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Public welfare and state-local government finance
0038~121/79/0801_0205/S02
Sono-Econ Plan Sci. Vol 13. pp 205412 0 Pergamon Press Ltd. 1979 Prmfed m Great Bntam
00/O
PUBLIC WELFARE AND STATE-LOCAL GOVERNMENT FINANCE FRED C. WHITE Department of Agricultural Economics, 301 Conner Hall, University of Georgia, Athens, GA 30602,U.S.A. (Received 17 January 1979) Abstract-Many state and local governments in the United States have experienced major financial problems during the economic recessions of the 1970s.These problems can be attributed to (1) the instability associated with the present tax structure, resulting from the increasing importance of unstable taxes and (2) the rapid increase in welfare expenditures which can be categorized as uncontrollable. In financing public services including welfare, state and local governments can organize their tax structures so as to dampen the effect of business cycles. This paper develops concepts and methodology to be used in identifying efficient tax structures.
INTRODUCTION
growing major expenditure categories in federal, state and local governments in the United States. These expenditures have more than doubled in the last five years in each of these budgets ([1], pp. 20-27). The reasons for this increase during the last decade are twofold: (1) poverty according to official definitions has increased, and (2) the American transfer system has grown enormously ([2], pp. 179-180). Compared with ten years ago, a larger percentage of people live in families whose earnings and other nontransfer income are unable to lift them above the poverty line. Broader coverage of the poor in welfare programs and expanded benefits has reduced official post-transfer poverty. Whether or not the current system of transfers will be modified by a new comprehensive welfare reform, it appears that the cost of welfare programs will continue to rise. The fact that welfare expenditures are accounting for an ever increasing share of federal, state and local budgets has important implications for public finance, particularly cyclical controllability of expenditures. Weidenbaum identified public welfare expenditures as an important component of uncontrollable expenditures at the federal level ([3], p. 361). As authorized and administered, public welfare is also uncontrollable at the state and local levels. More importantly for cyclical controllability public welfare expenditures are countercyclical: when economic conditions reduce revenue, the demand for welfare would be expected to increase. The Federal government has the major responsibility for financing public welfare. Federal outlays account for total welfare two-thirds of approximately expenditures [ 11. Consequently, most of the public finance literature concerning the finance of public welfare has concentrated on the Federal government.” While the Federal government is the dominant provider of public welfare, state and local expenditures for public assistance increased from $2.7 billion in 1%5 to $12.5 billion in 1975. Rising welfare expenditures at the state-local level create special financing problems that differ from those Public
welfare
is one of the fastest
“Typically, the literature on public welfare financing has recommended the Federal government assume full financial responsibility for the welfare function. For example, see Ref.[4].
at the federal level. State and local governments are not concerned with stabilization policies. Stabilization is a national objective which state and local governments are unequipped to handle primarily because of debt limitations. The use of debt is limited for state and local governments because of their lack of money creation authority; statutory limitations in many cases; and credit rating and access to markets which may also be cyclical. The overall objective of this paper is to explore the financing of public welfare by state and local governments. More specifically, the paper will address these two questions: What impact does the rise in welfare expenditures have on the vulnerability of state and local governments to recessions? How can state and local governments best finance the rise in welfare expenditures? RELATEDTHEORY
Numerous attempts have been made to establish guides for tax policies. Adam Smith in the famous “canons of taxation” made perhaps the greatest contribution to this theme. As a result of these efforts, several criteria have been developed and are widely used to appraise the quality of a tax system. First, there are several criteria concerning the fiscal budget directly that are quite evident to state governments. These criteria include the level and stability of revenue, as well as such factors as ease of administration and low cost of administration and compliance. The second broad category of criteria which can be applied in judging tax systems is concerned with adjustments in the allocations of resources and adjustments in the distribution of income and wealth. The following discussion will elaborate on these concepts. Perhaps one of the most important criteria to be used as a guide for tax policies is the adequacy criterion ([5], p. 104). Adequacy of tax revenue involves stability of revenue in periods of recession but also growth in revenue to finance increases in government goods and services demanded by an increasing society. These two goals are clearly in conflict as the growth criterion requires that tax revenues be responsive to changes in income, while the stability criterion requires that they be unresponsive to an economic slowdown which is also measured by changes in income. Public finance literature first described a stable tax
205
206
F. C. WHITE
system for state and local governments as one that would sustain a given volume and quality of governmental services throughout the various phases of a business cycle (163,pp. 87-88). However, this approach failed to account for the importance of growth in tax revenue to finance the increases in public services that have occurred. More recently, fiscal instability has been viewed as fluctuation in budgetary cash flows in response to the business cycle ([7], p. 2). Fiscal problems, from this viewpoint, are characterized as cash surpluses during economic booms and cash deficits during recessions. These cyclical fluct~tions in fiscal conditions could conceptually result either from cyclical behavior of a single major budgetary component or several of themtax revenues, intergovernmental transfers, expenditures, debt or stabilization reserves. Long-run and short-run income elasticities have been used to quantify growth and stability, respectively@]. Corporate and individual income taxes are generally classified as having high long-run and short-run income elasticities, general sales as having medium income elasticities, and excise and property taxes as having low income elasticities[S, 6,8]. As income taxes account for a larger proportion of total tax revenues and property taxes account for a smaller proportion, aggregate state and local taxes experience more rapid growth but are also more susceptible to short-run economic fluctuations. The revenue-expenditure process of government has broad social and economic effects, often beyond the immediate objective of satisfying public wants ([9], p. 17). These policies also affect economic efficiency through a vast array of individu~ choices-between work and leisure, consumption and saving, one kind of consumption good or financial asset and another ([lo], pp. 179-237). Tax and expenditure programs which are used to promote economic objectives may not distribute tax burdens fairly, according to either ability-to-pay or benefits-received principles. The general theoretical framework for incidence analysis is focused on how the burdens of different taxes are distributed vertically, according to family income. Tax incidence, as distinguished from tax impact, is the point where the final burden of the tax tests. If part of the tax burden ultimately rests at a point other than where it initially fell, tax shifting has occurred. This shifting takes place through the interaction of supply and demand ([ill, pp. 402-427). Adjustments in the distribution of income, resulting from changes in tax and expenditure policies, can be measured by examining tax burdens among income groups. Empirical estimates of tax burdens among income groups should take tax incidence and not just tax impact into account. Tax shifting and incidence are usually measured in a partial equilibria sense in terms of changes in selling prices for economic goods and purchase prices for resources. A higher selling price for economic goods indicates forward shifting of the tax to the consumer, while a lower price for a factor of production indicates that the tax burden has been shifted backwards to the owners of the factors of production. Tax incidence analysis ~iti~ly makes a distinction in household income according to its source and use. Then tax burdens can be estimated according to whether the tax is shifted forward, shifted backwards or borne directly by the person paying the tax with no tax shifting. Opinions on the incidence of the corporation income tax
range from complete shifting to shareholders, on the one extreme, to forward shifting to consumers on the other. The true corporate tax incidence pattern probably contains a mixture with tax burdens on owners of capital and on consumers. Sales and use taxes are generally considered to be shifted forward to consumers. The personal income tax is borne primarily by those persons paying the tax with little shifting to other income groups. Families with different levels of income derive their income, in general, from different sources. For example, wages and salaries represent a larger proportion of total income for low income earners, while business and property income is relatively more important for high income earners. A tax on wages and salaries would, therefore, be more regressive than one on business and property income. On the uses-of-income side of household budgets, taxes that fall on consumers are generally regressive. Aithou~ concepts of vertical equity, stability and growth provide an intuitive basis for choosing between two taxes, a systematic approach is required to analyze a complete tax structure. By varying the level of individual taxes, it is possible to develop a large number of tax structures, and each tax structure will have associated with it a specific level of equity, tax instability, and expected growth rate. This set of possible tax structures can be termed the attainable set. However, from the potential set of all possible tax structures that can be constructed, we are most interested in those tax structures that define the efficient frontier. For a given growth rate, an efficient tax structure provides the highest levef of equity for any degree of tax instability, or the lowest possible degree of tax instability for any level of equity. Any possible tax structures that are not on the frontier are inefficient, because for any level of equity these tax structures provide less stability than those tax structures on the efficient frontier. Public welfare expenditures are hypothesized to have an effect on the efficient frontier. These expenditures, which ~uctuate with the business cycle, increase during recessions when aggregate tax revenues decline. Therefore, the level of overall fiscal instability would be expected to increase with an increase in public welfare expenditures. It may be possible, however, for state and local governments to diversify away some of this instability through the proper selection of taxes to be used to finance public welfare expenditures. OPERATIONAL MODEL
To define an efficient tax structure, there are several concepts that must be defined in such a manner that they can be quantitatively measured. Such concepts for equity, instability, and growth are discussed in this section. Then a model is developed to integrate these concepts so that efficient tax structures can be identified. Progressivity and regressivity Income has been used predominantly as an indicator of taxpaying ability. A tax is said to be progressive if the amount of taxes paid as a percentage of income increases as income increases or regressive if the amount of taxes paid as a percentage of income decreases as income increases. The degree of progressivity (or regressivity) can, therefore, be measured by the slope of the-_.curve depicting tax liability as a percent of income or _ _. AIXJAJ. Since the slope of this curve can vary with the
Public welfare and state-local government finance
amount of revenue generated,b the curves are standardized so that each tax would generate one million dollars in tax revenue. A further complication arises as an individual tax may be more regressive or progressive over some income ranges than others. An overall measure of regressiveaess or progressiveness can be calculated as the weighted average slope of this curve over all income categories, where the weights are determined by the number of taxpayers in each category. The weighted average unit index of tax neutrality (9) for a particular point in time is given as: c--l
q=C
,=I
ATL Wj* I
where TL is average tax liability per thousand dollars of income, Z is average personal income in thousand dollars, c is the number of income classes, j is the income class (for example, j = 1 when the income class is under three thousand dollars), and W, is the weight based on the number of taxpayers in classes j and j + 1. If the value of the unit index for a particular tax is negative, then the tax is regressive. If the value is positive the tax is progressive. Having calculated the unit index for each tax, the overall index of tax neutrality (TV) for a particular tax structure is given by:
where TT is the index of tax neutrality for the total tax structure, 7, is the unit index of tax neutrality for the ith tax, and R, is the level of revenue generated by the ith tax. The sign of qT indicates whether the overall tax structure is progressive or regressive. Fiscal instability
Several approaches could be used in analyzing budgetary instability. The first approach might be to concentrate on tax instability. Governments may be interested in the possibility of actual revenues being less than their targets. This would suggest that revenue deviations below the target should be treated differently than those above. In the portfolio literature this has been handled by using semi-variance measures that ignore deviations above target levels[l2]. Similarly, tax instability could be introduced in a policy-making model as a safety-first rule. With this rule, selection of tax structures would depend on the security of generating a specified level of revenue in order to finance selected expenditure programs. A major shortcoming of such approaches in dealing with fiscal instability is that expenditures, as well as revenues may fluctuate with the business cycles. For example, public welfare, which is an increasingly important component of state and local government finance, is countercyclical. The approach used to measure fiscal instability in this analysis is an extension of the concept of portfolio selection as first reported by Harry Markowitz ([13], pp. 77-91) and further expanded by Markowitz[l2]. This approach, as described below, accounts for instability in revenues and expenditures. bAn increase in the tax rate would result in a proportionate increase in the slope of the curve depicting tax liability as a percent of income.
