from for efficiency

359

EMPIRICAL TESTS FOR ALLOCATIVE

EFFICIENCY IN THE LOCAL PUBLIC SECTOR

ANWAR M. (CHAUDRY) SHAHWorld Bank, Washington, DC, and Departmentof Finance, Government of Canada, Ottawa

This article reports evidence from two tests for allocative efficiency in the localpublic sector using micro-based data. The first test is based on Brueckner’s (1979,1982) theoretical result that a nonpositive relationship between public services andresidential property values is a definite indicator of over provision of local publicgoods beyond optimal levels in the case of typical mixed communities, that is,communities having substantial business property. This article points out the limi-tations of Brueckner’s empirical analysis and provides a stronger empirical test ofallocative efficiency in the local public sector using micro-based data. An alternativetest that uses the criterion that, when the level of local spending is optimal, abalanced budget change in local spending and residential property taxation shouldleave residential property values unaltered, is also presented. Both the tests suggestoverprovision of local public goods in metropolitan Edmonton, Canada.

This article carries out tests for allocative efficiency in thelocal public sector using micro-based data. For this purpose,two empirical approaches are considered here. The first approachoperationalizes Brueckner’s (1979, 1982) theoretical result that anonpositive relationship between public services and residential prop-erty values in mixed communities is a definite indicator of provisionof local public goods beyond optimal levels. The second approach usesthe criterion that, when the level of local public spending is optimal,a balanced budget change in local spending and residential propertytaxation would leave residential property values unaltered.

AUTHOR’S NOTE: The author is grateful to Professors Jan Brueckner, Bev Dahlby, MelvilleMcMillan, Wallace Oates, Sam Wilson, Dennis de Tray, Roger Smith, J. Ronnie Davis, Editor, andtwo anonymous referees of Public Finance Quarterly for helpful comments. The views expressedin this article are those of the author only and should not be attributed to the World Bank or theGovernment of Canada.

PUBLIC FINANCE QUARTERLY, vol. 20 No. 3, July 1992 359-3770 1992 Sage Publications, Inc.

at PENNSYLVANIA STATE UNIV on March 6, 2016pfr.sagepub.comDownloaded from

http://pfr.sagepub.com/

360

The second section discusses Brueckner’s model and its empiricalimplementation and results. The third section outlines a balanced bud-get test of allocative efficiency and describes econometric proceduresand results. The fourth section highlights the conclusions reached inthis analysis. An appendix provides an econometric procedure on themeasurement of public outputs.

AN EMPIRICAL TEST FOR ALLOCATIVEEFFICIENCY IN THE LOCAL PUBLIC SECTOR

BRUECKNER’S MODEL

Brueckner (1979, 1982) develops a theoretical model of propertyvalue determination to focus on the local public sector efficiencyquestions in a world that is not in Tiebout equilibrium. It is a bid rentmodel of housing market in which rents adjust to insure that the utilitylevels of identical consumers are equal regardless of which housingunit they transact. The most satisfying aspect of his theoretical formu-lation is that it &dquo;yields an estimating equation that can indicate whetheror not public goods are provided efficiently even in heterogenouscommunities&dquo; (1979, 224). For a community with mixed tax base, aheterogeneous housing stock, and within-community differences inhousehold incomes, Brueckner draws the conclusion that a zero, ornegative, relationship between public services and residential propertyvalues implies overprovision of local public services beyond optimallevels. The following paragraphs summarize Brueckner’s contribu-tions and reflect on the innovations presented by this article to improvehis empirical applications.

The key to Brueckner’s (1979, 1982) empirical studies is his resultthat aggregate property value in a bedroom community is insensitiveto a balanced budget increase in public spending when the public goodis efficiently provided. The absence of an effect indicates that aggre-gate value is at a maximum. Using this result, the 1982 paper per-formed a cross-section regression of aggregate property values onpublic spending levels and other determinants of aggregate values ina sample of Massachusetts communities. The public spending coeffi-



361

cients in various versions of this regression were never significantlydifferent from zero, suggesting that local spending levels in factmaximized property values and thus that expenditure levels wereefficient in the sample.

