Measuring Subjective Valuation and Demand For Government Services

Eli M. Noam, Columbia University
ABSTRACT - The paper describes a method by which demand equations for public seeds and services can be estimated. A model is described which is based on the revealed preferences in voting behavior by different groups, taking in particular account of abstentions and their frequency. The results permit the derivation of the absolute valuation for governmental services by different income groups.
[ to cite ]:
Eli M. Noam (1981) ,"Measuring Subjective Valuation and Demand For Government Services", in NA - Advances in Consumer Research Volume 08, eds. Kent B. Monroe, Ann Abor, MI : Association for Consumer Research, Pages: 534-539.

Advances in Consumer Research Volume 8, 1981      Pages 534-539


Eli M. Noam, Columbia University


The paper describes a method by which demand equations for public seeds and services can be estimated. A model is described which is based on the revealed preferences in voting behavior by different groups, taking in particular account of abstentions and their frequency. The results permit the derivation of the absolute valuation for governmental services by different income groups.


The problems of estimating demand functions in private markets, vexing as they are, still pale in comparison with those encountered in the Public sector. Here we have no markets, no customers, no sales, no products, and usually no data. We have to deal with "public goods" that are fuzzy conceptually, indeterminate distributionally, and measurable indirectly. At the same time it is important for decision makers in the public sector to have some sense of the demand for the many alternative public services because of the huge governmental outlays. Some sense of the demand for competing public services would be most helpful. This is not necessarily a matter of trial and error; mistakes in determining demand functions for public seeds are not self-correcting. With private goods, sooner or later a wrong demand function will come home to roost, provided that some decisions are based on them. With public goods, however, a government can go on for a long time supplying hospital beds and canals that no one wants in particular except for some small vocal groups.

Because the knowledge of public demand functions could be of considerable help in the allocation of the huge governmental budgets, a number of attempts to determine them have been made by researchers in the past. A first method of analysis is an opinion survey or controlled experiment (Bohm 1972). The difficulty with this approach, besides its cost, is that no real concept of cost exists in peoples' minds when it comes to large public expenditures. Sometimes, too, a survey is subject to manipulation by the subjects, since there is little to stop then from vastly exaggerating their politically oriented likes and dislikes. In order to avoid this problem, some authors have developed an entire theory of the type of questions that removes the incentive for manipulation (Green and Laffont 1976), or proposed methods to assign cost shares to the individual (Tideman and Tullock 1976). These methods are remarkably ingenious but probably too complex for use in practice.

A third approach is to take a look at the real world and to assume that its reality is an expression of public desires (Borcherding and Deacon 1972, Bergstrom and Goodman 1973). Thus one can compare expenditures in different jurisdictions and analyses and their relation to community characteristics such as income, education and tax rates. If affluent towns spend twice as much as poor ones on law enforcement, we have information about the relative preferences with respect to income. The question remains, however, whether the underlying assumption that political decision making accurately expresses public demand is reliable. Small bands of bureaucrats, insiders, and notables can obtain decisions according to their own preferences rather than of those of the public at large. In a society with free election contests and easy mobility such possible divergence will probably be bridged over time. The literature on log-rolling and election-posturing (Buchanan and Tullock 1972) explain the public choice mechanism by which public preferences become policy decisions, while the so--called Tibout hypothesis (1956) of locational mobility (voting with one's feet) provides a public finance mechanism.

A fourth approach looks at decisions on the individual level, namely by voting. Concretely, this means in the case of public good issues the use of results from referenda. The advantages here are, first the realism of data: they reveal preference in concrete expenditure matters, and typically after the voter has been subject to a fair amount of information about both sides of the issue at hand. Neither is there usually a reason to suspect that voters would disguise their true preferences for some strategic purpose, recognizing these advantages, several studies of referenda on public finance issues were undertaken. They fall into two broad categories, of which the first is an essentially empirical use of correlation studies of aggregate approval rates (Wilson and Banfield 1965, Frey and Kohn 1970, Birdsall 1965), and the second more theoretical, such as Deacon and Shapiro's study (1975) with a sophisticated model as an underpinning, but with application to only two referendum issues.