207
Instability associated with the cash flow of a particular revenue or expenditure category can be measured by the standard deviation. Similarly to the index of tax neutrality, the standard deviation is calculated on a per unit basis-the standard deviation per million dollars of revenue or expenditure. This concept of instability applies only to a single budgetary category and must be extended to measure fiscal instability for a budget that includes several revenue and expenditure categories. When financing a specified combination of expenditure programs, it may be possible to diversify away fiscal instability through the selection of a combination of taxes that will generate a given level of revenue and minimize the level of instability. The concept of diversification relates to the correlation that exists between budgetary cash flows. If two taxes are positively correlated, the movement in the level of revenue generated by these taxes would correspond throughout the business cycle. If the two taxes were negatively correlated, then an increase in the revenue from one tax would occur while revenue from the other tax would show a decrease. To diversify away instability, the tax structure would have to contain taxes that were not perfectly correlated, i.e. the movement in tax revenue would not be in exactly the same direction and proportion. The concept of diversification can be extended to expenditures, which also exhibit instability. For example, welfare expenditures are highest during recessions when tax revenues are lowest. Therefore, appropriate diversification measures for a particular government will be dependent on the level and instability of its expenditure programs, as well as its tax structure. To determine fiscal instability for an entire budget including several revenue and expenditure categories, we need to know the unit standard deviation for each cash flow. Expenditures, which represent a cash outtlow rather than a cash inflow, can be considered as a negative revenue. The overall measure of fiscal instability can be expressed as:
where uTz is the overall variance of budgetary cash flows, R, is the level of cash flow from the ith budgetary category (revenue or expenditure), pi) is the correlation coefficient between the ith and jth budgetary categories (expenditures are considered negative revenues when calculating p coefficients), ui is the unit standard deviation for the ith budgetary category, and n is the number of budgetary categories. Growth rate The measure of overall growth for a particular tax
structure is defined as a weighted average of growth rates for each individual tax considered.
where yT is the projected overall growth rate, RT is total tax revenue, ‘yi is the projected growth rate for the ith tax, R, is revenue generated from the ith tax, and n is the number of tax categories.
208
F. c.
The growth rate for the ith tax (7,) is weighted according to RJR=, the percent of total revenue generated by the ith tax. If the tax structure contains several taxes, the overall growth rate is a weighted average of the growth rates of the individual taxes. Therefore, given the growth rates of the individual taxes, the overall growth rate of the tax structure depends upon the amount of revenue produced by each tax. An integrated model The tax neutrality, fiscal instability, and growth concepts discussed above are integrated in this section to provide a systematic approach for analyzing a complete fiscal structure. By varying the level of individual taxes, it is possible to develop a large number of tax structures, and each tax structure will have associated with it a specific level of tax neutrality, instability, and expected growth rate. The set of possible tax structures can be termed the attainable set. Those tax structures with an overall index of neutrality greater than zero are considered progressive, while those with negative values are regressive. However, from the potential set of all possible tax structures that can be constructed, we are most interested in those tax structures that define the efficient frontier. For a given growth rate, an efficient tax structure provides the lowest possible degree of tax instability for any level of tax neutrality. Any possible tax structures that are not on the frontier are inefficient, because for any level of neutrality these tax structures provide less stability than those tax structures on the efficient frontier. Quadratic programming is used to develop the set of feasible tax structures having the property that variance UT*is minimum for associated level of tax neutrality VT.’ The quadratic programming model can be defined as follows: (9 such that
2 “%= A (A= 0 to
&?I=& R
-1
Rrzy~
T
R* I UZ+.(for all k, k = 1 to m) R,rLL~(foralli,i=ltom)
(9) (10)
where R, is the level of cash flow from the itb budgetary category (revenue or expenditure), ‘yi is the expected annual growth rate of the ith tax, ai is the standard deviation of the ith budgetary cash flow, pij is the correlation between the ith and jth cash flow, UL. is the upper limit on the kth tax, LL is the lower limit on the kth tax or expenditure, n is the number of budgetary cash flows, and A is a scalar. The summation term in eqn (5) is the variance and the ‘The quadraticprogrammingmodeldevelopedin this paper is an adaptationof the standardquadraticportfolioselection model developedby Freund([14], pp. 253-263).
summation term in eqn (6) is the aggregate index of tax neutrality. Parameterizing A produces a sequence of solutions of increasing tax progressivity (or declining tax regressivity) and increasing fiscal instability. The final solution in this sequence represents the maximum level of tax progressivity that can be achieved with the specified constraints. Solutions are obtained for critical turning points, such that for the current overall index of neutrality qT, determined by A, the variance a,’ is minimum. These solutions are sufficient to determine the efficient frontier. EMF’UUCAL RESULTS
Concepts and methodology developed in this paper are illustrated with budgeting data for the Georgia state government. Major own sources of revenue for the state government of Georgia, in order of importance, are taxes on sales, personal income, motor fuel, corporation income, alcoholic beverages, tobacco and motor vehicles. Measurement of growth and instability A major distinction between growth and instability in tax revenue is that growth is a long run phenomenon while instability refers to short run behavior ([8], p. 268). The reason for this distinction is that most state and local government expenditures are budgeted through the legislative process several months before actual revenues are known. Policymakers usually base expenditure decisions on “typical” growth patterns in tax revenue. Therefore, state and local government finance is based on predictable and steady growth over time. Instability in tax revenue can be measured by the degree to which actual revenue diEers from predicted revenue. It is possible to quantitatively measure both of these concepts from a single regression equatibn. Such an equation would be formulated to measure growth in tax revenue (and public welfare expenditures) over time. An important factor to take into consideration in this formulation is that tax rates and rate structures also affect tax revenue. The growth path is determined from the following eqn: lnRlt=a+bt+crit
Unfunded)
and
c“2_
WHITE
(11)
where R1, is revenue from the ith tax in year t, t is the time variable indicating year, rrtis the tax rate for the ith tax, and a, b and c are regression coefficients, The annual growth rate is simply (Rir-Rlt-l)/I&--l, and instability ui is calculated from the deviations between actual and predicted revenue. A similar equation was estimated for public welfare expenditures and used to estimate fiscal instability associated with these expenditures. For the regression analysis, tax revenue and welfare expenditure data for the period 1952-73 were obtained from U.S. Bureau of the Census, Governmental finances [15] and Census of governments [16]. Tax rates were obtained from Georgia Department of Revenue, Annual statistical report[l7]. The State government on several occasions changed the tax rate on motor fuel and tobacco. In addition, there was a major structural change in several taxes beginning in 1956. To represent this change, a dummy variable, with a value of 1 for 1952-55 and zero otherwise, was included where appropriate. An examination of the raw data indicated a structural shift in the rate of growth after VW. Consequently, a slope dummy variable, which was equal to zero for the
Public welfare and state-local government finance period 195244 and equal to the variable TIME for the period 1%5-73, was statistically tested in each regression equation. However, in one equation the Student r-value
209
individual tax and the overall growth rate for the combined taxes. The projected growth rates from these equations were used rather than actual growth rates to abstract from the effects of short-run fluctuations in aggregate economic activity, which are accounted for in the measures of variability. Also, projected growth rates would be more useful for planning purposes. Personal income and corporation income taxes have the highest growth rates among the seven major taxes (Table 2) and, also, the only growth rates above 10% annually. Growth rates on tobacco, alcoholic beverages,
on this variable was so small that the variable was deleted. The results of these regressions are shown in Table 1. In general, the results were quite satisfactory as indicated by the large Student r-values on each individual coefficient and large F-values for the entire equation. The regression equations of trends in tax revenue in Table 1 were used to estimate growth rates for each
Table l., Regression equations used to adjust tax revenues for time trends and tax rate changes” Dependent Variable in Natural Lags
Time
Il-hIU!pt
0.0596
Time If Year > 64
4.4339 (123.9862)**
(13.1279)**
0.0127 (3.9750)**
Motor Fuel
2.3197 (12.8243)**
0.0460 (12.0989)**
0.0060 (2.8974)**
Alcoholic Beverages
2.5174 (28.5509)**
0.0583 (6.1526)**
0.0196 (3.6323)**
Tobacco
1.7671 (16.0197)**
0.0847 (11.4945)**
-0.0138 (-2.1516)*
Motor Vehicle
2.3355 (74.6707)**
0.0617 (18.3512)**
0.0031 (1.6376)*
Personal Income
2.2857 (36.9924)**
0.1467 (31.1804)**
corporation
2.4429 (32.9441)**
0.0840 (8.9262)**
0.0186 (2.8108)*
3.9666 (114.5337)**
0.0573 (13.1239)**
0.1364 (15.5707)**
Sales
Public Welfare
Tax Rare
0.2598 (8.9601)**
_Y Shift Variable
RZ
F
651.2001
0.9856
-0 233&l (-6:2103)**
873.1319
0.9952
(-3:8366)** -0 301&/
380.2145
0.9845
322.8096
0.9818
(-20:3275)** -0 5657k' 2778.0484
0.9978
972.2190
0.9798
306.4175
0.9699
0.0808 (3.1201)**
(-14:5683)** -2 075&l
afStudeat t-values ate given in parentheses. a/ The dummy shift variable for taxes had a value of one for 1952-1955 end zero otherwise. cl The d-y wise.
