A choice consistent model of demand for government expenditures

European Journal of Political Economy 9 (1993) 125-140. North-Holland

A choice consistent model of demand for government expenditures

George Tridimas*

University I$ Reading, Reading, UK

In the tradition of the median voter hypothesis this paper presents a formal model of utility maximization to study voter demand for public expenditures. The model applies the median voter hypothesis to examine voter equilibrium when collective decisions concern the simultaneous determination of the tax rate to pay for the total size of public expenditures and the allocation of that total between exhaustive and transfer expenditures. Our findings suggest that the principal determinants of demand are relative prices, mean income, the trade-off between the disincentive effects of taxation and the benefits from public expenditures, and inequality in income distribution.

The issue of how far governments can and should tax income away from private households to finance the provision of public goods and redistribution transfer payments has always been at the centre of economic and political debate and has attracted the interest of a long line of scholars. Yet, as in other areas of economic research, the extensive theoretical and empirical literature is still unable to provide the policy-makers with a clear- cut answer to the question of how much public expenditure can a society afford and what is the precise trade-off between the different uses of those expenditures.

The aim of the present paper is to analyse in a formal and systematic way the behavioural insights that application of the principle of utility maximization can provide to understand the issue of demand for government programmes. Assuming that consumers-taxpayers are rational utility maximizers the paper examines the interdependence of taxation and voter demand for government expenditures and analyses the implications of the utility maximizing choices of individuals for the size of the government budget and its allocation between exhaustive and transfer expenditures.

Section I describes the salient characteristics of positive models of the

Correspondence to: G. Tridimas, Department of Economics, University of Reading, Whiteknights, P.O. Box 218, Reading RG6 2AA. UK,

*I wish to thank two anonymous referees for useful comments and suggestions on an earlier version of the paper. Of course, responsibility for any remaining errors is mine alone.

01762680/93/$06.00 ‘g? 1993-Elsevier Science Publishers B.V. All rights reserved

126 G. Tridimus. A choice consistent model

determination of government expenditures found in the literature and reviews those studies which have applied the hypothesis of utility maximization to examine voter demand. However, by considering taxpayer income as exogenous such studies have ignored the effects of the parameters of the tax system on earned income and therefore on the size of tax revenue and government expenditures. Section 11 extends this basic framework by relaxing the assumption of exogeneity of income and tax revenue and formulates a model of utility maximization to analyse the factors which determine the level of the tax revenue and its allocation between exhaustive and transfer expenditures. Section III uses the Stone-Geary utility function to derive more specific and detailed results and compares them with other approaches to demand for government expenditures, in particular, Wagner’s law and the displacement hypothesis. Finally, section IV summarizes the main conclusions of the paper.

I. Public choice models and the median voter equilibrium level of government expenditures

Positive, or public choice, models of government expenditure and taxation examine how the government actually behaves by analyzing the factors that determine the outcomes of collective choices.’ More specifically, the government sector is viewed as an agent granted with considerable revenue raising and spending powers to provide services, whose costs and benefits may vary substantially across individuals. Accordingly, public choice models examine issues such as the behaviour of voters, their preferences over government programmes, their perceptions of the costs and benefits of those programmes, the activities of interest groups, the impact of voting rules, and more generally, the mechanisms which are used to aggregate individual preferences into a collective choice and the behaviour of elected and appointed officials.’

There are many ways in which collective choices can be made varying from the one extreme of dictatorship to the other of unanimity, but in the tradition of a democratic society a distinct class of public choice models assumes a majority voting rule and applies the median voter theorem3 to determine the size of a government expenditure/taxation programme. More specifically, following in a way the paradigm of the perfectly competitive

‘This line of research is distinctly different from normative models of government expenditure and taxation, as for example the optimal tax literature [see Diamond and Mirrlees (1971) and Mirrlees (1971)], and the literature on the optimal provision of public goods [Samuelson (1954 and 1955)J which seek to determine the values of tax rates and government expenditures, which result in an efficient allocation of resources and an equitable distribution of income. A detailed account of this literature can be found, amongst others, in Atkinson and Stiglitr (1980).

‘See Mueller (1989) for a review and an assessment of various topics of public choice. “See Bowen (1943), Downs (1957) and Black (1958).

G. Tridimas, A choice consistent model 127

market equilibrium, and assuming that voters are utility maximizers, it is shown that under the conditions of single-peaked preferences, honest revela- tion of preferences, single dimension elections and binary choices, the outcome of majority voting is that the median voter’s preferences will emerge as the collective preference. In what follows we take the median voter, or rather the voter with median income, as the decisive factor in the election outcome and we explore the implications of this line of thinkings for the size of the government budget and its structure between different categories of expenditure.

