Public Choice105: 207–230, 2000.© 2000Kluwer Academic Publishers. Printed in the Netherlands.

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Is the median voter a clear-cut winner?: Comparing the medianvoter theory and competing theories in explaining localgovernment spending

SULTAN AHMED & KENNETH V. GREENEDepartment of Economics, Binghamton University, Binghamton, NY 13902-6000, USA;e-mail: econ@binghamton.edu

Accepted 3 April 1999

Abstract. This paper attempts to test the power of the median model against the respectivestrength of other alternate models based on redistributive, political-institutional and interestgroup theories in explaining the demand for public spending in New York state countiesduring 1990, 1980 and 1970. To execute the comparison of the performance of median votermodel with that of each of the nonmedian voter ones, various nonnested tests such as J and JAtests, N-tilde, W and encompassing tests have been employed. Results of the study show thatalthough the median voter model has a marginal edge over the rival models based on the altern-ative theories, it may not be relied upon solely when many other institutional, redistributiveand interest group factors are also relevant for explaining public spending. The results of thisstudy differ from those in Congleton and Bennett (1995). We do not find that interest groupmodels are substantially weaker than the median voter model.

1. Introduction

There continues to be a controversy over the ability of different models of thepublic sector to explain the size of government both across polities and acrosstime. In their overall review of attempts to explain government growth overtime Holsey and Borcherding (1997) conclude that complete explanations“will likely contain elements of both apolitical and political models”. Stilleconomists have shown continued interest in presenting results that tend tocollaborate one theory rather than another. So for instance Greene and Nel-son (1994) claim little support for special interest group theories as opposedto institutional theories. Congleton and Shugart (1990) report the growth ofU.S. social security is better explained by the median voter model than by thepolitical power of special interests and Congleton and Bennett (1995) presentevidence that this is also true in the case of U.S. state road expenditures. Thispaper will not resolve the controversy but will use accepted techniques forcomparing the explanatory power of the median voter model and some com-peting models. It does so by utilization of fiscal and socioeconomic measureswithin counties in New York State in 1970, 1980, and 1990.

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In the following section we briefly discuss the specifications of each of themodels. This is followed by a discussion of the relevant empirical tests of therelative power of the alternatives. A discussion of the results is followed bysome concluding remarks.

2. Specification of the models and measurement of the variables

While we will not provide a detailed discussion of the theoretical basis ofthe alternative models that we specify, we will provide a brief overview ofeach. The median voter model as implemented by Bergstrom and Goodman(1973) and Borcherding and Deacon (1972) relies on a rather sparse empir-ical specification that makes spending dependent on the median voter’s taxprice and income and on the polity’s population size,1 supplemented by a fewsocioeconomic variables. The empirical specification we use is a log linearone where

EXPC = f (YMR, POP, TXP, OWN, OLD GRANTM) (1)

where YMR is median family income, which is assumed to be the medianvoter’s income using the justification Bergstrom and Goodman provide, POPis the population in a county, TXP is the tax price of the median voter, OWNis the percentage of housing units owner occupied, OLD is the percentage ofthe population 65 and over, and EXPC is general nonschool expenditures ofall governments in the county per-capita.

The tax price term utilized here is rather unique. It goes beyond the usualformulation such as contained in Greene and Munley (1979) or Pommerehneand Schneider (1982) and elsewhere and estimates the tax price as theweighted share of both property, and sales taxes paid by the median voter.2

What we call the political-institutional model, is formulated along the linessuggested by Gilligan and Matsusaka (1995). Their purpose is to explain stategovernment expenditures and they focus upon some of the characteristicsof the legislature. They reason that where the number of seats is big, logrolling is facilitated and this increases expenditures. Moreover, where there isdomination of the legislative process by the liberal party and little competitionbetween parties expenditures also will be higher. Their empirical specificationcontrols for certain socioeconomic variables. We try to replicate it as nearlyas possible (all our legislatures are unicameral and not all county executivesare elected) and supplement it by controlling for certain institutions peculiarto New York counties and by the institutionalist literature perhaps first de-veloped by Wagner (1976) that reasons that revenue institutions matter as welland that complex and less visible revenue structures enhance public spending.So we specify it as

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EXPC = f(YPC, POPG, SIZE, GRANTH, DENSE, PCOMP, (2)

CHART, HERF, IDEO, VISIBLE, REVSH, PXPSAL).

Here YPC is per capita income, POPG is population growth in the pre-vious decade. The other variables are population per square mile, politicalcompetition,3 charter county,4 tax structure simplicity as calculated by aHerfindahl index,5 the ideological ratings of the Congressman represent-ing each county,6 visibility of taxes,7 percentage of revenues generated bycounty government, and percentage of sales and property taxes exported fromcounty.8

Meltzer and Richard (1981) in their seminal paper tried to explain thebulk of public expenditures as transfers of income from the upper classes tothe politically relevant poor. They focus solely on the ratio of median to meanincome predicting a negative sign and the aged. We supplement it followingPeltzman’s (1980) work and specify it as:

EXPC = f(YMDYB, REGISV, OLD, RATPAY, YPCG, DENSE, POPG) (3)

Here YMDYP is the ratio, which is expected to constrain spending, of medianto mean income, while REGISV is the percentage of the population registeredas voters which is expected to expand it. RATPAY is the ratio of earnings inmanufacturing to that in gasoline service stations and is meant as a proxy forthe skill differential between the wealthiest and poorest in the winning coali-tion as emphasized by Peltzman and this should reduce government size. Theother variables have been defined previously and were variables consideredby these redistribution theorists.