shift variable for public welfare expenditures had a value of one for 1965-1973 and zero other-
*Indicates a significance level of 0.10. **Indicates a significance level of 0.01.
Table 2. Empirical estimates of growth, instability and equity in tax revenue Taxes
Motor
vehicle
Unit Index ofa, Tax Neutrallty-
Unit covariance with Public Welfare
Growth R&G' (Percent)
-0.0081
6.68
0.000771
0.000133
Tobacco
-0.0198
7.35
0.007091
-0.001005
Alcoholic beverages
-0.0104
8.10
0.006151
0.000754
Sales
-0.0156
7.50
0.003577
-0.000133
0.0027
15.80
0.020148
0.002086
Corporation
-0.0067
10.81
0.015132
0.002459
Motor fuel
-0.0130
5.34
0.000853
-0.000040
Personal income
Public welfare
0.003022
a/Index of Equity per million dollars of tax. aiannual increase in tax revenue projected from trend regression equations. C'Variance and covariance per million dollars of tax revenue.
210
F. C. WHITE
and sales taxes range from 7.35 to 8.10%. Motor vehicle and motor fuel taxes are the two slowest growing taxes. The overall growth rate for 1976 is 9.62%. The variability in cash flows (taxes and welfare expenditures) were calculated from deviations in trend lines presented in Table 1. The measure of variability used in the quadratic programming model is unit variance, which is the variance per million dollars of tax revenue. The unit variances for the major taxes and welfare expenditures are presented in Table 2. Perhaps the easiest way to interpret one of these figures is to take its square root or standard deviation and convert it to a percent by multiplying by 100. This calculation yields the coefficient of variation. For example, the tobacco tax has a coefficient of variation of 8.42%. A comparison of unit variances indicates the relative variability among the taxes. Ranking the taxes according to unit variances reveals that motor vehicle, motor fuel, and sales taxes are the three most stable taxes.d Personal income and corporation income taxes are the most unstable taxes. As indicated earlier in this paper, covariance terms between each two taxes and between each tax and welfare expenditure are also important in determining the overall instability of the fiscal system. Since this paper is evaluating the role of public welfare expenditures in public finance, all of the welfare-tax covariance terms are presented in Table 2. The largest welfare covariance terms are with personal and corporation income taxes, which means that when the cash inflow from these taxes declines the cash outflow for welfare increases. Of particular interest, the welfare-sales tax covariance term is negative, indicating that if sales taxes were used to finance public welfare expenditures fiscal instability could be reduced through the diversification principle. Measurement
of tax neutrality
To determine tax burden, individual taxes had to be allocated among income categories.’ Data used to allocate taxes among income groups were obtained from three sources: U.S. Bureau of the Census, Census of population[19]; U.S. Department of Labor, Suruey of consumer expenditures 1201; and Georgia Department of Revenue, Statistical reports [17]. It was assumed that the same relative distribution of expenditures from the Survey of consumer expenditures 1201 would hold for Georgia. Consequently, it was the relative distribution and not the absolute level of these expenditures that was used in the present study. In general, the amount of taxes paid was positively related to family income. Personal income taxes ranged from $7 for families with less than $3ooOin income to $1482 for families with more than $25,000 in income. Sales taxes were $115 in the lowest income category and $554 in the highest income category. Average tax payments for the total of all seven taxes were eleven times greater in the highest income category than in the lowest income category-$2668 compared to $227. However, average income in the upper category was almost 30 times greater than income in the lowest category. The level of taxes paid was converted to taxes paid per thousand dollars of income as a measure of tax burden.
dStabiity is measuredby the size.of the unit variance. The most stable tax has the smallest unit variance. ‘Proceduresused to allocate taxes are similar to those used in Tax Foundationll81. - _
For six of the seven taxes the highest tax burden occurs in the lowest income category and the lowest tax burden occurs in the highest income category. This inverse relationship between tax burden and income indicates that these taxes are regressive. Only the personal income tax shows a positive relationship between tax burden and income. Although the tax structure appears to be regressive, calculating the index of tax neutrality for each tax will quantify the extent to which the tax structure is regressive. Empirical estimates of the unit index of tax neutrality, which indicate the regressiveness or progressiveness of generating one million dollars in revenue from a particular tax, are presented in Table 2. Ranking the seven major taxes from most progressive to most regressive reveals that the personal income tax and the corporation income tax are the two most progressive taxes. The sales tax and tobacco tax are the most regressive taxes. In summary, the taxes which are the fastest growingpersonal income and corporation income taxes-are the most progressive. However, these taxes are also the most unstable and, unfortunately for public welfare financing purposes, show the slowest growth during the recessions when welfare expenditures are increasing rapidly. Other taxes, such as the sales tax, are more stable and appear to be better sources to finance public welfare based on the covariance terms. However, these taxes are relatively inequitable and slow growing. All of these characteristics must be taken into consideration in a systematic manner to choose the appropriate tax structure. Programming
results
Efficient tax structures-minimum fiscal instability for any level of neutrality-were generated for the Georgia state government from the seven major taxes. In defining an efficient tax structure, any tax could be varied between 2 100% of its 1976level. Although the principle of vertical equity is considered in this analysis, no level of neutrality is predetermined as being most desirable. The results are presented in a manner so that policymakers could make a choice from among tax structures with various neutrality and stability characteristics, realizing the instability is minimum for any level of neutrality. Also, tax efficiency-the effect of taxes on such factors as resource allocation and business investment-is not considered directly, but the limits on individual taxes are imposed so that excess burdens beyond the current situation would be limited. This section reports on quadratic programming results which trace the trade-off in neutrality and stability. The model was restricted to generate the total 1976 level of tax revenue ($1586.46 million) and to achieve the 1976 overall growth rate in tax revenue (9.6%). The distribution of revenue by tax for that year is shown as the first row in Table 3. For the actual tax structure, the index of tax neutrality was - 15.02 and the standard deviation of tax revenue was $84 million. These figures are used for comparison with the various programming results. In comparison to the actual situation, the first solution in Table 3 is slightly less regressive and more stable than the actual situation. This solution would collect more taxes on motor vehicles, tobacco, alcoholic beverages, and corporation income and less taxes on sales, personal income, and motor fuel. In subsequent solutions, the tax structures were less regressive but the standard deviation
Public welfareand state-localgovernmentfinance
211
Table 3. Programming
Motor
Alcoholic PersO"& Vehicle Tobacco BeveraSes Sales Income
ay,te&
Neutrality Standard Index Variance Deviation
a
~llare)__-_______-___-______
---_____--__-_____--___~~ll~~”
1976
motor Corporation Fuel
Level
40
73
75
Sol"tio" 1
81
147
135
Sol"tio" 2
a1
147
151
Solutio" 3
81
147
Solutio" 4
81
80
Sol"tio" 5
81
62
Solution 6
81
0
413
133
233
-15.02
431
361
238
193
-0.00 -14.82
244
396
238
330
-225.62 -13.75
151
223
401
256
347
-252.30 -13.63
6447.96
80.30
151
130
423
265
466
-357.24 -12.46
6802.41
82.48
151
143
419
265
466
-451.40 -12.39
6836.54
82.68
151
206
418
265
466
-876.84 -12.14
6996.03
83.64
619
7057.32
84.01
6297.96
79.36
6418.16
80.11
Solutio" 7
81
0
151
0
624
265
466
-1344.58
-8.37
11219.32
105.92
Solution a
81
0
119
0
656
265
466
-1745.66
-7.96
11924.43
109.20
Solution 9
81
0
151
0
77.1
265
318
-2043.79
-6.06
15517.82
124.57
Solution 10
81
0
151
0
826
265
264
-2182.19
-5.20
17343.60
131.70
"ProSrammi"S restrictions include (a) attainment of the 1976 overall growth rate in taxes, (b) attainment of total tax revenue equal to the actual 1976 level, and (c) limit on individual taxes to 2100% of actual 1976 levels. b'Variability of the tax system concerns only the seven major taxes included in this table.
