Municipal welfare functions

Regional Science and Urban Economics 6 (1976) 5:-79. $2~North-Holland

MUNICIPAL WELFARE FUNCTIONS* Bernard M.S. VAN PRAAGt and Joop LINTHORSTD Leyakn University, Leyden, 7+heNetherlands IO this paper the concept of a municipal welfare function is defined. It reflects the evaluation by local authorities of several levels of local expenditures. On the basis of an extensive survey among all Dutch municipal authorities these functions are estimated for abc It 550 Dutch municipalities with respect to total expenditures and differentiated with respect to several portfolios, like public works, education, etc. The variation of the estimated mun,icipnl welfare parameters is explained by objectively measuixble municipal characteristics like the number of the inhabitants, age distribution of inhabitants and houses, number of unemployed, regional situation.

1. Introdoction

The Netherlands consist of about 842 municipalities, the size of which varies a good deal with respect to the number of inhabitants (from 300 to 800,000) and with respect to a.rea per inhabitant. The municipal authorities have a number of responsibilities, e.g., for education, traffic and roads, culturai and sporting facilities, and the allotment of social assistance to persons in need. This implies that the municipalities are big spenders. One-third of public expenditures is spent by municipalities. The own revenue of the municipalities from local taxation is legally restricted to very moderate proportions, while 90 percent of local spending is covered by money allotments by the central government to municipalities out of the state tax revenues. So the question arises how much money should be allotted to local authorities and according to which criteria this amount should be distributed among the municZpalities. It is evident that the criterion of an equal amount per inhabitant woulc! 5e too rough a criterion to do justice to the variation in regional function, the differences in urbanization and so on. We may compare the municipalities with a group of consumers with varying needs and varying obligations, who need money with different intensity. Actually what we need is an idea about the relation between the expenditure level and the mu&pal welfare level cadsed by it, or in short, an idea about the nwzic@d welfare

fumtion.

*This paper was read at the Third World Congress of the Econometric Socie6y .‘oror~o, 1975. Q’rofessor of Economics at the Economic Institute of Leyden University. OResearch fellow at the Economic Institute of Leyden University.

52

&. vm Praag and J. Linrhorst, Municipal we&arcjktions

Evidently the operationalization of this intuitive statement entails a number of problems to be solved. At first municipal welfare has t,o be defined in a way fit for measurement, secondly a method of measurement has to be developed. At a later stage we have to attempt an explanation of these subjective evaluation functions by objectively measurable municipzJity characteristics. Recently the first author developed an operational concept of an individual welfare function (of income) and in the meantime this function h;z; been estimated for well over 15,000 individuals in Holland and Belgium. In this paper we shall define a municipal welfare function (of local expenditures) by a measurement method analogous to the consumer concept. In section 2 we consider at first the concept of individual utility or welfare and its historical development. In section 3 we present a new approach of the individual welfare function concept which recently has been developed and which lends itself for empirical measurement. The municipal welfare function is introduced by analogy. In section 4 the functional form is specified and the way in which its parameters are estimated is explained in detail. In section 5 we report on the data survey held among all municipalities in the Netherlands. In section 6 we shall consider the estimation results with respect to the municipal welfare function of local expenditures as a whole and the municipal welfare function corresponding to parts of the local budget. In section 7 we shall make an attempt to explain the municipal needs by objective variables like number of inhabitants, percentage of old-aged, area, etc. In section 8 we summarize the main results, and in the appendix we present some additional results.

2. The concept of an individual welfare functicm From the very first days that economists attempted to explain consumer behaviour it has been recognized that the consumer is not looking for commodities themselves but for the satisfaction derived from their consumption. This satisfaction, mainly called utiZity (U), was considered to be a function of quantities consumed (x1, . . ., x,,), or in formula, U = U.-Y,, . . ., x,,). Edgewc rth and his contemporaries (1875) assumed, as Samuelson (1947) puts it, ‘that utility was as real as their morning jam’. The precise specification and measurement of utility functions was only a matter of progress of science. However, it appeared to be more difficult than expected. Fortunately, Pareto (1906) was able to show that (static) demand theory could be based equally well on the notion of ind$Erence curves described by iso-utility curves U(X) = c. This being the case, the function U(X) describes the same indifference curves system as U’(x) = $(U(x)), where $4.) is an order-preserving transformation function. In other words, Pareto proved that a cardinal utility function concept was not needed for an explanation of consumer demand, and that an ordinal utility function concept would suffice as well.

B. van Praag and J. Linthorst, Municipal welfare functiow

53

Although this development presented a nice way out of the difhculties met in measuring individual utility functions, it was not much ofa comfort to empirical demand analysts who derived only one certainty of this theory, viz., that they had no utility function from which demand curves could be derived. Demand theory proceeded Ento two directions. Either demand relationslips were specified on an intuitive basis [Prais and Houthakker (19§5)], or demand systems were specified by posing a number of plausible restrictions on the demand functions which specify them more or less [Stone (1954), Theil(1965)]. However, the utility function should not only be applicable in static demand theory (where we saw we may dispense with it), but also in a number of other fields. We mention savings and consumer behaviour under uncertainty. These problems have been tackled by the ordinal theory by introducing dated commodities and contingent claims [Debreu (1959j]. However, this is a rather artificial solution for it increases the dimensionality of the consumer’s decision space in such a way that it is hard to believe that such a structure can serve as a model for individual behaviour [Van Praag (I 968)]. In more practical applications like savings theory frequently a cardinal utility concept is used [Somermeyer and Bannink (1973), Hakansson (1970)]. Von Neumann and Morgenstern (1944) showed in their book that, if a set of plausible axioms is met, the individual’s choice behaviour under uncertainty can be described as the maximization of a sum of cardinal utilities attached to various states of nature weighted by their corresponding probabilities to come true. Actually, their theory yielded the basils for a method to measure cardinal utility functions (defined up to a positive linear transformation), developed and applied by Mosteller and Nogee (1951) and many others. Much more needed still than for individual behaviour is a cardinal utility concept when a kind of interpersonal cornparson of well-being is required [see Frisch (1959), Aumann (1975)J. Especially, we mention the quest for an optimal income distribution and redistribution problems. The theory of Von Neumann-Morgenstern yields a method for measuring utility by observing the individual’s gambling behaviour. This method suffers from several difficulties. It is a costly method, it neglects the ‘joy-of-gambling’ effect, and moreover gambling is such a specific setting that there is doubt whether the observed utility function will determine the individual’s behaviour in eq.reryday decisions. In Van Praag (1968) a different approach is suggested. A utility flJnction, called an indiuiduulwelfure function to create some distance from the tra.ditional utility concept, is considered simply as an evaluation scheme of the individual to evaluate specific commodity bundles or money amounts on a -bounded interval. This yields a new method of individual welfare function measurement winch does not take resort to gambling situations. Tt has a psychological flavour. We are going to explain it in the following section.