Finally, the special interest group model is formulated within the spirit ofMcCormick and Tollison’s (1981) attempt to explain all public sector activityas the sale of favors by the legislature to special interest groups. We specifyit as

EXPC = f(YPC, SIZE, OLD, HEALTH, OWN, GOVEM, DENSE, AGE)(4)

The original work here emphasizes the relative size of the legislaturewhich is expected to constrain spending and which we measure as Size-the per capita number of county legislators, but subsequent interpretationsof the special interest approach have emphasized employment and producergroups and age groups. Our ability to measure at the county level forced usto use OLD and OWN as well as Health-per capita health employment,9

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GOVEM, estimated per capita Government Employment10 and percentagebetween the ages of 5 and 18, on the grounds that this “special interest” couldhold down county (non-school) expenditures. Definitions of all variables andtheir sources are in Appendix A.

3. Comparison between models: Non-nested econometric tests

The specification of the models in the previous section suggests that it isappropriate to employ nonnested econometric tests to compare the medianvoter model and each of the other models. Previous studies in public choiceneglected the relevance of conducting nonnested tests for comparing models(Congleton and Bennett, 1995). In this section a discussion on the techniquesof nonnested tests will be outlined and an attempt will be made to evaluatethe individual strengths of various tests under discussion.

Assume that we have to make a decision on the relative appropriatenessof the two possible sets of regressors. Suppose they are:

H0 : Y = Xβ + ε0 (5)

H1 : Y = Zγ + ε1 (6)

3.1. The Davidson-McKinnon J test

Probably the test which deserves special mention among the list of such test-ing strategies is the J test as proposed by Davidson and McKinnon (1981). Toexecute this test, the two competing models as expressed in Equations (5) and(6) can be written in a compound model like the following (This discussionis from Greene, 1997):

Y = (1− α)Xβ + α(Zγ )+ ε (7)

In this formulation of the compound model, a test against H1 would followif α turns out to be zero. If the null is true, then Plimα = 0. To carry outthe test, the usual t ratio (α/SE(α)) which is distributed as standard normalis calculated. In a finite sample, the test of the H0 against H1 can give rise tosimultaneous rejection of both or of neither or of none of the hypotheses.

3.2. The Fisher and McAleer JA test

A modification of the J test called the JA test was proposed by Fisher andMcAleer (1981). Assuming two linear regression models:

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M1 : y = xβ1 + u1,u1 ≈ N(0, σ 2In) (7)

M2 : y = Zβ2+ u2,u2 ≈ N(0, ω2In), (8)

the JA test of M1 against M2 is based on the t-ratio ofλ in the OLS regression

y = Xβ1+ λ(A2Xβ1)+ u1, (9)

where

A2 = Z(Z′Z)−1Z′ (10)

And the relevant statistic for the JA test of M2 against M1 is the ratio ofµ

in the OLS regression

y = Xβ2+ µ(A1Xβ2)+ v, (11)

where

A1 = X(X ′X)−1X (12)

3.3. Encompassing tests

The ‘encompassing test’ derives from Deaton (1982), Dastoor (1983) andMizon and Richard (1986). The encompassing test is the same as the classicalF test if we test M1 against M2. It involves calculating the F-statistics fortestingδ = 0 in the combined OLS regression

y = Xa+ Z∗δ + u (13)

where Z∗ denotes the variables in M2 that cannot be expressed as exact linearcombinations of the regressors of M1.

3.4. The N-tilde and W test

The finite sample problems of Cox type tests like the J test and the JA testwhere the procedures have a tendency to reject the null hypothesis too fre-quently led Godfrey and Pesaran (1983, henceforth called (G&P)) to derivetesting procedures called N-tilde and W tests. An explanation for and descrip-tion of these tests, as well as the information criteria we subsequently report,is provided in endnote 11.11

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4. Results of nonnested econometric tests

The results for the different models specified for the different years arepresented in Appendix B. We will not provide a detailed review of the resultshere, but we do provide a summary. The median voter model’s explanatorypower appears greatest in 1990 and least in 1980. Changes in its explanatorypower across years is almost entirely due to three phenomena. While the taxprice term in each year is negative, it is strongest in 1990 and least in 1980.Second, the effect of medial family income is stronger in later years. Finally,grants from the state government, which became an increasing source of localfunds had a strongly positive explanatory power only in the last year.

The power of the redistributionist model (M-3) falls across time. Whilethe coefficient on the ratio of median to mean income is significantly negativeas Meltzer and Richard (1981) predict in the first two years and the pay ratiovariable is suggestively negative in line with Peltzmans hypothesis in the earlyyears it size and significance deteriorate.

The power of the political institutionalist model lies almost entirely withits socioeconomic elements. Political competition is the only truly polit-ical variable that sometimes works and in the opposite direction to thathypothesized by Gilligan and Matsusaka (1995).

The special interest group model’s explanatory power model improveswith time. While we cannot fault the model for our inability to obtain goodspecial interest measures, only legislative size, employment in health care,aged population (in 1980) and government employment (in 1990) workin the expected directions. The latter explains almost all of the improvedexplanatory power in 1990.

We focus on tests comparing the median voter model with the others viaTables 1 to 11. For each pair of models, the test is conducted by posing one ofthe models as null and the other as alternative. Then the roles of the modelsare reversed, i.e., the alternate is now posed as null and tested against theother. For example, M1 is tested against M2 initially and then M2 as nullis tested against M1 which is then the alternative. We shall discuss Tables 1to 3 that show the results of comparing model M1 with M2 in detail. Theinterpretations of the other tables should be self-evident after this discussion.A summary of the results of the nonnested tests is presented thereafter. Forthe Tables 1 to 10, a significant t ratio implies rejection of the null hypothesisthat the model above explains the phenomena in favor of the alternative thatthere is significant explanatory power in the second model and the entries inparentheses are probabilities of rejecting the null when it is in fact true.

