Acknowledgements

The author would especially like to thank Geoffrey Iverson,

Dorothy Keating, Daniel Sullivan, and Christopher Winship for their

help. Also, Yue-Hong Chou, James Clouse, R. Glenn Hubbard, Jeannine

Napoli, and Robert Sartain were of assistance.

No thanks whatsoever go to the Cook County Board of Education or

the Greater South Suburban Board of Realtors.

Abstract

This article uses housing prices in Chicago's south suburbs to

derive an estimate of the area's education demand curve. The analysis

improves upon the analysis of Jud and Watts (1981) by imposing fewer

researcher functional form assumptions through the usage of the

Box-Cox (1964) procedure. The result is a relatively inelastic demand

curve which displays expected derivatives with respect to local income

and college education levels.

Schools, Housing Values, and Public Policy

Edward Geoffrey Keating

5-26-87

Introduction

In this country, the provision of elementary and secondary

education has evolved into a major function of local government. A

major issue in virtually every American community is how much public

money should be spent on the provision of education. There is a

fundamental tradeoff involved: Taxpayers want their children to attend

high quality schools, but they do not enjoy paying the taxes needed to

support these schools.

Local school authorities appear to choose taxation and school

quality levels in a largely nonquantitative fashion. In Duckett

(1985), Thomas Payzant, superintendent of the San Diego city schools,

said that "educators tend to rely too much on intuition and subjective

judgment; we need more good data...Data-based decision making can

create a better balance in helping us to use both quantitative and

qualitative criteria as we make our decisions."

As Pomper (1984) noted, a vocal fraction of the electorate has

disproportionate influence on school officials - those individuals

with some large stake in the system such as parents and teachers. A

school official can only guess what the average taxpayer wants him to

do. Hence, school quality levels are chosen by school officials with

imperfect, perhaps biased, information.

This paper describes a method which may provide a better way for

school officials to gauge what their constituents actually want in

terras of school quality. When a person purchases a house, he

implicitly makes some statement as to how much he values school

quality. For example, if an individual purchases a house in an area

with good schools, he suggests that good schools are important to him.

By studying many buying decisions using the technique of regression

analysis, this paper will suggest what homeowners in Chicago's south

suburbs want in terms of school quality.

Using this information, a school official could make more

appropriate, better informed decisions. Theoretically, a school

official could compute the marginal benefit schedule for his district

and choose the optimal amount of quality by equating the marginal

benefit of quality and the marginal cost of quality (i.e. how much it

would cost to improve quality by some amount), which he presumably

already knows.

Starting with the original work of Ridker and Henning (1967),

regression analysis has been widely used to estimate the value of

particular components of a housing purchase. The underlying rationale

of regression analysis is that by controlling for other factors a

buyer may consider, it reveals the impact a particular factor has on

the housing price. In particular, regression analysis allows

statements of the following sort: "Given everything else is the same

between two houses, the house with trait X is worth $Y (or perhaps Z%)

more than the house without trait X." For a real estate regression,

the dependent variable (Y) is the price of a house. The independent

variables (X's) are the various house characteristics the researcher

deems relevant. Characteristics commonly included as independent

variables are such house traits as number of bedrooms, room sizes,

number of garages, house age, etc.

A controversial issue in the literature is the appropriate

functional form for a regression. One obvious option is a linear form

in which one simply regresses the untransformed housing price on the

vector of housing characteristics. However, as discussed below, some

researchers feel one should transform the housing price before running

a regression. These researchers often favor taking the natural log of

the housing price before running the regression (semilog form). When

one regresses in this fashion, the coefficients multiplying (or

weighting) the independent variables reflect the percentage change in

housing price resulting from a one unit increase in the independent

variable. In the linear form, the coefficients multiplying the

independent variables reflect the dollar change in housing price

resulting from a one unit increase in the independent variable.

