Testing Theories of Real GovernmentSize:
U.S. Experience, 1959-89*
J. STEPHEN FERRIS
EDWIN G. WEST
Carleton University
Ottawa, Canada
I. Introduction
In a recent article, West [17]arguedthat the existence of so many strandsof analysis attempting
to explain the growth of governmentcalls ultimatelyfor one consolidatedor generalizedtheory.
Accordingly he produced a model that integratedfour 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 presumptionis that each one
separately might contributein its own way to a composite explanationof governmentgrowth,
and that what is currentlymost needed is a set of jointly determinedempiricalestimatesshowing
relative importance.
While all our measuresof governmentsize consolidate federal, state and local government
expenditures,two other measurementissues shouldbe emphasizedsince they distinguishour work
from other contributionsto this literature.The government component of our main dependent
variable,the real size of government,is measuredin two differentways: the firstuses the National
Accounts definition of governmentpurchaseswhich excludes transferpayments from the measure of size; whereasthe second includes finalpurchasesplus net governmenttransferpayments.'
Since we are interested in the effects of changes in the productivityof supplying government
services, the first of these definitionsis 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 productivityof
government may affect the "output"of transfers,we also use the second definitionto produce
a more complete empirical exercise.
The other distinguishingfeatureof our analysisis thatboth definitionsof governmentsize are
analyzedin real as distinct from the more usual nominal shareof governmentin Gross Domestic
Product (GDP). This distinctionbecomes immediatelymore strikingwhen it is pointed out that,
while most authorshithertohave attemptedto explain the phenomenonof positive growth in the
ratio of nominals over the past half century,the ratio of reals has actuallyfallen for most of our
*We would like to thankKeith Acheson, Dennis Mueller, Soo Bin Park,LarrySchembri,Stan Winerand a referee
from this Journalfor comments that have alteredand improvedthe real size of this paper.None are responsible for any
remainingerrors. Finally we wish to acknowledge supportfrom a G6 grant from CarletonUniversity.
1. The first and second measures correspond,to the Citibase series GAGGEand GAGEX.
537
538
J StephenFerrisand Edwin G. West
time period, when that real shareis exclusive of transferpayments.2The distinctionbetween the
real and nominal shareis illustratedin Figure 1.3 Note that the coming togetherof the two series
reflects the rise in the relative price of government services that is characteristicof this time
period.4
Section II of our paperbrieflyrestatesthe theory in West [17]in a form amenableto testing.
Section III sets out the empiricalpredictionsand section IV outlines the datasourcesandvariable
names used in the tests. Section V then presents the three-stage least squares estimates of the
demandand supply curves used to determinereal governmentsize and discusses their meaning.
Section VI offers our main conclusions.
II. Theory
The equilibriumreal share of output producedby governmentis modelled as the outcome of a
competition among different factors to influence government size and is organizedin terms of
demandand supply analysis [17].In additionto traditionalvariablesinfluencingproductdemand,
our integratedmodel focuses both on Wagner's[16]propositionthat, at least in the early stages of
growth, there is a "high"elasticity of demandfor governmentservices, and on public choice hypotheses in which special interestgroupsare hypothesizedto influencereal governmentsize. The
particularinterest groups are drawnfrom the public choice literature,with particularemphasis
on the "bureauvoting power hypothesis" of Brennanand Buchanan[7]. On the supply side, we
test the Baumol [2] and Beck [3]postulatethatthe relativecost of providinggovernmentservices
rises over time, as well as Kau and Rubin'shypothesis [10] that governmenttax collection costs
fall as factors of productiontransferto occupations with more visible rewards.
The equilibriumdeterminingthe real size of government is illustratedby the intersection
of dashed full demandand supply curves in Figure 2. The full demandprice, pd, representsthe
marginalwillingness of the communityto pay for increases in the real shareof governmentservices (fully delivered), while the full supply price, pS, representsthe complete marginalcost of
providingthese services, i.e., the sum of the conventionalcosts of producinggovernmentservices
plus the deadweightcosts of raising necessary funds throughtaxation.These deadweightcosts, a
function of the distortionproducedby 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 demandand supplycurves
in Figure 2 are purely conceptual.For empirical purposes, observableprices and quantitiesare
2. The transferinclusive measure of real government services has stayed relatively constant at about thirty five
percent of real GDP since the early fifties.
3. Berry and Lowery [5, 734-35] note that "any valid assessmentof change in the size of the public sector must
reflect a recognitionof the differentialrates of change in the prices of goods and services between the public and private
sectors .. ." so that "when the numeratorand denominatorin the ratio of US governmentalexpenditureto total national
outputare adjustedwith price deflators... the apparentrate of governmentgrowthin the post war era falls substantially."
4. While we highlightthe choice over which quantityshouldbe used to measurereal governmentsize, there also
arises a choice over which price index to use to deflatethe differentnominalmagnitudes.Because we focus on the benefits
and costs of producinggovernment"output,"we deflatenominalgovernmentmeasuresby the governmentservices price
index from the GDP accounts.However some authorsarguethata more appropriateprice index would be one thatvalues
governmentexpenditurein terms of the private consumptionforegone to finance these services. In this case, it would
be argued,the CPI would be a more appropriatemeasureand that our measureof size would be biased against theories
that relate directly to willingness to pay. While this does not appearempiricallyto be a substantiveconcern in our time
period, its potential significanceis discussed and assessed in relation to our empiricalfindings in section V below.
THEORIESOF REAL GOVERNMENTSIZE
539
0.26
0.24
0.22
0.2
0.18
0.16
I 1
1959
1962
1965
1968
1971
I I
1974
I
1977
I I
I I
1980
1983
1986
1989
Year
SRatioof Nominals
e Ratioof Real Values
Sources: Citibase (see Appendix)
Government size -- net of transfers
Figure 1. Real versus Nominal GovernmentShareof GDP
the factorsaffectingdemandandsupplyto writethe
neededandto generatethesewe rearrange
in
condition
terms
of
net
demand
andsupply.A net demandforrealgovernment
serequilibrium
vicesis constructed
the
unobserved
tax
collection
and
costs
of
by subtracting
deadweight
financing
the government's
sharefromthe full willingnessto pay.Net demandmeasuresthe community's
costswill arisefromfundingthese
willingnessto payafterrecognizingthatadditional
deadweight
servicesthroughtaxation.By includingthis cost in the demandside of the problem,the cost
equationnow includesonly the productioncosts of governmentservices.Becausea measure
of the directcost of providingthese servicesis observable(fromthe NationalAccounts),our
540
J. StephenFerris and Edwin G. West
pip
. Full Supply
Full Demand
ProductionCosts
RELPRICE
d
en
SNet
n
Dp
Demand
gS=gd
Codes .... Conceptualbut unobservable
- Derived and measurable
GoodsandServices
Figure2. DemandandSupplyof Government
equilibriumis now formulatedin terms of the equalityof measurabledemandand supply prices.