Column 1 of Table 1 shows the test statistics when M1 is tested againstM2 whereas column 2 shows the same when M2 as null is tested againstM1 for the 1990 period. The t ratios for NT and W tests for column 1 are

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Table 1. Comparing model M1 with model M2 in 1990

Test statistic M1 against M2 M2 against M1

NT test –4.043 [.000] –4.592 [.000]

W test –3.152 [.002] –3.705 [.000]

J test 6.067 [.000] 4.904 [.000]

JA test 1.793 [.073] 3.010 [.003]

Encompassing F(12, 38) 3.846 [.001] F(6, 38) 5.155 [.001]

Akaike’s information criterion of M1versusM2 = –3.311 favorsM1.Schwarz’s Bayesian information criterion of M1versusM2 = 6.44favors M1.

Table 2. Comparing model M1 with model M2 in 1980

Test statistic M1 against M2 M2 against M1

NT test –2.280 [.023] –5.357 [.000]

W test –2.000 [.046] –4.602 [.000]

J test 5.733 [.000] 6.148 [.000]

JA test 1.222 [.222] 3.514 [.000]

Encompassing F(12, 38) 6.174 [.000] F(6, 38) 9.119 [.000]

Akaike’s information criterion of M1versusM2 = 591 favors M1.Schwarz’s Bayesian information criterion of M1versusM2 = 6.72favors M1.

respectively –4.04 and –3.15 which basically imply that the null hypothesisthat the median voter model is superior is rejected by both the tests.

Conversely, column 2 shows that when we reverse treating the models asnull and alternate, the idea that the political institution models is superior(M2) is now rejected. The NT and W tests then provide no indications thatone or the other is superior.

The J and JA test statistics show that the J test lends credence to both themodels (t ratios are highly significant in both columns 1 and 2), the JA testlends more support to the median voter model (a t ratio significant at only 8%level in column 1 is overpowered by a t ratio significant at 1% level in column2).

What about the encompassing test? The F value in column 1 is 3.85 andthat in column 2 is 5.15. The corresponding values in the F distribution Table

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Table 3. Comparing model M1 with model M2 in 1970

Test statistic M1 against M2 M2 against M1

NT test –1.385 [.166] –10.035 [.000]

W test –1.286 [.199] –7.050 [.000]

J test 4.063 [.000] 8.739 [.000]

JA test –.529 [.597] 6.925 [.000]

Encompassing F(12, 38) 4.413 [.000] F(6, 38) 15.263 [.000]

Akaike’s information criterion of M1versusM2 = 16.085 favors M1.Schwarz’s Bayesian information criterion of M1versusM2 = 22.214favors M1.

at 5% level of significance are only 2.04 and 2.34 which basically implies thatboth models are strong competitors.

While results of most of the above tests are inconclusive, the evaluationsof the information criteria support model 1. Using such tests as a criteria, themedian voter model seems to do a better job in 1990 in explaining governmentexpenditure compared to model M2.

How do we interpret the results of the various tests which show mutualrejection of the models through such tests? For example we have seen abovethat the NT, W, J and JA tests all show that both the models M1 and M2mutually reject each other. According to Bischoff and Terragrossa (1993), anull model even if it fits better than the alternative, is likely to be rejected ifthe alternate model contains sufficient independent observation. It cannot besaid that the alternative model should be preferred which, however, would betrue if the roles of the models are reversed and the alternate, now as null, isnot rejected. When models mutually reject each other, it is more likely thateach of them contain sufficient independent information on the phenomenonunder investigation. A case may be established here to linearly combine thetwo models for the purpose at hand. So when we see the models M1 and M2rejecting each other we believe that both of the models are potent competitorsin explaining the size of the governments and the demand for public expendit-ure. The N-tilde and W tests, in summary, show that we may not neglect eitherof the models. It is appropriate to say that the theoretical underpinnings ofeach model possess explanatory power.

In 1980 (Table 2) we observe similar results. Except for the JA test wesee significant t ratios in both columns 1 and 2 which implies that the modelsmutually reject each other or that the results are inconclusive. The JA test sup-ports the median voter model as an insignificant t ratio in column 1 pairs witha significant t ratio in column 2. Both the information criteria unanimously

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Table 4. Comparing model M1 with model M2 in 1990

Test statistic M1 against M3 M3 against M1

NT test –3.720 [.000] –25.131 [.000]

W test –3.550 [.000] –12.179 [.000]

J test 5.322 [.000] 17.499 [.000]

JA test 2.138 [.033] .706 [.480]

Encompassing F(6, 44) 21.7867 [.000] F(5, 44) 169.2362 [.000]

Akaike’s information criterion of M1versusM3 = 48.7152 favors M1.Schwarz’s Bayesian information criterion of M1versusM3 = 49.7368favors M1.

Table 5. Comparing model M1 with model M3 in 1980

Test statistic M1 against M3 M3 against M1

NT test –2.773 [.006] –6.656 [.000]

W test –2.556 [.011] –5.603 [.000]

J test 3.820 [.000] 5.244 [.000]

JA test .590 [.555] 2.120 [.034]

Encompassing F(6, 44) 5.025 [.001] F(5, 44) 8.639 [.000]

Akaike’s information criterion of M1versusM3 = 5.618 favorsM1.Schwarz’s Bayesian information criterion of M1versusM3 = 6.64favors M1.

favor the median voter model. Overall it can be said that model M1 appearsthe close winner in this year. In 1970 the NT, W and JA tests unquestionablysupport the median voter model because while there are insignificant t ratiosin column 1 there are significant t ratios in column 2. The other two nonnestedtests (W and encompassing tests) are inconclusive as both columns showsignificant t ratios. Again both the information criteria favor the median votermodel. Considering all three years, it appears that the median voter modelis stronger in explaining the government size in New York State countiesthan the political institutional model, but that the latter cannot be summarilydismissed.

