American Economic Association
The Distribution of Public Services: An Exploration of Local Governmental Preferences
Author(s): Jere R. Behrman and Steven G. Craig
Source: The American Economic Review, Vol. 77, No. 1 (Mar., 1987), pp. 37-49
Published by: American Economic Association
Stable URL: http://www.jstor.org/stable/1806727
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The Distribution
of PublicServices:
An Explorationof Local Governmental
Preferences
By JERE R. BEHRMAN AND STEVEN G. CRAIG*
A local governmental
welfarefunctionis specifiedto exploretwo of its central
characteristics:
the equity-productivity
tradeoffand differential
weightsacross
Themodelis estimated
neighborhoods.
usingserviceoutputs(safety)in thewelfare
as opposedtopubliclyprovidedinputs(police),overneighborhoods.
The
function,
is foundto be considerable,
and notall neighborhoods
equity-productivity
tradeoff
resultsraiseseveralquestionsaboutaccepted
are weighted
equally.The estimation
behavior.
analysisofgovernmental
The Serranov. Priestcase concerningthe
allocation of educational expenditurein
California broughtthe question of the nature of the distributionof local public
of policy debate.'
services to the forefront
Despite considerablesubsequentattentionto
related issues in the press and in political
and judicial arenas,therehas been littlesystematiceconomic analysis of importantdimensions of this process. The fairlysparse
related literatureto date, recentlysurveyed
by Edward Gramlichand Daniel Rubinfeld
(1982), has focusedon theempiricalpro-poor
vs. pro-richbias of local public expenditures.
A problem with examiningexpenditures,
however,is that what is of concernto residents is the actual level of service that is
The present
providedby local governments.
paper thereforerepresentsan importantdeparture from most previous literaturebecause we study distributionof local public
*Professor of Economics, Universityof Pennsylvania, McNeil 160/CR, Philadelphia,PA 19104, and
AssistantProfessorof Economics,Universityof Houston, 4800 Calhoun Road, Houston, TX 77004. We
thank Robert P. Inman and anonymousrefereesfor
usefulcomments,but the usual disclaimerapplies. The
crime survey is described in Criminal Victimization
Surveys... (1976). This referencehas a copy of the
questionnaire,as well as descriptivestatistics.Our data
set was especiallycreatedforus by the Bureau of the
Censiu.
'Serrano v. Priest (1971, L.A. 29820); subsequent
opinion December 30, 1976. This is the landmarkcase
in which the CaliforniaSupremeCourt ruled that the
school financesystemwas unconstitutional
due to the
equal protectionclause in the stateconstitution.
service outcomes,ratherthan expenditure.2
We hypothesizethat local servicesare distributed"as if" thereis a constrainedmaximization of a local governmentalsocial
3 defined over the distriwelfare function,
bution of local public servicesamong the
residentsof its jurisdiction.4Differentiation
between publicly providedinputs and final
service outcomes reflectsthat thereare two
welfare
separateconstraintson governmental
2This distinctionitselfis not originalwithus, though
a numberof studiesseem to ignoreit.
3The median voter model is the usual method for
However,this
preferences.
specifyinglocal governmental
model has some well-knowndisadvantages,especiallyin
of a large,heterogeneous
the modelingthe government
city (see Robert Inman, 1979, fora discussionof these
behavior
issues). Competing theoriesof governmental
are just beginning to be developed; they essentially
involve group decision-making models (Kenneth
Shepsle, 1979; Craig and Inman, 1985). These group
politibehavior models may involvean agenda-setting
cian, coalition building,or logrollingconcensusbuilding. We do not provide a structuralmodel of governmentalbehavior,but we model the "as if" preferences
concern,
of the governmentto allow fordistributional
prefwhateverthe cause. We model local governmental
erences to depend on public servicesoutcomes.Some
observers suggest that expenditures(or, for constant
inputs)may be arguments
prices across neighborhoods,
welfarefunction.Our approach
of a local governmental
is a start towards attemptingto explain the observed
distributionof publicly provided inputs given local
over the serviceoutcomes.
governmentalpreferences
ex4This process operationalizesand significantly
tends the local governmentalchoice frameworkfirst
suggested,to our knowledge,by Carl Shoup (1964). We
to
thank the refereesforbringingShoup's contribution
our attention.
37
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38
THE AMERICA N ECONOMIC RE VIE W
maximization.The firstis a resourceconstraint, which determinesthe amount of
publicly provided inputs that are available.
The second is a productionconstraintthat
determineshow much public service outcome is produced by a combinationof the
publiclyprovidedinputsand existingneighborhoodcharacteristics.5
The distinctionbetweenpubliclyprovided
inputs and service outcomes is crucial because the allocationof inputsand the distribution of outcomes across neighborhoods
can be verydifferent.
The difference
can be
illustrated in our model because we explicitlyincorporatethe productionfunction
constraint that converts inputs into outcomes. The model shows that the distribution of inputs (or expenditures)may respond in the opposite directionthan the
distributionof public service outcomes in
response to changes in neighborhoodcharacteristics.Further,we formulatethe model
to incorporatesystematically
different
welfareweightsfordifferent
that
neighborhoods,
may depend on characteristics
such as income or racial composition.6We estimate
the key parametersof our model using the
allocation of police and safetyfromcrime
across neighborhoodsin Baltimore.The empirical example shows how the distribution
of finalserviceoutcomesdependson thekey
parametersof the"as if" welfarefunction.