This is the intersection of the solid lines in Figure 2. In equilibrium,pns = pn, where p'S is
the marginalproductioncost of producinggovernmentservices (RELPRICE)and is measuredin
our empiricalwork as the ratio of the governmentservices deflatorin GDP,pg, to the aggregate
GDP price deflator,p. The correspondingmeasureof quantityis the real share of the National
Accounts measureof government,G, in GDP and is measuredas RSHARE- (G/pg)/(GDP/p).
III. The Basic Model
Beginning with the demand side, the net demandfor governmentservices can be written as
PCV, DCC),
gd(TDV,PCV, DCC) = gd (pnd, YPC,POVRATE,
(1)
where TDVrepresentsa set of traditionaldemandside expendituredeterminants,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 representsthe factorsinfluencing
deadweighttax collection costs.
From the set of traditionalvariablesthat would affect the median voter, we begin with the
first law of demandand predict a negative coefficient on net demandprice (RELPRICE).Note
thatbecause the demandfor governmentservices is determinedby the unobservedfull price, pd,
(ratherthan the observed net price, pnd), the measuredquantityresponse to the observed price
is expected to be smallerthan for the (underlying)full price. This follows from the observation
thatbecause deadweightcollection costs increaseat an increasingrate, their subtractionfrom the
full demandcurve results in a net demandcurve that is steeper in relationto price. Thus while
THEORIESOF REAL GOVERNMENTSIZE
541
the regression coefficient on RELPRICEis predicted to be negative, it would not be surprising
to find that that coefficient is small.5
Theory places no a priori restrictionon the sign of the income effect. However, if Wagner's
Law is interpretedas predictingan income elasticity on government services greater than one,
then that predictionwhen applied to the share of governmentin output would correspondto a
positive coefficient on per capita income, YPC. Unitary income elasticity implies constancy in
the real shareand hence a sharecoefficient of zero. In testing for the presence of Wagner'sLaw,
Peltzman [13]has arguedconvincingly that the use of actual ratherthan permanentincome will
result in an income coefficient that is downwardbiased (because it includes transitoryincome)
and hence biased against finding Wagner'sLaw. For this reason our analysis uses permanent,
PERMY,ratherthan actual income.6
To reflect the demandby the median voter for redistribution,we use a direct measureof the
size of the targetgroup to which substantialportionsof real governmentservices (and additional
governmenttransfers)are directed.Our measureof the desire for redistributionis the prevalence
An increasein POVRATEis then predictedto increase
of poverty or the poverty rate,POVRATE.7
the demandfor governmentservices either because the communityitself wishes greatergovernment involvementin improvingthe lot of the poor or because the poor, or their representatives,
are politically effective in obtaining increased transfers.The latter considerationraises public
choice issues and perhapsthe most importantreason for including POVRATEin the regression.
The presence of POVRATEcontrolsfor the potentialspuriouscorrelationthat could arise because
other (particularlypublic choice) variables are often correlatedwith both government size and
poverty. This increases our confidence in the economic importanceof those variablesfound to
be statisticallysignificant.
Consider next the proposition that the demand for government services is driven by the
relative strengthof special interest groups. Two groups that have often been the subjectof much
public choice speculation are: government employment (bureaucrats),GOVEMP;and farmers,
FARMPOP.The predictionis that as the share of these groups in the voting age populationincreases,the real shareof governmentwill also increase.Next, we expandthe publicchoice variables
to include two additional special interest groups that have received more recent critical attention: unions, UNION;and the fraction of the populationover sixty five, OLDPOP.The UNION
variable is of interest because of a conflict that has arisen between the more traditionalpublic
choice view thatunions favorstrongerandlargergovernments,and a morerecentlaborhypothesis
that workersview governmentas a substitutefor unions (so that declining union membershipis
associated with the absorptionof union-like functions within government [12]). The latterargument gains plausibility from the observationthat many of today's major social programs,such
as unemploymentinsurance,social security,workers' compensation,and health and safety laws,
5. This expectationis suggested by earlier findings of price inelasticity in such studies as Perkins [14]and Gramlich [9].
6. Our measure of permanentincome is the best fit of income per capita, YPC, regressed against past values of
itself (where the best fit was for three lags). Experimentationwith actual and permanentincome confirmedPeltzman's
conjecture.
7. The inclusion of the poverty series restricts our time period to the years after 1959. However, because the
presence of POVRATEon the demand side serves to counter more objections than it raises (by decreasingthe degrees
of freedom), we present the results for the shorterperiod. For the results of our tests over the longer 1948 to 1989 time
period (but excludingPOVRATE),see Ferris andWest, [8].The resultsare basically unchangedand complementthe ones
presented in the text.
542
J. StephenFerrisand Edwin G. West
were originally of union origin. A more recent strengtheningof this substitutioncan be seen in
the "employmentat will" doctrine, initiated by both the judiciary and some legislatures.Such
changes establish implicit but binding contractsthat requirejust cause before an employee can
be discharged.
The second variable,OLDPOP,is of growing interest because the over sixty five year old
age group is the fastest growing and most conservative segment of the population.Having the
highest level of disposableincome, the lowest rate of poverty,and owning one-thirdof all household assets and forty percent of all financialassets, senior citizens tend to have less than average
demandsfor governmentexpendituresand higher than averagedemandsfor lower taxes. In this
sense, their growth would act as a brake on governmentexpansion. Counteringthis, however,
is the considerationthat an older populationmay have a proportionallylarger demand for the
newer services and transfersthat governmentssupply,e.g., Medicaid and social security.There
then is no strong a priori case for believing that the coefficients on either of these two variables
must have one specific sign.