Table 4. Proarammirraresults of a 1976state budgetarymodel with revenue and expenditure variabilitp Motor Public Motor Alcoholic PWXKJ"al Welfare Vehicle Tobacco Beverages Sales Income Corporation Fuel
A
Fiscal Systek' Standard Neutralitv Index . Variance Deviation
_-_______-____-_______---(Million Dollars)--_____----------__------------1976 revel
40
73
75
619
413
133
233
645
-15.02
9015.24
94.95
Sol"tio" 1
a1
147
119
493
367
212
168
Sol"tio" 2
81
147
144
190
423
211
391
645
-0.00 -15.11
8333.13
91.29
645
-367.74 -13.37
8652.45
93.02
Sol"tio" 3
81
103
150
128
437
222
466
645
-435.75 -12.61
8957.47
94.64
Solution 4
81
22
151
183
418
Solution 5
81
5
151
200
418
265
466
645
-816.52 -12.23
9206.59
95.95
265
466
645
-978.87 -12.16
9267.54
96.27
Solution 6
81
0
151
196
Solution 7
81
0
151
0
428
265
466
645
-998.17 -11.96
9465.87
97.29
624
265
466
645
-1422.81
-8.38 13806.08 117.50
Solution a
81
0
113
0
662
265
466
645
-1831.01
-7.88 14682.88 121.17
Solution 9
81
0
Solution 10
81
0
97
0
678
265
466
645
-1883.19
-7.67 15071.87 122.77
151
0
826
265
264
645
-2320.16
-5.20 20207.92 142.15
~'ProSramminS restrictions include (a) attainment of the 1976 overall growth rate in taxes, (b) attainment of total tax revenue equal to the actual 1976 level, (c) limit on individual taxes to +100X of actual 1976 levelS, and (d) provision of public welfare at the 1976 level. a/ Variability in the fiscal system concerns the seven major taxes included I" this table and public welfare expenditures.
of tax revenue increased, indicating more tax instability. Several general trends can be noted in these solutions. The sales tax, which is the largest tax in the first solution, declines and is finally eliminated in subsequent solutions. The motor fuel tax increases with reduced regressivity through several solutions but then declines. The corporation income tax increases rapidly to its upper limit
(100% increase over its 1976 level). The personal income tax shows a steady increase throughout the solutions, not reaching its upper limit until the final solution. Increases in the two income taxes are primarily responsible for the reduction in regressivity, as well as the increase in tax instability. Only instability in the tax structure has been con-
212
F. C. WHITE
sidered to this point in the quadratic programming model. The next step is to incorporate the instability associated with public welfare expenditures into the programming model. Public welfare expenditures were held constant at their 1976 level and new programming results were generated. These results, which are presented in Table 4, indicate that including instability associated with public welfare increases actual aggregate fiscal instability to over $94 million compared to only $84 million when considering only instability associated with the tax structure. Thus, failure to consider instability from public welfare understates overall instability of the Georgia fiscal system by approximately twelve percent. Including public welfare expenditures in the model results in different tax structures identifying the efficient frontier. This is evident from comparing solutions in Tables 3 and 4. In the first solutions, the sales tax has been increased over $60 million, while taxes on corporation income, personal income and motor fuel have been reduced. This shift in the tax structure can be attributed primarily to the sign on the covariance terms between these taxes and public welfare expenditures; public welfare’s covariances with the sales tax were negative and with personal and corporation income taxes were positive. However, it would be incorrect to assume that at every level of stability more sales tax would be included in the efficient tax structure. As the tax structure becomes less regressive, the sales tax is reduced and eventually eliminated. IMPLICATIONS
Results from this analysis indicate that fiscal instability in state and local governments may be substantial. For the Georgia state government, the standard deviation for the budgetary system (taxes and public welfare expenditures) was $94 million. Based on the normal bellshaped distribution, the State government’s fiscal balance (the difference between revenue and expenditures) would range between -+$94 million of its expected level in two out of every three years. However, the government could experience a deficit as large as two standard deviations or $188 million in one out of twenty years. To put this figure into perspective, Georgia’s General Assembly had to be called into special session in 1975to deal with a projected $50 million deficit. This instability can be attributed to two general factors: (I) increased reliance on fast growing but unstable taxes such as personal income and corporation income taxes and (2) rapidly increasing welfare expenditures. Heavy reliance on income taxes in state and local government finance is advantageous for the process of raising revenue to finance the rapidly growing public service sector. However, these taxes increase the State’s susceptibility to the business cycle. Public welfare expenditures account for approximately twelve percent of Georgia’s measured fiscal instability and also make the State more vulnerable to recessions. Thus the combination of unstable taxes and uncontrollable welfare expenditures may result in severe fiscal problems during recessions. Given the level of public welfare expenditures that the State desires to maintain, it is possible to reduce fiscal instability through the selection of an appropriate tax structure. By considering a complete tax structure, it is
possible to diversify away instability by selecting a combination of taxes that will minimize instability for any level of tax neutrality. The results from this analysis indicate that there are no clear-cut rules of thumb, such as increasing the sales tax, that can be applied to identify efficient tax structures. Instead, it is necessary to develop a complete programming model for each state and local government. Once the efficient frontier is developed, the policymakers can choose the tax structure that is best for the particular governmental unit under consideration.
REFERENCES I
Advisory Commission on Intergovernmental Relations,
Significant Features of Fiscal Federalism 1976 Edition, M106,Washington, D.C. (1976). 2. Robert D. Plotnick and Felicity Skidmore, Progress Against Pooerty, A Reoiew of the 1964-74 Decade, Institute for Research on Poverty, Academic Press, New York (1975). 3. Murray L. Weidenbaum, Budget “uncontrollability” as an obstacle to improving the allocation of government resources. The Analysis and Eualuation of Public Expenditures: The PPB System, Joint Economic Committee, Congress of the United States, 91st Congress, 1st Session, Vol. 1, U.S. Government Printing Office, Washington, D.C. (1%9). 4. Committee for Economic Development, Welfare Reform and Its Financing, New York (1976). 5. Walton T. Wilford, State tax stability criteria and the revenue-income elasticity coefficient reconsidered. Nat. Tax J. XVIII, 304-312 (1%5). 6. Harold M. Groves and C. Harry Kahn, The stability of state and local tax yields. Am. Econ. Rev., 87-102 (1952). 7. Fred C. White and Wesley N. Musser, Financing state and local services in a cyclical economy. Southern J. Agricult Econ. 8, I-10 (1976). 8. William V. Williams, Robert M. Anderson, David 0. FroeNe and Kay L. Lamb, The stability, growth and stabilizing inthrence of state taxes. Nat. Tax J. XXVI, 267-273 (1973). 9. Richard A. Musgrave, The benefit approach. The Theory of Public Finance. McGraw-Hill, New York (1959). 10. George F. Break, The incidence and economic effects of taxation. The Economics of Public Finance. The Brookings Institution, Washington, D.C. (1974). II. Bernard P. Herber, Modem Public Finance, the Study of Public Sector Economics. Irwin, Homewood, Illinois (1971). Selection: Eficient Markowitz, Pot7folio 12. Harry Diversification of Investments. Wiley, New York (1959). 13. Harry Markowitz, Portfolio selection. J. Finance 7, 77-91 (1952).
14. R. I. Freund, The introduction of risk into a programming model. Econometrica 24.253-263 (1956). 15. U.S. Bureau of the Census, Governmental Finances in 197273. U.S. Government Printing Office, Washington, D.C. (1975). 16. U.S. Bureau of the Census, Historical statistics on governmental finances and employment. Census of Gouemments1972. U.S. Government Printing Office, Washington, D.C., April 1975and previous issues. 17. Georgia Department of Revenue, Statistical Rep., Atlanta, Georgia (Annual). 18. Tax Foundation, Inc., Tax Burdens and Benefits of Gonemment Expenditures by Income Class, l%l &d l-%5, New York (1967). 19. U.S. Bureau of the Census, 1970Census of Population. U.S. Government Printing Office, Washington, D.C., March (1972). 20. U.S. Department of Labor, Bureau of Labor Statistics, Survey of Consumer Expenditures 1972-73, Washington, DC. (1975).