Studies of public expenditures which have adopted the framework of the median voter theorem start from the premise that the utility function of each member of the society comprises private (or more generally market) goods and public goods and other social services4 which are supplied by the government, formally

U’ = lJ’( Q’, G) (1.1)

where Q denotes the vector of goods purchased privately by the individual in the ordinary-pecuniary markets and G denotes the vector of outputs, public goods and social services provided by the government and consumed collectively by the society.

Utility is maximized subject to the constraint that income is spent to finance private purchases and to pay taxes. A static framework is assumed, so there is no saving. The individual budget constraint is then written

pQi= yi_Ti (1.2)

where P denotes the vector of prices of private purchases, Y’ denotes the pre-tax income of the individual, which is typically assumed to be exogenous, and T’ denotes the tax paid by the individual. Solving the above maximization problem determines the demand functions for private purchases.5

On the other hand, the government. or rather the political party which has won the election, is assumed to provide the set of government services which are preferred by the decisive-median voter, denoted by the superscript M.

‘In order to avoid unnecessary complications it is assumed that the output of the government sector is consumed collectively by the society irrespective of whether it comprises both ‘pure’ public goods and publicly provided private goods; on this see also footnote 6.

5As a corollary. it follows that the demand functions for private purchases will, in principle, depend not only on relative prices and disposable income but on the composition of government expenditures as well. However, by invoking almost unquestionably the usual assumption that preferences between private purchases and government services are separable (which, in turn, imphes that the allocation of expenditures between private purchases does not depend on the composition of government expenditures) empirical specifications of consumer demand have failed to recognize the importance of government expenditures as a determinant of consumer demand. For an analysis of this latter issue see Courakis and Tridimas (1992).

128 G. Tridimas, A choice consistent model

Formally, the components of G are determined by maximizing the utility function of M, that is,

U”= U”(QM, G) (1.3)

subject to the budget constraint of the government, which is always assumed to be balanced, that is,

CG=CNTi=NT”. (1.4)

C denotes the unit cost of the output of the government sector, N is the number of taxpayers and TA the mean of the tax payments. The literature typically assumes that G is produced by a homothetic technology, so that the unit cost of production, C, is constant with respect to the level of government output produced. The latter, in turn, ensures that the budget constraint is linear, which is necessary to define demand functions for G in the usual way and to allow econometric estimation. The tax share of the median voter is defined as the proportion of the cost of the government sector output borne by the median voter, that is, S”= TM/NT”. By substituting the latter into the budget constraint of the median voter and taking into account the budget constraint of the government, the consumption of the median voter is written as Q”=(l/P){ Y”-(T”/TA)(C/N)G}.

Accordingly, the question of finding the voting equilibrium level of government expenditures takes the form of determining the value of G which maximizes

V”=UM((l/P)[IYM-(T”iTA)(C/N)G],G). (1.5)

It then follows that the level of government expenditures preferred by the median voter will in general depend on his income, Y”, the relative price of government services, (C/P), the amount of taxes paid by the median voter relative to the mean, (TM/T*), which, in turn, depends on the pre-tax income distribution and the progressivity of the tax system, and the size of the population, N. With respect to the latter, the literature has invested a good deal of effort to measure ‘the degree of publicness’ of the government service, that is, the extent to which there are economies of scale in consuming the service.’ However, more detailed qualitative results cannot be obtained unless the utility function, the tax system and the income distribution are specified in more detail.

A large number of studies has attempted to test the empirical validity of

‘In particular, the relationship between G *, the level of government services perceived to be consumed by the median voter, and G, the level of G actually provided by the government is assumed to be G* =GN-“, where n is the degree of publicness; if n=O the government service is of the pure public good variety, while if n= 1, it is of the pure private good variety and intermediate cases are denoted by 0 <n < I.


the median voter theorem and estimate demand functions for various services provided by the government sector. Studies which have applied this mode of analysis relate primarily to demand for local public expenditures.’ They typically assume that the tax basis (being either income or the value of the residential property of the individual) is exogenous and that taxes are proportional, so that the utility function is written as U”= U”{(l/P)[YM--t( Y”/YA)(C/N)G], G}, w h ere t is the proportional tax rate.8 Maximization of the latter yields the demand function for G. For ease of estimation the demand functions for the various components, k, of G are generally specified to be of the log-linear type, namely,

In G,=a,+a, In YM +a, In t( Y”/YA)(Ck/P)+a3N +BZ. (1.6)

A vector of socio-economic and institutional variables, Z, is typically added to the set of explanatory variables; these are thought to be instrumental in affecting the demand for the various services included in G, though they are not explicitly provided for in the utility maximization model.’

