which again bore only a loose relationship to income. (The tax on land, indeed, would be capitalized and have no necessary relationship to even property incomes at later times.) In the nineteenth century, in sum- mary, only unconcealable assets (real property) and commodities which passed through bottlenecks (a port, or large production processes) and were inelastic with respect to taxes were feasible objects of taxation.4

4 The elasticity of supply with respect to taxes is determined by both demand and supply elasticities. Let f(q) be the demand price and h(q) the supply price, so before tax f(qo) = h(qo). After a unit tax of t, the equilibrium is given by

f(qo + Aq) + t = h(qo +Aq), and expanding in a Taylor series,

Aq =

h'(qo) - f'(qo)

and the elasticity of output with respect to the tax is

Aq t 1

q p 1 1

where is the elasticity of supply and the elasticity of demand. where e is the elasticity of supply and q the elasticity of demand.




If the state is to be used to redistribute income, the activities itt under- takes are also limited. Normally it will not be possible to give any commodity (or sell it at subsidized prices) to a particular class, unless the allotments of the commodities to individuals can be effectively rationed, because the members of this class will simply resell the commodity to other classes. Redistribu- tion is a form of discrimination, and is subject to the usual limitation that the classes discriminated against not be able to deal with the classes who are favored. Services are generally non-transferable, and on reflection it is a remarkable fact that the state has almost never supplied anything but services."

In the nineteenth century there were relatively few services which the state could supply only to favored income groups. The protective functions (the courts and police functions, in particular) and a measure of trans- portation and educational services were of special value to the upper income classes, but as with taxes the relationship to income was not close.

With both expenditures and taxes largely unrelated to income in the nineteenth century, we are not surprised that relatively little use was made of the state as an instrument of income redistribution. One may conjecture that other bases of classes (regional, urban v. rural) entered largely into the de- termination of public activities.

Increasingly in the twentieth century income has become a more important basis of political classes. Income taxes and an almost unlimited variety of excise taxes gradually became feasible, that is collectible at tolerable costs. A modern state is by no means unrestricted in its ability to assign tax liabilities to various income classes-in fact even the ability of families to divide income among members is an important restriction. Nevertheless changes in economic organization (for example, employment by large organizations rather than self-employment) and in the recording of economic information have greatly increased the power and flexibility of taxation.

There has been a corresponding enlargement of the eligible expenditure programs. Services have increased generally as a part of modern living- education and health services are examples. Direct transfer payments have also become practicable, although many such payments are still unrelated to income (for example, the subsidies to sugar and farm products).

As income has become a widely usable basis for tax and expenditure

5When a commodity producing industry seeks governmental benefits, it generally prefers output or entry restriction because the benefits of direct subsidies are likely to be dissipated by competition of firms in the industry. Hence the opposition of farm groups to the Brennan plan: the supply of poor farmers is more elastic than the supply of farm land.




programs, we conjecture that both the extent of governmental activities and their income redistribution effects grow.

III. NOTES ON A THEORY

Let us henceforth assume that income is the strategic basis for the forma- tion of voting coalitions. The actual income distribution of a society may be

presented as a conventional frequency distribution, which is shown in Figure I. In each income interval there is also a given number of possible voters

(adults). The number of possible voters increases with income: low income families are often single persons, and high income families will also contain more grown children and dependents. If every adult were to vote, we would have a distribution of voters by income of the type (labelled "100 per cent

Vote") illustrated in Figure I.

Per cent of Total 30 - --Income 27- 24- / 21 / 18 --Actual Vote

15- --100% Vote

12 9-

6 -

income 1 2 3 4 5 6 7 8 9 10 Recipients (Deciles)

FIGURE I Source: U.S. Bureau of the Census, Statistical Abstract of the United States, Income,

1966 in Table 472, at 324 (1968).

The actual number of votes cast will differ from the maximum possible votes for two reasons. The first is that the dominant coalition can impose a a variety of restrictions upon voters which decreases the voter participation of other income classes. In particular, upper income classes increase their




share of votes if they impose literacy requirements, poll taxes, and residence requirements (which affect most the more migratory persons). Registration requirements have recently been shown to have a substantial influence upon the fraction of eligible voters who actually vote." The second reason for differential voting is that individuals outside the majority coalition will receive smaller benefits from voting. The distribution of actual voters will be skewed to the right; it is labelled "Actual Vote" in Figure I.

When only excises and real property were feasible bases of taxation, the distribution of tax revenues by income class would be relatively regressive,- perhaps similar to the tax revenue curve displayed in Figure II. The distribution benefits of eligible expenditures (education, justice) might be that shown in the same figure; other potential public functions would be excluded because they put a larger tax than benefit upon the majority coalition of voters. The net redistribution of income by income class would be obtained by sub- tracting the tax distribution from the expenditure distribution (assuming budget balancing). There would be as many possible income redistribution curves as there were possible combinations of tax and expenditure programs.