Sono-Econ Plan Sci. Vol 13. pp 205412 0 Pergamon Press Ltd. 1979 Prmfed m Great Bntam
00/O
PUBLIC WELFARE AND STATE-LOCAL GOVERNMENT FINANCE FRED C. WHITE Department of Agricultural Economics, 301 Conner Hall, University of Georgia, Athens, GA 30602,U.S.A. (Received 17 January 1979) Abstract-Many state and local governments in the United States have experienced major financial problems during the economic recessions of the 1970s.These problems can be attributed to (1) the instability associated with the present tax structure, resulting from the increasing importance of unstable taxes and (2) the rapid increase in welfare expenditures which can be categorized as uncontrollable. In financing public services including welfare, state and local governments can organize their tax structures so as to dampen the effect of business cycles. This paper develops concepts and methodology to be used in identifying efficient tax structures.
INTRODUCTION
growing major expenditure categories in federal, state and local governments in the United States. These expenditures have more than doubled in the last five years in each of these budgets ([1], pp. 20-27). The reasons for this increase during the last decade are twofold: (1) poverty according to official definitions has increased, and (2) the American transfer system has grown enormously ([2], pp. 179-180). Compared with ten years ago, a larger percentage of people live in families whose earnings and other nontransfer income are unable to lift them above the poverty line. Broader coverage of the poor in welfare programs and expanded benefits has reduced official post-transfer poverty. Whether or not the current system of transfers will be modified by a new comprehensive welfare reform, it appears that the cost of welfare programs will continue to rise. The fact that welfare expenditures are accounting for an ever increasing share of federal, state and local budgets has important implications for public finance, particularly cyclical controllability of expenditures. Weidenbaum identified public welfare expenditures as an important component of uncontrollable expenditures at the federal level ([3], p. 361). As authorized and administered, public welfare is also uncontrollable at the state and local levels. More importantly for cyclical controllability public welfare expenditures are countercyclical: when economic conditions reduce revenue, the demand for welfare would be expected to increase. The Federal government has the major responsibility for financing public welfare. Federal outlays account for total welfare two-thirds of approximately expenditures [ 11. Consequently, most of the public finance literature concerning the finance of public welfare has concentrated on the Federal government.” While the Federal government is the dominant provider of public welfare, state and local expenditures for public assistance increased from $2.7 billion in 1%5 to $12.5 billion in 1975. Rising welfare expenditures at the state-local level create special financing problems that differ from those Public
welfare
is one of the fastest
“Typically, the literature on public welfare financing has recommended the Federal government assume full financial responsibility for the welfare function. For example, see Ref.[4].
at the federal level. State and local governments are not concerned with stabilization policies. Stabilization is a national objective which state and local governments are unequipped to handle primarily because of debt limitations. The use of debt is limited for state and local governments because of their lack of money creation authority; statutory limitations in many cases; and credit rating and access to markets which may also be cyclical. The overall objective of this paper is to explore the financing of public welfare by state and local governments. More specifically, the paper will address these two questions: What impact does the rise in welfare expenditures have on the vulnerability of state and local governments to recessions? How can state and local governments best finance the rise in welfare expenditures? RELATEDTHEORY
Numerous attempts have been made to establish guides for tax policies. Adam Smith in the famous “canons of taxation” made perhaps the greatest contribution to this theme. As a result of these efforts, several criteria have been developed and are widely used to appraise the quality of a tax system. First, there are several criteria concerning the fiscal budget directly that are quite evident to state governments. These criteria include the level and stability of revenue, as well as such factors as ease of administration and low cost of administration and compliance. The second broad category of criteria which can be applied in judging tax systems is concerned with adjustments in the allocations of resources and adjustments in the distribution of income and wealth. The following discussion will elaborate on these concepts. Perhaps one of the most important criteria to be used as a guide for tax policies is the adequacy criterion ([5], p. 104). Adequacy of tax revenue involves stability of revenue in periods of recession but also growth in revenue to finance increases in government goods and services demanded by an increasing society. These two goals are clearly in conflict as the growth criterion requires that tax revenues be responsive to changes in income, while the stability criterion requires that they be unresponsive to an economic slowdown which is also measured by changes in income. Public finance literature first described a stable tax
205
206
F. C. WHITE
system for state and local governments as one that would sustain a given volume and quality of governmental services throughout the various phases of a business cycle (163,pp. 87-88). However, this approach failed to account for the importance of growth in tax revenue to finance the increases in public services that have occurred. More recently, fiscal instability has been viewed as fluctuation in budgetary cash flows in response to the business cycle ([7], p. 2). Fiscal problems, from this viewpoint, are characterized as cash surpluses during economic booms and cash deficits during recessions. These cyclical fluct~tions in fiscal conditions could conceptually result either from cyclical behavior of a single major budgetary component or several of themtax revenues, intergovernmental transfers, expenditures, debt or stabilization reserves. Long-run and short-run income elasticities have been used to quantify growth and stability, respectively@]. Corporate and individual income taxes are generally classified as having high long-run and short-run income elasticities, general sales as having medium income elasticities, and excise and property taxes as having low income elasticities[S, 6,8]. As income taxes account for a larger proportion of total tax revenues and property taxes account for a smaller proportion, aggregate state and local taxes experience more rapid growth but are also more susceptible to short-run economic fluctuations. The revenue-expenditure process of government has broad social and economic effects, often beyond the immediate objective of satisfying public wants ([9], p. 17). These policies also affect economic efficiency through a vast array of individu~ choices-between work and leisure, consumption and saving, one kind of consumption good or financial asset and another ([lo], pp. 179-237). Tax and expenditure programs which are used to promote economic objectives may not distribute tax burdens fairly, according to either ability-to-pay or benefits-received principles. The general theoretical framework for incidence analysis is focused on how the burdens of different taxes are distributed vertically, according to family income. Tax incidence, as distinguished from tax impact, is the point where the final burden of the tax tests. If part of the tax burden ultimately rests at a point other than where it initially fell, tax shifting has occurred. This shifting takes place through the interaction of supply and demand ([ill, pp. 402-427). Adjustments in the distribution of income, resulting from changes in tax and expenditure policies, can be measured by examining tax burdens among income groups. Empirical estimates of tax burdens among income groups should take tax incidence and not just tax impact into account. Tax shifting and incidence are usually measured in a partial equilibria sense in terms of changes in selling prices for economic goods and purchase prices for resources. A higher selling price for economic goods indicates forward shifting of the tax to the consumer, while a lower price for a factor of production indicates that the tax burden has been shifted backwards to the owners of the factors of production. Tax incidence analysis ~iti~ly makes a distinction in household income according to its source and use. Then tax burdens can be estimated according to whether the tax is shifted forward, shifted backwards or borne directly by the person paying the tax with no tax shifting. Opinions on the incidence of the corporation income tax
range from complete shifting to shareholders, on the one extreme, to forward shifting to consumers on the other. The true corporate tax incidence pattern probably contains a mixture with tax burdens on owners of capital and on consumers. Sales and use taxes are generally considered to be shifted forward to consumers. The personal income tax is borne primarily by those persons paying the tax with little shifting to other income groups. Families with different levels of income derive their income, in general, from different sources. For example, wages and salaries represent a larger proportion of total income for low income earners, while business and property income is relatively more important for high income earners. A tax on wages and salaries would, therefore, be more regressive than one on business and property income. On the uses-of-income side of household budgets, taxes that fall on consumers are generally regressive. Aithou~ concepts of vertical equity, stability and growth provide an intuitive basis for choosing between two taxes, a systematic approach is required to analyze a complete tax structure. By varying the level of individual taxes, it is possible to develop a large number of tax structures, and each tax structure will have associated with it a specific level of equity, tax instability, and expected growth rate. This set of possible tax structures can be termed the attainable set. However, from the potential set of all possible tax structures that can be constructed, we are most interested in those tax structures that define the efficient frontier. For a given growth rate, an efficient tax structure provides the highest levef of equity for any degree of tax instability, or the lowest possible degree of tax instability for any level of equity. Any possible tax structures that are not on the frontier are inefficient, because for any level of equity these tax structures provide less stability than those tax structures on the efficient frontier. Public welfare expenditures are hypothesized to have an effect on the efficient frontier. These expenditures, which ~uctuate with the business cycle, increase during recessions when aggregate tax revenues decline. Therefore, the level of overall fiscal instability would be expected to increase with an increase in public welfare expenditures. It may be possible, however, for state and local governments to diversify away some of this instability through the proper selection of taxes to be used to finance public welfare expenditures. OPERATIONAL MODEL
To define an efficient tax structure, there are several concepts that must be defined in such a manner that they can be quantitatively measured. Such concepts for equity, instability, and growth are discussed in this section. Then a model is developed to integrate these concepts so that efficient tax structures can be identified. Progressivity and regressivity Income has been used predominantly as an indicator of taxpaying ability. A tax is said to be progressive if the amount of taxes paid as a percentage of income increases as income increases or regressive if the amount of taxes paid as a percentage of income decreases as income increases. The degree of progressivity (or regressivity) can, therefore, be measured by the slope of the-_.curve depicting tax liability as a percent of income or _ _. AIXJAJ. Since the slope of this curve can vary with the
Public welfare and state-local government finance
amount of revenue generated,b the curves are standardized so that each tax would generate one million dollars in tax revenue. A further complication arises as an individual tax may be more regressive or progressive over some income ranges than others. An overall measure of regressiveaess or progressiveness can be calculated as the weighted average slope of this curve over all income categories, where the weights are determined by the number of taxpayers in each category. The weighted average unit index of tax neutrality (9) for a particular point in time is given as: c--l
q=C
,=I
ATL Wj* I
where TL is average tax liability per thousand dollars of income, Z is average personal income in thousand dollars, c is the number of income classes, j is the income class (for example, j = 1 when the income class is under three thousand dollars), and W, is the weight based on the number of taxpayers in classes j and j + 1. If the value of the unit index for a particular tax is negative, then the tax is regressive. If the value is positive the tax is progressive. Having calculated the unit index for each tax, the overall index of tax neutrality (TV) for a particular tax structure is given by:
where TT is the index of tax neutrality for the total tax structure, 7, is the unit index of tax neutrality for the ith tax, and R, is the level of revenue generated by the ith tax. The sign of qT indicates whether the overall tax structure is progressive or regressive. Fiscal instability
Several approaches could be used in analyzing budgetary instability. The first approach might be to concentrate on tax instability. Governments may be interested in the possibility of actual revenues being less than their targets. This would suggest that revenue deviations below the target should be treated differently than those above. In the portfolio literature this has been handled by using semi-variance measures that ignore deviations above target levels[l2]. Similarly, tax instability could be introduced in a policy-making model as a safety-first rule. With this rule, selection of tax structures would depend on the security of generating a specified level of revenue in order to finance selected expenditure programs. A major shortcoming of such approaches in dealing with fiscal instability is that expenditures, as well as revenues may fluctuate with the business cycles. For example, public welfare, which is an increasingly important component of state and local government finance, is countercyclical. The approach used to measure fiscal instability in this analysis is an extension of the concept of portfolio selection as first reported by Harry Markowitz ([13], pp. 77-91) and further expanded by Markowitz[l2]. This approach, as described below, accounts for instability in revenues and expenditures. bAn increase in the tax rate would result in a proportionate increase in the slope of the curve depicting tax liability as a percent of income.