II. Median voter equilibrium and the determination of government expenditures with endogenous income

The behavior of the individual

Despite the insights that the previous class of models of government expenditures provide, their ability to explain the equilibrium size of government spending is rather limited. In particular, the assumption that income is exogenous restricts severely their relevance to reality, since it ignores two important issues. First, how the tax arrangements, income tax and transfer payments, affect income. Second, how income changes impinge on the tax revenue and, therefore, the size of government expenditures. More specifically, there is very little in the previous model to limit the redistribution of income or the shifting of the burden of financing public goods and other services to wealthier groups of the population. Incentives are completely ignored. In deciding the level of public expenditures rational voters are concerned with three factors, namely, the utility that social services confer,

‘See, for example, Barr and Davies (1966) Borcherding and Deacon (1972), Bergstrom and Goodman (1973), Inman (1978) and Lovell(1978).

*The variable R”=SM(C/P)= t( Y”/Y”)(CjP) is the so-called tax price paid by the median voter; it is also known as the Lindahl price of the government service, that is, the personalized price that the median voter would have to pay to purchase the equilibrium quantity of the government service. More generally, when we allow for the degree of publicness of the government services (see footnote 6) the tax price is written as R”=SM(C/P)N-” or R”= P’(C/P)(G/G*).

‘For a reivew and a critique of this mode of analysis and of its econometric implementation see Romer and Rosenthal (1979) and Tridimas (1985).

130 G. Tridimas. A choice consistmt model

the extent by which they can shift the burden of taxation to finance those expenditures, and the disutility caused by the loss of income through distortionary taxation.

In order to take into account these considerations the utility function is generalized to include leisure, L, in addition to private goods and government services. Assuming that a linear income tax is levied at a rate t, and that all individuals receive a (per capita) transfer payment of X, the utility maximization problem of the individual takes the form of maximizing

U/’ = U’(Q’, L’, G)

subject to the budget constraint,

(2.1)

PQ’=(l-t)W’(l-L’)+X. (2.2)

W’ denotes the labour productivity of the individual and, accordingly, the wage rate that it receives. Following standard practice individuals are assumed to have identical utility functions, but to differ in their earning abilities, which, therefore, becomes the source of income inequality. With the earning ability W’ exogenously given and randomly distributed across the population, and the government setting t, X and G, individuals can only choose Qi and L’. This yields the first order condition

UL=(l -t)(W’/P)&. (2.3)

Subscripts denote first derivatives with respect to the corresponding variable. By solving this equation one can obtain the equilibrium levels of private consumption, and leisure of the individual; the latter in turn can be used to derive the level of his income, that is, Y’= (1 - t) W’( 1 -L’).

The behaviour qf the government

The objective of the government is to maximize the utility function of the decisive-median voter written as

UM = U"(QM, L”, G) (2.4)

In the context of this model, there are three variables under the control of the government, namely, exhaustive expenditures G, transfer payments, X, and the income tax rate, t. The three are related through the budget constraint of the government, that is,

CG+NX=NtYA

where YA = W”( 1 -LA) denotes the mean income.

(2.5)


The budget constraint implies that (any) two of the three policy variables can be set independently, determination of the third will follow automatically through the balanced budget constraint.” In other words, there are two decisions to be made, (a) the determination of the total size of the budget, that is, the selection of the tax rate t and (b) the determination of the composition of the budget, that is, the allocation of the budget between exhaustive and transfer expenditures, G and X. However, with two policy variables to decide the selection of the public expenditure/tax programme is no longer a single dimension election. In two-issue elections the assumptions required for the existence of a majority voting equilibrium are extremely restrictive, so that it becomes doubtful whether they hold in reality.”