The criticalattributesof the local governmental welfarefunctionare two. The first,
inequality aversion, refersto the tradeoff
betweenequityand productivity
as reflected
in the curvatureof the welfaresurface.The
degree of curvatureindicates the relative
5 Outcomes depend on bothpubliclyprovidedinputs
and privateresidentcharacteristics
(see D. F. Bradford,
R. A. Malt and W. E. Oates, 1969). For example,crime
may be less in a " safe" neighborhoodthan in a
"dangerous" neighborhoodeven if both have the same
level of police activity.
6 Distributional
concernsin thepolicyarenaare much
broader than simplyconcernover income. Inman and
Rubinfeld(1979), for example, show that racial concerns are potentiallyimportantin applyingthe Serrano
decision to jurisdictionsin whicha distribution
biased
towardshigh-incomegroupswould not be thebasis for
legal complaint.
MARCH 1987
tradeoffbetween equity and concern over
maximizingaggregatecity-wideoutput(productivity).The second attributeof the welfare function,unequal concern,pertainsto
weightsin thegovernmental
welfarefunction
for the serviceoutcomesof different
neighborhoods. Such weightsmay differ,for example, dependingon neighborhoodpolitical
support for the currentlocal governmental
incumbents,or on thepossiblemovementof
some residentsfromthe jurisdictionto the
detrimentof the local tax base.7 Unequal
concernis reflectedin the asymmetry
of the
welfaresurfacearound a 450 ray fromthe
origin.
Local government
inequalityaversionand
unequal concernmayunderlieimportantdifferencesbetweenthepubliclyprovidedinput
and public serviceoutcomedistributions.
A
pro-poor distributionof publicly provided
inputs across neighborhoods,for example,
may result froma numberof conceptually
different
phenomena:
1) The objectiveof thecitygovernment
is to maximize aggregateserviceoutcomes
over the entirecity,withno concernabout
distributionof thoseoutcomes.Equivalently,
thereis no inequalityaversionand thereis
no unequal concern. If publicly provided
inputswould have a highermarginalproduct
in poor neighborhoodsweretheydistributed
equally, resourcesare distributedin a proreasonsalone.
poor fashionforproductivity
2) The objectiveis to equalize service
outcomes for each neighborhood,in which
case thereis an extremecase of inequality
aversion,but no unequal concern.If publicly
providedinputs are moreproductivein rich
neighborhoods,a pro-poor distributionof
publiclyprovidedinputsresultsbecause concern about equity overrides productivity
considerations.
3) The objectiveof thecityis to provide
greaterservices for poor neighborhoodsso
7The group conflictmodels whichunderlieunequal
concern implymany possible reasonswhydistribution
Our specificationis
may matterto local governments.
not a structuralmodel of the causes of distributional
concern,but it allows an empiricaltestof whetherthe
investigation.
group conflictmodels meritfurther
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VOL. 77 NO. 1
39
BEHR MAN AND CRAIG: PUBLIC SER VICES
thereis unequal concernfavoringthe poor.
Even if publicly providedinputs are more
productivein richneighborhoods,
a pro-poor
distributionof such inputsmay result.
These alternativescenariosillustratethat
the distributionof inputsprovidedby a city
governmentdoes not necessarilyprovideinindistributional
sightinto the government's
terestsregardingserviceoutcomes.They also
highlightthe tradeofffaced by citygovernment between equity and productivity
and
the possibility of unequal concern about
different
neighborhoods.
Our general model of the welfare-maxiis presentedin Secmizinglocal government
tion I. SectionII discussesexplicitfunctional
formsand theirimplications.SectionIII presents the unique data set thatwe use, which
involves the level of safetyfromcrime in
each neighborhoodof a singlejurisdiction.
Section IV presentstheempiricalresults.We
of police
findin the case of the distribution
and of safetyfromcrimeamong neighborhoods in Baltimorethat the local government does sacrificesome productivityin
order to achieve a more equitable distribution of serviceoutcomes,and that unequal
concernis pro-poorand pro-young,but racially neutral.A briefsummaryand conclusion is presentedin thefinalsection.
I. The Model
We assume thatthelocal government
acts
as if it maximizesa welfarefunctiondefined
over serviceoutcomesin each neighborhood
of thejurisdiction.In thisone-periodmodel,
the resource constraintis assumed to be
fixed. Further,the political structureis assumed constant,so the formof the welfare
functionalso is exogenous. The model is
to accountfortheemdevelopedspecifically
pirical example, the distributionof police
and of safetyfromcrime across neighborhoods ofa singlecity.Nonetheless,themodel
is generalto any publicserviceoutcome,and
can be used to explorethe allocationof any
publiclyprovidedinput.8
8The model also is easilygeneralizableto a multitude
of service outcomes and a multitudeof publiclypro-
The welfare functionof concern to the
is
local government
(1)
W=W(S,N),
where S is a vector of outcomes such as
safetyfromcrime per capita in each of m
neighborhoodsand N is a vectorof populations in each neighborhood.
The firstderivativeswithrespectto both S
and N are assumed to be positive. This
welfarefunctionis maximizedsubjectto two
constraints.First, thereis a constrainton
total governmentalresources(R) whichcan
be used to purchase public inputs,such as
police:
m
(2)
R 2 E TPjNj,
j=1
where R is the total available governmental
resources(assumed to be fixedby thepolitical process fortheperiodof interest),P is a
vector of per capita publiclyprovided inputs,wherethejth elementis theamountof
the factorallocated to thejth neighborhood,
and T is the price of Pj.