The final set of demand side variables are a set of tax collection cost variablesassociated
with the Kau and Rubin (K/R) hypothesis that governmentsgrow when people transferto jobs
with more visible and thereforetaxableearnings.K/R arguethat growth in the proportionof the
laborforce that is self-employed, SE, leads to less visible earningsand thereforemore tax avoidance. The consequence is higher real costs of financinggovernmentservices. In our framework,
an increase in SE reduces the demandfor governmentservices. Next urbanization(URBAN),is
used by K/R as a measureof the largerset of opportunitiesavailableto closely located taxpayers
to avoid formal markets (throughsuch activities as barter).This, it is argued, will increase the
cost to governmentof detecting economic activity and allow individualssome escape from taxation. For both these variables,the predictedsign of the regressioncoefficient is negative. A third
K/R variableis the female participationrate (FPART).K/R argue that as women relocate from
areas of employment that are hard to tax (i.e., the home) and into market employment where
earningshave greatervisibility, the real cost of collecting taxes by governmentwill fall. To this
considerationwe add a variablemeasuringthe productionoutputratio of business equipmentto
consumergoods, BERATIO.With this fourth variablewe argue, in the spirit of K/R, that as the
accounts of the economy become more mechanized,the cost of keeping track of taxpayersand
realizing tax payments will be lower. For these reasons, positive coefficients are expected for
both FPARTand BERATIO.Finally, we add the ratio of foreign transactionsto nationalincome
(BPRATIO)as a measureof the degree to which the domestic economy is interconnectedwith
the rest of the world.8The predictionis that marketopenness constrainsreal governmentsize so
that the coefficient on BPRATIOis predictedto be negative.
The estimatingequationthat comes from these demandside considerationsis:
RSHAREd= al + a2RELPRICE+ a3YPC + a4GOVEMP+ asFARMPOP
+ Q6UNION+ a7OLDPOP+ asSE + Q9URBAN+ aloFPART
+ a 11BERATIO+ al 2BPRATIO+ e1.
(2)
To recapitulatethe predictionsof the analysis:c2,
and c12 are expected to be negative;
a•8, 9,
the sign of c3 is viewed as a test of Wagner'sLaw; and a4, Q5, c10, and
are all predicted
ac1
8. Alternatively,BPRATIOmay stand as a measureof the constrainton governmentsize imposed by the growth
of the internationalizationon economic activity where the ability of any particulargovernmentto tax is lower.
THEORIESOF REAL GOVERNMENTSIZE
543
to be positive. In addition,the negative coefficient on the observed price, c2, is expected to be
small, while a6 and a7 have no expected sign.
It is now time to turn to the supply side. When Baumol'sproductioncost theory is addedto
the more traditionalsupply side considerations,a supplyrelationshipof the following sort results:
=
gnS S (p', Relative Factor Costs, Population,Relative ProductivityChanges).
(3)
Beginning with the traditionalcost considerations,the supply price of governmentservices,
RELPRICE,is predictedto be positively associatedwith real governmentsize, RSHARE,reflecting a movementupwardalong the supplycurve. Similarlyan increasein relativelaborinput costs
should increase the relative cost of governmentservices, shifting upwardsthe supply curve and
decreasing quantity.This is measuredas the ratio of income received by governmentworkers
Another
relative to that received by workers in the private sector and denoted as PAYRATIO.
variableis suggestedby the Samuelsonianhypothesis that governmentsprovidepublic goods. To
the extent thatgovernmentservices are more public thanthose providedby the privatesector, the
relative cost of providinga fixed share of real governmentservices should fall with an increase
in population size. To test this predictionwe included the two variables,population,POP and
populationsquared,POPSQ.The public good hypothesispredictsthatthe coefficienton POP will
be positive. The presence of POPSQallows this relationshipto be nonlinear.'
Finally, Baumol'scost disease hypothesis states that because governmentservices are relatively labor intensive, the governmentsector should lag behind the rest of the economy in productivity growth. This implies that government services become increasinglycostly over time,
reducing the relative size of government. One measure of the disadvantagefacing government
is capturedin BERATIO.As organizationsbecome more business machine and computerintensive, labor intensive sectors should fall furtherbehind. Manufacturingoutputper hour (MPROD)
and time (YEAR)are two more direct measures of the relative rate of productivitychange in
manufacturing.Baumol'scost disease theory predictsthat all three coefficients will be negative.
Summarizing,the estimatingequationthat comes from these considerationsis:
RSHARE=
+ 04POP + P5POPSQ
+ /2RELPRICE+ /3PAYRATIO
+ 06MPROD + /7 YEAR+ 08BERATIO+ E2
/3
(4)
where the predictions are that /2 will be positive, and 3, /36, /37 and /8 all negative. The sign of
/4 indicates whether economies or diseconomies of scale exist in the relative provision of real
governmentservices and P5 tests for nonlinearityin the relationship.
Because of the mutualdependenceof price and quantityin equations(2) and (4), the demand
and supply relationshipsshould be estimated simultaneouslyusing a technique such as threestage least squares. To interpretthe resulting coefficients as tests of the proposed hypotheses,
however, the remainingrighthand side variablesmust be strictlyexogenous. On a priorigrounds,
however, it seems likely that while governmentemployees may form an importantspecial interest group demandinggreatergovernmentservices, more governmentservices also requiremore
employees, if only for purely technological reasons. There is then a two way relationshiprunning between GOVEMPand RSIlARE, and a model that does not separateout the aspects of
9. Borcherding[6] places POP on the demand side as a tax share price effect, i.e., reduces individualtax shares
as populationincreases.