We are therefore left with two options. The first is to assume that one of the three policy variables is set exogenously, so that the decision reduces again to a single issue election,r2 in which case the applicability of the median voter may be less problematic.13 Nevertheless, it is obvious that such an approach cannot provide a complete answer to the question at hand, i.e., the joint determination of t, X and G. The second option is to adopt a broader interpretation of the median voter theorem [in a way analogous to that adopted by the empirical studies of the allocation of various categories of public expenditures reviewed above, see eq. (1.6)] and assume that voters vote for political parties, whose policy platforms can be ranked on a single dimension continuum. Proposals about the income tax rate and the levels of exhaustive and transfer expenditures are part and parcel ?f the party policy platforms. In this case, and assuming again that individual preferences for party platforms are single peaked, the median voter model provides an accurate description of the aggregation process of voter demands.14 Conse- quently, we can again use the median voter (approximated as usual by the

‘% the short-run the ability of the government to adjust the instruments of policy may be limited as spending commitments are carried over from previous periods. However, the analysis takes a broader view and focuses on the policy design level. where the size of the budget and the shares of exhaustive and transfer expenditures are determined. In addition, even in the short-run, the government still has some discretion to adjust tax rates, spending on specific services and rates of benefit payments.

“Probably they are as restrictive as the condition of complete unanimity [see, Kramer (1973)].

12That is, the decision problem takes the form of either choosing t and X given G, or, choosing I and G given X, or, choosing X and G given t.

13Elements of this approach can be traced in the studies of Cooter and Helpman (1974). Romer (1975), Roberts (1977) and Meltzer and Richard (1981, 1983); it should be noted that these studies were concerned with the interaction of taxes and transfer payments ignoring the other possible choices listed in the previous footnote.

i41ndeed such a view of the median voter theorem, which considers it as mechanism to arrirulute refer demand for a government programme, appears to be considerably less objection- able than the more narrow interpretation, which contends that the size of the government programme is determined by the median voter. For a detailed discussion of this and other related points see Holcombe (1989).


voter with median income), to study the joint determination of tax rates, exhaustive and transfer government expenditures.

Mediun voter equilibrium, the size of the budget and its allocution between exhaustive und transfer expenditures

To maximize the utility function (2.4) subject to the budget constraint (2.5) we differentiate the Lagrangean with respect to G, X and t. Denoting the Lagrangean multiplier by ,U the first order conditions are written as follows

MM u,"Q? + U, Lx =pN(l -tY”,). (2.6)

MM U:Q?+ u, L, = -pN(YA+tY;).

Substituting from (2.3) into the system of (2.6) we obtain

U,MCQg+(l-t)(W”/P)L~]+Uf=pN(C-NtY$,

U$CQf+U -O(W”IJ’WXMI =pN( 1 -tY;), (2.7)

$CQfM+U -tNW”/‘P)L,M1 = -pN( YA + t Yf)

Further, by differentiating the budget constraint of the median voter we have

QF= -(I-r)(W”/‘P)L$‘,

Q$‘= -(1 -t)(W’+/P)Ly+(l/P),

Qy= -(Y”/P)-(1-t)(W”/P)Ly.

Substituting the latter back into (2.7) and rearranging we derive

Uf[(C/P)-(N/P)tY;]=U$V[(YA/YM)+(t/YM)Y;4].

U$[(C/P)-(N/P)tY;]=U:N[l -tY,“].

(2.8)

(2.9)

(2.10)

Eqs. (2.9) and (2.10) together with the budget constraint of the government, eq. (2.5), comprise a system of three equations in the three unknowns G, t and X. Eq. (2.9) shows the relation between the equilibrium size of exhaustive public expenditures and the tax rate preferred by the median voter; eq. (2.10) shows his preferred allocation of the total of public expenditures between exhaustive and transfer expenditures.

Eqs. (2.9) and (2.10) show that, in general, the desired combination of public expenditures and the tax rate depends on the ratio of mean to median


income, YA/YM (this ratio can be interpreted as an indicator of the distribution of income in the society); the relative price of government output, C/P; the size of population, N; and the effects that income taxes, transfer payments and public goods have on mean income, Yt, Yi and Yg respectively. The standard assumptions that distortionary income taxes generate disincentive effects and that leisure is a normal good (so that an increase in non-earned income decreases the supply of labour), imply that the derivative Y;’ and Yi are negative. However, the direction of the effect of government services on mean income is less clear. If preferences between exhaustive public expenditures and private consumption (including that of leisures) are separable, then the former has no effect on labour supply and mean income, that is, Y$=O. If, on the other hand, preferences are not separable the sign of the derivative may be positive or negative, depending on whether public goods and social services provided by the government are considered by households as conducive to earning a higher or a lower income respectively.i5

The choices and the trade-offs that the decisive voter has to resolve are summarized as follows. The median voter enjoys the benefits from the provision of public goods and of transfer payments (which allow him to take more leisure), but knows that he, along with the rest of the society, will have to pay taxes to finance their provision. He also recognizes the opportunity to shift part of the burden of finance to the wealthier groups of the society by favouring a high tax rate (which increases the tax bill of those with high income). An increase in the tax rate increases tax revenue and therefore the ability of the government to provide more public expenditures. However, the median voter realises that a high tax rate will induce some workers to withdraw from the labour force and live on subsistence redistribution, while it will induce those who are still working to work less. The overall effect of the latter is obviously to reduce tax revenues and the ability to finance public expenditures.