The second constraintspecifiesthat production of the output, S, is dependenton
the level of publiclyprovidedinputs,Pj, and
on a vectorof neighborhoodcharacteristics,
in Xj
Xj.9 The neighborhoodcharacteristics
are givenfortheperiodof thegovernmental
allocationproblem.Any neighborhoodcharacteristicsthat adjust to the allocation of
governmental resources within the time
period of concern (for example, private
securityguards maybe adjustedin response
to police allocations)are not includedin Xj.
Instead the private reaction functionsfor
privateinputs dependenton Xj and P. are
used to eliminate these inputs, so that Si
vided inputs. Here the one-outcome,one-inputcase is
presented since that is the case explored in our empirical estimates.See Behrman(1986) for a multipleinput, multiple-outputgeneralizationfor the intrahousehold allocationof nutrients.
9The neighborhoodcharacteristics( Xj) could include population or populationdensityto capturecontentioneffectsor scale economiesin the productionof
services.See Craig (1987b).
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depends only on Pi and Xj in the following
relation:'0
(3)
MARCH 1987
THEAMERICAN ECONOMIC REVIEW
40
Si
f (Pi, X)
of the
whereXj is a vectorof characteristics
jth neighborhoodthataffectthe outcomeof
interestbut are not adjusted during the
period.
conditions
We can obtain the first-order
undertheassumptionsthatthewelfarefunction in (1) and theproductionrelationin (3)
have thestandarddesirablepropertiesforan
interiormaximum to occur. The intuition
behind the model can be illustratedgeometricallyby consideringthe ratio of the firstorderconditionsforneighborhoods1 and 2:
d W/dS,
N, dS2/dP2
d W/dS2
N23dS,/dP
The leftside of (4) is theslope of thewelfare
function,forwhichW in Figure 1 indicates
an iso-welfarecurve."1The rightside of (4) is
the slope of the productionpossibilityfrontier,whichis the convexsolid line identified
by S, and S2. The productionpossibility
frontierillustratesthat the "price" of allocating more inputs to one neighborhoodis
the lost output in other neighborhoods.
Welfaremaximizationleads to a tangencyat
point 1, at whichpointthe marginalrate of
substitutionin the welfarefunctionequals
along
the marginal rate of transformation
theproductionpossibilityfrontier.
In general,the slopes of the production
forplanes betweendifferpossibilityfrontier
ent pairs of neighborhoodsdifferdue to
values of X. across neighborhoods
different
(throughequation (3)). Because thedifferent
pairwiseplanes of theproductionpossibility
frontierare tangent to the same welfare
allocationproblemin
loWe are assuminga short-run
which people do not move among neighborhoodsbecause of the distributionof serviceoutcomes.However,
such movementscould be made endogenousand dependent on S fora longertimehorizon.
"This iso-welfare curve is drawn symmetrically
around the 450 ray fromthe origin;it is not necessary
to do so (see below).
0
0
o
r1
\
mla
Z
_
_i
ui
ZN
Production
possibilityfrontier
forS1 and S2
1
\
possibilityfrontier
Production
for S3
and
S4
0
F-
o
OUTCOME IN NEIGHBORHOODS
2 AND 4 S2 AND S4
FIGURE 1. PRODUCTION POSSIBILITY FRONTIERS
ALLOCATIONS
AND WELFARE-MAXIMIZING
function,they trace out the curvatureand
location of thatwelfarefunction.For example, the dashed line in Figure1 indicatesthe
productionpossibilityfrontierin the plane
for neighborhoods3 and 4 witha tangency
at point 2. The curvatureof the welfare
functioncan be identifiedby consideringa
series of points tike 1 and 2. Note that
estimationof relation(4) gives estimatesof
characteristicsof the welfarefunctionand
not necessarilythoseof the productionrelation (3). Our analysisdoes account for the
and S may enter into
fact that both
relation (4), for which reason control for
simultaneityis required.
As we noted,the two criticalattributesof
welfarefunctionperthe local governmental
tain to its curvature(inequality aversion)
arounda 450 rayfrom
and to its asymmetry
the origin (unequal concern). Figure 1 assumes some inequality aversion (with a
curvaturebetweentheextremelinearcase of
and theL-shaped
focus only on productivity
case of focus only on equity) and equal
concern. Equal concern about neighborhoods does not generallyimplyequal service
outcomes across neighborhoodsbecause the
if the disproductionset is not symmetrical
Figure2
tributionof Xj is not symmetrical.
indicatesa case of unequal concernin which
neighborhood2 is favoredover neighborhood 1 in the sense that the weightsin the
welfare functionare greaterfor neighborhood 2 than for neighborhood1. Thus we
distinguishbetweenequal and unequal conof the isocern related to the symmetry
welfarecurves around the 450 line and in-
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VOL. 77 NO. ]
BEHRMA N AND CRAIG: PUBLIC SER VICES
where - is a productionfunctionelasticity,
and h is any functionalformwithpositive
forX1.
marginalproductivities
conditionforPj is
The first-order
0
0
o
o/
0/
= -cSy'PJ.
d35/dPj
(6)
I
z
:D
o
~
2,S
~~~~~
S 2
OUTCOME IN NEIGHBORHOOD
OF UNEQUALCONCERN
FIGURE2. ILLUSTRATION
OF THEOUTCOME
ABOUTDISTRIBUTION
equality aversion (or the equity-productivity
tradeoff)related to the shape of the isoof thewelfare
welfarecurves.Both attributes
functionare essential for determiningthe
distributionof outcomes.For example,unequal concern even with pure inequality
aversion (i.e., L-shaped iso-welfarecurves)
of service
resultsin an unequal distribution
outcomes.