544
J. StephenFerrisand Edwin G. West
their mutualinterdependencemay attributethe strengthof a particularcorrelationto the wrong
theoreticalreason.'1
This considerationsuggests that a three ratherthan a two equationsystem should be estimated to determinethe share of governmentemployment (GOVEMP)along with RSHAREand
RELPRICE.Moreover,the outputbasis for suspectinga positive bias in the demandside GOVEMP
variablesuggeststhatthe additionalequationshouldbe the deriveddemandfor employees,derived
from the conditionsfor cost minimization.From cost minimization,then, the government'sshare
of employmentis determinedwhen the relativevalue of the marginalproductof laborwithin the
governmentsector equals its relativewage cost. Similarly,a focus on input proportionssuggests
that the governmentsector should become more labor intensive with increases in the rentalrate
on capital. Finally, the use of a separateemploymentequationalso allows us to test for UNION
as a determinantof the government'semploymentshare as distinct from its role in determining
the government'sshare of real output. Union power may be focussed more effectively on the
immediate and direct benefit of a larger employment share ratherthan on the indirect benefits
derived from a larger governmentoutput share.
These considerationssuggest that a third equation of the following form be added to the
analysis:
GOVEMP= 61 + 62RELPRICE+ 63RSHARE+ 64RWAGEG+ 65RWAGEPS
+
(6 UNION+
67TBR+
E3,
(5)
where RWAGEGrepresentsreal earningsby governmentemployees, RWAGEPSrepresentsreal
earningswithin the private sector and TBRrepresentsthe treasurybill rate (3 month).
As predictionsfromthe theoryof derivedfactordemand,the coefficientson both RELPRICE,
62, and RSHARE,63, should be positive. The desire to economize on relative labor costs means
that the coefficient on own wages, 64, is predictedto be negative and the coefficient on private
sector wages, 5s,positive. The 67 coefficient on the treasurybill rate, TBR,is used to measurethe
degree to which capitaland labor substitutewithin the governmentsector and this is predictedto
be positive. Finally, (6 measuresthe effect of union strengthon governmentemploymentwhich
is expected to be positive.
IV.Data
With the exception of the variables URBAN, UNIONand POVRATE,all the data in this study
are taken from CiticorpEconomic Database,Citibase,for 1992. The variablenames were chosen
to briefly describe the measure of the variable and to correspondto those used by Berry and
Lowery [5]. A complete descriptionof the data and the manipulationsmade to the raw data is
availablein the Appendix and a brief descriptionof some of the more difficultvariablenames is
attachedto the table of results. The 1992 Citibase databaseincludes both quarterlyand annual
data,runningbetween 1947 and 1991.However, because the longest time series we could find for
the poverty rate began only in 1959, our time series was restrictedto the years following 1959.
10. A Hausmanspecificationtest on GOVEMPallows maintenanceof the null hypothesis that GOVEMPis uncorrelated with the error term in the demandequation, althoughnot with a great degree of confidence. The coefficient of
1.58 on the reduced form predictedvalue of GOVEMPis significantlydifferentfrom zero at twenty per cent.
THEORIESOF REAL GOVERNMENTSIZE
545
In addition,some of our variableswere availableonly through1989. The result is that our study
is limited to the thirty one observationsthat arise between 1959 and 1989.1
To assist in readingthe following table of results, we collect together in a list the empirical
counterpartsof the theoreticalvariables described in section III. They are:
RSHARE= Real governmentservices divided by real GDP.Columns (a) and (b) of Table
I (below) use a National Accounts measure of real government size, while
Column (c) uses a larger, transferinclusive measureof size.
RELPRICE= Price deflatorfor governmentservices in GDP divided by the GDP deflator.
PERMY= Per capita permanentincome = permanentreal GDP divided by population
(total).
GOVEMP= Ratio of total governmentemploymentto populationaged 20 and over.
FARMPOP= Ratio of farm populationto total population20+.
OLDPOP= Ratio of population65 or older to population20+.
UNION= Ratio of total union membershipto population20+.
SE = Ratio of self-employed workersto population20+.
URBAN= Ratio of urbanpassenger vehicle miles to total passengervehicle miles.
FPART = Female participationrate.
BERATIO= Productionoutput of business equipmentrelative to consumer goods.
BPRATIO= Ratio of balance of payments receipts from foreignersto national income.
POP = Population(in thousands);POPSQ = Populationsquared.
RWAGEG= Real earnings per governmentemployee.
RWAGEPS= Real earnings per private sector employee.
PAYRATIO
= Ratio of governmentto private sector earnings = RWAGEG/RWAGEPS.
RWAGEM= Real earnings per manufacturingemployee.
MPROD= Manufacturingoutput per hour.
TBR= Three month treasurybill rate.
V. Results
The equationestimatesare presentedin TableI using the datanames describedabove (anddefined
in the Appendix). The coefficient estimates of the three-stageleast squaresdemandand supply
system where governmentemploymentis treatedas exogenous are presentedfirstand labelled as
the set of (a) column equations (appearingas columns 1 and 4 in TableI). For direct comparison
with the results when the government'sshare of employment becomes endogenous, the threestage least squaresestimatesof the three equationsystem (RSHARED,RSHAREs,and GOVEMP)
are labelled as (b)'s and are placed directly to the right of the (a) columns (as columns 2, 5, and
7). By locating any variableof interestand moving to the right along that row, the changes in the
coefficient producedby accountingfor the endogeneity of governmentemploymentcan readily
be identified. Finally, Table I also includes the three equation system estimationfor the transfer
inclusive measureof real governmentsize (againwhen the government'sshareof employmentis
11. Results for a longer time period (1948/1989, excluding the poverty rate) can be found in the working paper
version of this paper [8]. The transferinclusive measureof real governmentsize is availableonly for the period between
1952 and 1989.
546
J. Stephen Ferris and Edwin G. West
TableI. Three-Stage
LeastSquaresEstimatesof RealGovernment
Size:1959-1989
REAL
REAL
SHARE
1.
2.
3.
SHARE
4.
5.
6.
GOVEMP
7.
8.
DEMAND
(a)
(b)
(c)
SUPPLY
(a)
(b)
(c)
(Endog)
(b)
(c)
1.
Constant
-.363
-.494* -.138
(1.75) (2.65) (.525)
2.
.022
.059
.122*
RELPRICE (0.632) (1.68) (2.53)
3.
.0035 -.0029 -.007
PERMY
(1.25) (1.12) (1.97)
4.
.771*
.781* .836*
POVRATE (5.62) (6.02) (4.70)
5.
3.23*
3.69* 4.18*
GOVEMP
(6.98) (6.17) (5.21)
6.
.531"* .739* .476*
FARMPOP (4.60) (6.09) (3.25)
7.