A perusal of Tables 4 through 6 indicates some mild superiority of themedian voter model as opposed to the redistribution model in 1990 and 1980.If we consider 1970, however, neither model obtains an advantage using thetests.

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Table 6. Comparing model M1 with model M3 in 1970

Test statistic M1 against M3 M3 against M1

NT test –5.078 [.000] –10.783 [.000]

W test –4.267 [.000] –7.361 [.000]

J test 4.811 [.000] 7.802 [.000]

JA test 3.554 [.000] 4.650 [.000]

Encompassing F(6, 44) 6.435 [.000] F(5, 44) 16.766 [.000]

Akaike’s information criterion of M1versusM3 = 13.44 favors M1.Schwarz’s Bayesian information criterion of M1versusM3 = 14.46favors M1.

Table 7. Comparing model M1 with model M4 in 1990

Test statistic M1 against M4 M4 against M1

NT test –2.629 [.009] –6.282 [.000]

W test –2.246 [.025] –4.489 [.000]

J test 3.108 [.002] 5.447 [.000]

JA test 1.807 [.071] 4.593 [.000]

Encompassing F(6, 44) 3.479 [.007] F(4, 44) 9.635 [.000]

Akaike’s information criterion of M1versusM2 = 8.8637 favorsM1.Schwarz’s Bayesian information criterion of M1versusM2 =10.9067 favors M1.

In Tables 7 through 9 we see nothing to recommend the conclusion that oursimple median votes model outperforms the special interest model. Unlike inthe other comparison not even the information criteria unanimously favor oneor the other.

The findings from all these tests are summarized in Table 10. The keys atthe bottom of the table indicate how to interpret the letters and symbols usedin the table.

In 1990 all the nonnested tests were inconclusive. Basically this meansthat both the median voter and each of the rival models (the combined as wellas single models) have some independent capacity to explain the variationin government expenditures in New York State counties. The JA test and thetwo information criteria favor the median voter model in a consistent manner.In 1980, however, while most of the tests are inconclusive, the rival modelsreceive some support from the JA test and also from the AIC in about 50%

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Table 8. Comparing model M1 with model M4 in 1980

Test statistic M1 against M3 M3 against M1

NT test –6.331 [.000] –2.661 [.008]

W test –4.997 [.000] –2.422 [.015]

J test 5.260 [.000] 2.606 [.009]

JA test 4.141 [.000] 1.781 [.075]

Encompassing F(6, 44) 4.70 [.001] F(4, 44) 2.549 [.052]

Akaike’s information criterion of M1versusM2 = –6.174 favorsM2.Schwarz’s Bayesian information criterion of M1versusM2 =–4.131 favors M2.

Table 9. Comparing model M1 with model M4 in 1970

Test statistic M1 against M3 M3 against M1

NT test –5.089 [.000] –6.416 [.000]

W test –4.038 [.000] –4.833 [.000]

J test 4.793 [.000] 5.287 [.000]

JA test 3.626 [.000] 3.836 [.000]

Encompassing F(6, 44) 5.722 [.000] F(4, 44) 10.304 [.000]

Akaike’s information criterion of M1versusM4 = 4.398 favors M1.Schwarz’s Bayesian information criterion of M1versusM4 = 6.443favors M1.

of the cases. The SIC supports the median voter model in more than 50% ofthe cases. The interest group model, in particular, receives support from thetwo information criteria as well as from the JA test. In 1970 again as in 1990overwhelming support for the median voter model seem to be obtained fromthe AIC and SIC and partially from the JA test although results from othernonnested tests are not definitive. The superiority of the median voter modelon the basis of the information tests, however, cannot conclusively build acase for the median voter model. As William Greene (1997) pointed out, theinformation measures, although intuitively appealing, have no firm basis intheory (pp. 401). And then our discussion in Section 3 suggests that for ourpurpose, the N-tilde and W tests should be more reliable than the J or JA tests.It, therefore, cannot be alleged that any strong case against the nonmedianvoter models (or in favor of the median voter model for that matter) has beenestablished through these econometric tests.

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Table 10.Summary of nonnested tests

1990 1980 1970

M1 versusM2 ?/A+/S+/JA+ ?/A+/S+/JA+ YES/A+/S+/

M1 versusM3 ?/A+/S+/JA– ?JA+/A+/S+ ?/A+/S+/

M1 versusM4 ?/A+/S+/JA+ ?/A–/S–/JA– ?/A+/S+?

Keys to the models

1. M1: The median voter model;2. M2: The institutional model;3. M3: The redistributive model;4. M4: The interest group model.

Keys to symbols

1. Yes: Model M1 fares better than the rival one as shown by most of the nonnested tests.2. No: Model M1 does not fare better than the rival one as shown by most of the nonnested

tests.3. ?: Result inconclusive through most of the nonnested tests.4. A+: Model M1 supported by the Akaike Information Criterion (AIC).5. A–: The rival model is supported by the Akaike Information Criterion (AIC).6. S+: Model M1 supported by the Schwartz’s Information Criterion (SIC).7. J+: Model M1 supported by the J test.8. J–: The rival model is supported by the J test.9. JA+: Model M1 supported by the JA test.