54

B, van Praag and J. Linrhorst, Municipal welfare functior,s

3. A new approach to individuai welfare functions and their measurement It is well-known that an individual is able to evaluate specific income levels in relatiqn to his own circumstances by means of verbal qualifications like ‘good’, ‘suticient’, ‘bad’, etc. People who have experience in evaluating things in more formalized systems like the American letter-qualifications A, B, C, used at school or the European value-scales on a [1, lo]-interval, a [l, 5]-interval or a [I, 20]-interval like at some Belgian universities, are even able to evaluate iacame in such a formal evaluation system. This observation led the first of the authors to the formal evaluation assump tion [Van Praag (1968,1971), Van Praag and Kapteyn (1973)J that the individual is able to evaluate income levels on a finite interval scale, e.g., a [O, l]-scale, provided of course that he knows to which reference period the specific amounts refer, e.g., a month, a week, a year. This supposed relationship between income and i,ts evaluation is described by the individual’s welfare function of income, where we assume more or less traditionally that negative income is excluded from comideration, that an income level 0 is evaluated by zero and that the situation ,of ‘Bliss’, i.e., total satisfaction, is only reached asymptotically. The specific choice [0, l] is suggested by tradition. This normalization implies that the individual welfare function becomes formally similar to a (probability) distribution function. The concept is similar to but not identical with a cardinal utility function of the Von Neumann-Morgenstern type. In Van Praag (1971) and Van Praag-Kapteyn (1973) there has been reported in detail about empirical investigations in order to estimate this individual welfare function. These attempts have succeeded and at this moment there are estimates for about 15,000 individuals. The method of measurement, extensively described and motivated in the papers referred to above, may be briefly described as follows. Let ;he function sketched in figure 1 be denoted by U(y) with U(0) = 0 and lim Y__ U(j) = 1. If we want to know the shape of an individual’s welfare function of income we have to know some points on the curve. This may be done either by asking the individual to evaluate some income levels, or by presenting to the individual. some evaluations and asking the individual which income levels he would identify with the evaluations mentioned, The first method does not work. Imagine for instance, that we would supply a millionaire with the levels DA. 10,000, Dfl. 20,000 and Dfl. 30,000 per year, asking him for the difrerence in his eyes between these income levels. All three levels being far below his actual income level, he could not tell the difference between these levels, evaluating them all as equally bad. Hence we prefer the other method. This means supplying the individual with a number of evaluation levels say 0.1, 0 2, 0.3, . . ., 0.9, and asking the individual which income level he associates with these income levels. Obviously most individuals will have problems with this type of question since they do not have the habit of evaluating income levels by figures on a [0, II-scale. Difficulties

B. wn Praag and .I. Linthorst, Municipar welfare jimctiuns

55

will reduce when we ask evaluations on a scale used m school like 0, 1,2,3, . , ., 10, or A, B, C, D, E. The latter qualification scheme is non-numerical and this raises a translation difficulty. The most usual qualification scheme is cerbainly verbal in terms of ‘good’, ‘sufficient’, ‘bad’, etc. Whatever qualification system we choose, say for instance in n levels, we get a set of income levels, yl , . . ., yn, as a response to v&ich we may add y, = 0 with U(yO) = 0 and y,,, = 00 with U(JJ~+~)= 1. In our empirical investigations we always found a typical response pattern, viz., the incomes in the middle say, y, to y7, were located at short distances from each other while the tails where interspaced by considerable monetary distances.

1.00 t c90.

0.80 i 0.70 c 0.60 .

0.40 1 2

0.50 . 0.20

0.10 0.30 0.00 I

/ ’

/. 1

2

3

c

5

E------

i Y

Fig. 1. Individual welfare function of income.

This conveyed to us the idea that the respondent attempts to give us as much his individual welfare function as possible by giving us relatively many points of the function over the interval where it shows a steep slope and relatively few where the function is nearly horizontal. Let the evaluation of yk be U&) and of yk +1 be U(yk+ 1). If the individual evaluates his income by ‘good’ #hen it is between yk and _Iyk+1, yk is at the left extreme and hence just the margical income level he would call ‘gcod’, while yk+, , being at the right extreme, is somewhat underrated by the term ‘good’, since if it were only somewhat more he would definitely call it ‘very good’. Actually the income level j+ defined by U&) = ~(U(‘&I+ U’(Y~+,)), is evaluated by the term ‘good’ reserved for the whole interval. Since all incomes in [yk, y&+11are indiscriminately evaluated by the same term, an error is made which may be defined as the weighted average of least-squares, information about

B. van Praag and J. Linthorst,Municipal welfarefactions

56

Then the information error by offering the response yl, Yl , . . ., yn are chosen In such a way that

. . ., y,,

is minimal if

i; minimized with respect to Y1, . . ., yn subject to the trivial condition Y. = c < Y* < . . . < yn < 00 = yn+ 1 . In Van Pra ag (197 1) and Van Praag-Kapteyn (1973) it has been shown that the minimization has the unique solution

Uh+J- Wd =

n&, for

k = 0,

. . ., n.

In words this means that the individual responds to the question by giving l/(n+ 1) percentiles. If n = 9 this would mean the deciles of U(y). In Van Praag (1968) it has been shown that this solution remains the same if the criterion flunction defined above is changed for instance into absolute errors and more generally that most sensible criterion functions lead to the same solution of equai percentiles. It is clear that this method may be translated straightforwardly into municipaliq terms. Here the spender of municipal expenditure has to be asked how he would evaluate in his circumstances specific expenditure levels. Since in Dutch municipalities spending is decentralized among a limited number of separate portfolios we have to adapt the questionnaire to this framework by differentiating expenditures with respect to specific departments. So we pf)sed, among others, questions of the following type, where we have inserted a typical answer in Roman letters. Evduation question with respect to the portfolio ‘Public Works’, as filled in by municipality A (ca. 28,OOCl inhabitants) :

Taking into account the specl@c circumstances and needs of your municipality (number ofinhabitants, location, etc.) you would call the level of welfare as regards public works: Welfare Level Excellent Good AI qp@ suficien t S$%ient Bare !y suflcien t Inn4j~cient Very insuflcient Bad Very bad

EqpeRditure Level ( x Dfl. 1000)

if the expenditure level were above

Dfl. 5,800 if the expenditure level were between Dfr. 5,500 if the Pxpen&ure level were between Dfl. 5,200 if the expenditure level were between Dfl. 5,000 if the expenditure level were between Dj?. 4,000 if the expenditure level were between DJ. 3,800 [f the expenditure level were between Djl. 3,600 if the expenditure level were between D$. 3,500 if the expenditure level were below Dfl. 3,500

and and and and and and and

DjZ. 5,800 Dj?. 5,500 Qfl. 5,200 DJ. 5,000 Dfl. 4,COiI Djl. 3,800 DjL 3,600

B. L’cNIPraag and J. Linthorst, Municipal welfare functions

57

This answer supplies the series y, , . . ., ye needed, e.g., y1 = 3,500, y2 = 3,500. Identifying these levels by the 11.1 percent quantiles of the U-function we get a nine-point approximation of the U-function when y. = 0 is included. , 4. Specification and interpretation or the model In Van Praag (1968) or has been derived that the individual welfare function of klcome must be approximately a lognormal distribution function if spending on a broad variety of commodities is possible.

02=0.5

p=o

Fig. 2. The lognormal distribution function for different parameter values.

A lognormal distribution function is defined as

where N is a normal distribution function [see Aitchison and Brown (1957)3. The same conclusion holds if the spending room is limited to a specific subclass of commodities, say food, non-food, housing, etc. provided that the class r:onsists of a broad variety of commodities. The theoretically derived result has been verified since then in a number of large-scale surveys in The Netherlands and Belgium [see Van Praag (3971), Van Praag and Kapteyn (1973)]. It lies at hand to transfer this specification by analogy to the munici;3zl level ,ls the evaluation function used by rmmicipui spenders when evaluating municipal expenditures. The interpretation of the parameters ,Uand B is as follows: Consider figs. 2a and 2b. It can be shown that &e”; ,u, a) = 0.5. Hence efi is the median value.

B. van Praug and J. Linthorst, Municipal welfare functions

5&

Using the well-known. standardization formula of normal distribution theory,

we see that the spender evaluates y by considering the ratio y/e”. We call ep the natural unit.

Whatever its name, ec is a location parameter as shown in fig. 2a. From fig. 2b it is seen that Q determines the slope of the welfare function. If the function increases over a wide range we call the spender welfare-se&the. If the function inlreases steeply over a small interval we call the spender insensitive. It seems that the value of cr says something about the fantasy to do something with more money and the ability to adapt to a decreasing expenditure level. It stands to reason that p must have something to do with a number of objective factors. For instance if the number of inhabitants would increase it seems natural that the median value would increase as well. The explan-&on of p by objective factors will be attempted in section 7. The estimation oi p and Q has been performed as follows: The respondent has given us a number of expenditure levels yl, . . ., yR, which according to the theory exposed in section 3 correspond to evaluation levels l/(n + l),. 2&n+ I), . . ., n/(n + 1). Hence there must hold N((ln ,yi-JJ)/l; 0,l) S5 i/(n+ l),

for

i=

1, . . .,

n.

Now the l/(n+ 1) quantiles, ul, . s ., u,, of the standard-normal can be found in the usual table. TLere holds by definition

distribution

N(z$; 0, 1) = i/(n+l).