II. ExplicitFunctionalFormsand
Relativevs. AbsoluteInequalityAversion
This section presentsexplicit functional
formsforthe welfarefunctionin (1), and for
the production functionconstraintin (3).
These functionalformsallow estimationof
the first-order
conditions.From theseresults
conclusions can be drawn as to what extent the local governmenttrades offequity
of public serviceoutcomesfor productivity
(inequality aversion) and whetherwelfare
(unequal
weightsdifferacrossneighborhoods
concern).
A.
Production Function Specification
The productionconstrainton local governmentalwelfaremaximizationis assumed
to have a partiallog-linearform:
(5)
41
lnSj =elnPj
+ h(Xj),
Since S. depends on Xj, thispartialderivativedepends on theneighborhoodcharacterchangesas X. changes,
isticsX. and therefore
of the
as is required for the identification
welfare surface,even though Xj does not
appear explicitlyin (6).
B. WelfareFunctionSpecification
We have exploredtwo alternativespecifications of the welfarefunction(1). One is
the relativelywell-knownCES form; the
otheris the Kohm-Pollak(KP) specification
(see Charles Blackorbyand David Donaldson, 1980, and Behrmanand Raaj Kumar
in the specificaSah, 1984).12 The difference
tions is in theirtreatmentof the inequality
aversion parameter. Empirically,we find
which
more supportfortheKP specification,
is presentedhere. The CES specificationis
presentedin the Appendixsince thisspecification probablyis morefamiliarand maybe
more appropriatethantheKP formin other
applications.The KP welfarefunctionis
(7)
WKP =
-ln [aj}y
esq |
for
where N is Y_jajNj.The parameterq sumThe
tradeoff.
marizesthe equity-productivity
inlower is q, the greateris governmental
the
distribution
aversion
concerning
equality
As
of public servicesamongneighborhoods.
q -* 0, the KP welfarefunctionapproaches
the pure productivitysum over individual
outcomes withno concernabout inequality.
For qi -* - o, the KP welfarefunctionap'2We also have considereda generalizedCES form
with displacementfromthe originby a set of parameters bj. These bj a prioricould relateto unequal concern. However, we findno empiricalsupportfor such
displacements,so we do not considerthemfurtherin
thispaper.
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THE AMERICAN ECONOMIC REVIEW
42
MARCH 1987
AKP. However, it is possible to identify
proachesthe L-shapedpureequityform.For
values of q between these two extremes, whetherthe a1 reflectequal concernby subtradeoff.
stitutingfor ai. a relation dependent on
thereis an equity-productivity
neighborhood characteristicsinto (9). If
The parametersa1 relateto equal vs. unequal concern. If there is equal concern, neighborhood characteristicsare found to
influencethe aj, thehypothesisthatall resiaj = a for all m neighborhoods.If thereis
unequal concern, a. depends on neighbor- dents are weightedequally in the allocation
process can be rejected."3 Simultaneous
such as racial composihood characteristics,
estimationis requiredfor (9) because it intion or income level.The a1 parameterscan
volved S. and Pj, as does the production
be interpretedto control for the political
influenceof the jurisdiction,and therefore relationin (5).
allow theparameterq to representthedirect
CrimeandPolice
III. Data: Safetyfrom
tradeoff.
equityvs. productivity
inBaltimore
Allocation
of inequalityaversion
The representation
in the KP welfarefunctionis absolute.This
Our empirical illustrationof the model
can be seen fromcalculatingtheshape of an
considersthe allocationof police to produce
isowelfarecurve between neighborhoods1
safetyfromcrimein thecityof Baltimorein
and 2:
fiscal year 1972. The unit of observationis
an individual neighborhood.The allocation
N2a2
dS1
examof police in Baltimoreis an interesting
e
(8)
dS2 WKP Nla,
ple for two reasons. First, therehad been
considerablelocal (Democratic)politicalstaThis relationsays that along an iso-welfare bility in Baltimore at that time, with the
in expected same police chief (D. D. Pomerleau) since
curveit is the absolutedifference
theallocation
outcomes across neighborhoods(not their 1968, so the factorsunderlying
relative values as in the CES case in the
processes probably are not masked by too
much noise fromadjustmentprocesses.SecAppendix) thatis relevant.
condition ond, a unique data base existsforBaltimore
The logarithmof the first-order
in 1972 whichpermitsthe estimationof our
for the constrainedmaximizationof the KP
welfarefunction(7) is
model, includingthe explorationof whether
crime or officiallyreit is survey-reported
ported crime that mattersin the allocation
ln P. = AKP+ qSj +lnS. +lna.
(9)
process.
on 79
The data base containsinformation
where
residentialneigh(out of 240) representative
borhood police beats.14 It combines data
for=/?)