-.454
-.490 -.765*
UNION
(1.59) (1.94) (2.15)
8.
0.900
1.47 -1.95
OLDPOP
(.911) (1.45) (1.43)
9.
-.764
-1.13 -1.13
SE
(1.03) (1.28) (1.01)
10.
-.193
-.418" .118
URBAN
(1.37) (2.32) (.578)
11.
.026
.327* .387*
FPART
(.254) (2.55) (2.87)
12.
.034
.051"* .007
BERATIO
(1.56) (2.36) (.266)
13.
-.442* -.472* -.014
BPRATIO
(6.37) (6.17) (.150)
30.19* 24.57*
(2.76) (2.47)
RELPRICE .641* .691*
(5.11) (6.00)
PAYRATIO -.728* -.801*
(4.80) (5.74)
POP
-.007* -.010*
(2.45) (3.60)
.0003* .0004*
POPSQ
(6.54) (7.28)
YEAR
-.022* -.012*
(3.94) (2.23)
MPROD
-.003* -.002*
(4.38) (4.08)
BERATIO -.058* -.052*
(2.49) (2.47)
Constant
-25.35
(1.89)
.511*
(3.43)
-.561*
(3.12)
-.008*
(2.07)
.0001
(1.70)
-.014
(1.92)
-.003*
(4.72)
-.113*
(3.90)
-.150" -.165*
(14.09) (11.84)
RELPRICE .158* .190*
(3.69) (3.32)
RSHARE
.183* .394*
(7.22) (12.94)
RWAGEG -.008* -.012*
(4.08) (4.77)
RWAGEPS
.010* .013*
(10.43) (11.86)
UNION
.394* .394*
(16.40) (12.94)
TBR
.0005* .0002
(3.15) (.292)
Constant
S.E.
.003
.0037 .0049
.007 .0069
.008
.0014 .0016
F-stat
160.3
120.1
10.2
59.3
56.0
3.26
118.2
192.4
D.W.
1.69
1.85
1.72
1.32
1.37
1.35
1.70
1.41
Column(a) TwoequationestimatewithGOVEMPexogenous
(b) ThreeequationestimatewithGOVEMPendogenous
size
(c) Threeequationestimatewithtransferinclusivemeasureof government
* significantly
t-statisticsin parentheses;
differentfromzeroat 5%;Variable
namesanddefinitions
in Appendix
endogenous). The coefficients for these equationsappearas the set of (c) columns (or columns
3, 6, and 8) in the same table.
We begin our discussion of the resultsby firstreviewing the combined findingsrepresented
the
set of equations as a whole. At this the most comprehensivelevel, the combined set of
by
public finance hypotheses used to predictthe real share of governmentoutput in GDP perform
well in all forms of the test, even when using the broadertransferinclusive measureof real government size (the set of equationsappearingin (c)). For the size specificationmost appropriate
to our analysis (i.e., the service outputor net of transferincome measureof real governmentsize
in columns 2, 5, and 7), all three F-statistics allow rejectionof the null hypothesisthat the set of
THEORIES OF REAL GOVERNMENTSIZE
547
variablesin each equationhas no explanatorypower, while the Durbin-Watsonstatistics suggest
that serial correlationis not a significantconcern.12Similarly as a general statementabout the
individualhypotheses-that is, their conformity to the sign predictionsof the analysis-almost
all of the coefficients with specific sign predictionsare found to have their expected sign and most
of these are significantlydifferent from zero. The exceptions are the demand price coefficients
(in row 4, columns 1-3). This finding of general conformity to predicted values is repeated in
all formulationsof the model (although,as expected, the findingsare less significantfor transfer
inclusive form of the model). Overall, then, the group of findings are consistent with all of the
majorhypothesis groupingsand do not suggest the particularimportanceof one set of hypotheses
relative to the others.
Demand Side Variables
To structureour discussion of the individual findings, we begin by discussing the hypotheses
associated with the traditionalchoice variables (income and price) and then continue down the
set of demand side variables in order of their appearancein the first column of Table I. Beginning then with permanentincome (PERMY)and the hypothesis associated with Wagner'sLaw,
supportfor Wagner'sLaw of an income elasticity of real governmentspending greaterthan one
requires the regression coefficients in row 3 (columns 1-3) to be significantlypositive. This is
because a rise in the share of governmentin income is requiredfor real government spending
to have an elasticity greater than one. None of the coefficients of PERMY(row 3 columns 13), however, are found to be significantlydifferentfrom zero when the traditionalfive per cent
confidence intervalis used. If the confidenceintervalis increasedto seven per cent, however,the
transferinclusive measureof real governmentsize is found to decrease with increases in permanent income (implying a less than in proportionincrease in demand for increases in permanent
income).
When we turnto look at the own-price coefficients (on RELPRICE)in row two of the table,
we see that the findingsare somewhatmixed. On the one hand,all three supply price coefficients
12. Although spuriouscorrelationdoes not seem a significantconcern, the system was also estimatedin difference
form. While some variableslose their significancein this form, the general patternof result remains.We reportthe three
equation (transferexcluded) estimates:
ARSHARED= -.038ARELPRICE +.002APERMY + 3.42AGOVEMP+.791AFARMPOP
(.317)
(.560)
(2.59)
(1.99)
- .072AUNION - 2.36AOLDPOP- .084ASE - .073AURBAN - .235AFPART
(.115)
(.978)
(.061)
(.240)
(.598)
- .367ABPRATIO+.013ABERATIO+ .697APOVRATE D.W. = 1.86
(1.67)
(.308)
(2.44)
- .005APOP
ARSHAREs= -.012 +.024ARELPRICE - .097APAYRATIO
(.400) (.055)
(.204)
(.333)
+ .00001POPSQ- .002AMPROD- .049ABERATIO D.W. = 1.20
(.044)
(.851)
(.738)
AGOVEMP= .073ARELPRICE+.232ARSHARE - .003ARWAGEG+ .006ARWAGEPS
(.752)
(2.39)
(.599)
(1.95)
+ .255AUNION + .0005ATBR D.W. = 1.69.