207
Instability associated with the cash flow of a particular revenue or expenditure category can be measured by the standard deviation. Similarly to the index of tax neutrality, the standard deviation is calculated on a per unit basis-the standard deviation per million dollars of revenue or expenditure. This concept of instability applies only to a single budgetary category and must be extended to measure fiscal instability for a budget that includes several revenue and expenditure categories. When financing a specified combination of expenditure programs, it may be possible to diversify away fiscal instability through the selection of a combination of taxes that will generate a given level of revenue and minimize the level of instability. The concept of diversification relates to the correlation that exists between budgetary cash flows. If two taxes are positively correlated, the movement in the level of revenue generated by these taxes would correspond throughout the business cycle. If the two taxes were negatively correlated, then an increase in the revenue from one tax would occur while revenue from the other tax would show a decrease. To diversify away instability, the tax structure would have to contain taxes that were not perfectly correlated, i.e. the movement in tax revenue would not be in exactly the same direction and proportion. The concept of diversification can be extended to expenditures, which also exhibit instability. For example, welfare expenditures are highest during recessions when tax revenues are lowest. Therefore, appropriate diversification measures for a particular government will be dependent on the level and instability of its expenditure programs, as well as its tax structure. To determine fiscal instability for an entire budget including several revenue and expenditure categories, we need to know the unit standard deviation for each cash flow. Expenditures, which represent a cash outtlow rather than a cash inflow, can be considered as a negative revenue. The overall measure of fiscal instability can be expressed as:
where uTz is the overall variance of budgetary cash flows, R, is the level of cash flow from the ith budgetary category (revenue or expenditure), pi) is the correlation coefficient between the ith and jth budgetary categories (expenditures are considered negative revenues when calculating p coefficients), ui is the unit standard deviation for the ith budgetary category, and n is the number of budgetary categories. Growth rate The measure of overall growth for a particular tax
structure is defined as a weighted average of growth rates for each individual tax considered.
where yT is the projected overall growth rate, RT is total tax revenue, ‘yi is the projected growth rate for the ith tax, R, is revenue generated from the ith tax, and n is the number of tax categories.
208
F. c.
The growth rate for the ith tax (7,) is weighted according to RJR=, the percent of total revenue generated by the ith tax. If the tax structure contains several taxes, the overall growth rate is a weighted average of the growth rates of the individual taxes. Therefore, given the growth rates of the individual taxes, the overall growth rate of the tax structure depends upon the amount of revenue produced by each tax. An integrated model The tax neutrality, fiscal instability, and growth concepts discussed above are integrated in this section to provide a systematic approach for analyzing a complete fiscal structure. By varying the level of individual taxes, it is possible to develop a large number of tax structures, and each tax structure will have associated with it a specific level of tax neutrality, instability, and expected growth rate. The set of possible tax structures can be termed the attainable set. Those tax structures with an overall index of neutrality greater than zero are considered progressive, while those with negative values are regressive. However, from the potential set of all possible tax structures that can be constructed, we are most interested in those tax structures that define the efficient frontier. For a given growth rate, an efficient tax structure provides the lowest possible degree of tax instability for any level of tax neutrality. Any possible tax structures that are not on the frontier are inefficient, because for any level of neutrality these tax structures provide less stability than those tax structures on the efficient frontier. Quadratic programming is used to develop the set of feasible tax structures having the property that variance UT*is minimum for associated level of tax neutrality VT.’ The quadratic programming model can be defined as follows: (9 such that
2 “%= A (A= 0 to
&?I=& R
-1
Rrzy~
T
R* I UZ+.(for all k, k = 1 to m) R,rLL~(foralli,i=ltom)
(9) (10)
where R, is the level of cash flow from the itb budgetary category (revenue or expenditure), ‘yi is the expected annual growth rate of the ith tax, ai is the standard deviation of the ith budgetary cash flow, pij is the correlation between the ith and jth cash flow, UL. is the upper limit on the kth tax, LL is the lower limit on the kth tax or expenditure, n is the number of budgetary cash flows, and A is a scalar. The summation term in eqn (5) is the variance and the ‘The quadraticprogrammingmodeldevelopedin this paper is an adaptationof the standardquadraticportfolioselection model developedby Freund([14], pp. 253-263).
summation term in eqn (6) is the aggregate index of tax neutrality. Parameterizing A produces a sequence of solutions of increasing tax progressivity (or declining tax regressivity) and increasing fiscal instability. The final solution in this sequence represents the maximum level of tax progressivity that can be achieved with the specified constraints. Solutions are obtained for critical turning points, such that for the current overall index of neutrality qT, determined by A, the variance a,’ is minimum. These solutions are sufficient to determine the efficient frontier. EMF’UUCAL RESULTS
Concepts and methodology developed in this paper are illustrated with budgeting data for the Georgia state government. Major own sources of revenue for the state government of Georgia, in order of importance, are taxes on sales, personal income, motor fuel, corporation income, alcoholic beverages, tobacco and motor vehicles. Measurement of growth and instability A major distinction between growth and instability in tax revenue is that growth is a long run phenomenon while instability refers to short run behavior ([8], p. 268). The reason for this distinction is that most state and local government expenditures are budgeted through the legislative process several months before actual revenues are known. Policymakers usually base expenditure decisions on “typical” growth patterns in tax revenue. Therefore, state and local government finance is based on predictable and steady growth over time. Instability in tax revenue can be measured by the degree to which actual revenue diEers from predicted revenue. It is possible to quantitatively measure both of these concepts from a single regression equatibn. Such an equation would be formulated to measure growth in tax revenue (and public welfare expenditures) over time. An important factor to take into consideration in this formulation is that tax rates and rate structures also affect tax revenue. The growth path is determined from the following eqn: lnRlt=a+bt+crit
Unfunded)
and
c“2_
WHITE
(11)
where R1, is revenue from the ith tax in year t, t is the time variable indicating year, rrtis the tax rate for the ith tax, and a, b and c are regression coefficients, The annual growth rate is simply (Rir-Rlt-l)/I&--l, and instability ui is calculated from the deviations between actual and predicted revenue. A similar equation was estimated for public welfare expenditures and used to estimate fiscal instability associated with these expenditures. For the regression analysis, tax revenue and welfare expenditure data for the period 1952-73 were obtained from U.S. Bureau of the Census, Governmental finances [15] and Census of governments [16]. Tax rates were obtained from Georgia Department of Revenue, Annual statistical report[l7]. The State government on several occasions changed the tax rate on motor fuel and tobacco. In addition, there was a major structural change in several taxes beginning in 1956. To represent this change, a dummy variable, with a value of 1 for 1952-55 and zero otherwise, was included where appropriate. An examination of the raw data indicated a structural shift in the rate of growth after VW. Consequently, a slope dummy variable, which was equal to zero for the
Public welfare and state-local government finance period 195244 and equal to the variable TIME for the period 1%5-73, was statistically tested in each regression equation. However, in one equation the Student r-value
209
individual tax and the overall growth rate for the combined taxes. The projected growth rates from these equations were used rather than actual growth rates to abstract from the effects of short-run fluctuations in aggregate economic activity, which are accounted for in the measures of variability. Also, projected growth rates would be more useful for planning purposes. Personal income and corporation income taxes have the highest growth rates among the seven major taxes (Table 2) and, also, the only growth rates above 10% annually. Growth rates on tobacco, alcoholic beverages,
on this variable was so small that the variable was deleted. The results of these regressions are shown in Table 1. In general, the results were quite satisfactory as indicated by the large Student r-values on each individual coefficient and large F-values for the entire equation. The regression equations of trends in tax revenue in Table 1 were used to estimate growth rates for each
Table l., Regression equations used to adjust tax revenues for time trends and tax rate changes” Dependent Variable in Natural Lags
Time
Il-hIU!pt
0.0596
Time If Year > 64
4.4339 (123.9862)**
(13.1279)**
0.0127 (3.9750)**
Motor Fuel
2.3197 (12.8243)**
0.0460 (12.0989)**
0.0060 (2.8974)**
Alcoholic Beverages
2.5174 (28.5509)**
0.0583 (6.1526)**
0.0196 (3.6323)**
Tobacco
1.7671 (16.0197)**
0.0847 (11.4945)**
-0.0138 (-2.1516)*
Motor Vehicle
2.3355 (74.6707)**
0.0617 (18.3512)**
0.0031 (1.6376)*
Personal Income
2.2857 (36.9924)**
0.1467 (31.1804)**
corporation
2.4429 (32.9441)**
0.0840 (8.9262)**
0.0186 (2.8108)*
3.9666 (114.5337)**
0.0573 (13.1239)**
0.1364 (15.5707)**
Sales
Public Welfare
Tax Rare
0.2598 (8.9601)**
_Y Shift Variable
RZ
F
651.2001
0.9856
-0 233&l (-6:2103)**
873.1319
0.9952
(-3:8366)** -0 301&/
380.2145
0.9845
322.8096
0.9818
(-20:3275)** -0 5657k' 2778.0484
0.9978
972.2190
0.9798
306.4175
0.9699
0.0808 (3.1201)**
(-14:5683)** -2 075&l
afStudeat t-values ate given in parentheses. a/ The dummy shift variable for taxes had a value of one for 1952-1955 end zero otherwise. cl The d-y wise.