Kain and Quigley (1970) used regression analysis to assess the

impact of racial discrimination in the St. Louis housing market. Li

and Brown (1980) used regression to measure the effects of air

pollution and noise levels on housing prices. Harrison and Rubinfeld

(1978) performed a somewhat similar analysis to evaluate the societal

willingness to pay for better air quality. Brown and Pollakowski

(1977) used housing prices to measure the value of proximity to the

shoreline.

A most creative example of regression analysis is Nelson (1981).

He tried to analyze the effect of the Three Mile Island nuclear

accident of March 28, 1979 on housing prices in the Three Mile Island

region. Curiously, none of his "Three Mile Island-related" variables

was statistically significant. Indeed, most of Nelson's post-accident

dummy variables had positive coefficients (generally in the $1,000 to

$3,000 range) but with very low t statistics (all less than .8).

Nelson suggested this result implies the accident caused neither an

absolute decline nor a slower appreciation rate for housing prices in

the Three Mile Island region. However, it should be noted that

Nelson's sample size was quite small. (He ran tests for a variety of

regions around the plant but his largest sample size was just 118

houses. His main regression involved a total of 100 housing

transactions, only 41 of which occurred after the accident.) His

results may be insignificant merely for lack of adequate sample size,

not because, in practical terms, the nuclear accident was regarded as

unimportant by the public.

In an ambitious study, Jud and Watts (1981) attempted to derive a

societal demand curve for educational improvement using Charlotte,

North Carolina housing price information. Jud and Watts' housing

price model included variables in seven categories - the quality of

local public schools, the land-use pattern of the neighborhood, the

socioeconomic characteristics of the neighborhood, the quality of the

structure, the size of the structure, the lot size, and the zoning

classification of the structure. Some of these categories were in

turn characterized by as many as six variables. In total, their

housing model had twenty-three independent variables plus a constant

term. This sort of model is generally similar to other authors'

housing price models.

Sherwin Rosen ( 197-4) pointed out that simple regression results

do not provide a demand curve for a housing component as unknown

supply influences intrude. The results of a regression represent a

price schedule, not a demand curve.

To address this problem, he described a multiple stage

simultaneous equation method to derive a demand curve for a housing

component.

Under Rosen's procedure, the first step is to regress observed

differentiated products* prices on all of their characteristics using

the best fitting functional form.

Rosen's next step is to compute a set of implicit marginal prices

for each buyer and seller evaluated at the amounts of characteristics

actually sold. In the semilog format, these prices are the targeted

variable regression coefficient multiplied by each house's selling

price.

The third step is to use these estimated marginal prices in a

simultaneous demand and supply system. The existence of one or more

variables in the supply system but not in the demand system will allow

identification of the demand curve.

Using this procedure, Jud and Watts (1981) concluded that the

residents of Charlotte would be willing to pay an additional $675 per

capita for a one-half year increase in average grade-level performance

in the Charlotte public schools, or a total of $48 million summed over

the whole city.

Wetzel (1983) argued these suggestions were inappropriate; that

schools actually compete with one another so a society-wide upgrade is

likely to have limited positive effect.

Brown and Harvey Rosen (1982) criticized Sherwin Rosen's (1974)

procedure saying any results are dependent upon arbitrary restrictions

on functional forms. Brown and Rosen said that implicit marginal

prices constructed in the second step of Rosen's procedure will not

necessarily play the same role in estimation that direct observations

on prices would play if they were available. They said that because

such constructed prices are created only from observed sample

quantities, any results can only come from restrictions placed on the

functional form of the price function.

Jud and Watts' (1981) procedure contained a sequence of

assumptions and restrictions which underscore the arbitrariness Brown

and Rosen (1982) found endemic to Rosen's (1974) procedure. For

instance, Jud and Watts chose a semilog form for their price function

without any concrete justification for that functional form. More

notably, Jud and Watts imposed a restriction from Rubinfeld (1977)

that the ratio of the income to the price elasticity of demand for

public education is -1.7. The odd thing about this insertion is that

Rubinfeld's study was based on survey results from Troy, Michigan in

1973 - not Charlotte of 1977. Yet, without this restriction, Jud and

Watts would not have derived a downward sloping school quality demand

curve.