The 1979 paper offers a similar test using median rather thanaggregate property values. The basic idea is that if public spending isat the level where aggregate property value is maximized, then thevalue of the average property is maximized as well. Because themedian-valued house will offer a good approximation to the averageproperty in a community with little business property, it follows thata regression of median house values in a sample of bedroom commu-nities has a similar interpretation to an aggregate value regression. Inparticular, a zero spending coefficient indicates that public good levelsare set to maximize median (and hence aggregate) property value andthus that public spending levels are efficient.When a community has substantial business property, the interpre-

tation of a median house value regression must be modified slightly.The problem is that because business property does not benefit frompublic spending in Brueckner’s model (public goods are pure con-sumption goods), at a public spending level that maximizes totalproperty value, residential value must still be increasing in the publicgood level. Using the previous reasoning, this in turn implies that whenthe public good level is efficient, additional public spending raisesmedian house value. Therefore, in contrast to the bedroom communitycase, a median house value regression from a sample of typical mixedcommunities should exhibit a positive spending coefficient if the localpublic sector is efficient.

With this understanding of Brueckner’s approach, the innovationoffered by this article can be appreciated. Rather than running amedian value regression, my approach is to construct a sample of alarge number of houses in a relatively large number of communities.To interpret a house value regression in such a sample, note that theabove discussion implies that in an efficient mixed community, morehouse values will be rising than falling in response to an increase inpublic spending (this must be true for the median value to be rising).As a result, a regression on a random sample of houses from severalcommunities should show a positive spending coefficient if the local



362

public sector is efficient. Basically, then, my approach is similar to thatof Brueckner (1979) but it relies on data from a large number of housesrather than a single (median) observation within each community. Byusing a rich micro-based data set, this article provides a strongerempirical test of Brueckner’s theoretical results.1

EMPIRICAL IMPLEMENTATION

A stronger empirical test of efficiency of local public goods basedon Brueckner’s theoretical model can be carried out using disaggre-gated data on house value based on a stratified random sample of 875residential properties sold in the summer of 1977 in 35 communities inmetropolitan Edmonton, Alberta, Canada. Basic data on house char-acteristics and property taxes were obtained from the Multiple ListingsService. Supplementary data on spending and output measure of localpublic services were assembled from a variety of sources (see Chaudry-Shah 1989 for details on data construction).An empirical test of Brueckner’s model requires that the property

value equation should omit the tax variable but include communitycharacteristics and indicators of business profits and business contri-butions to property tax base or property taxes. The equation presentedin Table 1 closely follows Brueckner’s empirical formulation andincludes POOR (low income population), Y (median income), POP(community population), and OLD (population 65 years and over) ascommunity characteristics. NRA% (nonresidential assessment/totalassessment) serves as a proxy for business contribution to the propertytax base or property taxes. This equation is noteworthy for its omissionof tax variables. This is because in Brueckner’s model, the inclusionof a tax variable as well as expenditure variables in a housing priceequation violates local government budget constraints. Communitycharacteristics and business property values and profits variables needto be included because these are considered important in interpretingthe implications of spending coefficient for allocative efficiency, asdiscussed earlier.

To carry out a stronger test of equality of regression coefficients forpublic sector variables than is available with the help of the Chow test,differential slope dummies are introduced for the local public spending



363

TABLE 1: An Empirical Test of the Efficiency of Local Public Sectors in Metro-politan Edmonton (Two stage least squares estimation)

NOTE: 875 observations were made. Dependent variable = P (house sale price).a. Per capita equalized assessment, business assessment per capita, populationdensity, population growth rate, roads per square kilometer of areas, and municipalgrants were used as instrumental variables in TSLS estimation.

variable (LOCAL) for communities in the sample (see Maddala 1977;Judge et al. 1980). Individual local public spending dummies are usedfor communities having a 1977 population greater than 25,000



364

(LOCAL24 and LOCAL25). The communities having a 1977 popula-tion of 7,000-10,000 and those having a population of 2,000-3,000are grouped and assigned separate dummy variables (LOCALA andLOCALB, respectively). It may be noted that LOCAL24 (St. Albert)and LOCALB (Morinville, Stony Plain, and Devon) are bedroomcommunities, whereas LOCAL25 (Sherwood Park) and LOCALA(Spruce Grove, Leduc, and Fort Saskatchewan) are mixed communi-ties. Thus regression results would help to determine if the samplecommunities’ performance in the provision of local public goodsdiffers in any significant manner among those groups.