In these studies an important problem remains unresolved: voting results indicate the direction of public preference, but they do not necessarily reflect its intensity. [Deacon and Shapiro (1975) use "Utility" to overcome this problem, but only as an intermediate theoretical construct.] An issue may be mildly preferred or passionately desired by the same percentage of people; this will nor be obvious from the voting results.

This paper describes a method to overcome such problems by deriving a model by which measures of preference for public goods can be obtained. There, preference measures can be analyzed for factors that influence them, and demand functions can then be found.


The key element of the model is its recognition of a previously completely ignored source of information from voting data, namely the rate of abstention. It is obvious that the active voting in favor or in opposition to a proposal reflects some preferences; but so does non-voting. Implicit in non-voting by a large group of people who vote on other occasions is an indication that the issue is of limited importance to them. This is particularly true with voters who are frequently called to the polls and where, therefore, the consumption aspect of voting--the exercise of the franchise--becomes secondary. In such a situation, voters are more selective in their voting; they go to the polls when the issue is subjectively important to them, and do not when they perceive the issue to be of only minor significance. It is important to contrast this analysis of differential behavior of the same group of voters over elections with those studies that compare voting behavior of different voting jurisdictions within the same election.

It may be argued that another reason for abstention exists, namely that the outcome of a vote is so predictable that an individual's vote hardly matters anymore, thus reducing participation (Frohlich et al. 1978). Empirically, however, this claim turns out to be untrue, at least for the jurisdiction which was analyzed. In the course of this study an analysis of the participation rates in hundreds of referenda showed practically no correlation (.081) with the closeness of the vote. Maybe the reason is that in local voting normally no sophisticated polls are taken that predict the outcomes of the voting with a reasonable degree of accuracy; or perhaps because it requires some stake in the outcome to mount a drive in order to "get the vote out", so that such attempt will succeed only in important votes.

Thus we make two assumptions about voting behavior, denoting the perceived benefit with B and defining a voting "threshold" S such that a voter acts according to the following rules:

(A) Vote Yes if B > S

(B) Vote No if B < -S

(C) Abstain from voting in -S < B < S

Let us postulate next that the voter is a member of a subgroup of the total population, of which we assume that

(D) Their perceived benefits are normally distributed around some mean m and with some variance s. [Normal distribution is a common assumption in much of the public choice of literature on spatial electoral analysis. See, e.g., Hinich and Ordeshook (1970) and Hinich, Ledyard and Ordeshook (1972).]

(E) They follow decisions rules (A) - (C)

These assumptions are represented by Figure 1. The abscissa represents the magnitude of benefits, both positive and negative, around point 0. The units are as yet undefined. The vertical axis represents the frequency distribution of these benefits in the subgroup. Points to the right of 0 reflect positive benefits, and points to the right of S represent "yes" voting. Similarly, at points left of -S "no" voting occurs, while people whose potential benefits lie between -S and S abstain. The abstainers' proportion of total voting population is the area A, and Y and N represent yes and no voting proportions.


The objective for analyses is to determine the mean benefit for the group. Formally, this amounts to determining the unknown mean m of a normal distribution whose variance s is also unknown, but where we know the areas Y, N, and A to exist, respectively, right of S, left of -S, and between S and -S. This can be expressed as the probabilities.

P {B<-S} = N   (1)

P {B<S} = N + A   (2)

These equations can be standardized into:

EQUATION    (3)  and   (4)

Let ZX be the cumulative distribution function of the standardized normal distribution, and therefore

EQUATION   (5)  and   (6)

Thus, the variance s can be expressed, after substitutions, as


and the mean m, using (5) and (7), is found to be


This means that m can be readily calculated as a multiple of S once the proportions of N and A are known and once their cumulative Z values are obtained from tables of normal distribution.

This procedure can be repeated for any number of subgroups i, resulting in a series of mean benefits mi which can be analyzed for chair susceptibility to factors of demography, economics, etc. For most of such estimations the actual magnitude of the voting threshold S is immaterial, as long as we assume that it is constant for all subgroups. But this assumption can be relaxed, and S can instead be estimated by reversing the above procedure. Let there be observed voting behavior for certain issues, where the mean benefit m of the normally distributed random variable B is known from some outside information as well as the proportions Y, N, and A. Then, from equations (5) and (6) we have


which substituted into (5) results in

EQUATION    (10)

Thus Si can be determined if Ni, Ai, and mi are known for subgroup t. Of course, for most issues mi will be unknown. To deal with this situation, it is assumed that

(E) An individual's voting threshold S is constant in the short and medium term.