Like Jud and Watts (1981), this paper evaluates school quality

demand within Rosen's (1974) framework. I shall address Brown and

Rosen's (1982) criticisms using a procedure due to Box and Cox (1964)

which reduces the number of assumptions made pertaining to functional

form.

No evidence is found to support Wetzel's (1983) hypothesis of

interschool competition. If anything, results suggest improving one

region's schools provides a positive externality to neighboring

regions. However, the results do not imply a uniform societal

schooling upgrade, as Jud and Watts proposed and Wetzel criticized, is

in any way appropriate.

In the end, this paper derives a demand curve for educational

quality. However, the ability of people to move to communities best

suiting their tastes noted by Tiebout (1956) as well as the presence

of local elections suggests this curve is not necessary for an optimum

amount of school quality to be provided in the long run. Yet, in the

short run, such a demand curve approximation may provide a school

official with a useful measure to be considered, if not studiously

obeyed.

Data Set

The data set is composed of selling price and house description

information for 621 houses sold by realtors in Chicago's south suburbs

during the first quarter of 1986. There were 701 eligible houses in

the area, but 80 had to be excluded due to suspicion of inaccuracy or

because key information was omitted in the house description.

Each house is described by a number of characteristics, some of

which are internal to the house (i.e. room sizes, number of

bathrooms, number of garages) and some of which are related to the

house's area or town (i.e. distance from downtown Chicago, average

income of the community) .

One such area characteristic provided for each house is a measure

of the quality of the local public elementary school. This measure is

related to the percentile achievement level of the school's third

graders on a statewide standardized test. There are 72 public

elementary schools attended by third graders in the area and having at

least one house in the school district in the data set.

A more complete description of the school quality variable as

well as the rest of the house description variables is found in

Appendix A.

Functional Form and Regression Results

Jud and Watts (1981) employed a semilog form in their regression.

Their justification for this form stemmed from their observation that

housing attributes cannot always be mixed and matched to a buyer's

specifications so the implicit price of any characteristic is

dependent upon the level of that, and perhaps other, characteristics.

This reasoning suggested a non-linear transformation of housing price

was most appropriate. Harrison and Rubinfeld (1978) also felt a

non-linear form was justified as housing attributes cannot be untied

and repackaged to produce an arbitrary set of attributes at all

locations.

Halvorsen and Pollakowski (1981) stated that an appropriate

functional form for a hedonic equation cannot in general be specified

on theoretical grounds. Most researchers seem to have had similarly

pragmatic outlooks. Kain and Quigley (1970) chose the semilog form

for some of their data set (analysis of owners) and the linear form

for the rest (analysis of renters) simply on the basis of goodness of

fit. Grether and Mieszkowski (1980) used semilogs on the grounds of

simplicity. Mayo (1981), Linneman (1981), and Ridker and Henning

(1967) used linear models because they fit better in their cases.

Griliches (1971) and Freeman (1979) suggested using the procedure

of Box and Cox (1964) as an objective way to determine the best

transformation for the dependent variable in a regression. In the Box

and Cox procedure, one transforms the housing price variable Y by

and finds the optimal k by maximizing the likelihood function

Employing this procedure on the data, one finds the maximizing k

10

to be k=-0.13 (to 2 decimal places). The maximized likelihood

function value is -1303.65 while the k=0 (semilog) value of the

likelihood function value is -1307.48. The value corresponding to the

k=0 value is not within the (-1303.65,-1305.57) 95$ confidence

interval for the likelihood function value described by Draper and

Smith (1981), but it is sufficiently close to suggest the semilog form

is the most appropriate common transformation. Appendix B shows the

likelihood value for a variety of k's and the accompanying plot of the

likelihood as a function of k.

Table 1 displays the regression results using this semilog

transformation. One sees positive coefficients in most categories

where one expects a positive coefficient (i.e. the room size

variables, neighborhood income level, full basement, central air

conditioning), and negative coefficients where that outcome is

expected (house age, mobile homes). More surprising, perhaps, is

a) The negative coefficient on the number of bedrooms.