AKP = ln(P x[EaNieqsjj
Surveys
from: 1) the CriminalVictimization
crimeper capita; 2) the
on survey-reported
is a constantwithina period,and X is the
Lagrangian multiplierfor the budget constraint.
dependent
13The estimatesof q are not particularly
on the choice of variables includedin the aj for our
For empiricalwork,a stochastictermcan
of the impact of neighborsample. The identification
be added to representthe factthatobserved
hood characteristicson aj, however,is more probex post outcomes differfrom ex ante exlematic.See fn.20 below.
pected outcomes. Estimates then can be
14This includes all the police beats on which data
obtained of absolute inequality aversion were collected in the crime survey.The beats fairly
(q) with data on outcomes and govern- representneighborhoodsin Baltimore(see Craig,1987a,
includedare not all
ment-allocatedinputsacross neighborhoods. for more detail). The policewebeats
contiguous.For thisreason have avoided thecompliWithoutfurtherassumptionsor a prioriincations of including"spillover"effectson otherneighformationit is not possible to identifythe
borhoods in the models of SectionsI and II; such an
but tedious.
extensionwould be straightforward,
absolute magnitudesof the componentsof
2e(S2-S1)
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VOL. 77 NO. ]
43
BEHRMA N AND CRAIG: PUBLIC SER VICES
STATISTICSa
TABLE1-DATA DEFINITIONSANDDESCRIPTIVE
Means
Variables
Outcomesb
reportedcrime
Per capita safetyfromofficially
Per capita safetyfromsurveyreportedcrime
Officiallyreportedcrimepercapita
Surveyreportedcrimepercapita
Inputs
Police patrolsper capita (X 10-3)
Tested
NeighborhoodCharacteristics
forRelationto Unequal Concern
Mean householdincome
Percentresidentswhite
Percentresidentsover65
housing
Percentresident-owned
OtherInstruments
Percenthouseholdswithincome < $5000
Percenthouseholdswithincome > $15000
Percentsinglehomes
Percentwith? 10 unitsperbuilding
Percentmarried
Percentmale
Percentbetween16 and 24-years-old
Percentunemployed
Percentcompletedhighschool
Percentinsuredforloss
Percentcriminalsobservedwho are white
Percentcrimevictimsemployed
Averageage of householdhead
Averagedollar loss per crime
Standard
Deviations
Ranges
1.28
.54
.32
.26
.28
.14
.28
.14
.04-1.55
.09-.75
.05-1.56
.05-.71
1.010
.880
.095-5.195
$6928
36.6
13.1
29.8
$2941
39.0
8.4
22.5
$2795-18179
0-100
0-35.2
0-82.0
44.6
7.9
60.8
13.6
39.1
42.8
21.3
2.4
85.9
18.0
18.6
58.5
38.4
$246.9
23.2
10.5
26.7
24.4
14.3
7.6
7.7
3.6
16.6
19.0
31.4
22.9
6.1
$365.8
0-91.1
0-56.1
0-100
0-100
0-69.4
16.7-62.3
0-44.4
0-21.6
19.3-100
0-100
0-100
0-100
25.6-53.2
$0-3000
a
There are 79
b
neighborhoodsin the sample.Data are forBaltimorein fiscalyear 1972.
reported
Per capita safetyfromcrimeis definedas is indicatedin relation(10): per capita safetyfromofficially
crime is 1.6 minus officiallyreportedcrime and per capita safety from surveyreportedcrime is 0.8 minus
crime.
survey-reported
Baltimore Police Departmenton officially
reportedcrimeper capita and thenumberof
police per capita; and 3) census data on
Table 1 gives
neighborhoodcharacteristics.'5
summarystatisticsof the variablesthat we
use.
We use two outcomes:safetyfromsurveyreportedcrime per capita and safetyfrom
officiallyreportedcrimeper capita. One interestingfact in the studyof crimeis that
about one-halfof all crimeis unreportedto
the police. Because a survey measure of
neighborhoodcrimeis available, these data
permit examinationof whetherthe police
reportedor surveyauthoritiesuse officially
"5The data base was preparedby RobertHighsmith
whilehe was at Towson StateUniversity.
We are grateful to him forkindlymakingit available forthisstudy.
reportedcrime in makingpolice allocation
thesurveymeasure
decisions.Unfortunately,
of crimehas some deficiencies;in particular,
in
it does not measurecrimeto nonresidents
an area, while it includescrimeto residents
sufferedin otherareas. We restrictour analysis to residentialcrime to minimizethese
problems(see Craig,1987a,formoredetails).
For both outcomes,we definesafetyfrom
crime" to be
(10)
Sj=c-cj,
16Some outcomes may lessen "bads" such as crime
(but perhaps in other contexts,disease) ratherthan
increase"goods." Of course,goods can be consideredto
be the absence of bads. Because our functionalforms
use logarithms,for empiricalpurposes we use safety
fromcrimeas definedin relation(10) as theoutcomeof
interest.
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44
THE AMERICAN ECONOMIC RE VIEW
where C > max(C.) and C1 is the per capita
crime rate (reportedor actual) in the jth
neighborhood.The empiricalresultsare not
qualitativelysensitiveto a range of values
for C. We use a value slightly above
max(Cj) in the estimatesthat we present
below.17
The equation of interestforestimationis
(9). The problem is a simultaneousone, as
not onlydoes theallocationof police depend
on safetylevels, but safetylevels are prowe use an instruduced by police. Therefore,
mental variable estimator,witha list of instrumentsthat accounts for the supply of
crime, the private demand for safety,the
propensityto reportcrime,and exogenous
determinantsof the probabilityof arrest.
are derivedfroma simultaThe instruments
neous equation model of urbancrime;Craig
These
(1987a) presentsthe fullspecification.
instrumentsinclude the 4 neighborhood
characteristicsindicatedabove, plus 14 additional characteristics(see Table 1). The
basic thrustof our resultsis not sensitiveto
the exact instruments
used.