(1.88)
(1.59)
548
J. StephenFerris and Edwin G. West
(row 2, columns 4-6) conform to the predictionthat price increases will result in movements
up or along an upwardsloping supply curve. Moreover,all of these positive coefficient estimates
are significantlydifferent from zero. Evaluatedat their mean, the coefficients suggest that the
supplycurve for governmentservices is highly elastic. In contrast,the estimatesof the own-price
effect on demandequations (row 2, columns 1-3) contradictthe expected sign in all three cases,
althoughonly in the transferinclusive measureof governmentsize is the coefficient found to be
significantlydifferentfrom zero. The set of demandcurve estimates in row 2 suggest essentially
no responsivenessto price and imply that the net demandcurve is virtuallyinelastic."
The demandside variableused to meter the intensityof the public'swish to providegovernment services to the disadvantaged,POVRATE(in row 4 columns 1-3), does have a significant
positive effect on the real size of governmentin all system specifications.'4The real scale of governmentactivity increases with increases in the poverty rate. It is worth repeating,however,that
in additionto havingits own significanceas a direct indicatorof demand,an importantreasonfor
including POVRATEis to separateits influenceon size from the effect on size producedby such
public choice variablesas GOVEMPand OLDPOP.The presence of POVRATEin the regression
equationand the consistent findingthatits coefficientis significantlypositive increasesour confidence that the regressioncoefficients on the other public choice variableswill not simply reflect
a spuriouscorrelationwith size throughpoverty. Over the whole of our time period, the effect
of the change in the poverty rate has been to decrease governmentsize. Beginning at twenty two
per cent in 1959, the poverty rate fell at firstdramaticallyand then more slowly throughthe early
seventies where it bottomed (at 11.2%).Since then the poverty rate has risen marginally.
After controllingfor the desire to use governmentto amelioratepoverty and/or effect redistribution,we turnto assess the significanceof the set of public choice variablesas determinantsof
size. Here there are two sets of variables.First for the two public choice variablesfor which there
are specific sign predictions,the relativesize of governmentemployees (GOVEMP)and the size
of the farm population(FARMPOP),the coefficient findingsin rows 5 and 6 (columns 1-3) suggest thatboth have significantpower in explainingvariationsin RSHARE.All six coefficients are
significantlypositive and hence conform to the hypothesis that increases in the relative strength
of these special interestgroups will increasegovernmentsize. Because the coefficient values are
not independentof the units chosen to measure size, the coefficients were converted into elasticities so that the relative size of differenteffects could be compared.Evaluatedat the means,
the coefficientestimatesimply governmentemploymentshareelasticitiesthat are all significantly
larger than one (the smallest in row 5 column 1 being 1.8), while the FARMPOPelasticities are
found to be positive but smaller than one (at about .3 for the entry in row 6 column 3). It was
the power of the governmentemployee variable to "explain"government size that first led us
to consider the possible endogeneity of employment.However, as can be seen by looking at the
two coefficients when GOVEMPis endogenized (i.e., row 5, columns 2 and 3), the employment
coefficients retainboth their size and significance.Governmentemploymentthen helps to explain
changes in government'sshareof real outputboth in the sense that more employmentis required
13. Previousstudies suggest thatthe full-demandfor public goods is inelastic (see footnote 6). Hence given thatour
net demandcurve requiresthe furthersubtractionof an increasingmarginalcost curve, the slope of net demandshould
appearsteeper and the estimated coefficient would be expected to be smaller.
14. As might be expected, the point estimate for the effect of POVRATEon the transferinclusive measureof government size is found to be larger than the point estimate of the narrowermeasure. The difference, however, is not
statisticallysignificant.
THEORIESOF REAL GOVERNMENTSIZE
549
to fulfil the functions of a largergovernmentand also in the sense that a largerbureaucracywill
itself increase political and group pressurefor larger government.
The values of the coefficients on the second set of public choice variables (OLDPOPand
UNION) help to resolve the quantitativestrengthof opposing factors seen to be at play within
these groups. In the case of the fraction of the populationthat is sixty five or older, the coefficient findings for the narrowerservice definition of governmentsize (in row 8, columns 1 and
2) suggest that increases in OLDPOPincrease the real size of government.However, while both
coefficients are positive, neither is significantly different from zero. For the transferinclusive
measure of real size, on the other hand, the coefficient is negative (row 8 column 3), but again
insignificantlydifferentfrom zero. Thus while our results hint at the conflictingincentives facing
the older proportionof the population,the data cannot resolve this issue and are consistent only
with the hypothesis that the "grey panthers"are not yet an effective lobby group. For UNION,
however, the coefficient estimates are negative in all three forms of the test (row 7 columns 13) and become significantlynegative as we move to the transferinclusive measurein column 3.15
These results are more consistent with the hypothesis that governmentservices have substituted
for traditionalunion activities than they are with the hypothesis that the enhancementof union
power will increase the provision of real governmentservices.
The final set of demand side predictions (see rows 9-13, columns 1-3) involve the five
hypotheses associated with the K/R collection cost hypothesis that changes in the structureof
economic organizationmakingit easier for governmentsto monitoreconomic activity will lower
the cost of raising taxes and hence increase the real size of government.For the K/R variables,
virtuallyall coefficients had their expected sign and, in the preferredspecification (in column 2)
where governmentspending excludes transferpayments, not only do all coefficients have their
expected sign but only the SE coefficient (in row 9 column 2) is insignificantlydifferentfrom zero.
This suggests that increases in the rate of female participationin the work force, the increases in
the mechanizationof business activities and its accounts, and increasesin the internationalization
of marketactivity have all workedtowardsdecreasingtax avoidance,while increases in urbanization and to some degree self-employmenthave tended to work in the opposite direction.What is
also of interest is that as we broadenthe measureof real size to include transferactivities (rows
9-13, column 3), all the K/R coefficients except that for the female participationrate lose their
significance.Overall, the data is stronglysupportiveof the K/R hypothesis when the measureof
size is centered on the provision of real services, but is only mildly supportivewhen transfers
are added to the measure.