However, since bedroom square footage is also included and

achieves a significant positive coefficient, this result is really not

surprising i.e. given total bedroom area, more bedrooms translates as

tinier (less desirable) bedrooms. When the regression is run omitting

bedroom square feet, number of bedrooms receives a significant

positive coefficient (t=2.87).

b) The insignificant coefficient for minutes to downtown

Chicago.

One would expect housing prices to fall, cet.par., as the time it

Table 1

Dependent Variable

Source

Model Error Total

Parameter

Intercept Lot Size Age of House Bedrooms Baths Garages Fireplaces Living Room Kitchen Ft. Bedroom Ft. Other Ft.

DF

25 595 620

Ft.

Town Blacks/1000 Town Income Brick Aluminum Frame Distance to Chgo Full Basement Crawl Space Partial Basement Central Air Window Air Split Level Two Story Mobile Home School Quali ty

: Natural Log of Housing Price

Sum of Squares R-squared

69.11857188 11.36636318 80.48493506

Estimate

3.08001065 0.00000770 -0.00382559 -0.03003716 0.08421091 0.04422775 0.06383700 0.00032148 0.00031472 0.00053939 0.00023822 -0.00004640 0.00003700 0.02302936 -0.04994257 -0.01758755 0.00033375 0.04538941 0.03223914 0.06358772 0.09806630 0.03312822 0.03562991 -0.00903231 -0.89350445 0.00004470

85.9%

Std Error T-

0.07264483 0.00000093 0.00058967 0.01448474 0.01474417 0.00765485 0.01274490 0.00012517 0.00012896 0.00009191 0.00003790 0.00004298 0.00000306 0.02982089 0.03192308 0.03097641 0.00072454 0.01428871 0.02088741 0.01867994 0.01703298 0.02098294 0.01644208 0.01865857 0.10359445 0.00001375

-Statistic

42.40 8.30 -6.49 -2.07 5.71 5.78 5.01 2.57 2.44 5.87 6.29 -1.08 12.10 0.77 -1.56 -0.57 0.46 3.18 1.54 3.40 5.76 1.58 2.17

-0.48 -8.63 3.25

11

takes to commute to downtown Chicago increases. Yet, Kain and Quigley

(1970), Daniels (1975), Berry (1976), Li and Brown (1980), and Jud and

Watts (1981) also reported insignificant coefficients for distance to

downtown variables for other cities. Ridker and Henning (1967) even

reported a significant positive coefficient for miles from the Central

Business District (for St. Louis).

Rizzuto and Wachtel (1980) suggested that input measures (i.e.

expenditure per pupil, teachers per pupil, etc.) are more appropriate

measures of a school's quality than achievement-related variables such

as the school quality variable used in Table 1. Schnare and Struyk

(1976), Jud and Walker (1977), and Longstreth, Coveney, and Bowers

(1985) used input measures as proxies for local school quality in

regressions. However, for this data set, the achievement variable was

found to be significant using F tests while input variables were not.

Of special interest to this research is the positive significant

coefficient (t=3.25) for the school quality variable. This

coefficient suggests that (holding everything else constant) a buyer

will indeed have to pay some percentage more for a house in an area

with "good" schools than for one in an area with "bad" schools.

Wetzel (1983) suggested such a regression finding does not

necessarily imply there would be any gain from a society-wide upgrade

in school quality. Wetzel asserted that property valuation may be

viewed as a zero-sum game for society as a whole. Though individual

schools might increase their property values by increasing their

quality, it may be at the expense of neighboring districts' property

12

values.

In an attempt to test Wetzel's hypothesis, for each elementary

school a cohort of its five closest neighboring schools is defined.

The mean school quality of each cohort is computed.

In order to control for any positive externality related to

living near rich people which might be correlated with and hence

reflected in this neighboring school quality variable, for each house

the mean per-capita income of the nearest other community to the house

is also included in the regression structure.