This assumption implies that a rational voter remains rational and that his decision calculus as to whether it is worthwhile to vote is stable, at least over a few years. The reasonableness of this assumption will receive support in the empirical part of the paper. Hence, if S can be determined in several issues, and provided that the results are reasonably similar to each other, the average S will be used for other issues as well.

The variables that are investigated for their influence on the attitude toward government services are income and other demographic factors such as education, number of children, age, occupational category, etc. Let this be expressed by the equation [A linear function does not seem likely in light of some of the high incomes observed.]:



Y/Y = relative income as a measure for socio-economic status

C = tax cost to the individual

Xi = other demographic factors

and d, l, hi = elasticities.

A special problem in the analysis of public goods is that under almost all tax systems their cost to the individual varies with his income. To the individual the tax price depends both on the total cost of the public good, V, and on his relative share of the tax burden, T/R, where T is his tax payment and R is total revenue. The tax price is therefore


Normally, tax contributions are an increasing function of income, either through taxation of income, property, or consumption such that

T = eYy   (13)

Substituting into equation (12) we then have

EQUATION    (12')

Substituting this in turn into the earlier equation (11)

EQUATION    (11')

l and i can be estimated exogenously by

t = eYy  (13)

and an expression for the cost-elasticity

m = rCl   (14)

which is subject to independent estimation. If i and l are obtained exogenously, equation (11') simplifies into


where the parameters a and b are shorthand for

EQUATION    (15)

b is the "raw" or observed income elasticity. It has been corrected in the way described for changes in the tax price in order to yield the "true" income elasticity, which takes into account that as income rises the tax price also increases. d = b - il, i.e., the "real" income elasticity d is equal to the observed "raw" income elasticity minus the product of price elasticity and the elasticity of the tax system.


The data analysis utilized voting results from Switzerland, a country with an unusual degree of direct participation by the electorate. Among Swiss jurisdictions, Basel-Stadt is the smallest urban canton(state) [The use of Basel was inspired by Frey and Kohn (1970).]; it was chosen in order to reduce the effect of geographic location on voting behavior. Basel is a highly developed middle-sized city with a long civic tradition and an international location, and the preference of electorate should be illustrative.

The main method of estimation involves a cross-section analysis across relatively homogenous polling districts, where the relative income and the demographic characteristics of the district are the independent variables and the intensity of preference that is found through the model is the dependent variable.

Voting results for referenda by polling place are available in the official gazette. [Kantonsblatt, Basel-Stadt, on days following the referenda.] Demographic information is found in the Swiss national census; specifically analyzed, in addition to income, were education, number of dependent children, age, and occupation (self-employed vs. employees). The source of income data is a market re search survey. [PROGNOS, Konsumpotential and Filialnetz, Untersuchung nber die Investitionsplanung des ACV, includes the distribution of household income of 1965 in districts. Tables made available by L. Kohn.] Cost data for the public goods were found, quite laboriously, in the resolutions by the cantonal government to the electorate (Ratschlaege) which precede voting. [Collected at the Cantonal Chancery and the Cantonal Archives.] The active electorate--i.e., the electorate excluding habitual non-voters against which percentages of Y, N, and A are calculated--is defined as the highest number of participants that voted in a referendum concerning cantonal matters. [Respectively in each decade, maximum participation rates are for referenda held on 12/11/49; 12/5/54; 2/28/65; 10/20/74.] In order to avoid a systematic bias, one must ascertain that the average voting participation of the active electorate is not different for different income groups. An analysis of this question determined that the defined L did not display bias; average participations by the active electorate in the nearly two hundred issues that are investigated in this paper are nearly identical: for the lowest income district, 55.6%; for the median income district, 56.5%; and for the highest income district, 56.2%. This active electorate's participation rate must be distinguished from average general voting participation rate, in which low income groups display the usual lower rates.