Hence there must hold

which yields the linear regression model lnyi = @UiS/J+Ejp

for

i=

l,...,n.

(4.1)

Making the normal assumptions about the disturbance terms ef of being normal, homoskedastic and mutually independent, ,u and D may be estimated as rergession coefficients frcm (4.1). This has been done for five functions for about 525 municipalities, yielding in total about 2,663 regressions. If the evaluation question is completely responded, we have to our disposal 8 observations (n = 8). In a minority of cases the questiornaire was onl;f partly filled in, leaving us with less than eight points in the (u, In y)-space. Only when less than three points were given we did not estimate p and 6.

B. van Praag and J. Lin?horst, Municipal Herfarefunctions

59

5. Data In order to collect the data needed we held a survey by mail among all 842 Dutch municipalities during Spring 1974. The survey could. be split up into a series of subjective questions, viz., questions with regard to the evaluation of the expenditure levels as quoted in section 3 and a series of objective questions with the aim to gather informatic _Iabout a number of physic;,1 and financial variables. The Dutch municipality is governed by an elected city council which elects from its midst a number of aldermen who constitute the Executive Committee which is chaired by the burgomaster appointed by the central government. In most municipalities the aldeimanship is not a full-time job and the aldermen earn their living in their own profession. In the large municipalities the aldermen are fulltime protessional politicians who are adequately salaried. The Executive Committee gets assistance from a municipal administration headed by the Town Clerk. The municipal tasks are split up into a number of portfolios which are held by the aldermen. In most of the municipalities each portfolio corresponds to an administrative department of its own headed by a chief. In our survey we considered only t!le following portfolios : (I) public works (roads, sewerage, public parks, etc.); (2) education (primary and secondary education); (3) culture, sports and recreation (arts, sporting facilities, etc.); (4) social affairs (social work, unemployment and sccial assistance). These departments cover on the average 55 percent of all municipal expenditures. As in the state government the minister of finance, the municipality has an alderman of finance He is the countervailing power to the spending departments. Obviously this department is the only one to get an idea of total spending and what a Dfl. 1,000,000 more or less means to the municipality as a whole. The evaluation question with respect to total municipal expenditures has been posed as well. Preferably the respondents to these questions should be both municipal experts who have experience in thinking over and handling the municipal expenditures and are representative for the municipality as a whole. When mailing the survey we expressed our preference that the aldermen themselves should fill in the evaluation questions. The result was different although expected. In the smaller municipalities nearly always the full-time officials filled in the questionnaire instead of the part-time (amateur-) aldermen. We do not think that this will do harm to the intermunicipal comparability of the results since in the smaller communities the aldermen and the clc:ks who assist them are mainly of the came opinion, as we found from our frequent oral contacts with the respondents. -!so in the large municipalities the aldermen appeared to consult their clerks before filling in the questionnaire. In table 1 we present as an example numerical evidence on who filled in the

B. om Praag and J. Linthorst, Municipal welfare functions

60

evaluation question of total expenditures, distinguished according to four categories of population size. The expenditure concept itself is not unambiguously defined. Although the central government requires the municipalities to set up &eir adminisnations acccrding to strict rules, in practice there remains room for substantial variation. Hence, we asked C number of questions to get more insight in the expenditure concept the respondent had in mind. Using the varying answers it appeared possible to correct (and deflate) the individual answers towards a more unified expenditure concept. Although there is still some room left for ambiguity, we believe that the figures stated are such that intermunicipal coinparison is justified. Table 1 Djst.riWion of the various respondents, politicians as well as officials, to the evaluation question of total expenditure, subdivided to four categories of town size. Politicians

Number of inhabitants

Officials

Executive Committee Burgo- Alder(asa whole) master man

0- 5,000 5,000 - 20,000

0 1

10 24

1

20,000 - and 50,000 50,000 more

,!I L

i

:: 11

Town Town Official Clerk Treasurer (unspecified)

Vdcnown

51 35

125 181

12 10

1;:

51

40 14

:

:

A few of the pitfalls encountered in this respect are the following: (a) Most municipalities stated their expenditure levels a~ budgeted for 1974 on the basis of 1973 prices and wages, while a substantial minority applied inflation percentages of different size, although this is not a legal procedure. We asked for the inflation percentage used. (b) The major municipalities have their own municipal services such as municipal engineering, public utilities, etc. In that case the service has a’budget of it:, own and only its profit or (more likely) deficit is booked over to the municipal budget. Hence the municipal budget shows only the balance cf such a more or less independent service. This applies especially to the social service. If a municipality has a separate social service the state contributions which are distributed via the social se?,-ice are booked directly to that social service, by-passing the

B. van PraGg and J. Linthorst, Mrrnicipnl welfare functions

61

municipal administration. On the other hand, if there is no independent service the state contributions flow to the municipal administration and are distributed by it. Hence, if the social service is not integrated in the municipal bookkeeping we find much lower anounts for t,Gal algairs expenditures (and revenues) ,nian in the case where it is integrated. The first situation applies mainly to larger munic;palities, and the second situation to smailer ones. (c) Finally, one of the peculiar points in the Dutch school system is Its falling apart in state schools and private schools (mainly on a religious basis). The first type is financed completely by the municipality which in its turn gets the money for nearly 100 percent from ihe state. The second type is also nearly completely fmanced by the state, but the school gets a considerable part directly without intervention of the municipality. Hence, it looks as if highly religious communities spend much less on education than more liberal communities, but this is simply caused by history-based differences in the finance procedures. Table 2 Frequency table for the reactions of 671 municipalities according to specified expenditure levels (0 - 8) for each evaluation qkstion (I - V). 0

1

2

3

4

5

6

7

8

-1 Public works II Education III Culiure, sports, and recreation IV Social affairs V Total expenditures -

86 ;I; zi

34 37 32

:3

z:

14

22

::

31 8

30 23

41 :t

28 27 25

22 13 17

10 14 8

416 411 424

37 45

22 26

9 18

3 5

403 436

Evidently these problems of measurement could have been avoided, at least theoretically, by providing our own definitions of expenditures, etc., to the respondents. However, these would not have conformed with the locally varying concepts used for years in the municipal accounts and this would have raised a lot of confusion and decreased the response rate considerably. The survey in its present form did quite well. Eighty percent of the municipalities reacted and of the returned questionnaires 80percent proved completely fit for our investigations. All in all we base our investigation OIR552 municipalities. Especially interesting is the response behaviour with respect to the subjective evaluation questions. In table 2 we present the frequency distribution for the five questions with respect to the number of expenditure levels tiled in. With respect to the question:; of an objective type, we asked, among others, for the number of inhabitants, the age distribution of perr,ons and houses, the area, an in,dication of the income level of the population, unemployment E

62

B. van Praag and J. Linthwst, Municipal welfare functions

percentag.:, etc. A number of those variables will be used as explanatory variabks in section 7. 6. Es-ted

municipalwelfare functions

According to the method described in sections 3 and 4 we estimated from the linear regression model (4.1) lognormal municipal welfare functions for the 552 municipaht.ies. Due to the fact that some questionnaires are not filled in with respect to each portfolio the number of observations with respect to each portfolio is somewhat less. For each municipality we estimated, if possible, 5 municipal welfare functions. Table 3 Welhre parameters for municipality A.

I

Public works

II Education III L’uhuw, sports ,“nd

recreation IV Social affairs V Total expenditure

P&E (0.022) 8.856 (0.007) 7.250

(0.010) 7.534 CO.Oc2) 10.412 (0.010)

0.243 (0.029) 0.149 (0.009) 0.846 (0.013) 0.081 (0.002) 0.192 (0.014)

0..338

0.960

0.504

0.990

0.638

0.999

0.570

0.998

0.338

0.960

--

In table 3 we present as an example the regression results for municipality A: the estimated values for p and cr(with in parentheses their corresponding standard errors), the welfare evaluation U and the unsquared correlation coefficient R. The welfare evaluation U can be found by substituting the actual level of e>.penditure y in the estimated municipal welfare function, hence &; cc,a); that is the municipal evaluation of its own actual welfare position. In fig. 3 we present a graphic representation of the four partial municipal Nelfare functions of municipality A, corresponding to table 3. (Municipality A has about 28,000 inhabitants and may be characterized as a small regional town with center function.) In this figure on the x-axis the nctuztl expenditure level for the four portfolios and their corresponding vtelfare evaluation on the y-axis has been indicated. Obviously it is impossible to consider each municipality separately. Hence we divide the municipalities into a few subgroups (size n) and consider the average value of ,u, 6, U and R for each subgroup, denoted by ji, 3, l7 and R. By d$ng so

B. van Praag and J. Linthorsr, Municipd welfare functions

63

it is evident that we get no good idea about the variation about those averages. Therefore we present the sample standard deviations of ,q 6, W,'Rdenoted by s@), s(a), s(v) and s(R)as well. Since p and u are estimated regression coefficients their standard errors denoted by s.e.(uj,s.e.(a) are important. In parentheses below ji and C we present the average value of s.e.@) and s.e.(o) in the corresponding subgroup, denoted by s.e.fir) and s.e.(a).