Table 1 presents regression results for a Brueckner-type equation.Because the results using both OLS and TSLS were essentially equiv-alent, only the TSLS results are reported. All the structural character-istics have statistically significant coefficients at least at the .05 levelwith correct signs. As expected, LSIZE and Y appear with positivesignificant coefficients (.05 level) and DCBD and POOR with nega-tive significant coefficients (at .10 and .05, respectively). NRA% hasa positive coefficient but it is not statistically significant at the .05level. The theory is ambiguous about the sign of coefficients for POPand OLD. Both appear with negative signs that are not statisticallysignificant at the .05 level. The coefficients for LOCAL, LOCAL24,and LOCAL25 are negative, whereas for LOCALA and LOCALB theyare positive. The former three coefficients are, however, not statisti-cally different from zero. LOCALA and LOCALB are positive andsignificant at the .25 level only.

The coefficients of LOCAL and differentials slope dummies forLOCAL imply that the marginal net impact of the local public sectoron residential property values is negative (but statistically not differentfrom zero) in the larger mixed communities of Edmonton and Sher-wood Park and for the bedroom community of St. Albert. For smallmixed communities (LOCALA) and small bedroom communities(LOCALB), this marginal net impact is positive but statistically signif-icant at the .25 level only. Thus the null hypothesis of the zero coef-ficient cannot be rejected for the spending variable or for any of thespending slope dummies, suggesting that a value of zero for all thosecoefficients be accepted provisionally. Recall that according to Brueckner’smodel, a zero coefficient in the case of a bedroom community indicates



365

efficiency but implies overprovision of local public goods in the caseof mixed communities. Thus the regression results suggest a tendencyto overprovide local public goods in all mixed communities, but thenull hypothesis of efficient levels of public services provision cannotbe rejected for bedroom communities in this sample. Bedroom com-munities nevertheless constitute only 7% of total population and 8%of total area of the sample communities. Therefore, for the sample asa whole, overprovision conclusions are warranted.

A BALANCED BUDGET APPROACH TO TEST THE

EFFICIENCY OF LOCAL PUBLIC GOODS PROVISION

EMPIRICAL MODELS

Alternately, a simple test of efficiency can be carried out by esti-mating the impact on house price of a dollar increase in per capita lo-cal expenditures financed solely by residential property taxes (AP/ALOCAL). A negative net impact would indicate overprovision ofpublic services. Positive or zero impacts have ambiguous interpreta-tions. More specifically, consider the following simple model:

If TA, = (TAX)I = tax payment on property i, where -r is the nominal taxrate and A, is the assessed value of property i, then t, = T(4jP,) and



366

Equation (1) shows the effect of an increase in expenditure of onedollar per capita financed through a residential property tax. It showsthat the balanced budget impact can be approximated by the coeffi-cient of per capita local expenditure minus the coefficient of effectivetax rate multiplied by the ratio of assessed value to market valuedivided by per capita assessment.An application of the balanced budget approach outlined above is

more appropriate for regressions that estimate capitalization of bothwithin- and across-jurisdictions tax differentials because the approachrequires incorporating the independent influence of interjurisdictionaltax capitalization. The capitalization literature has advanced the fol-lowing models to estimate both influences using either the effectivetax rate variable (modified Oates approach) or the tax burden variable(modified King-Reinhard approach).2 These approaches and theirmotivations are outlined in the following paragraphs.As a powerful and prescriptive tool of analysis, the Tiebout hypoth-

esis that &dquo;voting with feet&dquo; in a multijurisdiction environment leads toPareto-optimal provision of local public goods remained dormant forseveral years due to the lack of an empirical framework to test theimplications of &dquo;voting with feet&dquo; for the supply of local public goods.Oates (1969) provided the first empirical test of this idea by arguingthat, if consumers shop among local communities, then fiscal differ-entials among communities will be capitalized into residential prop-erty value, that is, the discounted present value of a future stream ofcosts and benefits will affect housing prices. This simple idea, whichis often referred to as the &dquo;capitalization hypothesis,&dquo; is potentiallyvery powerful because it not only provides a simple measure ofindividual preferences for local public goods but it also has importantimplications for the equity and efficiency of local public goods provi-sion. To examine the existence of capitalization, Oates used a hedonicindex approach, where the price of a house is depicted as a functionof the valuation of the various characteristics of the house, such asstructure, site, neighborhood, public services, and taxes. The correctspecification of the tax price term in such an equation is the subject of