10. JA–: The rival model is supported by the JA test.11. W+: Model M1 supported by the Wald-test.12. W–: The rival model is supported by the Wald-test.

5. Median voter or interest group?: Comparing the results with thosein Congleton and Bennett (1995)

The results we obtained through the various econometric tests point out thatthe influence of interest groups can indeed be important in explaining thesize of local governments. Congleton and Bennett’s (1995, henceforth calledC&B) exercise in explaining the state highway expenditure reached a conclu-sion that is somewhat different than what we obtain here.12 They point outthat in the case of roads with near universality of usage and earmarked taxes,it is probably more likely that median voters control and this can help explaintheir conclusion that the median voter model is superior. But that conclusionis reached by comparing coefficients of determination, F statistics and stand-ard errors of the regressions. A fuller application of techniques for testingalternative nonnested hypothesis seems warranted and we have provided that.

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Table 11. Goodness of fit statistics.

Model Year

1990 1980 1970

M-1

R2 .823 .345 .588

F 44.45 5.91 14.32

SD .240 .218 .101

Combined M-1 and M-4

R2 .864 .413 .528

F 36.38 4.46 6.49

SD .211 .163 .079

M-4

R2 .766 .442 .338

F 27.87 6.35 4.44

SD .277 .155 .093

In Table 11, we present results for using essentially their methodologyon our observations. We present the goodness of fit statistics for the medianvoter, combined model and the special interest model.

In 1990, the combined model has a slight edge over the interest groupmodel. The fit improves in the sense thatR2 rises from .77 to .86. The standarderror of regression falls from .277 to .211. On the other hand if we comparethe combined model with the median voter model alone, the fit improves,but by a lesser extent. TheR2 rises from .82 to .86 and the standard error ofregression falls from .24 to .211.

In 1980 if we start from the median voter model, we find that adding theinterest group variables to the median voter model improves the statisticalfit by some margin. TheR2 goes up from .35 to .41. The standard error ofregression falls from .218 to .163. On the other hand adding the factors inthe median voter model to the interest group model lowersR2 from .44 to.41, and standard error of regression rises from .159 to .163. There is reasonto believe that the interest group model has outperformed the median votermodel in explaining public expenditure across counties in 1980.

In 1970 adding the interest group factors to the median factors lowersR2

from .59 to .53. The standard error of regression falls marginally, from .101 to

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.079. On the other hand adding the median voter factors to the interest groupfactors raisesR2 considerably, .34 to .53. The standard error of regressionfalls from .093 to .079. These results indicate that the median voter modelfares relatively well in terms ofR2 and standard error of regression in 1970.

The above results show that even if we apply the same procedures used byC&B, their result that interest group model fares much worse than the medianvoter model in explaining public expenditure demand cannot be observed inthe present study. Our evidence corroborates that in New York state counties,in addition to median voter’s preference, various other forces are at work andinterest group’s influence on the local government expenditure demand areimportant as well.

6. Conclusions

This study makes a modest attempt to compare the power of the median votermodel with each of three nonmedian voter models based on institutional-political and redistributive and interest group theories. Comparison amongthese models indicates that the median voter, one of the most widely usedmodels in the public choice literature may hold some slight advantage overthe other models. However, this does not undermine the importance of certaininstitutional, redistributive and interest group factors that can have significantimpact on the expenditure of local governments in New York State. To admitthat the median voter model has some edge over the nonmedian voter model,does not necessarily imply that we discard those models because no strongcase against them can be deduced from the nonnested tests. We are led tobelieve that both the median voter model and the rival model are strongcompetitors in their ability to explain the subject of investigation. Whichmodel to choose from in any particular research will depend partially at leaston the purpose of the study and partially on the availability of the data. Nogeneralized prescription can be made with respect to which model to choose.

So far as the comparison of the median voter model with the interest groupmodel is concerned, this study reaches a conclusion different from those inCongleton and Bennett (1995). While they conclude that the median votermodel does a much better job in explaining the state highway expenditure percapita than the interest group model, the present study does not support theirconclusion about its clear-cut superiority. The nonnested tests conducted inthis study shows that the interest group factors are important in county juris-dictions in New York State and may at times be stronger (as in 1980) in theirimpact on the public expenditure demand than the median voter parameters.

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Notes

1. The population size influences the price of the ultimate good that enters the utility functionif it has any of the characteristics of a public good.

2. GRANTM has been calculated by multiplying the total grants received by each county(GRANT) by the tax price of the median family. A possible simultaneity problem mightexist between the left hand variable and ‘GRANT’ which is all the more probable if grantsare of a matching nature. Concern was also expressed that this probable simultaneitybetween ‘GRANT’ and the left hand variable will lead to biased and inconsistent estimatesof all coefficients and invalid conclusions from the associated tests of hypotheses (Mar-shall, 1991). To correct for this simultaneity, we employ again a two stage least squarestechnique whereby we estimate the grant variable first using various outside exogenousvariables plus the various regressors in the current expenditure model and then use theunbiased consistent estimator of the ‘GRANT’ factor in the second stage to estimate theoriginal expenditure model (institutional model). These exogenous factors are: FAMIL:Percentage of family below poverty line; FEMALE: Percentage of female workers in totallabor forces; POPSQ: Population squared; DENSE: Population density; UNEMP: Per-centage of unemployed; RCOMP: Percentage of nonwhites to total population; GOVSQ:Number of governments per square miles.