Aversion
andUnequal
IV. Estimates
ofInequality
Concernin BaltimoreAllocationof Police Patrols
The firstset of empiricalresultsthat is
presented utilizes a two-outputversion of
rethe model to examinewhetherofficially
crimeis the more
ported or survey-reported
relevantdecision variable in the local governmentwelfarefunction.Results are then
presentedforboth the KP and CES specifications of the welfarefunction,althoughwe
KP
concentrateon the empiricallypreferred
specification.
A. SafetyfromOfficially
Reportedvs.
Crime
Survey-Reported
As noted in Section III, our sample includes data on crime as reportedin police
crimeas indirecords,and survey-reported
cated in the National Crime Victimization
Survey. We estimate a nonlinear relation
17To be explicit,we use C = 1.6 forper capita safety
reportedcrimeand C = 0.8 forper capita
fromofficially
crime.
safetyfromsurvey-reported
MARCH 1987
FUNCTION
TABLE2-ESTIMATIONOF KP WELFARE
OFFICIALLY
PARAMETERS
WITHTwO OUTCOMES:
REPORTEDANDSURVEY-REPORTED
CRIMEa
Right-SideVariables
Parametersin
Two-OutcomeExtension
of First-Order
Condition
in Relation(9)
of b
MultiplicativeCoefficient
SafetyfromOfficially
ReportedCrime
SafetyfromSurveyReportedCrime
InequalityAversionParameterc
SafetyfromOfficially
ReportedCrime
SafetyfromSurveyReportedCrime
R2
SEE
45.Id
(14.9)
- 5.6
(5.4)
- 2.9d
(.51)
- 3.0
(1.7)
.76
27.5
aBeneath the point estimatesare the standarderrors
of estimates.The R2 are pseudo R2 calculatedas one
minussum of squares of theerrorover the totalsum of
squares of the dependentvariable.
hThe firsttwo rows give the weightson the safety
fromreportedand surveycrimeterms,respectively.
c The thirdand fourth
rowsgivetheestimatesforthe
inequalityaversionparameter(i.e., q in (9)).
d Point estimatesthatare significantly
nonzeroat the
5 percentlevel.
parallel to the antilog of (9), but with an
extensionto the two-outputcase withsafety
fromofficially
reportedcrimeand safetyfrom
crime as the two weighted
survey-reported
outcomes,in order to examinewhichmeasure of public serviceoutcomeis morerelevant empirically.18
Since the resultsare robustwithregardto
we reportin Tavariationsin specification,
ble 2 theestimatesforthesimplestcase-the
basic KP model withequal concern.We find
that the weights on safetyfrom officially
reportedcrimes are positiveand significant
while those for safetyfromsurvey-reported
crimeare negativeand insignificant.
There are at least two possible explanationsforfindingthatofficially
reportedcrime
18In such an estimationthe weightscannotbe identifiedseparatelyfromthe productof the equal concern
parameters(aj), the constants(A KP), and the producof the
tion functionparameter(?). But the significance
product that includes the weightscan be determined
fromthe estimates.
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45
BEHRMA N AND CRAIG: PUBLIC SERVICES
VOL. 77 NO. ]
TABLE 3-KP
AND CES WELFARE FUNCTION PARAMETERESTIMATES
WITH AND WITHOUT EQUAL CONCERNa
AbsoluteInequality
Aversion
KP-Equation (9)
Right-Side
Variables
Estimatesof InequalityAversion:
In SafetyfromCrime
per Capita (c forCES)
Safetyper Capita (q forKP)
Determinantsof Unequal Concern:
a (or a)
Mean householdincome
Equal
Concern
(1)
Unequal
Concern
(2)
-4.0c
(.30)
- 3.4C
(.39)
4,5C
(.38)
.53
24.7
-.55C
(.17)
-.02
(.02)
-.06c
(.03)
- .01
(.03)
8.8c
(1.3)
.67
17.1
Percentresidentswhite
Percentresidentsover65
housing
Percentresident-owned
Constant
R2
SEE
RelativeInequality
Aversion
CES -Equation (A2)
Equal
Concern
(3)
Unequal
Concern
(4)
- 1.6c
(.30)
- .90c
(.30)
- .04
(.10)
.27
48.3
-.66c
(.20)
-.02
(.02)
-.08c
(.04)
-.06c
(.03)
6.0c
(1.7)
.55
25.8
aSee fn.a, Table 2.
b In theseestimatesthecoefficient
of ln safetyis constrainedto be one as requiredin
relation(9).
cSee fn.d, Table 2.
empiricallydominatesas a determinantof
the allocation process. First, the officially
reportedinformationmay be the best (or
only) informationavailable to the allocator
of police across neighborhoods.Even if the
surveycrime measure is better,the police
on how
may not have accurateinformation
officiallyreportedand actual crimediverge
systematicallyacross neighborhoods.Second, evenif theallocatorof police knowsthe
pattern of actual in addition to officially
crimeis
reportedcrimesand survey-reported
a better measure of actual crime than is
officiallyreportedcrime,attentionmay be
reportedcrimesbecause
focusedon officially
of the perceptionthat they are more importantin thepoliticalprocess."9If eitherof
19See Craig (1987a) foradditionaldiscussionof this
issue, an estimateof the causes of the propensityto
reportcrime,and a discussionof theproblemswiththe
surveycnme measure.
these explanationshold, theremay be social
gains in termsof controlof totalcrimefrom
improving the data on officiallyreported
crime to reflectbetterthe patternsof actual
crime.