_~ ..._

.__- _._... _ II i I

i ij

EXPENDITURES

/f

I

I

j

IN DFL hlo’i

Fig. 3. Pulial municipal welfare functions of municipality A (ca. 28,ooO inhabitants). Public Works: actual expenditures (y) = Dfl. 4,036,OOO; welfare evaluation (u) = 0.338. II Educution: y = Dfl. 7,02S,OOO; U = 0.504. III Ckfture, Sports, and Recreation: y = IX 1,900,OW; U =- 0.638. IV Social Affairs: y = Dfl. 1,897,OOO;U = 0.570.

The results with respect to total expenditures are printed in table 4. Tile results with respect to partial expenditures are presented in table i: in the appendix. Horizontally table 4 (and table 6) is subdivided according to two classification criteria, borrowed from the NetherIan& Central Bureau of Statistics. The first criterion is the number of inhabitants, the second criterion is the degree of urbanization, where there are 3 main categories, viz., countryside, urbanized countryside and towns. With respect to the countryside we distinguished according to the percentage of agrarians in ttce working population. A specific type of community in the urbanized countryside is the ‘commuter village’, the ;vorking population of which works for a considerable part outside the munici-

Table 4 Characteristics of the municipal welfare function with respect tc total expenditures, subdivided to town size. and urbanization degree. Total expenditures

InhabitantS o1,000

7

l,OOO-

2,000

33

2,000-

5,000

139

5,000 -

10,000

149

lO,OOO- 20,000 20,ooo -

so,ooo

ill 76

50,ooo- 100,000

19

100,000 - and more

9

Urbanizationdegree (Al) countsyside”

Urbanized CpmWstcieb

(A.2) W)

39

83 104

(A41

85

(Bl)

69

(B2)

65

(J33)

30

(Cl)

21

(C2)

29

(C3)

8

(C4)

18

l-OWLC

Netherlands

551

0.10

0.53

0.16

0.99

0.01

0.31

0.50

0.17

0.98

0.02

0.22

0.49

0.17

0.98

0.03

0.19

0.50

0.15

0.98

0.03

0.10

0.51

0.16

0.98

0.03

0.10

0.49

0.15

0.98

0.03

0.06

0.41

0.14

0.98

0.02

0.06

0.45

0.20

0.99

0.01

0.19 (0.02) 0.21 (0.02) 0.21 (0.02) 0.17 (0.61)

0.17

0.47

0.17

0.98

0.02

0.23

0.49

0.15

0.98

0.02

0.24

0.52

0.17

0.98

0.03

0.16

0.50

0.16

0.98

0.02

8.44 0.62 (0.01) 9.78 0.58 (0.01) 9.77 0.72 (0.01)

0.18 (0.W) 0.13 (;;;)

0.19

0.49

0.16

0.98

0.02

0.10

0.51

0.17

0.98

0.04

0.10

0.50

0.17

0.97

0.05

9.13 (0.01) 10.36 (0.01) 11.08 (0.01) il.93 (0.00)

0.17 (0.02) 0.12 (0.01) 0.15 (0.01) 0.10 (0.01)

0.13

0.48

0.18

0.98

0.01

0.10

0.47

0.11

0.98

0.03

0.09

0.47

0.14

0.99

0.01

0.07

0.43

0.15

0.99

0.01

0.18

0.50

0.16

0.98

0.03

6.72 (0.00) 7.17 (0.02) 7.99 (0.01) 8.73 (0.01) 9.48 (0.01) 10.25 (0.01) 11.41 (0.01) 12.36 (0.00) 8.33 (0.01) 8.33 (0.01) 8.52 (0.01) 8.48 (0.01)

8.95 (0.01)

0.52 0.51 0.40 0.32 0.27 0.35 0.22 0.58

0.82 0.82 0.91 0.78

0.60 0.28 0.46 0.61 1.15

0.17 (0.01) 0.31 (0.03) 0.22 (0.02) 0.17 ~0.01) 0.14 (0.01) 0.12 (0.01) 0.13 (0.01) 0.08 (0.00)

(0:ol)

0.17 (0.01)

*Agricuhural employment : (Al) over SO%, (A2) 40-SO%, 0.‘:) 30-40 %, (A4) 20-30 x. bbs thau 20% agricultural employment. Main urban resid?ntial kernel: (Bl) less than 5.000 inhabitants, (B2) S,OOO-20,000inhabitants, (B3) commuter village. CTown residential kernel: (Cnj 2,000-lO,OOOinhabitants, 22) lO,oOo-30, inhabitants, (C3) 3O,OOQ-50,000inhabitants, (C4) 50,000 and more inhabitants.

pality. A more precise definition of the subdivision in urbanization degrees is given in table 4 [see also the Netherlands Central Bureau of Statistics (1964)j. From the last two columns containing the average R for the individual regressions, corrected for the number of observations, it appears that the quality of the individual regressions is vet’ good. Although we are aware of the fact that the transformation of the data as described in sectiotl3 may be of some influence to the value of R a:;d that the number of obsenations is small, the conclusion remains imminent that a lognormal function serves as a very good approximation of municipal welfare functions, apart from the fact that there is a theoretical motivation possible. As shown in table 4 and table 6, we see that there is a big difference between the values of c corresponding to the various welfare fun&Ions. Generally the 0 ‘total’ is the smallest, followed by ‘social affairs’ and ‘ed:!cation’, then ‘public works’, with nearly always ‘culture, etc’, as the largest. This is an overall-pattern, which may have something to do with the degree rf independence the municipality has with respect to the portfolios. For social affairs and education municipalities act almost as executors of the regulations fixed by central government, while in the portfolios of culture and public works there are a lot of local problems and needs which have to be solved by local authorities themselves in their own way. I-?ence the fantasy of what to do if one gets more or less money to spend is stimulated in the latter fields. The variable ji varies a good deal with the number of inhabitants. We shall make an attempt to explain this variation systematically in section 7. The standard errors of ~1and C, denoted by s.e.(& and s.e.(a) are invariably small. With respect to the welfare evaluation U we see ;! considerable variation about the means, the standa-d deviation being of the order of 0.16 throughout. The mean value U is always in the neighbourhood of0. iO,although there is substantial variation in the sample. It may be observed that the portfolio of social affairs yields the highest welfare evaluation (about 0.56) while ‘culture’ scores the lowest evaluation throughout (0.45). 7. A first explanatory attempt In this section we shall consider the question whether the p and 0 values found depend on and may be explained by objective determinants. In the case of the individual consumer we found that/r could be explained to a considerable extent, while d was not capable of systematic expianation, except for a small but not insignificant relation with the consumer’s education level. The explanatory variables which propose themselves as obvious candidates are many. Actually the state contributions to municipalities depend on a number of objective characteristics like (1) the number of inhabitants, (2, the area,

66

B. van Praag and J. Linthorst, Municipal welfare functions

(3) the building density, (4) the ‘social structure’, e.g., the number of unemployed, the number of people enjoying social assistance, etc. Morcover the state applies a number of ‘refinements’ to do justice to specific circunstances like the nature of the soil (for building drilling may be necessary), the area of a historic town-center, the number of residentisl kernels, etc. A very limited number of specia.1 municipalities, like municipalities on an island, municipalities at the national frontier or municipalities intersected by a large river, is specially subsidized by the state to do justice to their specific difficulties. These latter location refinements will be neglected for the meantime in order to concentrate on the main variables. Certainly the explanation might be improved by including the latter variables in the explanatory set. Apart from the variables above we may think of another complex of variables, viz., the political composition of the City Council and the Executive Committee. In this article we shall neglect this interesting feature. We met in this application to municipal welfare functions the same phenomenon as with respect to individual welfare functions: the welfare sensitivity G proved to be utit for explanation by any series of variables considered. Our conjecture is that it has something to do with the political composition which we did not take into account at the moment. For the time being we consider only /.4. When considering the value of CL,or rather ep, we see that eP is commensu.rable to municipal expenditures, It is evident that it is not so much total expenditures as expenditures per inhabitant which interest us. Let I be the number of inhabitants then ti/l or rather its logarithm @-In (r)) will be our varable to be explained. In the sequel we shall present for the four portfolios and total expenditures the best explanation we were able to find with a limited number of variables using ordinary least-squares regression. We have used two categorizations side by side, namely according to size and according to urbaprizationdegree.