SupplySide Variables
On the supply side of the problem (i.e., the RSHARESequationsin columns 4-6), the findings
are broadly consistent with the hypotheses that changes in the real size of government will respond to traditionalcost considerations(includinginput costs), scale variables (populationsize)
as well as the set of Baumol/Beck variablesindicatingrelativeproductivitychange.As mentioned
earlier,the positive price coefficients (in row 2) confirmthe predictionthatincreasesin quantities
supplied can be achieved only at higher cost. In addition,the coefficients in row 3 columns 4will reduce
6 suggest that a rise in the real input cost of government employees, PAYRATIO,
15. If the confidence interval is expandedto ten per cent, UNIONis significantlynegative.
550
J. StephenFerrisand Edwin G. West
significantly the real size of government (all coefficients are significantly negative). The data,
however, contradictthe hypothesis of significantpublicness in the provision of real government
services. The POP coefficients in row 4, columns 4-6 indicate that populationis inversely associated with real size, suggesting diseconomies ratherthan economies of scale in the provisionof
real services." Finally, the data provide broad supportfor Baumol's "cost disease" hypothesis.
For example, in rows 7 and 8 (columns 4-6) the coefficients on both BERATIOand MPRODare
consistently and significantlynegative as predicted.Thus to the extent that increases in the ratio
of businessmachineproductionrelativeto consumergoods captureindirectlythe degree to which
labor intensive sectors such as governmentfall behind more innovativecapital intensive sectors
andmanufacturingoutputper laborhourcapturesthis directly,the findingsfor both BERATIOand
MPRODare consistent with Baumol's "cost disease" hypothesis. Similarly,because the relative
productivitydisadvantageheld by governmentis predictedto be an increasingfunction of time,
the significantlynegative coefficients found for YEAR(in row 6 columns 4 and 5) are consistent
with the predicteddecline in the relativeefficiency of providinggovernmentservices over time."
GovernmentEmploymentEquation
As expected, the coefficients of the thirdequation (the GOVEMPequationsin last two columns,
7 and 8, of the table) addedto endogenize governmentemploymentand so accountfor the supply
side interactionof employmentand output conform closely to the predictionsof cost minimization theory. All coefficients have their predicted signs and almost all are significantlydifferent
from zero at five per cent. The coefficients on both real government size (RSHAREin row 3,
columns 7 and 8) and the relative price of governmentservices (RELPRICEin row 2, columns
7 and 8) conform to the predictionsthat expansions in real governmentoutput will increase its
relative use of labor (as a factor of production)and that an increase in the relative sector price
will similarly attractlabor and so increase government'sshare of employment. Along the same
lines, the positive coefficientfound for the interestrate variable(TBRin row 7, columns 7 and 8)
suggests a significantdegree of substitutabilitybetween capital and labor within the production
activities of the governmentsector (althoughthis disappears,as might be expected, in the more
transferinclusive measure of real government size). Finally, the UNIONcoefficient (in row 6,
columns 7 and 8) is consistentlyand significantlypositive in its effect on GOVEMP.This suggests
thatalthoughwe found earlierthatgovernmentgrowthmay be substitutedfor union-likeservices
on the demand side of the problem, union power has been more successful on the supply side
in promotingemployment.
Focusing specificallyon the changesthatarise once governmentemploymentis endogenized
(in equation sets (b) and (c)), the most general comment is that the concern expressed earlier
over the potentialloss in significanceof GOVEMPas a demandside variable (because of reverse
causationfromRSHAREto GOVEMP)is not realized."The coefficienton GOVEMPrises slightly
despite findinga significantpositive relationbetween RSHAREand GOVEMPin the employment
equation. The relative employment size of government, then, remains a large and significantly
16. The point estimates of POP and POPSQin the transferexcluded measureof governmentsize suggest that the
negative effect of POP on RSHAREwill disappearat a populationsize of around244 million. This would then reconcile
our results with those usually found [6, 367].
17. The coefficient on MPRODfor the transferinclusive measureof real governmentsize (row 6 column 6) would
be significantlydifferentfrom zero only if the significanceinterval were extended to seven per cent.
18. These results confirm the outcome of the Hausmannspecificationtest of footnote 11.
THEORIESOF REAL GOVERNMENTSIZE
551
of RSHARE(i.e., the elasticitiesrepresentedby the coefficientsin row 5,
positivedeterminant
columns2 and3 remaingreaterthanone).Thethreeequationsystemresultsthenallowus to retain
thepublicchoicehypothesislinkingthe size of government
employmentwiththerealsize of the
the
of GOVEMP
In
of
the
other
sector.
terms
endogenization
appears
hypotheses,
government
of the demandandsupplyhypotheses,marginallyimprovingthe
to producea cleanerseparation
significanceof mostcoefficientsrelativeto theirpredictedvalue.Thisis moststronglythe case
all becomesignificantlydifferent
for the K/R predictions(e.g., URBAN,FPART,andBERATIO
fromzero)in the product(transferexcluded)measureof realgovernmentsize. The K/R varitransfer
ables,however,arealsothevariablesthatdo mostpoorlywhenthemorecomprehensive,
inclusivemeasureof realsize is used.
is designedto explainthe growthin
on the size of government
Whilemuchof the literature
in
thatthe realshareof government
the shareof government
throughtime,it is worthreiterating
beWar
before
the
the
Korean
GDPhasdeclined.Therealsize of government
peakedduring
just
to reachtwentypercentby 1978.Overthe
ginningof ourtimeperiodanddeclinedcontinuously
remainedroughlyconstant.Whilethe size of governmentmeaperiodof the eighties,RSHARE
suredin realtermshasfallen,theratioof nominalhastendedto remainconstantat abouttwenty
The differencebetweenthe two is the trendin the realcost of providinggovernment
per cent."19
servicesandthe impliedcontinuousrise in the relativecost of governmentservicesthroughout
this periodwas the focus of an influential1984articleby BerryandLowery[5] (hereafterBL).
costdisease"
In thatworkBL testedthecomparative
explanatory
powerof "Baumol/Beck's
of the conandTullock'sbureauvotingpower"hypothesisas an explanation
versus"Buchanan
In
their
relative
services
1970.
in
cost
of
rise
the
terms,
findings
through
government
tinuing
[5, 745].In contrast,ourresultsfor a
"clearlylend supportto the Beck/Baumolinterpretation"
morerecenttimeperiodsuggestthatbothhypothesesareequallywell supported
by the data.It
the
two
to
allows
that
our
be
however,
hypotheses be separated
testingprocedure
may significant,
acrossthe estimationof separatedemandandsupplyequations,one in the demand,the otherin
the supplyequation,ratherthanhavingthe two combinedtogetherin one reducedform.