shift variable for public welfare expenditures had a value of one for 1965-1973 and zero other-
*Indicates a significance level of 0.10. **Indicates a significance level of 0.01.
Table 2. Empirical estimates of growth, instability and equity in tax revenue Taxes
Motor
vehicle
Unit Index ofa, Tax Neutrallty-
Unit covariance with Public Welfare
Growth R&G' (Percent)
-0.0081
6.68
0.000771
0.000133
Tobacco
-0.0198
7.35
0.007091
-0.001005
Alcoholic beverages
-0.0104
8.10
0.006151
0.000754
Sales
-0.0156
7.50
0.003577
-0.000133
0.0027
15.80
0.020148
0.002086
Corporation
-0.0067
10.81
0.015132
0.002459
Motor fuel
-0.0130
5.34
0.000853
-0.000040
Personal income
Public welfare
0.003022
a/Index of Equity per million dollars of tax. aiannual increase in tax revenue projected from trend regression equations. C'Variance and covariance per million dollars of tax revenue.
210
F. C. WHITE
and sales taxes range from 7.35 to 8.10%. Motor vehicle and motor fuel taxes are the two slowest growing taxes. The overall growth rate for 1976 is 9.62%. The variability in cash flows (taxes and welfare expenditures) were calculated from deviations in trend lines presented in Table 1. The measure of variability used in the quadratic programming model is unit variance, which is the variance per million dollars of tax revenue. The unit variances for the major taxes and welfare expenditures are presented in Table 2. Perhaps the easiest way to interpret one of these figures is to take its square root or standard deviation and convert it to a percent by multiplying by 100. This calculation yields the coefficient of variation. For example, the tobacco tax has a coefficient of variation of 8.42%. A comparison of unit variances indicates the relative variability among the taxes. Ranking the taxes according to unit variances reveals that motor vehicle, motor fuel, and sales taxes are the three most stable taxes.d Personal income and corporation income taxes are the most unstable taxes. As indicated earlier in this paper, covariance terms between each two taxes and between each tax and welfare expenditure are also important in determining the overall instability of the fiscal system. Since this paper is evaluating the role of public welfare expenditures in public finance, all of the welfare-tax covariance terms are presented in Table 2. The largest welfare covariance terms are with personal and corporation income taxes, which means that when the cash inflow from these taxes declines the cash outflow for welfare increases. Of particular interest, the welfare-sales tax covariance term is negative, indicating that if sales taxes were used to finance public welfare expenditures fiscal instability could be reduced through the diversification principle. Measurement
of tax neutrality
To determine tax burden, individual taxes had to be allocated among income categories.’ Data used to allocate taxes among income groups were obtained from three sources: U.S. Bureau of the Census, Census of population[19]; U.S. Department of Labor, Suruey of consumer expenditures 1201; and Georgia Department of Revenue, Statistical reports [17]. It was assumed that the same relative distribution of expenditures from the Survey of consumer expenditures 1201 would hold for Georgia. Consequently, it was the relative distribution and not the absolute level of these expenditures that was used in the present study. In general, the amount of taxes paid was positively related to family income. Personal income taxes ranged from $7 for families with less than $3ooOin income to $1482 for families with more than $25,000 in income. Sales taxes were $115 in the lowest income category and $554 in the highest income category. Average tax payments for the total of all seven taxes were eleven times greater in the highest income category than in the lowest income category-$2668 compared to $227. However, average income in the upper category was almost 30 times greater than income in the lowest category. The level of taxes paid was converted to taxes paid per thousand dollars of income as a measure of tax burden.
dStabiity is measuredby the size.of the unit variance. The most stable tax has the smallest unit variance. ‘Proceduresused to allocate taxes are similar to those used in Tax Foundationll81. - _
For six of the seven taxes the highest tax burden occurs in the lowest income category and the lowest tax burden occurs in the highest income category. This inverse relationship between tax burden and income indicates that these taxes are regressive. Only the personal income tax shows a positive relationship between tax burden and income. Although the tax structure appears to be regressive, calculating the index of tax neutrality for each tax will quantify the extent to which the tax structure is regressive. Empirical estimates of the unit index of tax neutrality, which indicate the regressiveness or progressiveness of generating one million dollars in revenue from a particular tax, are presented in Table 2. Ranking the seven major taxes from most progressive to most regressive reveals that the personal income tax and the corporation income tax are the two most progressive taxes. The sales tax and tobacco tax are the most regressive taxes. In summary, the taxes which are the fastest growingpersonal income and corporation income taxes-are the most progressive. However, these taxes are also the most unstable and, unfortunately for public welfare financing purposes, show the slowest growth during the recessions when welfare expenditures are increasing rapidly. Other taxes, such as the sales tax, are more stable and appear to be better sources to finance public welfare based on the covariance terms. However, these taxes are relatively inequitable and slow growing. All of these characteristics must be taken into consideration in a systematic manner to choose the appropriate tax structure. Programming
results
Efficient tax structures-minimum fiscal instability for any level of neutrality-were generated for the Georgia state government from the seven major taxes. In defining an efficient tax structure, any tax could be varied between 2 100% of its 1976level. Although the principle of vertical equity is considered in this analysis, no level of neutrality is predetermined as being most desirable. The results are presented in a manner so that policymakers could make a choice from among tax structures with various neutrality and stability characteristics, realizing the instability is minimum for any level of neutrality. Also, tax efficiency-the effect of taxes on such factors as resource allocation and business investment-is not considered directly, but the limits on individual taxes are imposed so that excess burdens beyond the current situation would be limited. This section reports on quadratic programming results which trace the trade-off in neutrality and stability. The model was restricted to generate the total 1976 level of tax revenue ($1586.46 million) and to achieve the 1976 overall growth rate in tax revenue (9.6%). The distribution of revenue by tax for that year is shown as the first row in Table 3. For the actual tax structure, the index of tax neutrality was - 15.02 and the standard deviation of tax revenue was $84 million. These figures are used for comparison with the various programming results. In comparison to the actual situation, the first solution in Table 3 is slightly less regressive and more stable than the actual situation. This solution would collect more taxes on motor vehicles, tobacco, alcoholic beverages, and corporation income and less taxes on sales, personal income, and motor fuel. In subsequent solutions, the tax structures were less regressive but the standard deviation
Public welfareand state-localgovernmentfinance
211
Table 3. Programming
Motor
Alcoholic PersO"& Vehicle Tobacco BeveraSes Sales Income
ay,te&
Neutrality Standard Index Variance Deviation
a
~llare)__-_______-___-______
---_____--__-_____--___~~ll~~”
1976
motor Corporation Fuel
Level
40
73
75
Sol"tio" 1
81
147
135
Sol"tio" 2
a1
147
151
Solutio" 3
81
147
Solutio" 4
81
80
Sol"tio" 5
81
62
Solution 6
81
0
413
133
233
-15.02
431
361
238
193
-0.00 -14.82
244
396
238
330
-225.62 -13.75
151
223
401
256
347
-252.30 -13.63
6447.96
80.30
151
130
423
265
466
-357.24 -12.46
6802.41
82.48
151
143
419
265
466
-451.40 -12.39
6836.54
82.68
151
206
418
265
466
-876.84 -12.14
6996.03
83.64
619
7057.32
84.01
6297.96
79.36
6418.16
80.11
Solutio" 7
81
0
151
0
624
265
466
-1344.58
-8.37
11219.32
105.92
Solution a
81
0
119
0
656
265
466
-1745.66
-7.96
11924.43
109.20
Solution 9
81
0
151
0
77.1
265
318
-2043.79
-6.06
15517.82
124.57
Solution 10
81
0
151
0
826
265
264
-2182.19
-5.20
17343.60
131.70
"ProSrammi"S restrictions include (a) attainment of the 1976 overall growth rate in taxes, (b) attainment of total tax revenue equal to the actual 1976 level, and (c) limit on individual taxes to 2100% of actual 1976 levels. b'Variability of the tax system concerns only the seven major taxes included in this table.