At first we attempted to explain (pPw-- In (I)). The main variables of influence were In (I), the logarithm of the land area In (area) and the log-percentage of houses built after 1965 In (H 1965+). The outcomes are different for the various categories. For the small municipalities R2 (corrected for the number of observations) is virtually zero, while for the larger municipalities the variar,ce explained is very considerable. The standard errors of the coefhcients (denoted in parentheses) are mostly acceptable. It is interesting to see that municipalities work under diseconomies of scale: the larger the number of inhabitants and/or the higher the urbanization degree,

B. vun Praag and J. Linthorsr, Munkipal welfare firnctions

67

the more per-capita expenditures are needed to keep the municipal welfare with respect to,public work constant. In the bigger municipalities the elasticity of needed expenditures with respect to inhabitants is about 1.4. For the sparsely inhabited communities it appears that the area is a drawback, an increase of which causes an increase of public works expenditures as well. In the more urbanized municipalities we find the inverse pattern pointing to the costs Qf congestion of small crowded areas. 1 able 5a

Public works - Regression results. ;.-

n -.

Inhabitam o- 5,000 5,000 - 20,000

173 265 69

50,000 mindmore

27

Urbanized countryside Town

In (T)

In (area) In (H1965’“) corr. R*

-..-

20,000 - 50,000

Urbanization degree Countryside

Constant

308 154 71

-

5.338 (0.685) 1.796 (0.358) 0.212 (0.279) 0.080 (0.325)

- 0.050 (0.095)

4.955 (0.360) 2.395 (0.324) 1.214 (0.401)

- 0.088 (0.049) 0.204 (0.055) 0.262 (0.071)

0.2+, (0.050)

0.425 (0.048)

0.109

--

0.055

0.133 (0.031) 0.010 (0.036) - 0.050 (0.084)

-0.211 (0.096) -0.002 (0.071) 0.101 (0.088) 0.129 (0.181)

0.189 [0.042) - 0.032 (0.047) -0.115 (0.080)

-0.188 (0.068) 0.279 (0.089) 0.620 (0.115)

0.123

(0.050)

0.273 0.789 0.897

0.290 0.566

The influence of the age distribution of buildings is very puzzling. For small communities a good part of modern building seems to be lowering the need for public works, while in ihe larger communities it is inverse (cf. - 0.188 in rural municipalities OC~SUS +0.620 in towns). This is possibly a reflection of the fact that rural communities when extending may still offer a location of good quality, while towns being rather crowded can offer only marginal locations. The same holds for facilities like public parks, parking grounds, etc. It may bc explained by Ricardo’s and Von Thunen’s ideas about land use. The quality of the soil varies a lot among the Netherlands. In some municipalities every building and sometimes even the sewerage-system, must be based on piles of often more than 20 meters. Of course expenditarres on public work; are influenced b! this fact quite a lot. To our surprise we could not find any substantial influence of ‘the nature of the soil’ (n*eflectedby the drilling depth

68

B. van A sag and J. Linthorst, iUunicipI welfare functions

needed). Neither did .we find any influence of other variables which might influence the expenditures on public works like ‘the area of a historic town center’ (high maintenance costs of old buildings, canals, roads, etc.) and ‘the number of residential kernels’ (relatively great length of roads, etc.). 7.2. EdtmSion We considered @n - In (I’)) and present the results in table Sb. The explanatory ‘E. variables are In (I), the percentage of young in the population, viz., the logpercentage of people below 19 years In (Alg’j, the log-distance (in km) with Table Sb Education - Regression results. .n

Constant

Inhabitants 0- 5,000

172

5,000 - 20,000

257

20,000 - 50,000

73

50,000 and more

24

Countryside

299

UhatkZed countryside Town

154

In (0

In (A19”)

In (dist)

In (polo)

-0.081 (Q.54ci)

- 0.024 (0.069) 3.266 iO.044) 0.293 (0.072) 0.273 (0.154)

0.021 (0.119) 0.259 (0.093) 0.315 (0.194) 0.372 (0.445)

0.012 (0.051) 0.038 (0.035) 0.048 (0.051) 0.046 (0.143)

(0.017) 0.181 (0.015) 0.294 (0.029) 0.277 (0.114)

3.711 (0.401) 0.985 (0.321) 0.400 (0.472)

0.041 (0.029) 0.151 (0.036) 0.146 (0.055)

0.092 (0.086) 0.503 (0.115) 0.732 (0.194)

0.011 (0.035) 0.093 (0.048) 0.028 (C,.O89)

0.194 (0.014) 0.195 (0.019) 0.222 (0.014)

4.470 i0.724) 1.020 (0.336) 0.012 (0.289)

0.194

corr. RZ

0.448 0.516 0.850 0.808

Urbanization degree

72

0.421 0.626 0.651

respect to the nearest municipality of more than 100,000 inhabitants In (dist) and the variable In solo), being the log-percentage of pupils in the schoolpopulation going to state schools. We see that with increasing population size the needed p.c. expenditures increases. This accounts probably for the fact that larger municipalities have more diversified education facilities and needs than the smaller municipalities. The age distribution has an obvious effect, but also here we find diseconomies of scale. ff a municipality has a large distance to a big town we would expect a s&i-ring for self-sufficiency. Hence, the larger the distance to a large center, the more education facilities the community is providing itself.

B. van Praag md J. Linthrsr, Municip&Iwelfare futzcrions

69

This tendency proves to be non-significant. The variable ‘polo’ has been included for reasons explained in section 5, because the private (mostly confessional) schools are directly subsidized by the state for a part of their expenditures without intermediation of the local authorities contrary to the procedure for non-private schools. As expected we find a considerable positive effect if private education decreases, for it implies a larger p.c. ‘burden’ to the municipality. We could not find a substantial influence for ‘the number of residential kernels’ which might cause diseconomies of scale by the necessity of ha$ng relatively many small-school-facilities. 7.3. Culture, sports and recreation Cu!ture, sports and recreation is a somewhat difficult department. The expenditures are heterogeneous. Superficial investigation shows that there is a lot of political influence, being a non-technical department the expenditures of which have a directly traceable influence on individuals in the population. Therefore the explanation is more dificult, since a number of imponderable influences are intervening. We present the most Fuccessful results, where (riiCSR-In (I)) is the variable I, to be explained. The first variable included is again In ( 3 and it appears that also for this Table 5c Culture, sports, and recreation - Regression results. n

Constant

In (I)

In(U)

2.924 (Q.901) 0.642 (0.403) 0.019 (0.453) 0.015 (0.293)

0.021 (0.104) 0.310 (0.044) 0.355 (0.050) 0.366 (0.034)

0.110 (0.054)

Inhabitam Cl- 5,ooo

169

5,000 - 20,ooo

251

20,ooo - 50,ooQ

73

50,000 and more

27

-___

In (dist) corr. it2 ---.-0.028

0.168 (0.036) 0.113 (0.078) 0.083 (0.121)

0.095 (0.078) - 0.008 (0.044) 0.090 (0.083) 0.941 (0.082)

8.171 (0.039) 0.085

0.040 (0.051) 0.051

0.072

0.2,6 0.528 0.893

-_

CJtbuttization degree

Countryside

29:

3.118 (0.423)

0.018 (0.044)

Urbanized CountrysiJe Town

153

0.519 (0.376)

0.319 (0.037)

(0.0449

(0.058)

0.144 (9.312)

0.339 (0.030)

0.204 (0.077)

0.076 (0.066)

75

0.346

0.703

B. uw Praag and J. Linthorst, Municipal we/fare ,cWrctio~r~

70

portfolio there are increasing costs to inhabitl.nts, except in the small rural m.unicipalities. In the second place the log-percentage of unemployment In (v), proves to be of some importance. This can be exphtined by interpreting the unemployment ratio as a measure of good or weak social structure. Municipalities tend to take care of a weak social structure by the supply of welfare facilities like sporting accommodations, pleasure grounds, etc. The influence of the variable ‘log-distance to nearest big city’ In (dist) is weak. We might expect that a high average level of personal income in a municipality would raise the expenciitures and needs for culture, etc. Unfortunately we have no good figures TabIe Sd Social affairs - Regression results. n

CoLIstant

Ld%&#m!s o- 5,000

163

5,OQO- 2o,Oi#

246

20,000 - 50,000

69

5WOO and more

24

In (I)

4.774 (0.897) 0.829 (0.427) 0.231 (0.624) 0.205 (0.596)

-0.009 (0.101) 0.405 (0.047) 0.436 (0.072) 0.366 (0.119)

4.09? (0.47L) 1.453 (0.403) 0.880 (0.528)

0.069 (0.047) 0.302 (W342) 0.286 (0.069)

In (A65+)

In (U)

sose

corr. R’

0.035 (0.114) 0.197 (0.075) 0.160 (0.200) 0.424 (0.494)

0.237 (0.050) 0.149 (0.037) 0.094 (0.102) 0.264 (0.225)

- 1.097 (0.323) -1.124 (0.086) -0.996 (0.173) - 1.092 (0.281)

0.158

0.067 (0.078) 0.366 (0.098) 0.618 l.O.282)

0.193 (0.039) 0.169 (0.045) 0.207 (0.120) -I

- 0.982 (0.125) -1.345 (0x0) -1.204 (0.165)

0.214

0.497 0.523 0.761

Urbanization degree Countryside

286

Urbanized countryside Town

145 70

0.603 0.564

on average personal income; the only rough measure as yet available - the principal sum p-c. of ‘inhabited house duty’ - pruved to be of no relevance. Moreover it must be observed that it is official Dutch policy to intermingle rich and poor inhabitants in order to avoid ghettos either of the rich or of the poor. This policy is supported by admitting only a small relationship between the revenues of the municipality and the income level of its inhabitants. We tried also several other variables as area, the age distribution and the - number of residential kernels, but no variable yielded satisfactory results. I

7.4. Social afluirs As

outlined before a good deal of the expenditures in the field of social

B. wn Praag and 3. Linthrst,

Municipal w&are _bctions

71

assistance is repaid by central government according to certain standards. If a municipality does more than the standard, it has to find the money herself from other sources. Hence, there is a certain degree of freedom although the room for manoeuvring is costly. From a bookkeeping Gewpoint a difficulty arises since especially the larger municipalities have their own social service, in which case only its negative balance appears on the city a,xounts. Therefore we introduced a dummy variable ‘sose’ which equals 0 if the municipality does not have a separate service and which equals 1 otherwise. In table Sd we present the regression results for the explanation of bSA-ln

(I))*

As before the quali:y of the regression increases when the municipality becomes larger and more urbanized. The principle variables are In (I) and the unemployment log-percentage In (U) for most cases. Evidently the dummy variable of social services ‘sose’ has a considf:rable negative effect, while the log-percentage of old-aged In (A65+) in urban areas seems to be important. This may be explained by the fact that support by family and neighbours is still quite common in the countryside, while virtually absent in urban areas. The measure of average personal income and the age distribution of houses (we might expect a ‘positive’ effect in relatively old municipalities) yielded n ) satisfactory results. 7.5. To tat expenditures seems predictable that the explanation of the evaluation of total expenditures, being an aggregate of the four portfolios considered plus some additional non-considered portfolios, must be a blurred reflection of the previous explanations. Hence we lose the main explanatory variables already introduced. The quality of the regression coefficients and the correlation coefficients is equal or better than wnth the separate portfolios. Some random influences are compensating each other. In table 5e we present the regression results where &-In (I)) has been regressed on In (I), In (area), In (A65+), In (dist), In (H1965+), In @olo) and SOYC. As in all regressions considered, the explanation for the small municipalities is weak, while the size ot the constant krm is rather large. This can be ::xplained by the fact that n lot of different circumstances can have 3 relatively great iufluence on these sm:tll municipal budgets, while on the other hand any municipality in this subclass has a rat her considerable part of conc;tnnt overhead costs in the budget (like the costs of’ a tou 11,hall, the salaries of the burgomaster, aldermen, town clerk, etc.). Again we find considerable diseconomies when the population increases, indicating an optimal size from this uoint of view s:)mewhere between’2W-N and 10,000 inhabitants. It

76

2s

20,000 - 50,000

SO,000 and more

158

Urbanized countryside Tow

74

303

Cwutryside

Urbanization &gree

261

174

s,OOO- 20,ONI

o- s,ooo

InJrabitants

n

(O-306) 1.36S (0.266)

6.299

w64) 1.296 CC2.246) 0.161 (0.215) 0.116 (0.292)

6.619

constant

-0.015 (0.035) 0.391 (0.043)

-0.015 (0.069) 0.405 (0.035) 0.584 (0.041) 0.515 (0.089)

lu (I)

o.os2 (0.03Oj -0.118 (0.036)

0.01s (0.036) -O.ZJ (0.023) -0.085 (0.027) -0.104 (0.087)

In (area)

0.012 (0.045) 0.473 (0.062)

0.114 (0.072) 0.228 (0.045) 0.200 (0.080) 0.323 (0.264)

h (A65 ‘)

0.086 (0.028) 0.148 (0.039) 0.110 (0.047)

0.086 (0.044) 0.116 (0.027) 0.101 (0.078) 0.029 (0.078)

In (dist)

Total expenditures - Regression results. ._

Table Se

-0.06s (0.047) 0.359 (0.071) 0.511 (0.079)

-0.143 (O.c!57) 0.257 (0.051) 0.197 (0.131) 0.424 (0.131)

In @I1965+)

0.039 (0.010) 0.019 (0.016) 0.002 (0.028)

0.031 (0.015) 0.041 (0.011) 0.037 (0.078) 0.029 (0.078)

In (polo)

-0.121 ww -0.218 (0.066) -0.246 ~0.08s)

- 0.282 (0.203) -0.174 @.OSO) -0.121 (0.056) -0.182 (O.!SO)

sose

0.871

0.727

0.142

__--

0.959

0.929

0.667

0.128

corr. P

B. van Prmg and J. Linthorst, MunicipaI welfare functions

73

The negative coefficient attached to the area reminds us of congestion troubles in crowded municipalities [see also Van den Berg (1956)]. The influence of the proportion of old-aged appears to be even more marked than in the previously considered portfolio of social affairs. Probably this is due to the fact that total expenditures also inciude other expenditures which are probably heavily dependent on the fraction of old-aged in the population (like public health and housing). The influence of the distance to the nearest big city is very pronounced. This may be caused by the portfolios not considered, like public health, fire protection, etc. The proportion of modem housing is also important. The influence of the ‘polo’ variable is considerably reduced when compared to the education portfolio, reflecting the fact that education is only a fraction of total expenditures. The same may be observed with respect to the dummy variable ‘so&l service’. We could not find a substantial infIuence of the variables ‘average personal income’, ‘the area of a historic town-center’ and ‘the number of residential kcmels’. 8.