367

ongoing debate. Oates (1969,1973,1981) used effective tax rate (taxbill/house price) as the tax price term in his empirical investigation,and until recently most subsequent studies followed suit. King (1977)and Reinhard (1981) have recently argued that the tax effect is incor-rectly treated in an Oates-type equation and have advocated an alter-nate approach using annual property tax payments ($) per householdas the tax price term. Reinhard (1981) has argued that the dependentvariable should be the total cost of homeownership, that is, house priceinclusive of tax costs. Chaudry-Shah (1988,1989) finds that both spe-cifications yield comparable estimates if intrajurisdictional variationsin taxes are also captured by the model. Both the Oates and King-Reinhard approaches are therefore modified to distinguish empiricallyintrajurisdictional capitalization of taxes due to systematic assessmenterrors within each jurisdiction (Hamilton 1976) and interjurisdictionalcapitalization due to differences in the effective tax rates amongjurisdictions. The respecification of these models to capture the sepa-rate effects of the two above-mentioned influences is reported below.

The first approach (modified Oates approach) reflects the view thatit is the differentials in tax rates both within and across jurisdictionsthat matter for capitalization of tax burdens. Mathematically,

The MT variable in the above equation captures interjurisdictionalinfluences, TMT measures the effect of intrajurisdictional property taxdifferentials for the sample communities, and the measures of localpublic services estimate the influence of alternate mixes and levels oflocal public sector output.



368

The second approach uses tax payments in estimating tax capital-ization. This view can be implemented by the following basic estimat-ing equation, which captures public sector capitalization both withinand across jurisdictions based on the King-Reinhard methods:

The above equation can also be rewritten in effective-tax-rate form asfollows:

In the above specification, MT is used to estimate interjurisdictionalinfluences, whereas T - MT captures systematic assessment differen-tials within jurisdictions. The model specified is nonlinear both invariables and parameters and would be best estimated by a nonlinearregression using a quasi-Newton algorithm.

Because the King-Reinhard approach uses tax burden variables,balanced budget impacts (M’/ MOCAL) can be calculated in astraightforward manner. Thus, for these equations, (AP/ALOCAL) isobtained simply by multiplying the coefficient of MTAX (mean mu-nicipal property tax per household) by the size of the household andthen adding this negative value to the positive effect obtained from thecoefficient of LOCAL (per capita local expenditure). For regressionsusing the public services index (PSI), a translation of the coefficient



369

of PSI in terms of equivalent coefficient for LOCAL is first attemptedas follows:

Values for the first expression on the right-hand side of equation(4) are easily obtained from capitalization regressions. (dP.S7/dZ,0-CAL) is approximated from the following equation: Where PSI = Oo +(31LOCAL or

is estimated empirically.3For regressions using the effective tax rate variable, the balanced

budget impact can be approximated by substituting the estimatedvalues of the parameters in equation (1).

In investigating public sector capitalization based on the effectivetax rate variable (the Oates approach), I estimated several equationsusing a variety of models and data. Of these models, equation (2) (seeTable 2) appears to be most satisfactory based on theoretical consid-erations and empirical results. It distinguishes between intra- andinterjurisdictional aspects of property tax capitalization. It also incor-porates quality indices for public sector output that are theoreticallypreferable over expenditure measures. Moreover, these measures areneighborhood specific in contrast to expenditure measures of publicservices, which are only available at the municipal jurisdiction level.Empirically, the equation overcomes the multicollinearity problem byincorporating a composite measure of public services that is notcollinear with other regressors. All the independent variables appearwith statistically significant coefficients having sizes and signs con-sistent with a priori expectations.As an alternate approach to tax capitalization, I also estimated

models using the annual property tax bill ($) per household as anexplanatory variable (the King-Reinhard approach). These modelsalso differed as to the choice of public sector variables and economet-ric technique employed. Of these models, equation (3) (see Table 3)



370

TABLE 2: Estimation of Within- and Across-Jurisdictions Public Sector Capi-talization : Modified Oates Approach