At the same time the median voter chooses the composition of the revenue secured through taxation between exhaustive and transfer expenditures. The latter, however, is a noticeably more complex decision than, for example, the allocation of private consumption expenditures of the standard utility

IsThere is no simple resolution of this ‘crowding in’ or ‘crowding out’ issue. If government services are perceived as enhancing human capital and increasing the productivity of the individual (e.g. spending on health and education) one would expect that they would increase mean income. If on the other hand, they are perceived as wasteful and obstructing productive private initiatives, they would decrease mean income. It is more likely that some components of government spending may fall into the former category, while others may fall into the latter. A full consideration of the complementarity-substitutability relationships of government expenditures and private income taking into account its intertemporal aspects lies beyond the purpose of this paper, for a more detailed account see Tridimas (1992).

134 G. Tridimus. A choice consistent model

maximization problem (where total budgetary expenditure is assumed exogenous). Transfer payments not only compete against the rest of public expenditures, but also by giving the incentive to take more leisure decrease tax revenue and the size of the budget. The ultimate outcome of those conflicting factors cannot be predicted at this level of generality, a more detailed specification of the decision problem of the consumer is required to obtain more explicit results. For this we turn to the next section.

III. An algebraic example

Let us assume that the utility function is of the Stone-Geurg type, i.e.,

U’=aln(Q’+Q,)+hln(L’+L,)+c~n(G+G,) (3.1)

with CI + ht C= 1. Maximization of utility subject to the budget constraint (2.2) yields the following equations for demand for private consumption, Q’, leisure, L’, labour supply, Hi = 1 -L’, and income Y’= W’H’,

Q’=(u[(l+L,)W’(l-r)+X]-bhPQ&(u+h)P,

L’= {h[ W’( 1 -t) +X + hPQo] -&Wi( 1 - t)}/(a + h) w’( I- t), (3.2)

H’={u(1+L,)W’(I-r)-h(X+PQ,))/(u+h)W’(l-t),

Y’=ju(l+Lo)Wi(l-t)-h(X+PQ,)j/(a+b)(l-t).

Letting L’= 1 we derive from (3.2) the level of the wage rate W” at which the individual chooses not to work (and finances his consumption from the transfer payment X), i.e.

W” = h(X + PQ,):‘(r( 1-t I!,,)( 1 -t).

Substituting the latter into (3.2) yields Y’=a( 1 + I,,)( W’- W’). Letting F( .) be a distribution function for individual productivity, so that F(W) is the fraction of the population with productivity less than W, then mean income is [where A I = u/(u + h)]

Y”=A,(I+L,)+~’ (W’-WO)dF(W) W”

(3.3)

Eq. (3.3) determines mean income, and therefore aggregate income NY”, once the productivity of the last non-worker, W”, is known. Differentiation of (7.3) with respect to t, X and G yields the following expressions for the first derivatives [where A z = h/(a + h)]

G. Tridimas. A choice consistent model 135

Y:=-A,(X+PQ,)(1-F0)/(1-t)2,

Y$= -A,(1 -FO)/(l -t),

Y$=O.l6

(3.4)

1 -F” = 1 - F( W”) denotes the rate of non-participation, that is, the fraction of the population that does not work.

Differentiating the utility function of the median voter with respect to Q and G, using (3.4) and substituting into (2.9) and (2.10) and rearranging we obtain

a(G + Go) =c(QM + Q,)(P/C)N(( YA/YM)

-t[A2(X+PQo)(l-F0)/(1-t)2YM]J. (3.5)

a(G+Go)=c(QM+QO)(P/C)N{1+t[A2(1-F’)/(l-t)]ji. (3.6)

Dividing (3.5) by (3.6) we obtain after the relevant manipulations

A,t[(l-F’)/(l-t)][Y”(l-t)+X+PQO]=(YA-Y”)(l-t). (3.7)

From the system of eqs. (3.2) we obtain

Q”+QO=[(l-t)Y”+X+PQo]/P. (3.8)

Substituting the latter into (3.6) we have

a(G+Go)=c(N/C)~1+t[A,(1-F0)/(1-t)]j[(1-t)YM+X+PQO].