con&sion

In this paper we developed the concept of a municipal welfare function by analogy to the concept of an individual welfare function of income On the basis of an extensive surwey among all Dutch municipalities estimates of these municipal welfare functions are derived for about 550 municipalities. The main resuIts are the following: (a) The municipal welfare function of total expenditures and partial welfare functions with respect to portfolios are measurable and operational concepts. (b) The lognormal specification of these functions cannot be rejected. (c) The welfare sensitivity CTof the municipal spenders varies a lot among spenders but there is a definite pattern of order between the several portfolios considered. (d) Tile natural unit er - except for the very small municipalities -may be explairied for a good deal by objectively measurable factors like the number of inhabitants, unemployment, area arid age distribution of houses and population. (e) Welfare sensitivity does not seem capable of explanation by these factors. It has to be stressed that these results are orply the first results of an exploration just started. At a later stage other model specifications. more advanced estimation methods and the influence of other variables - like the regional environment and interrelationships - shall be investigated. Moreover the political composition has to be brought into the picture, However, it does not seem a prema.ture statement, when we express our belief

74

B. oan Praag and J. Linthrst, Municipal wdfare functions

that this approach will shed new light on the behaviour of local authorities. Moreover it may serve as an additional basis for the distributior, of public goods. It goes without saying that our results are of special relevance for the Dutch context and that concepts have to be redefined somewhat for application in other countries with a different financial regime at the local level. References Aitchison, J, and J.A.C. Brown, 1957, The lognormal distribution (Cambridge University

Press, Cambridgr). Aumann, R.J., 1975,Values of markets with a continuum of traders,Econometrica 43,61 l-646. Berg, C. van den, 1956,De structuur van de gemeentelijke uitgaven (Stenfert Kroese, Leyden). Debreu, G., 1959, Theory of value (Wiley, New York). Frisch, R., 1959, A complete scheme for computing all direct aud cross demand elasticities in z made1 with many sectors, Econometrica 27,177-196. Hakansson, N.H., 1970, Optimal investment and consumption strategies under risk for a class of utility functions, Econometrica 38,587~607. Mosteller, F. and P. Nogee, 1951, An experimental measurement of utility, Journal of Political Economy 59,3714&I. Netherlands Central Bureau of Statistics, 1964, Typologie van de nederlandse gemeenten near urbar risatiegraad, 31 mei 1960 (NCBS, The Hague). Neumatm, J. von and 0. Morgenstem, 1944, Theory of games and economic behavior, 3rd ed. 1953,3rd print 1967 (Wiley, New York) Pareto, V., 19%, Manuel d%conomie pohtique (V. Giard and E. Briere, Paris). Praag, B.M.S. van, 1968, Individual welfare functions and consumer behavior (North-Holland, Amsterdam). Praag, B.M.S. van, 1971, The welfare function of income in Belgium: An empirical investigation, Euroytian Economic Review 3,337-369. Praag, B.M.S. van and A. K;tpteyn, 1973, Further evidence on the individual welfare function of income: An empirical investigation in the Netherlands, European Economic Review 5, 3362. Prais, S.J. and H.S. Houthakker, 19JS, The analysis of family budgets (Cambridge University

Press, Cambridge). Samuelson, P.A., 1947, Foundations r.)feconomic analysis (Harvard University Press, Cambridge, Mass.). Somermeyer, W.H. and R. Bannink, 1973, Aconsumption-savings model and its applications (North-Hoiland, Amsterdam). Stone, J,R.N., 1954, Linear expenditure systems and demand analysis: An application to the pattern of British demand, The Economic Journal 6451 l-527. Theil, H., 1965, The information approach to demand analysis, Econometrica 33,67-87.

B. van Praag and J. Linthorst, Municipal welfare functicm

75

Appendix

Table 6 presents the characteristics of the partial municipal welfare functions, subdivided to town size and urbanization degree. Table 6a Public works.

Inhabitants o1,000

8

r,ooO-

2$00

31

2,ooo-

5,000

138

s,ooo- 1O~ooo

147

lO,oOO-

20,000

118

20,000-

50,000

68

5o,ooo- 100,ooo

19

100.000 - and more

8

4.52 (0.02) 5.38 (0.02)

0.96

6.28 (0.02) 7.09 (0.02) 7.74 (0.02) 8.36 (0.01) 9.34 (0.01) 10.11 (0.01)

0.53

0.73

0.42 0.39 0.31 0.26 0.36

0.32 10.04) 0.36 (0.03)

0.26

0.51

0.20

0.97

0.04

0.21

0.49

0.17

0.98

0.02

0.29 (0.03) 0.30 (0.03) 0.28 (0.02) 0.25 (0.02) 0.28 (0.02) 0.23 (0.02)

0.30

0.46

0.16

0.98

0.02

0.26

0.49

0.15

0.98

0.02

0.17

0.51

0.16

0.98

0.02

0.17

0.49

0.14

0.98

0.02

0.15

0.43

0.13

0.94

0.01

0.12

0.49

0.12

0.98

0.02

0.28 (0.02)

0.22

0.46

0.17

0.98

0.02

0.26

0.48

0.14

0.98

0.02

0.33

0.52

0.15

0.98

0.02

0.19

0.48

0.16

0.98

0.03

0.25 (0.02) 0.27 (0.02) 0.28 (0.02)

0.15

0.49

0.16

0.99

0.02

0.16

0.52

0.18

0.98

0.02

0.14

0.55

0.13

0.98

0.02

0.38 (0.04) 0.24 (0.02) 0.30 (0.02) 0.26 (0.02) I- I-0.29 (0.03)

0.41

0.45

0.15

0.98

0.U

0.16

0.45

0.14

0.98

0.01

0.11

0.41

0.13

0.98

0.01

0.16

0.46

0.13

0.99

0.01

“_--- -_~- ____~ _-.__ 0.24 0.49 0.16

0.98

0.02 --

Urbanization digree

Countryside’

Urbanized countrysideb

(Al)

39

(A2)

81

(A31

107

(A4)

85

W)

65

(B2)

6”.

(B3)

27

(Cl)

20

(C2)

25

(C3)

8

(Cd)

16

6.53 (0.02) 6.72 (0.02) 6.79 (0.02) 6.76 (0.02)

1.16 0.96 1.05 0.79

6.76 (0.01) 7.92 (0.02) 7.95 (0.01)

0.62

7.40 (0.02) (E)

0.57

8.94 (0.02) 9.70 (0.01)

0.38

7.17 (0.02)

1.12

0.59 0.59

0.25

Town8

537 ~‘%ce footnotes

to table A.

0.50

&i) 0.33 (0.03) 0.27 (0.03)

B. van Praag and J, Linthorst, Munici.aI welfare Jicnctions Table 6b Education.

inhabitants o1,OOQ

7

l,OOO-

2,Ooo

33

2,000-

5,ooo

136

5,000 -

10,000

141

lO,OOO- 20,000

119

50,000

73

so,000 - 100,000

19

100,000 - and more

7

UrBanization degree WI

39

cul intry-

81

20,000-

WI

side”

Urbanized countrysid@

CA31

102

C44)

83

IW

65

m21

64

(B3)

28

W)

19

C2)

29

TOWIP (C3) (W

8 17

4.27 (0.02) 5.35 (0.02) 6.09 (0.01) 6.83 (0.01) 7.63 (0.01) 8.52 (0.01) 9.47 (0.01) 10.78 (0.01)

1.28 0.75 0.60 0.50 0.48 0.51 0.68 0.82

0.81 6.41 (0.01) 6.69 (0.01) 6.54 (0.01)

1.06 1.03 0.96 0.74

(&?I) 7.89 (0.01) 7.95 (0.0%) 7.32 (0.01) 8.62 (0.01) 8.95 (0.01) 10.15 (0.01)

0.73 0.74 0.93 0.44 0.75 0.89

0.37 (0.03) 0.31 (0.02) 0.22 (0.02) 0.23 (0.02) 0.23 (0.02) 0.19 (0.01) 0.23 (0.02) 0.19 (0.01)

0.47

0.41

0.22

0.99

0.01

0.23

0.60

0.16

0.99

0.01

0.21

0.50

0.17

0.98

0.02

0.21

0.52

0.18

0.98

0.03

0.18

0.52

0.16

0.98

0.02

0.16

0.52

0.14

0.98

0.03

a.13

0.52

0.18

0.98

0.01

0.19

0.47

0.11

0.98

0.02

0.23 (0.02) 0.25 (0.02) 0.26 (0.02) 0.22 (0.02)

0.20

0.48

0.19

0.99

0.01

0.18

0.51

0.16

0.98

0.02

0.28

0.54

0.17

0.98

0.02

0.16

0.53

0.19

0.98

0.02

0.24 (0.02) 0.21 (0.02) 0.24 (0.02)

0.23

0.49

0.15

0.98

0.02

0.17

0.53

0.16

0.98

0.02

0.17

0.54

0.15

0.97

0.03

0.23 (0.02) 0.14 (0.01) 0.17 (0.01) 0.22 (0.01)

0.21

0.47

0.14

0.99

0.02

0.10

0.51

0.14

0.98

0.03

0.07

0.52

0.20

0.98

0.01

0.14

0.46

0.13

0.98

0.02

0.17

0.98

0.02

-_I

Netherlands

535

gYhe footnoks to table 4.