The results of this upgraded regression are shown in Table 2. As

expected, there is a positive significant coefficient for the

neighboring community income variable. There is a positive but

insignificant coefficient for the neighboring school quality variable.

If the Wetzel hypothesis that improving neighboring schools would

reduce property values is valid, one would expect a negative

coefficient for this neighboring school quality variable. Hence, this

result casts doubt upon the Wetzel hypothesis.

Of course, it could be that the Wetzel argument applies to a

somewhat larger area e.g. a school competes with the schools two

towns away. The data were not available to test this version of the

Wetzel theory. In a sense, the Wetzel hypothesis is impossible to

disprove since one can redefine "neighborhood" in a broader and

broader fashion ad infinitum.

Thus, the regression results do suggest a buyer has to pay more

to live in an area with better schools, while finding no evidence of

Table 2

Dependent Variable

Source

Model Error Total

Parameter

Intercept Lot Size Age of House Bedrooms Baths Garages Fireplaces Living Room Kitchen Ft. Bedroom Ft. Other Ft.

DF

27 593 620

Ft.

Town Blacks/1000 Town Income Brick Aluminum Frame Distance to Chgo Full Basement Crawl Space Partial Basement Central Air Window Air Split Level Two Story Mobile Home School Quali •ty Neighbor Quality Neighbor Income

: Natural Log o f Housing Price

Sum of Squares R-squared

69.34124834 11.14368672 80.48493506

Estimate

3.02946389 0.00000740 -0.00376715 -0.03109236 0.08373472 0.04388085 0.06228603 0.00029814 0.00029953 0.00054298 0.00023852 -0.00005820 0.00003660 0.02073741 -0.04722511 -0.01998511 0.00061186 0.04536826 0.03152633 0.06658682 0.09502112 0.03415737 0.03172655 -0.00780537 -0.87661760 0.00003620 0.00000820 0.00000610

86.2%

Std Error T-

0.07506780 0.00000093 0.00058619 0.01437559 0.01463185 0.00759330 0.01266473 0.00012433 0.00012802 0.00009123 0.00003762 0.00004459 0.00000310 0.02958913 0.03168348 0.03073248 0.00073979 0.01436706 0.02074207 0.01860571 0.01691724 0.02082980 0.01640318 0.01862281 0.10363437 0.00001394 0.00003199 0.00000203

-Statistic

40.36 7.94 -6.43 -2.16 5.72 5.78 4.92 2.40 2.34 5.95 6.34 -1.31 11.77 0.70 -1.49 -0.65 0.83 3.16 1.52 3.58 5.62 1.64 1.93

-0.42 -8.46 2.60 0.26 3.01

13

Wetzel's interschool competition.

Simultaneous Equations

In an attempt to employ Rosen's (197*0 procedure, I assert a

simultaneous system of the form

Quality Demand Q(d) = G(P,Y,E)

Quality Supply Q(s) = H(P,F)

where

P = Average Marginal Willingness to Pay for Quality

by district

Y = Average Income by district

E = Number of Adults per 10000 with a College degree

by district

F = Fixed (Non-salary) Cost per Pupil by district

To some extent these variable choices were arbitrary, though F

tests were used in choosing to include Y and E, and F was chosen as

the lone supply variable because other potential supply curve

variables (Pupils per Teacher, Average Teacher Salary) seem to behave

more like demand variables. Intuitively, it makes sense that the

level of teacher salary and the ratio of pupils to teachers in a

district are influenced by local demand factors. Districts that pay

their teachers well and hire a lot of teachers relative to their

number of students in all probability do so because their constituents

are interested in obtaining high quality education. Hence, variables

along this line do not truly shift the quality supply curve so they

11*

should not be included as supply curve variables in simultaneous

systems.

A similar argument could suggest the fixed cost per pupil

variable is also adulterated by influence from demand factors. To

some extent, this criticism is valid. For example, a more expensive

facility might be built in a district that has greater demand for

education. However, in the short run at least, districts would have

difficulty adjusting fixed costs to constituent demand levels. More

pragmatically, there must be at least one supply variable to identify

the demand curve and this variable is apparently preferable to all

other options.