3. With Gilligan and Matsusaka (1995) we define political competition as D(1-D)×100where D is the fraction of Democrats in legislative size. It is to be noted that we cannotavoid some degree of measurement error from using the variables ‘SIZE’ and ‘PCOMP’(which respectively stands for the size of the county legislature and political compet-ition within the legislature), when the dependent factor is expenditures of all countygovernments within the county (rather than the expenditure of the individual county gov-ernment). The individual county government expenditure is roughly about 50% of thetotal expenditures of all county governments. Variables like ‘SIZE’ and ‘PCOMP’ closelyreflect individual county government (rather than all governments within the county)characteristics and may not accurately measure the desired effects.

4. A charter county has the ability to create and abolish county departments and agencies,make appropriations, impose property, sales and various other taxes besides providing fora variety of governmental functions like dividing legislative and executive responsibility.The non-charter counties operate under the New York State County Law and the executiveor administrator of such a county is not independent of the legislature. We postulate thatit could provide some constraint on spending by controlling logrolling. If, however, thecharter county designation proxies for something else, for example, if it represents bigcounty jurisdictions having bigger needs for public expansion, then the impact of thecharter status on spending should be positive.

5. The complexity of the tax system can be expressed by a Herfindahl-like index whichcan be constructed in the following manner: Calculate the relative shares for each of thelarge taxes like property and sales taxes. Each share is then squared and summation of thesquares gives the Herfindahl index. This index represents, in essence, the concentrationof locally generated revenues by source. The simplest tax structure can be conceived asone in which the local governments collect all the revenues from a single source and,therefore, is easiest for the taxpayers to comprehend. The higher the value of this index,the lower the degree of complexity of the tax structure and so by assumption the lowerthe degree of fiscal illusion on the part of the tax payers that leads to a lower governmentexpenditure per capita.

222

The usual measure for complexity includes quite a few revenue sources. In the presentstudy, three sorts of revenue sources have been utilized: ‘Sales tax’, ‘Property tax’ and‘all other taxes’. Sales and property taxes are the major sources of revenue in the countyjurisdictions and other sources of revenue are few and far between and do not even existfor all countries (e.g., utility and liquor store revenue; see County Government Finances,U.S. Department of Commerce, Bureau of Census). It can be alleged that if all othertaxes are not strong revenue generators and also, since, it is found that the sales tax asa percentage of sales and property taxes is always less than half, a Herfindahl-like indexconstructed in the above manner, may reflect the degree of reliance on the sales tax whichis only likely to be used at a high level where expenditures are high and in big metropolitanareas. Since in the county jurisdictions in New York, there are two major category of taxes,namely sales and property taxes, it is likely that the Herfindahl and visibility indices,as defined, will be strongly and negatively correlated. While the two variables are notstrongly correlated in 1990 (Correlation coefficient –.55), they appear to be so in 1980(–.82) and especially in 1970 (–.95).

6. The rating system is the AFL-CIO’s COPE index in the year in question. The majorlimitation of this measure arises from the fact that many counties have more than (inwhich case we average their ratings) or less than one congressman (in which case we usethe same rating for several counties).

7. Here measured as percentage of sales tax revenue in total.8. In order to determine the extent to which property taxes can be exported to non-residents,

we assume, following Bradbury and Ladd (1985), that taxes on commercial and industrialproperty are borne primarily by company owners and landowners and that many of theseowners are nonresistant stockholders. Greene and Munley (1984) discuss the possibilitythat people may perceive such taxes as borne locally but we assume that 100% of thetaxes on nonresidential property is exported out of the counties. The calculation of theexportation of property taxes involves the following steps: First we calculate how muchtaxes the non-residential property holders pay. Unfortunately, we do not have the dataon the composition of property taxes for the New York State counties. A roundaboutway to tackle this problem is to calculate the fraction of the valuation of industrial andcommercial properties in total valuation of all properties and then assign tax amounts tothose categories by multiplying the above fraction by total property taxes in each county.The resulting figure will be the calculated amount of property taxes paid by the industrialand commercial property holders. We then calculate the percentage of such exportedtaxes in total taxes of each county. The resulting figure is the percentage of propertytaxes exported out of each county jurisdiction. This variable substitutes for Gilligan andMatsusaka’s (1995) mineral production per capita variable.

9. Nelson (1994) documents that there is evidence that those employed in the health sectorprefer a larger public sector. About the only other special interest group we could identifyby county was those employed in education, but it is unclear in what direction they wouldaffect the non-educational expenditures.

10. Greene and Munley (1979) examine the hypothesis that government employment canhave a significant independent positive effect on public sector size. The fact that wecannot possibly use the government employment directly in a model where the left-handvariable is government expenditure per capita, is the reason which leads us to estimate theabove equation using a two stage least squares methodology. There is reason to suspectthat the size of government employment is endogenous to the model. As a result thepublic employee size will also be influenced by the dependent factor and we will beunable to interpret the resulting coefficients as tests of the proposed hypotheses (Ferris

223

and West, 1995). We therefore estimate the government employment in the first stage inthe following manner using various extra exogenous factors as instruments plus all theremaining factors in the interest group model: LOCM=f(GOVSQ, DENSE, POPG, SIZE,POP, POPSQ, FEMALE, FAMIL, YPC, HEALTH, OLD, OWN, YAGE, UNEMP).

Where, LOCM: Government employment per capita; GOVSQ: No. of governments persquare mile; DENSE: Population density; POPG: Population growth; SIZE: Size of le-gislature per capita; GRANT: Grants per capita from higher levels of governments; POP:population; POPSQ: Population squares; FEMALE: Percentage of female labor force;FAMIL: Percentage of family below poverty line; YPC: Per capita income; HEALTH:Per capita health employees in counties; OLD: Percentage of population 65 and over;OWN: Percentage of owner occupied houses; YAGE: Percentage of population between5 and 18 years of age.