(3.9)

Substituting (3.7) into (3.9) and rearranging we derive the level of G that maximizes the utility function of the median voter [where B, =~/(a +c) and

&=a/(u+c)]

G=[B1(N/C)(YA+PQo)]-B2Go. (3.10)

The important feature of the demand for exhaustive public expenditures which emerges from eq. (3.10) is that, with the type of consumer preferences assumed, the level of real exhaustive public expenditure chosen by the median income voter depends positively on the mean income of the society, but it is independent of his own median income. This implies that to the extent that there is a general increase of aggregate income, demand for exhaustive expenditures by the median voter will increase. However, if only

“It should be borne in mind that all the conclusions derived below are conditional on this last result, which implies that labour supply is independent of exhaustive government expenditures.


the median income increases (that is, the relative position of the median income earner in the income distribution improves) his preferred level of G will be unaffected.’ ’

Substituting (3.10) into the budget constraint of the government, eq. (2.4), and solving for X we obtain

X=(t-B,)YA-B,PQo+B2(C/N)Go. (3.11)

Substitution of the latter into (3.7) yields after the relevant manipulations

(a+C)[(a+hF0)/h(l-F0)](M-1)(1-t)2

+[Cu(M+K+Z)+(u+C)(M-l)](1-f)-u(M+K+Z)=0. (3.12)

where M = YA/YM, K =PQ,/YM and Z=CGo/YM. The solution to eq. (3.12) is the preferred tax rate for the decisive voter who works and decides t>O. Solving with respect to 1 -t and concentrating on the positive root, we have

1 - t = [(a + bF0)/2(a + c)(a + bF”)( M - 1)]

(-u(M+K+Z)-( u+c)(M- l)+-(M+K+Z)[l +px+q.~~]~:~1

(3.13)

where p = 2(u + c)(2u + h( 1 + FO)/ub( 1 - FO), q=(u+c)2/u2 and x= (M-l)/(M+K+Z).

Using the approximation [l +px +q~‘]“~ zz 1 +(p/2)x + [(q/2)-(p2/8)]x2, and substituting the latter into (3.13) we obtain after the relevant manipulations

tzD,[(M-l)/(M+K+Z)] (3.14)

where D, = [(a+b)(a+c)/ub(l -F’)]. From (3.14) we obtain the first derivative of t with respect to M

tM=D,(1+K+Z)/(M+K+Z)2>0. (3.15)

Eq. (3.14) shows that the income tax rate chosen by the median voter, when he is working, will be higher as the ratio of mean income to median income, M, rises. Interpreting the latter ratio as an index of income inequality, eq. (3.14) postulates a positive relationship between the relative size of the budget (its proportion to aggregate income) and income inequality.

“Eq. (4.10) also shows that G depends positively on the price of private purchases, P (and also on Qo). Such a ‘complementarity’ relationship, however. is model specific. That is, given the form of the utility function assumed, one cannot claim to have discovered that public and private expenditures are complements, since the latter is a consequence of the adding-up property of demand.

G. Tridimas. A choice consistent model 137

A further implication of eq. (3.14) is worth noting. Since it is the same policy process, which determines the desired level of the tax/transfer combination and the decision to work, t and F” are simultaneously determined rather than the tax rate affecting the rate of non-participation (as it might have been thought from the way that eq. (3.14) is written).‘* It then follows that the rate of non-participation, F”, is negatively related to the degree of inequality.

Using (3.14) to substitute into (3.11) we derive for the level of the transfer payment chosen by the median voter

X=([D,(M-l)/(M+K+Z)]-B,}YA-&PQO+B2(C/N)Go. (3.16)

Eq. (3.16) reveals that, similarly to the preferred rate of taxation, the desired level of the per capita transfer payment increases when the degree of income inequality rises. However, no such clear-cut inference can be made when mean income increases. More specifically, the following conditions relate to the sign of the dX/dY* derivative:

dX/dY*<O, for O<M<M, and dX/dY*>O, for M>M, (3.17)

with M,=[(a+b)(a+~)~+abc(1-F~)(K+Z)]/[(a+b)(a+c)~-ubc(1-F~)] as the critical value of M. The two inequalities imply that whether or not a genera1 proportional increase in income (that is, one which leaves the ratio of mean to median income unaffected) will lead the decisive voter to select a higher level of per capita transfer payments depends on the absolute value of the inequality index. In particular, the higher value of M the more likely it appears that the preferred level of the transfer payment will be rising with mean income.