In order to increase the accuracy of the system, analysis was

restricted to those school districts having at least H houses sold in

the sample (which was 53 of the 72 districts). Appendix C displays

the means and standard deviations of these variables.

In order to derive the demand curve, one must regress the

Willingness variable on the income, education, and fixed cost

variables, deriving an estimate of Willingness. Then one must run the

school quality variable on that estimate, the income variable, and the

education variable, thus deriving, within this framework, the demand

curve for school quality.

To reduce the arbitrariness of this procedure, the Box-Cox (196-4)

procedure was used to determine the optimal J for

P~J = a + bY + cE + dF

where "~" can be read as "raised to the power of". (The

15

computer's printing capacity does not include superscripts.)

J= -.23 was determined to provide the best fit. Appendix D

displays the Box-Cox statistics for this equation.

Then the Box-Cox procedure was again used to determine the

optimal K for

Q~K = e + fP~(-.23) + gY + hE

K = .63 was determined to provide the best fit. Appendix E

displays the Box-Cox statistics for this equation. Table 3 shows the

results of these regressions.

The same procedure was also attempted using lnY, InE and InF, but

the result was less satisfying, as the resultant curve was not

downward sloping. The Box-Tidwell (1962) procedure in which the

powers of independent variables are allowed to vary was also

attempted, but no convergence was found.

Hence, the best approximation of the school quality demand curve

found is

P = (.413 - -00003Y - .00005E + .013Q~(.63)T(-4.348)

where

P = Average Marginal Willingness to Pay for Quality

by district

Y = Average Income by district

E = Number of Adults per 10000 with a College degree

by district

Q = School quality measure

and where "~" is read as "raised to the power of".

Table 3

Stage 1

Dependent Variable

Source DF

Willingness to Pay for Quality to the (-.23)

Sum of Squares R-squared

Model Error Total

Parameter

Intercept Income

3 49 52

College Education Fixed Cost

0.07411685 0.03879915 0.11291600

Estimate

0.82581589 -0.00000990 -0.00001710 0.00000900

65

Std Error

0.02597781 0.00000305 0.00000759 0.00000907

.6%

T-Statistic

31.79 -3.26 -2.26 1.00

Stage 2

Dependent Variable : School Quality to the (.69)

Source DF Sum of Squares R-squared

Model Error Total

Parameter

Intercept Income

3 49 52

College Education Willingness--Hat

2348.07685714 16 11745.44524984 14093.52210699

Estimate

-32.80249451 0.00261092 0.00417009 79.46421344

Std Error

466.01696480 0.00585501 0.00977945

552.60964963

.7%

T-Statistic

-0.07 0.45 0.43 0.14

16

This formulation has several positive characteristics:

a) It provides an intuitively correct downward sloping demand

curve.

b) It imposes no external restrictions in order to achieve this

downward slope.

c) It has fewer arbitrary functional form assumptions due to the

usage of the Box-Cox procedure.

Discussion

Assuming for the moment that this curve does represent demand for

school quality in Chicago's south suburbs, several key points emerge.

First, and perhaps trivially, the curve is downward sloping given

fixed levels of income and education. Appendix F shows this curve

with income and education held constant at their mean levels. Holding

other things constant, an area with poor schools is likely to receive

a larger benefit from an upgrade than an area with good schools would.

Second, the level of demand in a district is affected by the

level of income and education in the district. Both dP/dY and dP/dE

are positive - marginal willingness to pay for quality is greater in

more affluent and educated areas.

Both of the above points call into question the wisdom of

speaking of uniform societal schooling upgrades as Jud and Watts

(1981) proposed. Demand levels vary depending upon present quality

level, area income level and area education level. If one looks at an

average homeowner in an area with average schools, average education

17

level, and average income level, one would find that he would realize

a gain of approximately $191.50 from a 1055 upgrade in his school.

However, such "average" computations obfuscate the real point which is

that demand levels vary from area to area so any suggestions of

society-wide quality changes are inappropriate.