To estimate the threshold value Si, the procedure described earlier in equation (10) is used and issues are chosen for which the mean benefits can be estimated independently. The referendum issues that are used are votes on public utility charges and ration, [Referenda held 12/11/49; 1/19/50; 11/24/68; 7/12/75; 6/12/77.] for which the financial consequences are known or are officially forecast in the above mentioned Ratschlaege or resolutions; we use these as mi in order to determine Si. Table 1 shows an example for such calculation. The resultant Si are all relatively similar to each other, with values in a band 23-34 Sfr. Very similar results were also found for the other voting precincts. Thus we find support for our assumption of a constant S. The average value (28 Sfr. or approximately $20) is therefore assumed as the voting threshold. As mentioned before, a different magnitude of S would not change the elasticities.



Also calculated from statutory tables of income tax is the progressivity of the tax rate [Kanton Basel-Stadt, Steuertafeln, 1977.] with respect to income as T = eYi = .0000036 Y1.98. This progressivity is assumed to apply in general to the cantonal tax system, there being no sales or consumption tax and only a moderate property tax.

To find the cost elasticities l, time series for benefits are estimated in the following way. From the multitude of referenda, those voting issues were selected that were over the years repetitive or similar to each other so as to make comparison possible over time. For example, there are several referenda about the public support to the municipal theater. Similarly, public expenditures for roads, for administrative buildings, and for schools are a frequent subject of voting. We chose therefore seven categories of public goods and services for which a number of similar referenda are available and run time series of the form (14) over the median income precinct, with different cost figures as variable. The results are listed in Table 2. The cost elasticities are found to have the negative sign which one would expect. The magnitude of the coefficients is small and fairly similar for each category. It is interesting to note that preferences are less elastic for upper class issues such as law enforcement and culture, and more elastic for lower class categories such as social programs. For the latter the cost-sensitivity is larger.

The results for the cross-section analysis of equation (12) are listed in Table 3. Nearly all of the coefficients of "true" income elasticity are statistically significant, and are reported. The other variables, however, do not show any consistent significance. Thus the most important variables are reported, while the others were omitted and the regression re-calculated. The results follow.





Turning first to the income elasticities, we can observe that most are of a good size and either statistically significant or nearly so. Positive income elasticities are found for law enforcer (prosecution, prison), for education and culture, foreign aid, and highways. Negative elasticities exist for mass transit and redistributive social programs such as unemployment compensation, welfare subsidies and public hospitals. None of the other demographic factors shows consistent statistical importance; age is significant for road and -mass transportation (younger people prefer highways, hospitals and old age homes), however the coefficients are fairly small. Self-employment occupation contributes to the negative attitudes towards welfare and unemployment compensation. The number of children affects the preference for mass transit, unemployment compensation, sports facilities, and education (in favor of all). Finally, education affects the preferences for support of an art museum as well as of education itself.

Because all the coefficients are fairly small, we find that relative income explains the predominant part of the preferences for public goods and services.

It is also interesting to estimate and compare preferences in absolute terns. One way to interpret the meaning of such preference values is to think of them as the maximum payment the individual would be willing to make to have the public good. Another interpretation is to think of the individual as being indifferent between having the public good, or having the stated sum of money. A larger sum would be preferable to the public good. Thus the value can also be seen as a schedule of "bribes" to have a voter change his mind if he thinks that his vote makes the difference. The income of the highest and of the lowest 20 percent of the population are substituted into the equations, and other variables are kept at median values. The results are shown in Table 4. As can be seen, the



high-income individuals have a strong absolute valuation for education and law. enforcement expenditures; their preferences for roads, and the art museum is positive but moderate in size. For social programs their preference is normally negative, but not strongly so. It does not equal the strong positive demand by the low income group for these expenditures. For low income people, not surprisingly, the user important issues involve services from which they benefit: public hospitals, old age homes, unemployment compensation and welfare support. Nearly all other public goods are demanded positively--which is not irrational considering their low cost to poor people--but not very intensely.


This paper describes a method to derive measures of the demand for public goods. It uses the results of referenda and incorporates variations in non-voting into a model and calculates both the elasticities of the preference intensities with respect to income and other demographic variables, and finds absolute measures of preference. The model itself is a useful extension of the analysis of voting outcomes to demand function for public goods. The empirical results are specific to a Swiss jurisdiction; similar studies should be undertaken for other countries, and this is a next step for research.


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