NOTE: 875 observations were made for 35 communities. Dependent variable = P(house sale price).a. General Accessibility Index (CM/): A Gaussian accessibility index was computed asfollows:

where

cL = distance between i and j, andv = diameter of the smallest circle circumscribing all communities in this study.This accessibility index, the sum of a series of relative point accessibility values,indicates the degrees of spatial proximity for an area vis-a-vis all other areas in thesample. This measure of relative accessibility has the desired properties of smoothnessand asymptotically approaches zero as distance increases. This measure also givesgreater relative importance to communities within the City of Edmonton because theydominate the sample. It is a superior measure of accessibility because it does notmeasure accessibility with respect to a fixed point.

presents better results than do alternate estimating equations. Recallthat the model incorporating the King-Reinhard suggestions is nonlin-



371

TABLE 3: Public Sector Capitalization Estimation Based on Modified King-Reinhard Approach (Nonlinear estimation)

a. Canonical composite index based on number of rooms, dwelling size, living roomarea, age, fireplace dummy, recreation or family room dummy, number of 3- or 4-piecebathrooms, garage size, and brick/stone exterior dummy.b. Canonical composite index based on lot size, General Accessibility Index, distancefrom central business district, distance from a bus stop, and population density.c. Canonical composite index based on achievement score, park area, recreationsprograms index, residential fire safety index, per capita weekly bus trips, and neighbor-hood personal and property safety indices.d. Log-likelihood function.

ear both in variables and parameters. Equation (3) estimated thismodel by a nonlinear method based on a quasi-Newton algorithm. Thisprocedure enabled me to obtain more precise estimates of all regres-sors without encountering the heteroskedasticity problem often en-countered with the use of iterative linear methods. Furthermore, theequation used composite indices of structure, site, and public servicescharacteristics, and thus a very small set of significant regressorsexplained most of the variations in the house price. All the regressorsappear with the expected signs. Like equation (2), it also enables meto estimate the extent of both within- and across-jurisdictions taxcapitalization.

The above-mentioned equations are used to determine the alloca-tive efficiency of the local public sector in Edmonton. Table 4 presentsestimates of a change in average residential property value as a resultof a dollar increase in per capita expenditure financed solely byresidential property taxes. The estimated impact is a decrease ranging



372

TABLE 4: Estimates of a Change in Average House Price as a Result of a DollarIncrease in Per Capita Expenditure Financed Solely by ResidentialProperty Taxes

from a low of $41.9 to a high of $133.2 based on a 68% confidenceinterval. The average decrease is $81 using the Oates approach [equa-tion (2)] and $86 based on the King-Reinhard model [equation (3)].Both equations suggest overprovision of local public goods in metro-politan Edmonton.

CONCLUSION

This article employed two alternative empirical approaches to testthe allocative efficiency of local public goods provision in metropol-itan Edmonton, Alberta, Canada. The results based on two alternativemodels reach the same conclusion, that local public goods are over-provided in metropolitan Edmonton. These results are to be expecteddue to the generous availability of provincial assistance to localgovernments in the area.



373

APPENDIXOn the Measurement of Public Outputs

This appendix provides a brief description of the Public Services Index (PST) andits estimation. This index incorporates an interesting innovation in the measurementof public outputs.

In examining public sector allocative efficiency questions, using expendituremeasures of output, although helpful and often used, are not sufficient. The use of theexpenditure measures for local public output is based on the supposition that differ-ences in public expenditures reflect only differences in output. This implies thatcommunities have the same cost structure, the same technology, and are equallyefficient in providing local public services. These conditions are generally not met inpractice, and therefore observed differences in expenditures may not reflect differ-ences in public goods. In fact, using expenditure measures might lead one toerroneously characterize the community with higher costs as having greater provisionof local public goods (see also Schlack 1977). Even if some of these shortcomings ofthe expenditure measures of output could be overlooked, it is simply not possible towork out a geographical distribution of city expenditures among city neighborhoods.An attempt was therefore made to construct output measures of public services at theneighborhood level. In this respect, only the five major &dquo;soft&dquo; services-education,police, fire protection, public transit, and parks and recreation services-were in-cluded in this analysis. Education services are measured by school achievementscores, and police protection by neighborhood personal and property safety indexesdeveloped from crime incidence statistics. The output of fire protection services isaccounted for by four alternate measures: community fire classification developed bythe Provincial Superintendent of Fire Insurance; a measure of fire prevention effec-tiveness (6-year average fire rate); a measure of fire suppression effectiveness (6-yearaverage per capita fire loss in dollars); and a residential fire protection index (FSR)calculated as follows:

where HP is the number of single family dwellings in the neighborhood and RFC isthe residential fire count of the neighborhood.