Median voter, Wagner’s law and the displacement hypothesis

One of the best known and most often tested demand-theoretic explanations of the growth of public expenditures is Wagner’s 1aw;19 our findings have important implications for this line of enquiry. The standard statement of Wagner’s law postulates that government expenditures increase more rapidly than income, because the income elasticity of demand for government expenditures is greater than unity. Accordingly, numerous studies have examined the empirical validity of the law by estimating a log-linear specification of the form

ln(G/N)=c,+c,ln(RY*) (3.18)

“On this see also Meltzer and Richard (op. cit.). “See A. Wagner (1883).

138 G. Tridimas. A choice consiscenf model

where RYA denotes per capita real income, and testing whether cr > 1.20 Our findings, in particular those of eqs. (3.10) and (3.16) raise the following points in relation to the standard specification of Wagner’s law.

Focusing on exhaustive public expenditures, eq. (3.10) first indicates that real public expenditures is conditional on the relative price of government output, an aspect which has been omitted by studies adopting the log-linear specification (3.18). ” More specifically, exhaustive government expenditures will grow more rapidly than the rest of the economy if demand is price inelastic (elastic) and their relative price, C/P, has been rising (declining).22 Second, eq. (3.10) also shows that in order for Wagner’s law to hold, that is, (dG/dYA)( YA/G) > 1, it must be cPQ, < a(C/N)G,. Since, in general, one cannot presume that such a condition is necessarily satisfied, one should not expect Wagner’s law to be a proposition of general applicability either across different countries, or different periods, or different components of public expenditures.

Turning to eqs. (3.16) and (3.17) two more observations follow. In view of our discussion of the sign of the derivative dX/dYA, with regard to transfer expenditures at least, the possibility of the reverse of Wagner’s law cannot be ruled out. That is, depending on relative income inequality, it is possible that as per capita income rises transfer expenditures decline. Moreover, eq. (3.17) suggests that, by excluding income distribution considerations, Wagner’s law offers an incomplete account of the determinants of demand for government expenditures. In particular, our results suggest that changes which increase the number of voters with relatively low incomes (lowering therefore the median income relative to the mean), like an extension of the franchise to poorer groups of the population, or greater participation of them into the political process, lead to a higher demand for government expenditures.‘3

Moreover, our results can be seen as offering a formalization of the displacement hypothesis of Peacock and Wiseman. Indeed, the equilibrium value of the tax rate in eq. (3.14) can be interpreted as the ‘tolerable level of taxation’ which in normal times vote-seeking politician cannot overstep.

‘“See Courakis, Roque and Tridimas (1993) for a critical discussion of this standard econometric specification of Wagner’s law.

“Indeed, rewriting YA as P.RY*, eq. (3.10) makes clear that the ratio of the price of private purchases to the unit cost of government expenditures, P,‘C, must be included in the set of the explanatory variables in regression equations of Wagner’s law. Specifications which feature such relative price as an explanatory variable, although still in a less formal way than that derived here. are estimated in the study of Courakis. Royue and Tridimas (ibid.) who have> derived negative and statistically significant relative price elasticities.

“In connection to this. see Baumol’s (1967) paper which argues that the relative price of government expenditures has been rising, because productivity growth in the government sector lags behind that of the private sector.

‘“On this see also Meltzer and Richard (op. cit.); for a critical review of the latter see Mueller (1987).

“‘See Peacock and Wiseman (1961).


However, during national emergencies, like wars, natural disasters and other social upheavals, voters’ perceptions of their contribution to society and attitudes to the role of government are most likely to change, shifting thereby the tolerable level of taxation. This is formally modelled by introducing changes in the relevant parameters, a, b and c, of the utility function, which imply an increase in the upper threshold of taxation. In addition, changes in the parameters of the utility function point to possible restructuring of the composition of government expenditures, see eqs. (3.10) and (3.16), exactly as argued by the ‘inspection effect’ of Peacock and Wiseman, that is, following the displacement government spending is reallocated to other priority areas.

IV. Conclusion

The aim of this paper has been to explore the implications of the theory of choice for the demand for public expenditures and the composition of that demand between exhaustive and transfer expenditures. Folowing the tradition of the median voter model it was assumed that the levels of budgetary outlays, which maximize the utility of the decisive-median voter, will emerge as the collective choice of the society. The latter does not imply that the levels of public expenditures actually provided are those preferred by the median voter, since in reality the observed pattern of expenditures reflects a variety of other factors, like supply and constraints on the choices of the median voter. Rather, it implies that in elections where the contest can be depicted along a single dimension, as for example in the choice between left and right, the median voter model describes successfully the process of aggregating individual preferences.