Incomparative
terms,then,ourfindingsdonotreducetheexplanatory
powerof theBuchanan/
cost hypothesis
to
the
relative
Tullockbureaucratic-voting
Baumol/Beckproduction
hypothesis
is endogenized.As such,our resultscontradictthe generaltenorof BL's
even afterGOVEMP
findingsin this moregeneralsetting.In addition,we confirmthe significanceof the generalset
of hypothesesadvancedby K/R [10].On the otherside of the market,ourfindingssuggestthat
cost variables(real
roleto be playedby the conventional
thereremainsa substantive
production
in
considerations
with
the
scale
and
explainingthe relative
Baumol/Beck
wages
variables)along
the
and
as
services.
cost of supplyingrealgovernment
Finally,
expected, hypothesesas a group
workless well at explainingthe transferinclusivemeasureof governmentsize (in column(c))
19. The ratio of the nominal values could also be interpretedas a ratio of real outputs when both nominal expenditurecategories are deflatedby the CPI index. This interpretationof the appropriatereal ratio would be preferred
by theories focusing less on the quantityof real services providedby governmentand more on consumers' willingness
to pay and hence on the foregone value of the funds needed to finance governmentactivity. If the ratio of nominals is
used as the dependent variable in our test (with transfersexcluded), the results do change slightly (these findings are
availableupon request). As a general statement,all coefficients signs are unchanged,however, on the demandside three
of the K/R variables (URBAN,FPARTand BERATIO)lose their significance.On the supply side equation,only YEAR
lost significance. In relative terms, then, the definition of real output used in this analysis is somewhat more favorable
to the K/R hypothesis than is the more traditionalmeasure.On the other hand, the public choice and the Baumol/Beck
hypotheses appearto perform equally well in either form of the test.
552
J. StephenFerrisand Edwin G. West
than they do the size measurethat excludes transferpayments. The K/R variablesreceive least
supportin terms of the more comprehensivemeasure.
VI. Conclusion
Our purpose in this paper has been to present a simplified demandand supply system approach
to explain the determinationof the real share of governmentin GDP and suggest reasons and
instanceswhen the neglect of a more generalsetting may bias single equationresults.The conclusion that arises from our empirics is that over the later postwarperiod the evidence is consistent
with three of the four majortheories used to explain government size, the exception being the
theory associated with Wagner'sLaw of a propensityto spend greaterthan one. Depending on
the particularset of regressions chosen one can find evidence that is more or less favorableto
one's favorite approach.However, when viewed as a whole, there seems no strong reason for
preferringany of the three to a more comprehensiveapproachthat nests these theories within a
traditionaldemandand supply setting. What may be more surprisingis that even after accounting for the endogeneity of GOVEMP,the data remainconsistent with a significantdemandside
role for GOVEMPin government'sreal size, whether measuredas exclusive of transfersor not.
Finally, while there is strong evidence for the presence and significance of "unobservable"tax
collection costs in determiningreal governmentsize when the service measureof size is used,
the weakeningof this effect when transferpaymentsare included (combinedwith a similarweakening of demand price effect) is consistent with some degree of fiscal illusion. In view of the
significanceof transfersas an ever increasingproportionof governmentspending,this becomes
discouragingnews for economists who wish politicians and voters to both recognize and internalize deadweighttax collection costs when making allocative political decisions. As such, our
findings echo and supportthe recent call by Baumol [1]for greaterinformedcommunicationto
overcome the illusions held by the public of the real costs of providing governmentservices.
Appendix
VariableDefinitionsand Sourcesfrom CITIBASE
RSHARE(Columns(a) and (b) = GGE/GDPQ(bothconvertedfromquarterly
data);
RSHARE(Column(c)) = GGEX/GDPQ(fromquarterly
data);
GDPDEF= GDP/GDPQ(fromquarterly
data);
GOVDEF= GGE/GGEQ(fromquarterly
data);
RELPRICE = GOVDEF/GDPDEF; POP = PAN;
POPSQ = PAN x PAN; YPC = GY/(PAN x GDPDEF);
PERMY= .261 + 1.22YPC(-1)- .524YPC(-2)+.304YPC(-3);
GOVEMP= GATG/PAMF20;FARMPOP= GATAFl/nPAMF20;
OLDPOP = PAN19/PAMF20; SE = LHNASE/LF;
FPART = LHFP16; WAGEMAN = GAPM/GAFM;
RWAGEM= WAGEMAN/GDPDEF;
GOVWAGE= GAPG/GAFG;
RWAGEG = GOVWAGE/GDPDEF; WAGEPRIV = (GAP - GAPG)/(GAF - GAFG);
= GOVWAGE/WAGEPRIV;
RWAGEPS= WAGEPRIV/GDPDEF;
PAYRATIO
BERATIO = IPE/IPC;
BPRATIO= GEXF/GY (convertedfrom quarterlydata);
MPROD = LOUTM.
THEORIESOF REAL GOVERNMENTSIZE
553
Variable Names and Definitions from Non-Citibase Sources
URBAN: 1947-1965-Urban streets to total travel;
1966-1985-Urban interstate+ other urbanto total Urbanand Rural;
1986-1990-All Urban to Total Urban and Rural
Source: Office of Highway InformationManagement,U.S. Departmentof Transportation,FederalHighway
Administration.Tables entitled Annual Vehicle-Miles of Travel and Related Data (by Highway Category
and Vehicle Type) 1936-1985 and by year through 1990.
UNION: Total Membershipof National and InternationalUnions (exclusive of CanadianMembership)
-1947-1978, U.S. Departmentof Labor,Handbookof Labor Statistics,1975 (Table 164) and 1979
(Table 165).
-1983-1990, U.S. Departmentof Labor,Employmentand Earnings,Januaryissues, 1985,7,9 and 1991.
-1979-1982, interpolated.
POVRATE: PovertyRate for Individualsin Selected DemographicGroups (Overall)Bureauof the Census,
TechnicalPaper 56, Table 1; CurrentPopulationReports series P-60.
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