Intercommunity public transit service variations are captured by the per capitaweekly bus trips (PBT). This variable measures the frequency of public transit servicesto each community. Finally, parks and recreation services are accounted for byneighborhood park area (PARK) and a recreations programs index (PKIS~.

Transportation and environmental health (sewage, water, etc.) were excludedbecause the sample municipalities now routinely require developers to provide forsuch infrastructure (such as local streets, water and sewer lines, etc.) in new subdivi-



374

sions. These municipal functions are being performed by developers and are not fullyaccounted for in municipal spending. Furthermore, other than expenditure measuresthere is no accepted basis for comparing these services. General government, health,and welfare were also not considered because these are not assumed to have anydifferential impact on intracity neighborhood residential property values.

The original data set was collinear, and the application of ridge regression did notoffer any significant improvement. Therefore, as a possible solution to the multi-collinearity problem, the first stage of the analysis uses canonical analysis to formcomposite variates. In subsequent regression analysis, one or more of these variatesreplace the original variables. The canonical index has a long tradition of acceptancein the econometric literature (Hotelling 1936; Judge et al. 1980), but its applicationshave been few and far between partly due to greater availability of routines for doingprincipal component analysis in most software packages. Note that the canonicalanalysis is preferable to the principal component analysis for the purpose of this study.The latter technique selects components on the basis of intercorrelation of availablevariables and attempts to maximize the explained variance in these variables alone.Thus, although the first principal component may pick up the major portion of thevariance of independent variables, it may not necessarily be the one that is mostcorrelated with the dependent variable. Furthermore, a linear combination of allvariables representing the weighted sum of diverse classification of characteristicsmay not be open to any meaningful interpretation. Canonical analysis, on the otherhand, forms linear combinations of original variables in such a way that the resultingcomposite indexes are maximally correlated with the dependent variable, and thecomposite indexes afford meaningful economic interpretation.

Formally, in canonical analysis, coefficients are chosen to form a linear combina-tion of a set of standardized independent variables (Z) in such a way that, of the infinitenumber of possible linear combinations for the standardized independent variables(Z), the resultant linear combination of Z is maximally correlated with the dependentvariable (or a linear combination of dependent variables). Let x and y be definedas x = &dquo;.f..a7&dquo; and y = y, where Z, = (X, - X )/o~. Canonical correlation analysis selectsthose values for the as such that the correlation coefficient between x and y is the

maximum possible value. Thus x represents that combination of Z set variables thathas the highest correlation with the y vector. Thus the pair x and y are most highlyrelated to one another. The correlation coefficient between x and y is termed the

canonical correlation, r, and the x and y pairs are called canonical variates. Themaximum number of such variates that can be extracted depends on the maximumnumber of variables in the smaller set. If the smaller set is only a vector then therewill be only one solution for each subset of independent variables. This formulationof the index suggests that it will have a zero sample mean. By using a simpletransformation (adding a constant), the sample mean of the index in our analysis waschanged to a positive number. It should be noted that such a transformation has noeffect on regression coefficients.



375

The canonical analysis was used to develop a composite score of public sectoroutput indicators by each community. With this procedure I was able to develop ameaningful comparative index of public outputs and also to use some valuable datathat could not be used in regressions ignoring multicollinearity correction. Thecanonical composite index of public services, the PSI index, is composed entirely ofoutput indicators of public services. The index is positively related toAS (achievementscore), PARK (park area), PKIS (park and recreation subprograms index), and PBT(per capita bus trips per week by each neighborhood), and it is negatively related toRFR (residential fire rate) and PTC (per capita total crimes by each neighborhood) 5Thirty-five canonical indices representing composite public services output charac-teristics for 27 communities within the City of Edmonton and 8 neighboring munic-ipalities were formed. These indices, based on a chi-square test, indicated highlysignificant association with the house price. These indices thus proved useful inderiving improved estimates of public sector capitalization within and across thesample municipalities.

