Testing theories of real government size: U.S. experience, 1959-89.

• Author: Ferris, J. Stephen

1. Introduction

   In a recent article, West [17] argued that the existence of so many strands of analysis attempting to explain the growth of government calls ultimately for one consolidated or generalized theory. Accordingly he produced a model that integrated four such theories, two on the cost side and two on the demand side. The purpose of the present paper is to derive empirical measures of all four theories, using U.S. data for the period 1959-1989. The presumption is that each one separately might contribute in its own way to a composite explanation of government growth, and that what is currently most needed is a set of jointly determined empirical estimates showing relative importance.

   While all our measures of government size consolidate federal, state and local government expenditures, two other measurement issues should be emphasized since they distinguish our work from other contributions to this literature. The government component of our main dependent variable, the real size of government, is measured in two different ways: the first uses the National Accounts definition of government purchases which excludes transfer payments from the measure of size; whereas the second includes final purchases plus net government transfer payments.(1) Since we are interested in the effects of changes in the productivity of supplying government services, the first of these definitions is expected to be more relevant and is so used as the basis of our empirical work. However, since there is a sense in which changes in the productivity of government may affect the "output" of transfers, we also use the second definition to produce a more complete empirical exercise.

   The other distinguishing feature of our analysis is that both definitions of government size are analyzed in real as distinct from the more usual nominal share of government in Gross Domestic Product (GDP). This distinction becomes immediately more striking when it is pointed out that, while most authors hitherto have attempted to explain the phenomenon of positive growth in the ratio of nominals over the past half century, the ratio of reals has actually fallen for most of our time period, when that real share is exclusive of transfer payments.(2) The distinction between the real and nominal share is illustrated in Figure 1.(3) Note that the coming together of the two series reflects the rise in the relative price of government services that is characteristic of this time period.(4)

   Section II of our paper briefly restates the theory in West [17] in a form amenable to testing. Section III sets out the empirical predictions and section IV outlines the data sources and variable names used in the tests. Section V then presents the three-stage least squares estimates of the demand and supply curves used to determine real government size and discusses their meaning. Section VI offers our main conclusions.

2. Theory

   The equilibrium real share of output produced by government is modelled as the outcome of a competition among different factors to influence government size and is organized in terms of demand and supply analysis [17]. In addition to traditional variables influencing product demand, our integrated model focuses both on Wagner's [16] proposition that, at least in the early stages of growth, there is a "high" elasticity of demand for government services, and on public choice hypotheses in which special interest groups are hypothesized to influence real government size. The particular interest groups are drawn from the public choice literature, with particular emphasis on the "bureau voting power hypothesis" of Brennan and Buchanan [7]. On the supply side, we test the Baumol [2] and Beck [3] postulate that the relative cost of providing government services rises over time, as well as Kau and Rubin's hypothesis [10] that government tax collection costs fall as factors of production transfer to occupations with more visible rewards.

   The equilibrium determining the real size of government is illustrated by the intersection of dashed full demand and supply curves in Figure 2. The full demand price, [p.sup.d], represents the marginal willingness of the community to pay for increases in the real share of government services (fully delivered), while the full supply price, [p.sup.s], represents the complete marginal cost of providing these services, i.e., the sum of the conventional costs of producing government services plus the deadweight costs of raising necessary funds through taxation. These deadweight costs, a function of the distortion produced by taxing real activities with "imperfect" taxes, are assumed to increase with the real size of government [15].

   Because not all the costs of tax collection are observable, the full demand and supply curves in Figure 2 are purely conceptual. For empirical purposes, observable prices and quantities are needed and to generate these we rearrange the factors affecting demand and supply to write the equilibrium condition in terms of net demand and supply. A net demand for real government services is constructed by subtracting the unobserved tax collection and deadweight costs of financing the government's share from the full willingness to pay. Net demand measures the community's willingness to pay after recognizing that additional deadweight costs will arise from funding these services through taxation. By including this cost in the demand side of the problem, the cost equation now includes only the production costs of government services. Because a measure of the direct cost of providing these services is observable (from the National Accounts), our equilibrium is now formulated in terms of the equality of measurable demand and supply prices. This is the intersection of the solid lines in Figure 2. In equilibrium, [p.sup.ns] = [p.sup.nd], where [p.sup.ns] is the marginal production cost of producing government services (RELPRICE) and is measured in our empirical work as the ratio of the government services deflator in GDP, [p.sub.g], to the aggregate GDP price deflator, p. The corresponding measure of quantity is the real share of the National Accounts measure of government, G, in GDP and is measured as RSHARE [equivalent to] (G/[p.sub.g])/(GDP/p).

3. The Basic Model

   Beginning with the demand side, the net demand for government services can be written as

   [g.sup.d](TDV, PCV, DCC) = [g.sup.d] ([p.sup.nd], YPC, POVRATE, PCV, DCC), (1)

   where TDV represents a set of traditional demand side expenditure determinants, price (p), income per capita (YPC) and a measure of perceived need, the poverty rate (POVRATE); PCV represents a set of public choice or "Leviathan" variables; and DCC represents the factors influencing deadweight tax collection costs.

   From the set of traditional variables that would affect the median voter, we begin with the first law of demand and predict a negative coefficient on net demand price (RELPRICE). Note that because the demand for government services is determined by the unobserved full price, [p.sup.d], (rather than the observed net price, [p.sup.nd]), the measured quantity response to the observed price is expected to be smaller than for the (underlying) full price. This follows from the observation that because deadweight collection costs increase at an increasing rate, their subtraction from the full demand curve results in a net demand curve that is steeper in relation to price. Thus while the regression coefficient on RELPRICE is predicted to be negative, it would not be surprising to find that that coefficient is small.(5)

   Theory places no a priori restriction on the sign of the income effect. However, if Wagner's Law is interpreted as predicting an income elasticity on government services greater than one, then that prediction when applied to the share of government in output would correspond to a positive coefficient on per capita income, YPC. Unitary income elasticity implies constancy in the real share and hence a share coefficient of zero. In testing for the presence of Wagner's Law, Peltzman [13] has argued convincingly that the use of actual rather than permanent income will result in an income coefficient that is downward biased (because it includes transitory income) and hence biased against finding Wagner's Law. For this reason our analysis uses permanent, PERMY, rather than actual income.(6)

   To reflect the demand by the median voter for redistribution, we use a direct measure of the size of the target group to which substantial portions of real government services (and additional government transfers) are directed. Our measure of the desire for redistribution is the prevalence of poverty or the poverty rate, POVRATE.(7) An increase in POVRATE is then predicted to increase the demand for government services either because the community itself wishes greater government involvement in improving the lot of the poor or because the poor, or their representatives, are politically effective in obtaining increased transfers. The latter consideration raises public choice issues and perhaps the most important reason for including POVRATE in the regression. The presence of POVRATE controls for the potential spurious correlation that could arise because other (particularly public choice) variables are often correlated with both government size and poverty. This increases our confidence in the economic importance of those variables found to be statistically significant.

   Consider next the proposition that the demand for government services is driven by the relative strength of special interest groups. Two groups that have often been the subject of much public choice speculation are: government employment (bureaucrats), GOVEMP; and farmers, FARMPOP. The prediction is that as the share of these groups in the voting age population increases, the real share of government will also increase. Next, we expand the public choice variables to include two additional special interest...