Each income class would of course prefer that income redistribution which benefited it the most, and if a single income redistribution met this require- ment for 51 per cent of the voters, it would be chosen. As a rule, however, different fiscal programs would be preferred by different income classes, and then the program to be chosen must represent a compromise. The program displayed in Figure II would be chosen only if the area under the votes curve to the right of A contained a majority, and if no alternative program offered more to some majority.

At the present time both taxes and expenditures can be much more closely assigned to particular income classes. Suppose now that taxes could be made strictly proportional to income, and expenditures consisted of uniform family subsidies. Then the difference between the income curve and a uniform curve (1/10 of subsidies received by each income decile) would represent the gains or losses to an income class from recourse to the political machinery.

Under these restrictive conditions-proportional taxation and uniform subsidies-the gain to any decile income class from a K per cent tax would be readily calculated:

1. Let its pre-tax income be (siN), where N is national income. 2. The tax upon it would be KsiN.

6 See Stanley Kelley, Jr., Richard E. Ayers, & William G. Bowen, Registration and Voting: Putting Things First, 61 Amer. Pol. Sci. Rev. 359 (1967).




Per cent of Total

Expenditures

Votes

Tax Revenue

Income Redistribution

o A Income Recipients

FIGURE II

3. The uniform income class subsidy would be one-tenth of the total tax receipts, or KN/10.

4. Hence the subsidy to the class would exceed its tax if

KN > KsiN 10

or 1

10

Hence all income deciles with less than one-tenth of income would gain. If they contained a majority of the votes, they would vote for redistribution, and if they had less than a majority, the government would not engage in redistributive activities. Since the gain to an income decile from redistribution is

KN - - ssi< 10 10)




it rises with the tax rate until K = 1. Absolute leveling of income would have

self-defeating disincentive effects upon the rich, so that rate of taxation would be imposed which maximized the present value of a perpetual stream of

redistributions, taking account of the effects of taxes upon the supply of

large incomes. A variant of this scheme is analyzed in the mathematical notes to this paper.

The fiscal machinery of government is not limited to such simple policies as proportional taxation and uniform subsidies. Tax systems may be made

regressive in certain regions and progressive in others, not only by income tax rate schedules but by deductions (costs of owned homes) and by excises on suitably chosen commodities. Expenditures, as we have seen, can be con- centrated on certain income classes by subsidizing goods and services which

primarily these income classes consume. The increase in the flexibility of taxes and expenditure programs works

toward a larger role for government, and toward programs which redistribute income increasingly toward lower income classes. As the amount that can be collected from upper income classes increases, and the amount that can be

given directly to the lower income classes increases, the potential rewards from redistribution rise for the lower income classes. In the long run the middle classes may have been beneficiaries of this process because they were in coalition with the rich in the nineteenth century, and are entering into coalition with the poor today.

MATHEMATICAL NOTES

1. Let families be ranked over the interval (0,1) by income. At any point x on the interval,

v(x) is the number of votes of family x

y(x) is the income of family x.

The votes in the successful coalition are given by

Ve = -j1 v(x)dx> 1/2, (1)

where Vt is the total number of votes. Let us consider a case in which taxes are levied at a uniform rate t on families outside the coalition, and the receipts distributed only to members of the majority coalition. The tax receipts will be

T= t o y (x)dx + yf(x)dx . (2)

Suppose we add a small increment of wealthier families to the coalition: they will possess

v(xI) (Ax)u votes.




Correspondingly we must subtract an equal number of votes from the lower incomes to maintain a minimum majority:

v(x0) (Ax)L such that

v (x1) ((Ax)u = v(xo) (Ax)L. (3) This reconstitution of the coalition will reduce aggregate taxes (and hence benefits for the members of the coalition) if

t {y(x1) (Ax)u - y(xo) (Ax)L} < 0, or, using equation 3, if

v(xl) y(xi) (Ax)u -- y(xo) (Axu) < 0 y (xo)

or

v(xo) v(x1) (4)

Y(xo) y(xl)

v(x) But is a decreasing function of x for all x, so (4) holds for all x. Hence the success-

y(x)

ful coalition is that for which xo = 0, and x1 is given by (1). This conclusion ignores the question of marginal incentives, to which we turn. 2. The system of uniform taxation of the non-members of the coalition founders on the problem of marginal incentive, that is, the families with income above x1 have after tax incomes of (1 - t) y(x), x > x1, and this may be less than x1. If one exempted y(xl), the tax would become t'[y(x) - y(xl)], where t' is the new rate. The reconstitution of the coalition by adding (Ax)u and deleting (Ax)L must be such that the limits set by disin- centives be taken into account.



Director's Law of Public Income

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