7.07 (0.01) --

1.27

0.23 (0.02)

0.20

0.52

._

B. mm Praag and J. Linthorst, Mwdcipal welfare functions

77

Table 6c Culture, sports and recreation. -

n

inhabitants o1,000

P

I,OOo-

2,000

32

2,000-

5,ooo

137

s,ooo-

10,ooo

143

lO,ooa-

20,000

116

2o,ooo-

50,ooo

72

5oJloo - 100,000 100,000 - and more

2.99 (0.01) 3.82 (0 05)

8

4.75 (0.03) 5.45 (0.03) 6.34 (0.02) 7.35 (0.02) 8.52 (0.02)

17 Y

642)

5.17 (0.03)

82 (z!) 5.25 (0.03) 5.14 (0.03)

side@ (A3)

Urbanized countrysidcb

loo

(A4)

83

031)

65

os2)

61

033)

29

(Cl)

20

C2)

29

(C3)

a

(C4)

18

5.19 (0.03) 6.66 (0.02) 6.79 (0.03)

_

Netherlands ‘-%x

F

534

1.11

0.47 (0.02) 0.71 (0.09) 0.48 (0.04) 0.47 (0.05) 0.42 (0.W

0.77 0.65 0.51 0.49 0.51 0.36

1.Ol

(E) 0.45 (0.04) 0.36 (0.02)

0.48

s(o)

v

~(0)

R

s(f0

0.40

0.44

0.19

0.99

0.01

0.53

0.46

0.18

0.98

0.02

0.31

0.44

0.18

0.98

0.02

0.32

0.43

0.18

0.98

0.02

0.30

0.46

0 17

0.98

0.02

0.25

0.46

0.19

0.98

0.02

0.30

0.47

0 14

0.98

0.02

0.18

0.46

0.08

0.99

0.01

0.35

0.41

0.16

0.98

0.02

(0.W 1.06

0.51 (0.0s)

0.31

0.45

0.17

0.98

0.02

1.07

0.49 (0.W 0.50 (0.05)

0.37

0.45

017

0.98

0.02

0.37

0.44

0.19

0.98

0.02

0.49 (0.05) 0.38 (0.03)

0.35

0.45

0.20

0.98

0.02

0.25

0.46

0.20

0.99

0.02

0.23

0.48

0.17

0.98

0.01

0.17

0.39

0.13

0.98

0.03

0.31

0.50

0.17

0.98

0.02

0.15

0.34

0.13

0.97

0.04

0.23

0.50

0.08

0.99

0.01

0.88

0.85 0.62 0.91

,S:C$ 0.76

(XX) 7.43 (0.3’2) a.33 (0.02) 9.31 (0.02)

Town“

_.---P

8

0.88

39 collntry-

SW

OS8 0.30 0.88

0.34 (0.04) 0.41 (0.03) 0.28 (0.03) 0.42 (0.03)

-.----

5.76 (0.03) -..---footnotes to table 4.

---

1.38

0.46 (0.04)

0.33 -

0.45 ---_

0.18 -I_-~---

0.98

0.02 --.-

._

8. van Praag and J. Lintkorst, Municipal welfare functions

78

Table 6d Social affairs. -.--.----.

n hzhabitants O1,000

ii

S(D)

d

sk$

.-

0

s(u)

R

s(R)

7

4.79 (0.01)

o.r9

0.22 (0.01)

0.31

0.57

0.24

0.99

0.00

l,OOO-

2,OOO

30

5.19 (0.02)

0.77

0.29 (0.03)

0.25

0.61

0.17

0.98

0.01

2,000 -

5,000

132

6.14 (0.02)

0.63

0.24 (0.02)

0.25

0.57

0.15

0.98

0.02

5,OOO- 10,OOO

135

6.93 (0.01)

O.&?

0.22 (0.02)

0.22

0.58

0.15

0.98

0.04

lO,OOO- 20,OOO

111

7.49 (0.01)

O.ti8

0.20 (0.02)

0.13

0.55

0.17

0.98

0.02

2O,OOO- 50,OOO

67

7.77 (0.01)

0.15

0.24 (0.02)

0.20

0.53

0.13

0.98

0.03

50,OOO- lOO,OOO

15

8.91 (0.01)

0.75

0.21 (0.02)

0.14

0.51

0.09

0.98

0.02

lOO,OOO - and more

9

10.14 (0.02)

0.74

0.27 (0.02)

0.15

0.51

0.14

0.98

0.01

Urbanization degree (Al)

38

6.42 (0.01) 6.50 (0.01) 6.51 (0.02) 6.63 (0.01)

1.03

0.25 (0.03) 0.21 (0.02) 0.27 (0.02) 0.19 (0.02)

0.26

0.53

0.14

0.98

0.02

0.24

0.58

0.13

0.98

0.02

0.27

0.57

0.16

0.98

0.05

0.16

0.6O

‘5.17

0.99

0.01

0.20

0.56

0.18

0.98

0.03

0.19

0.58

0.15

0.98

0.02

0.15

0.58

CL14

0.98

0.02

0.15

0.47

p*lS

0.99

0.01

0.12

0.52

j.12

0.98

0.02

0.13

0.45

5.07

0.99

x01

0.16

0.52

(‘,12

0.99

0.01

0.21

0.56

_-.__.__

_ ..,

77 96

Urbanized countryside”

(A4)

77

(Bl)

61

@2)

59

(B3)

28

Cl)

21

(C2)

24

(C3)

8

G4)

17

TOW5=

6.65 (0.02) 7.70 (0.01) 7.33 (0.01) 7.06 (0.01) 7.76 (0.01) 8.58 (0.01) 9.67 (0.0 1)

0.96 1.14 0.87 0.70 0.72 0.78 0.64 0.80 0.79

0.24 (0.03) 0.21 (0.01) 0.22 (0.02) 0.20 (0.01) 0.18 (0.02) 0.20 (0.01)

0.91

__-----Netherlands -+%ee

506

6.94 (0.01)

footnotes to table 4.

1.15

0.23 (0.02)

_.--.-_ -... ._ .,_ 0.15

0.98 -

0.03

_~-___,___l

B. can Praag and J. Linthorst,

Mutticipal welfare fimctions

79

For curiosity we present table 7 which makes a distinction according to the position of the respondent, i.e., poDician, town clerk, town treasurer or others. It is seen that most respondents are nonpoli!icians. There is a marked difference in evaluation. The town treasurer nt:ar!y always evaluates highest while the town clerk always evaluates most moderately. The politicians are somewhere in between We have no explanation for this phenomenon at the moment. Table 7 Welfare evaluations according to the position of the respondents.

I Public

works 0

n ---Politicians Town clerk Town treasurer

Official (unspec.) Unknown

Total

I1 Education --n 0 ___ __~

II Culture, spzmts, and recreation ---.n 0 ---___-

IV Social affairs n

u

V Total expenditures -_.n 0 93 0.49 81 0.45 339 0.51 23 0.52 16 0.55

99

0.48

93

78 251 82 28

0.45 0.50 0.50 0.56

81 242 89 31

0.45 0.53 O..c? 0.:3

0.54 0.52 0.58 0.55 0.57

538 0.49 _~______

536

535 0.45 509 0.52 -._.__.. - .._----~.-~._-~_

0.56

Y3 021

I .

94

0.44

77 261 75 28

0.36 0.48 0.45 0.47

72 219 106 19

552 ___--

0.50