NOTES

1. Brueckner’s empirical work suffered from omitted variables bias (having an inadequateset of regressors), a severe degree of multicollinearity among a subset of sample variables, andhaving only one observation for each community and thereby implicitly assuming that allcommunities in his sample were identically efficient or inefficient in providing local publicgoods.

2. See Chaudry-Shah (1988,1989) for a critical evaluation of both the approaches. See alsoOates (1969,1973, 1981), King (1977) and Reinhard (1981).

3. The following equation was used in its estimation:

where LOCAL* = local expenditures for services included in PSI.

4. This technique was introduced in econometrics by Hotelling (1936), and brief summariesof the general model are given in Tintner (1952), Theil (1971), Johnston (1972), and Judge et aL(1980). A detailed account of the procedure appears in Kendall and Stuart (1966) and Levine(1977).

5. Some readers might question the validity of the index on the grounds that achievementscores, crime rates, and fire rates are poor measures of public services because they depend onother "inputs"; areas with high crime and fire rates probably receive more public services but



376

they enter negatively into the index. Problems alluded to above refer to public services effortsor expenditure measures. This study has argued that effort/expenditures are a poor indicator ofquality of public services in any neighborhood and therefore represent a poor choice for acapitalization regression. Attractiveness of a neighborhood for location depends on precisely thekind of indicators used in developing the public services index in this study. For example, simplybecause the District of Columbia spends relatively higher amounts on most public services,including crime prevention, than do neighboring jurisdictions does not make it a more attractiveplace for residential location.

REFERENCES

Brueckner, Jan K. 1979. Property values, local public expenditure and economic efficiency.Journal of Public Economics 11:223-45.

—. 1982. A test for allocative efficiency in the local public sector. Journal of PublicEconomics 19:311-31.

Chaudry-Shah, Anwar. 1988. Capitalization and the theory of local public finance: An interpre-tative essay. Journal of Economic Surveys 2:209-43.

—. 1989. A capitalization approach to fiscal incidence at the local level. Land Economics65:359-75.

Hamilton, Bruce W. 1976. Capitalization of intrajurisdictional differences in local tax prices.American Economic Review 66:743-53.

Hotelling, H. 1936. Relation between two sets of variables. Biometrika 28:321-77.Johnston, J. 1972. Econometric methods. 2d ed. New York: McGraw-Hill.

Judge, G. D., W. E. Griffiths, R. C. Hill, and T. Lee. 1980. The theory and practice ofeconometrics. Toronto: Wiley.

Kendall, M. G., and A. Stuart. 1966. The advanced theory of statistics. London: Griffin.King, A. T. 1977. Estimating property tax capitalization: Acritical comment. Journal of Political

Economy 85:425-31.Levine, Mark S. 1977. Canonical analysis and factor comparison. Beverly Hills, CA: Sage.Maddala, G. S. (1977. Econometrics. New York: McGraw-Hill.Oates, Wallace F. 1969. The effects of property taxes and local public spending on property

values: An empirical study of tax capitalization and Tiebout hypothesis. Journal of PoliticalEconomy 77:957-71.

—. 1973. The effects of property taxes and local public spending on property values: Areply and yet further results. Journal of Political Economy 81:1004-08.

—. 1981. On local finance and the Tiebout model. American Economic Review 71:93-98.

Reinhard, R. M. 1981. Estimating property tax capitalization: A further comment. Journal ofPolitical Economy 89:1251-60.

Schlack, R. F. 1977. Residential site choice, land use patterns, and local public service provision:An integrative model and econometric study of the Detroit metropolitan area. Ph.D. WayneState University.

Theil, H. 1971. Principles of econometrics. New York: Wiley.Tintner, G. 1952. Econometrics. New York: Wiley.



377

Anwar M. (Chaudry) Shah is a Senior Economist with the Public Economics Division,World Bank, and Department of Finance, Government of Canada, Ottawa. His currentresearch interests are in the areas of global environment, fiscal federalism, fiscalincentives, and productivity of public spending and sectoral allocation choices. Hisrecent articles have appeared in the Review of Economics and Statistics, Land Econom-ics, International Journal of Transport Economics, Journal of Economic Surveys, WorldBank Economic Review, and Finance and Development.



Documents

from for efficiency