11. As is usual for this kind of purpose i.e., testing of nonnested models, G&P consider tworegression models:

H0 : Y = Xb0+ u0, u0 ≈ N(0, σ20 I), (Equation 1 in G&P)

H1 : Y = Zb1+ u1,u1 ≈ N(0, σ21 I), (Equation 2 in G&P)

The N-tilde test is conducted on the basis of the following adjusted Cox type teststatistics:

N0 = N0{V0(T0)

}0.5 , (Equation 20 in G&P)

where

V0(T0) = (σ20/σ

410)

{e′100e100+ 0.5σ2

0 tr(B2)}

(Equation 21 in G&P)

and

T0 = 0.5(n− K1)log(σ21 /σ

210) (Equation 19 in G&P)

and where

(a) σ20 =

e′0e0(n−K0)

and e0 is the OLS residual vector of the regression of Y on Xn: number of observationsK0: number of regressors in the null model.

(b) e100: the OLS residual vector of the regression of e10 on X, e10 being theOLS residual vector of the regression ofY0(= Xb0) on Z

(c) σ21 =

e′1e1(n−K1)

e1: OLS residual vector on regression of Y on Zn: number of observations in the alternative hypothesisK1: number of regressors in the alternative model.

224

(d) is an unbiased estimator ofσ210= E0(σ

21 ) defined by

σ10={e′10e10+σ2

0 tr(M0M1)}

(n−K1)(Equation 12 in G&P)

(e) e10 stands for the OLS residual of the regression of e10 on X

(f) tr(B2) = K1 − tr(A0A1)2 −

{K1−tr(A0A1)

2}

n−K0, (Equation 17 in G&P)

(g) tr(A0A1) = tr{(Z′Z)−1Z′X(X′X)−1X′Z}

The W-test is conducted on the basis of the following statistics:

W0 = (n−K1)(σ2−σ10){

2σ40 tr(B2)+4σ2

0 e′10e10}0.5 (Equation 18 in G&P)

The adjusted Cox type of statistics as given by the above two tests reveals thatthe unadjusted Cox type of statistics have undergone three sorts of corrections:

(1) σ20 , σ

21 andσ2

10 have been replaced by their unbiased estimators.(2) Upward adjustment to the variance of the test statistics has been made by the

magnitude of

0.5

{σ2

0

σ210

}tr(B2).

(3) To computeT0, (n− K) has been used instead of n.

G&P argue that these adjustments affect the asymptotic properties of Cox type tests.Afterwards they conduct monte carlo experiments to test the small sample performanceof the W and the N-tilde test. The experiments show that adjusted Cox type statisticsproposed by G&P were effective in removing the tendency of the Cox type nonnestedtests to reject a true null hypothesis too frequently. These adjusted tests have finite samplesignificance levels very close to the asymptotically achieved value of 5% not only whenthe disturbances are normal but also when they are nonnormal or there are lagged de-pendent factors in the set of regressors. For the latter case of lagged dependent factorsthe ‘W’ test is more appropriate. Also, it was found in the experiments that the N-tildeand W tests led to the correct decision more frequently than the F test. The J test wasfound to have a high significance level with very large values (20% for example). TheJA test of Fisher and McAleer (1981) did not fare very well in either case, especiallywhen k0 > k1. Although in this test, the probabilities of type 1 error were satisfactory,the identity of the true model being unknown, the JA tests can only be recommendedwhen both models, null and alternate, have the same number of nonoverlapping variables.Thus G&P’s paper suggests that an N-tilde and W test rather than the J, JA or Cox testsfor comparing nonnested regression models will be more appropriate especially when thesample size is finite.In addition to the nonnested tests we also invoke Akaike and Schwarz’s InformationCriteria (AIC and SIC for short) for our purpose. The AIC can be expressed as:

AIC(M1 : M2) = LL1 − LL2 − (k1− k2) (7.12)

225

where LL1 and LL2 are respectively the log-likelihood functions of the models M1 andM2. Model M1 is preferred to M2 if AIC>0, otherwise M2 is preferred to M1.Whereas the criteria devised by Akaike is an extension of the maximum likelihood prin-ciple, Schwarz’s attempt was to find a Bayesian solution for the selection of one of anumber of models of different dimensions through evaluating the leading terms of itsasymptotic expansion. His procedure ultimately reduces to the following expression:

SIC(M1 : M2) = LL1 − LL2 − 0.5(k1− k2)Log(n) (7.12)

where n is the sample size. Model M1 is preferred to M2 if SIC>0, otherwise M2 ispreferred to M1.

12. In their model the pure interest group model had the highest standard errors whereasthe reduced form median voter model has the lowest. C&B find that the pure medianvoter model estimates have better fits and are more robust than the special interest groupestimates in that the values are more stable and are likely to be statistically significant.When they add the special interest variables to the median voter model the explanatorypower of the combined model does not substantially improve. In spite of the fact thatthe special interest variables have signs and magnitudes consistent with the theory, theycontributed little to the overall fit of the combined model.