Having established in this light the median voter as the decisive voter, we set to identify the conditions for voter equilibrium, when collective decisions regard the simultaneous determination of the tax rate to pay for the total size of public expenditures and the allocation of that total between exhaustive and transfer expenditures. Our tindings suggest that the principal determinants of demand are relative prices, mean income, the trade-off between the disincentive effects of taxation and the benefits from public expenditures and inequality in income distribution. Finally, they also imply that explanations of the phenomenon of government growth relying on simple relations of income to demand for government expenditures provide an incomplete, if not erroneous, account of a highly complex process.

References

Atkinson, A.B. and J.E. Stiglitz, 1980, Lectures in public economics (McGraw-Hill, New York). Barr, J.L. and O.A. Davies, 1966, An elementary political and economic theory of the

expenditure of local governments, Southern Economic Journal 33, 149-165.

140 G. Tridimas. A choice consistent model

Baumol, W.J., 1967. The macroeconomics of unbalanced growth: The anatomy of urban crisis, American Economic Review 57, 4155426.

Bergstrom, T.C. and R.P. Goodman, 1973, Private demand for public goods, American Economic Review 63, 28@297.

Black, D., 1948, The theory of committees and elections (Cambridge University Press, Cambridge).

Borcherding, T.C. and R.T. Deacon, 1972. The demand for services of the non-federal governments, American Economic Review 62, 891-901.

Bowen, H.R., 1943, The interpretation of voting in the allocation of economic resources, Quarterly Journal of Economics 58, 27748.

Cooter. R. and H. Helpman, 1974. Optimal income taxation for transfer payments under different social welfare criteria, Quarterly Journal of Economics 88, 656670.

Courakis, AS., F. Moura-Roque and G. Tridimas, 1993, Public expenditure growth in Greece and Portugal: Wagner’s Law and beyond, Applied Economics 25, 1255134.

Courakis, A.S. and G. Tridimas, 1992, Public consumption expenditures and private consumer demand, Mimeo. I

Diamond. P.A. and J.A. Mirrlees, 1971. Optimal taxation and public production 1 and II, American Economic Review 61, g-27 and 261-278.

Downs, A., 1957, An economic theory of democracy (Harper and Row). Holcombe, R.G., 1989, The median voter model in public choice theory. Public Choice 61,

115-125. Inman, R.P.. 1978, Testing political economy’s as if proposition: Is the median voter really

decisive?, Public Choice 33, 45-66. Kramer, G.H.. 1973, On a class of equilibrium conditions for majority rule, Econometrica 41.

2855297. Lovell, M.C., 1978, Spending for education: The exercise of public choice, Review of Economics

and Statistics 60, 487495. Meltzer, A.H. and SF. Richard, 1978. A rational theory of the size of government, Journal of

Political Economy 89, 914-927. Meltzer, A.H. and S.F. Richard, 1983, Tests of a rational theory of the size of government,

Public Choice 41, 403418. Mirrlees, J.A., 1971, An exploration in the theory of optimum income taxation. Review of

Economic Studies 38, 175208. Mueller, D., 1987, The growth of government: A public chocie perspective, International

Monetary Fund Staff Papers 34, I 155149. Mueller, D., 1989, Public choice I1 (Cambridge University Press). Peacock, A.T. and J. Wiseman, 1961, The growth of public expenditure in the United Kingdom

(George Allen and Unwin, London). Roberts, K.W.S., 1977, Voting over income tax srhedules, Journal of Public Economics 8,

3299340. Romer, T., 1975, Individual welfare. majority voting and the properties of a linear income tax,

Journal of Public Economics 4, 1633185. Romer. T. and H. Rosenthal, 1979, The elusive median voter, Journal of Public Economics 12,

143-l 70. Samuelson, P.A.. 1954, The pure theory of public expenditures, Review of Economics and

Statistics 36, 387-389. Samuelson, P.A., 1955, Diagrammatic exposition of a theory of public expenditures, Review of

Economics and Statistics 37, 350-356. Tridimas, G., 1985, Economic theory and the allocation of public expenditures in Greece. Greek

Economic Review 7, 34-52. Tridimas, G., 1992, A note on the effects of government expenditures on prtvate consumptton,

Public Finance/Finances Publiques 47, 153-l 61. Wagner, A., 1883, Three extracts on public finance, in: R.A. Musgrave and A.T. Peacock. eds.,

Classics in the theory of public finance (Macmillan, London, 1958).

Documents

A choice consistent model of demand for government expenditures