Table 4. Proarammirraresults of a 1976state budgetarymodel with revenue and expenditure variabilitp Motor Public Motor Alcoholic PWXKJ"al Welfare Vehicle Tobacco Beverages Sales Income Corporation Fuel
A
Fiscal Systek' Standard Neutralitv Index . Variance Deviation
_-_______-____-_______---(Million Dollars)--_____----------__------------1976 revel
40
73
75
619
413
133
233
645
-15.02
9015.24
94.95
Sol"tio" 1
a1
147
119
493
367
212
168
Sol"tio" 2
81
147
144
190
423
211
391
645
-0.00 -15.11
8333.13
91.29
645
-367.74 -13.37
8652.45
93.02
Sol"tio" 3
81
103
150
128
437
222
466
645
-435.75 -12.61
8957.47
94.64
Solution 4
81
22
151
183
418
Solution 5
81
5
151
200
418
265
466
645
-816.52 -12.23
9206.59
95.95
265
466
645
-978.87 -12.16
9267.54
96.27
Solution 6
81
0
151
196
Solution 7
81
0
151
0
428
265
466
645
-998.17 -11.96
9465.87
97.29
624
265
466
645
-1422.81
-8.38 13806.08 117.50
Solution a
81
0
113
0
662
265
466
645
-1831.01
-7.88 14682.88 121.17
Solution 9
81
0
Solution 10
81
0
97
0
678
265
466
645
-1883.19
-7.67 15071.87 122.77
151
0
826
265
264
645
-2320.16
-5.20 20207.92 142.15
~'ProSramminS restrictions include (a) attainment of the 1976 overall growth rate in taxes, (b) attainment of total tax revenue equal to the actual 1976 level, (c) limit on individual taxes to +100X of actual 1976 levelS, and (d) provision of public welfare at the 1976 level. a/ Variability in the fiscal system concerns the seven major taxes included I" this table and public welfare expenditures.
of tax revenue increased, indicating more tax instability. Several general trends can be noted in these solutions. The sales tax, which is the largest tax in the first solution, declines and is finally eliminated in subsequent solutions. The motor fuel tax increases with reduced regressivity through several solutions but then declines. The corporation income tax increases rapidly to its upper limit
(100% increase over its 1976 level). The personal income tax shows a steady increase throughout the solutions, not reaching its upper limit until the final solution. Increases in the two income taxes are primarily responsible for the reduction in regressivity, as well as the increase in tax instability. Only instability in the tax structure has been con-
212
F. C. WHITE
sidered to this point in the quadratic programming model. The next step is to incorporate the instability associated with public welfare expenditures into the programming model. Public welfare expenditures were held constant at their 1976 level and new programming results were generated. These results, which are presented in Table 4, indicate that including instability associated with public welfare increases actual aggregate fiscal instability to over $94 million compared to only $84 million when considering only instability associated with the tax structure. Thus, failure to consider instability from public welfare understates overall instability of the Georgia fiscal system by approximately twelve percent. Including public welfare expenditures in the model results in different tax structures identifying the efficient frontier. This is evident from comparing solutions in Tables 3 and 4. In the first solutions, the sales tax has been increased over $60 million, while taxes on corporation income, personal income and motor fuel have been reduced. This shift in the tax structure can be attributed primarily to the sign on the covariance terms between these taxes and public welfare expenditures; public welfare’s covariances with the sales tax were negative and with personal and corporation income taxes were positive. However, it would be incorrect to assume that at every level of stability more sales tax would be included in the efficient tax structure. As the tax structure becomes less regressive, the sales tax is reduced and eventually eliminated. IMPLICATIONS
Results from this analysis indicate that fiscal instability in state and local governments may be substantial. For the Georgia state government, the standard deviation for the budgetary system (taxes and public welfare expenditures) was $94 million. Based on the normal bellshaped distribution, the State government’s fiscal balance (the difference between revenue and expenditures) would range between -+$94 million of its expected level in two out of every three years. However, the government could experience a deficit as large as two standard deviations or $188 million in one out of twenty years. To put this figure into perspective, Georgia’s General Assembly had to be called into special session in 1975to deal with a projected $50 million deficit. This instability can be attributed to two general factors: (I) increased reliance on fast growing but unstable taxes such as personal income and corporation income taxes and (2) rapidly increasing welfare expenditures. Heavy reliance on income taxes in state and local government finance is advantageous for the process of raising revenue to finance the rapidly growing public service sector. However, these taxes increase the State’s susceptibility to the business cycle. Public welfare expenditures account for approximately twelve percent of Georgia’s measured fiscal instability and also make the State more vulnerable to recessions. Thus the combination of unstable taxes and uncontrollable welfare expenditures may result in severe fiscal problems during recessions. Given the level of public welfare expenditures that the State desires to maintain, it is possible to reduce fiscal instability through the selection of an appropriate tax structure. By considering a complete tax structure, it is
possible to diversify away instability by selecting a combination of taxes that will minimize instability for any level of tax neutrality. The results from this analysis indicate that there are no clear-cut rules of thumb, such as increasing the sales tax, that can be applied to identify efficient tax structures. Instead, it is necessary to develop a complete programming model for each state and local government. Once the efficient frontier is developed, the policymakers can choose the tax structure that is best for the particular governmental unit under consideration.
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Advisory Commission on Intergovernmental Relations,
Significant Features of Fiscal Federalism 1976 Edition, M106,Washington, D.C. (1976). 2. Robert D. Plotnick and Felicity Skidmore, Progress Against Pooerty, A Reoiew of the 1964-74 Decade, Institute for Research on Poverty, Academic Press, New York (1975). 3. Murray L. Weidenbaum, Budget “uncontrollability” as an obstacle to improving the allocation of government resources. The Analysis and Eualuation of Public Expenditures: The PPB System, Joint Economic Committee, Congress of the United States, 91st Congress, 1st Session, Vol. 1, U.S. Government Printing Office, Washington, D.C. (1%9). 4. Committee for Economic Development, Welfare Reform and Its Financing, New York (1976). 5. Walton T. Wilford, State tax stability criteria and the revenue-income elasticity coefficient reconsidered. Nat. Tax J. XVIII, 304-312 (1%5). 6. Harold M. Groves and C. Harry Kahn, The stability of state and local tax yields. Am. Econ. Rev., 87-102 (1952). 7. Fred C. White and Wesley N. Musser, Financing state and local services in a cyclical economy. Southern J. Agricult Econ. 8, I-10 (1976). 8. William V. Williams, Robert M. Anderson, David 0. FroeNe and Kay L. Lamb, The stability, growth and stabilizing inthrence of state taxes. Nat. Tax J. XXVI, 267-273 (1973). 9. Richard A. Musgrave, The benefit approach. The Theory of Public Finance. McGraw-Hill, New York (1959). 10. George F. Break, The incidence and economic effects of taxation. The Economics of Public Finance. The Brookings Institution, Washington, D.C. (1974). II. Bernard P. Herber, Modem Public Finance, the Study of Public Sector Economics. Irwin, Homewood, Illinois (1971). Selection: Eficient Markowitz, Pot7folio 12. Harry Diversification of Investments. Wiley, New York (1959). 13. Harry Markowitz, Portfolio selection. J. Finance 7, 77-91 (1952).
14. R. I. Freund, The introduction of risk into a programming model. Econometrica 24.253-263 (1956). 15. U.S. Bureau of the Census, Governmental Finances in 197273. U.S. Government Printing Office, Washington, D.C. (1975). 16. U.S. Bureau of the Census, Historical statistics on governmental finances and employment. Census of Gouemments1972. U.S. Government Printing Office, Washington, D.C., April 1975and previous issues. 17. Georgia Department of Revenue, Statistical Rep., Atlanta, Georgia (Annual). 18. Tax Foundation, Inc., Tax Burdens and Benefits of Gonemment Expenditures by Income Class, l%l &d l-%5, New York (1967). 19. U.S. Bureau of the Census, 1970Census of Population. U.S. Government Printing Office, Washington, D.C., March (1972). 20. U.S. Department of Labor, Bureau of Labor Statistics, Survey of Consumer Expenditures 1972-73, Washington, DC. (1975).