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227

Appendix A

List of variables: Definitions and sources of data

EXPC: General (non-school) expenditure of all governmentsexcept school districts in the county (SRMA)

YMR: Real income of the median family, in 1987 dollars(COPH)

TXP: Tax price of the median voter (Calculated)

POP: County population (CCDB)

GRANTM: Estimated Amount of state and federal grant receivedby the median family

OWN: Percent of owner occupied houses (CCDB)

OLD: Percent of population 65 years and over (CCDB)

YPC: Per capita county income (CCDB)

POPG: Population growth in the current study period since thefirst year of the last decade (NYSSYB)

DENSE: Population density (CCDB)

GRANT: Federal and State Government grant to County govern-ment (SRMA)

GRANTH: Estimated Federal and State Government grant toCounty government

SIZE: Per capita size of county legislature (CD and informa-tion collected from each county legislative offices

PCOMP: Political competition (Calculated)

HERF: A Herfindahl-like index to represent complexity of thetax system (Calculated)

CHART: Type of county, charter or noncharter (NYSAC CD)

VISIBLE: Proportion of sales taxes in total tax revenue (Calcu-lated)

REVSH: County government share in total revenue of all gov-ernments in a county (SRMA)

228

IDEO: Ideological ratings for the Congressman representingeach county as rated by the ‘Committee on PoliticalEducation of the AFL-CIO’ (AAP)

YMDYB: Ratio of median to mean family income (COPH)

REGISV: Registered voters as a percentage of total population invarious counties (NYSSYB)

RATPAY: Ratio of earnings in the manufacturing to that in thegasoline service stations used as a proxy for skilldifferential (CBP)

YPCG: Growth of income in the current period since the firstyear of the last decade (CCDB)

HEALTH: Employment per capita in the health service sector(CBP)

GOVEM: Estimated government employment per capita in NYstate counties (CCDB)

YAGE: Percentage of population between 5 to 18 years of agein different counties (CCDB)

PXPSAL: Percentages of property and sales taxes exported out ofthe counties.

Abbreviations

CCDB: County and City Data Book (U.S. Department of Com-merce, Bureau of Census)

COPH: Census of Population and Housing (U.S. Departmentof Commerce, Bureau of Census)

NYSSYB: New York State Statistical Year Book (The Nelson A.Rockefeller Institute of Government)

SRMA: Special Report on Municipal Affairs (Office of StateComptroller, New York State)

NYSAC CD: County Directory (New York State Association ofCounties)

CBP: County Business Patterns (U.S. Department of Com-merce, Bureau of Census)

AAP: Almanac of American Politics (National Journal,Washington D.C.)

229

Appendix B

OLS results for individual models

YEAR

Model M-1 (1990) (1980) (1970)

Constant –10.24 [3.18] –11.83 [3.19] 4.03 [1.52]

YMR 1.40 [5.60] 1.25 [2.97] .440 [1.39]

TXP –1.45 [10.32] –.886 [2.29] –.709 [7.02]

POP –.068 [1.33] –.041 [.73] .020 [.89]

OLD .520 [2.30] .439 [2.10] –.254 [2.26]

OWN –1.40 [3.03] –.864 [2.00] –.287 [1.34]

GRANTM .535 [5.50] .265 [.88] .093 [.45]

R2 .823 .345 .588

F 44.45 5.91 14.32

s.e. .240 .218 .701

Model M-2 (1990) (1980) (1970)

Constant –20.80 [6.56] –25.38 [6.63] –4.34 [1.00]

YPC 2.17 [6.36] 2.72 [5.72] 1.18 [2.95]

POPG .585 E-02 [.72] –.078 E-02 [.23] –.215 E-02 [1.56]

SIZE .01 [.23] –.066 [.90] –.072 [1.64]

GRANTH 1.01 [8.39] .59 [1.96] 1.29 [.97]

DENSE- .348 [4.18] –.342 [5.44] –.183 [4.24]

PCOMP 1.64 [1.86] 1.42 [2.02] .14 [.35]

CHART .21 [1.69] .20 [2.03] .08 [1.19]

HERF –.302 [.72] –.300 [.69] .255 [.80]

IDEO –.023 [.37] .003 [.06] .003 [.08]

230

VISIBLE –1.125 [.98] .32 [.52] .88 [1.55]

REVSH .789 [2.48] –.113 [.41] .218 [2.23]

PXPSAL –.299 [1.02] .246 [1.13] .137 [.91]

R2 .783 .431 .346

F 17.83 4.54 3.47

s.e. .266 .203 .128

Model M-3 (1990) (1980) (1970)

Constant –5.10 [2.38] –4.56 [6.26] 5.78 [13.27]

YMDYM .645 [1.29] –2.92 [2.47] –2.38 [4.32]

REGISV .318 [1.97] .111 [1.64] .054 [1.39]

OLD .478 [.75] .395 [1.76] .039 [.30]

RATPAY –.023 [.15] –.058 [ 1.05] –.070 [1.50]

YPCG 6.17 E-02 [1.54] .109 [2.39] –.923 E-02 [1.98]

DENSE- .316 [2.21] –.053 [.94] –.075 [2.13]

POPG –.016 [.93] .613 E-03 [.14] .480 E-02 [3.46]

R2 .081 .214 .350

F 1.70 3.17 5.30

s.e. .548 .239 .127

Model M-4 (1990) (1980) (1970)

Constant –6.39 [1.75] –12.39 [4.34] –.642 [.34]

YPC .973 [2.84] 1.10 [3.18] 54.81 [2.94]

SIZE –.026 [.30] –.118 [2.42] –.086 [3.13]

OLD –.089 [.35] .227 [1.33] .199 [.86]

HEALTH .106 [.96] .118 [1.96] .068 [2.16]

OWN .032 [.05] –.248 [.66] .26 [1.37]

GOVEM –1.028 [8.01] .902 E-04 [.04] –.548 E-02 [.21]

DENSE –.074 [1.04] –.134 [2.21] –.098 [2.97]

AGE .384 [.55] .206 [.52] .200 [1.24]

R2 .799 .525 .436

F 27.87 6.35 4.44

s.e. .277 .159 .093