In any case, because of this evidenceon
the relativeimportanceof safetyfromofficially reportedcrimein thepolice allocation
process, we focus exclusivelyon officially
reportedcrimein whatfollows.
B. WelfareParametersUnderlying
PoliceAllocation
Table 3 presents estimatesof specifications with equal and withunequal concern
conditionsderived from
for the first-order
the KP (9) and CES (A2) welfarefunctions.
These resultsare robustin threecrucialrespects. First, and most important,theyindicate substantial governmentalinequality
aversion,but still withsome equity-productivity tradeoff.Second, they indicate that
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46
THE AMERICA N ECONOMIC RE VIEW
unequal concern prevails in the allocation
decisions,so that all neighborhoodsare not
weightedequally in the"as if" social welfare
function. Third, they suggest that police
patrol allocations are more consistentwith
the KP absolute inequality aversion than
with the CES relativeinequalityaversion
welfarefunction(see the
local governmental
Appendixforthe CES specification).
significant
inequalityaverThe statistically
sion is in addition to any unequal distribution of inputs resultingfrom different
neighborsocial welfareweightsfordifferent
hoods. The KP resultsallowingforunequal
concernyield an estimateof q of - 3.4. This
less than zero, indiestimateis significantly
cating aggregateoutcomeis not maximized.
At the same time, however,there also is
as the
concernabout productivity,
significant
inequalityaversionparameteris significantly
greaterthan the extremeof concernsolely
with equity. Results for the CES case are
similar; the estimatedvalue of c is significantlynegativewithboth the equal and the
unequal concernspecifications.
In addition to the inequalityaversion,Ftests reject the hypothesisof equal concern
across neighborhoods.20
As discussedin Section II, thismeans thatpublic serviceoutput
20Estimation of a model thatallows unequal concern
may have a greaterproblem with identificationthan
does estimationof a model assumingequal concern
because of the introductionof neighborhoodcharacteristics. We have noted in Sections I and II that our
conditionsthatpermitidenestimatesare of first-order
of the welfarefunctificationof certaincharacteristics
tionand notof productionrelations,whichalso involve
in Xj. If theneighbortheneighborhoodcharacteristics
in X. wereexactlythesame as the
hood characteristics
on whichunequal concern
neighborhoodcharacteristics
conditionswould be
depends, however,our first-order
identifiedfromproductionrelationsonly by the functionalforms(and, as a refereehas noted,some alternativeproductionrelationto thatin (5) maymakeidentification by functionalform impossible). On a priori
groundswe do not thinkthatthe set of neighborhood
characteristicsthat we explore in our estimatesare
identicalto the elementsof Xj in the productionrelation(also see Craig, 1987a). Moreover,our estimatesof
the inequalityaversionparametersdo not change significantlyif we allow unequal concern,as mightbe
expected were we switchingfromestimatingthe firstorder condition to the productionfunction.Therefore
we interpretour estimatesto relateto unequal concern
and not to the productionprocess.
MARCH 1987
is weightedmoreheavilyin thelocal governmental welfarefunctionforsome neighborhoods than for others.The estimateswith
unequal concern are robust in suggesting
preferencesforgreatersafetyfromcrimefor
lower income and younger(in the sense of a
smaller percentage of residents over 65)
neighborhoods,but there is no significant
impact of racial composition.The estimates
are mixed for the percentageof residentnegative
owned housing,with a significant
imeffectin the CES case, but insignificant
pact in the preferredKP case. Thus the
preferenceweightsseem to be pro-poorand
pro-young,but neutralregardingrace and
housing.
probablyresident-owned
Some importantimplicationsof our estimates of inequalityaversionand of unequal
concerncan be seen by solvingrelations(5)
and (9) forthe reducedformfortheratioof
safetyfromcrime:21
e h(_X2)(
2
)
s2)
e -qS2
Since 0 < - < 1 (because it is the elasticityof
safety from crime with respect to police
patrols) and q is estimatedto be less than
zero (see Table 3), all of the powerson the
rightside of relation(11) are positive;therefore, if neighborhood1 has more of the
characteristicsthat produce safety from
crime and thereis equal concern(a1 = a2),
neighborhood1 has greatersafety(S1 > S2).
Relation (11) also is usefulforexamining
the optimal allocation of safetyfromcrime
in neighborhood1 vs. 2. The more unequal
concern favors neighborhood1 (i.e., the
greateris a1/a2), the greateris safetyfrom
crimein neighborhood1 relativeto 2. Since
the mechanism for increasingsafetyfrom
crime in neighborhood1 vs. 2 is through
allocation of police patrols(givenneighborrelation(11) also imhood characteristics),
plies that the more unequal concernfavors
neighborhood1, the greaterthe relativeal-
21Closed-formexpressionsfor the ratio of police
patrolsand safetyfromcrimecannotbe derivedforthe
KP case. See the Appendixforsuch expressionsin the
CES case.
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VOL. 77 NO. 1
BEHRMAN AND CRAIG: PUBLIC SERVICES
location of police patrols to that neighborhood.
These estimates imply an allocation of
police resourcesthat partiallycompensates
for the distributionof neighborhoodcharacteristicsthatpreventcrime.While thereis
ambiguity in the KP case about which
neighborhoodshave greaterpolice patrols,
relation(11) does show that the relativeallocation of police is greaterto neighborhoods with more crime-causingcharacteristics. But compensation does not offset
completely the impact of neighborhood
so neighborhoodswithmore
characteristics,
crime preventioncharacteristicsare more
safe than are those with relativelygreater
police patrols. In addition,those neighborhoods that are favoredby unequal concern
are allocated further
police and have greater
safetyfromcrime than would be the case
withequal concern.
V. Summary
andConclusions
We have presenteda model which explicitly examines the distributionalpreferences of a local governmentover service
outcomes.An important
featureof themodel
is that it distinguishesinequalityaversion
fromunequal concernin the social welfare
functionof a local government.
The modelis
estimatedfora particularcase, theallocation
of safetyfrom crime and of police across
neighborhoodsin Baltimorein 1972. All the
major results hold with both alternative
specificationsof the welfarefunction.These
empiricalresultsindicatea significant
degree
of inequalityaversion,so that some aggregate productionis sacrificedin orderto obtain the equity goals of the local government. Further,thereappears to be unequal
concern so that the safetyfromcrimeoutcomes are weighteddifferently
forresidents
in different
neighborhoods.Subject to qualificationsabout the conditionalityof our
estimateson our assumptionsand data, our
empiricalresultshave potentiallyfar-reaching implicationsformodels of local governmentbehavior.
First, we have shown that at least one
major local governmentappears to have
substantial concern about equity in the
47
distributionof a local public service.The
parametersthat we estiinequality-aversion
negative,even after
mate are significantly
accountingforthefactthatresidentsmaybe
weighted unequally in the social welfare
function.This suggeststhatthelocal government compensates for the distributionof
characteristicsacross neighborhoodsregardtheimpact
ing safety,ratherthanreinforcing
in its allocation of
of such characteristics,
police across neighborhoods.While a structural model that would explain stronginequality aversion has not yet been developed, our contributionshows that pursuing
such a researchgoal may yield interesting
behavior.
new insightsinto governmental
Second, we also showthatin thiscase not
all residentsare weightedequallyin thelocal
welfare function.These results also merit
furtherexamination.Unequal concernmay
exist, for example, because residentswho
receive less safetyfromcrime may receive
more of other publicly provided services,
such as education. Conversely,the results
may reflectthat certainresidentsare more
"in favor" with the authorities,and receive
more of all locally providedservices.While
our single-input,single-outcomeestimates
betweenthesetwo
are not able to distinguish
or froma hostof otherexplanaalternatives,
tions, the point is that a distinctionamong
residentsapparentlyis being made by the
government.Research with a multi-output
extension of our model, if data become
the situation.
available, could clarifyfurther
In any case, our resultsimplythat models
which a prioriassume that all residentsare
of governtreatedequally in thedistribution
mental servicesare ignoringthe potentially
importantfact thatunequal welfareweights
may prevail.
Third, our empiricalsupportin this case
for both aspects of unequal serviceallocation by neighborhoodimplies potentially
in studiesof aggreserious misspecification
gate local public servicedemand. Models of
mayneed to takeheed
preferenceaggregation
of the fact that people pay taxes based on
the city-wideamount of purchasedinputs,
but base theirdemand and votingbehavior
on the perceived level of neighborhood
serviceoutput.The standardassumptionof
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48
THE AMERICAN ECONOMIC RE VIEW
median voter models is that residentsparticipate equally in serviceoutputs and tax
shares. These models calculate residenttax
sharesbased upon theirsharein the cost of
the aggregate level of purchased inputs.
However, the frameworkand results presented here show that residentsmay share
unequally in the benefitof those inputs to
the extentthat serviceoutcomesdifferfrom
the allocationof inputs.Thus,residentsmay
perceive differentservicelevels even when
they have equal tax shares,causing differences in the votingbehaviorof people who
prima facie may appear to face the same
constraints.
where
ACES =ll(P
(I(X
of thewelfarefuncThe CES specification
tion is
(Al)
WCE
(Njaj
Sj)
I/
The parameterc refersto inequalityaversion.
Like q forthe KP specification,
as c is more
negative,inequalityaversionis greater.At
the extremewithonlyconcernabout equity,
c is - so; for the intermediate
Cobb-Douglas case, c is zero; and forthe extremewith
only concernabout productivity,
c is one so
that WCES is the weightedsum of the Sj.
The aj parametersrepresentunequal concern,in the same manneras the a1 parametersin theKP version.Inequalityaversionin
the CES case is relative(i.e., along an isowelfarecurveit is the relativeoutcomesthat
matters),ratherthan absolute as in the KP
case. Nonetheless,the estimationresultsare
similarforthe two cases (see Table 3).
Maximization of (Al) subject to the resource and productionconstraintsyieldsan
estimatingequation fromthefirst-order
conditionsthatis similarto (9) forthe KP case:
(A2)
lnPj = ACES + cln Sj + ln a1,
ENjajSjc)(
)
is a constantwithina period.
One advantage of the CES case is that
closed-formexpressionscan be derivedfor
the ratiosof P1/P2 and S1/S2 forneighborhoods 1 and 2, analogous to equation (11)
forthe KP specification:
APPENDIX
The CES WelfareFunctionSpecification
MARCH 1987
S(
(A4)
P2
(
1
(a
(2)
eh
2
)
-/(
EC)
eh(XI)
e(
A/( -EC)
2)
Again, the implicationsof theseexpressions
are similarto those forthe KP version,except thereis no ambiguity;the allocationof
police patrolsis greaterto theneighborhood
for
withless crimepreventioncharacteristics
our estimateof c in Table 3.
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