Another factor suggesting any wholesale changes would be

inappropriate is the general inelasticity of quality demand.

Elasticity is not constant, but as Appendix G shows, it is inelastic

throughout all relevant quality levels. (The demand elasticity is

generally around -.H.) Hence, this curve suggests people are unlikely

to support large changes in school quality in either direction.

It is important to note that this demand curve does not consider

the other key component a school official must consider, namely the

supply curve he faces. Increasing quality costs money - if it did

not, every district would do it. Hence, this demand curve, even if

totally accurate, does not remove the school official's role. He must

equate the demand curve's marginal benefit with the marginal cost he

is facing.

The extent to which this curve actually describes the area's

demand level is in question. The repeated usage of the Box-Cox (1964)

procedure reduces the number of arbitrary assumptions, but hardly

eliminates the researcher's subjective role. For instance, the

seemingly inconsequential decision to use Y, E, and F as opposed to

lnY, InE, and InF meant the difference between a downward and an

upward sloping curve. Further, the R-squared of the estimated demand

18

curve is not good (16.7?). Hence, it is difficult to have much

confidence in conclusions derived from this demand curve.

Even given that this procedure may, in the end, do policymakers

little good, there is some reason to believe an optimal outcome will

occur.

In a seminal work, Tiebout (1956) introduced a model of the

consumer-voter as one who chooses the community whose local government

best satisfies his set of preferences. If an individual approves of

the local government's performance in his area, he stays; while if he

disapproves, he moves to a more favorable area. Of course, there

tends to be enormous inertia in housing due to the costs of moving,

but the Tiebout effect does guarantee that, at least in the long run,

the level of school quality provided in an area approximates the

optimal quantity for the area.

The local school board election process provides another means of

pushing policymakers to an optimal solution. If a school official's

choice of school quality level differed markedly from that of his

constituents, the constituents could rise up and remove the official.

However, there is question as to the extent to which citizens are

active and interested in local school affairs. Boardman and Cassell

(1983) surveyed a stratified random sample of adults listed in the

telephone directories of six geographically representative areas of

one midwestern state. Only 22.2? of those surveyed correctly stated

the number of members of their local school board. Only 5.6? reported

having ever attended a board meeting. In general, the degree of

19

knowledge displayed about how school boards function and what issues

they consider was very poor.

Many school board elections are little-publicized, staid affairs.

Of 2H elementary school board elections in the south suburban area

held in November, 1985, eleven of the 2H involved no contest

whatsoever, six of the 2-4 involved only one more candidate than seats

available (i.e. 5 candidates for H seats), while only seven of the 2k

involved more than one more candidate than seats available. Indeed,

of the noncontested elections, two actually involved fewer candidates

for office than seats available. Presumably, the elections are this

way either because residents are basically pleased with the

performance of their elected officials or because residents are too

ignorant of the political process to act upon their displeasure.

Hypothetically, if the performance of the elected officials was

poor enough, the residents would find it in their interest to end

their ignorance of and apathy toward the system. However, it is

entirely possible a school official could keep his job over the long

run despite a nonoptimizing solution, as long as that solution did not

aggravate his constituency sufficiently to end their inactivity.

Hence, I have derived an approximation of the demand curve for

school quality in Chicago's south suburbs. However, it is fair to

question its accuracy as well as the extent to which such a demand

curve would be needed to assure an optimizing outcome.

Conclusions

20

Employing a data set of 621 housing sales in Chicago's south

suburbs from the first quarter of 1986, this study finds a positive,

significant premium is paid by housing buyers to live in areas with

better schools.

Analysis finds no evidence of the interschool competition

asserted by Wetzel (1983).

Using the method of Rosen (197*1), a demand curve for school

quality is derived which contains fewer of the arbitrary assumptions

criticized by Brown and Rosen (1982) due to the repeated usage of the

Box-Cox (1964) procedure.

Theoretically, this demand curve could be used by a policymaker

to determine the wisdom of increasing (or decreasing) a district's

school quality. Another potential usage would be to aid a school

official in reacting optimally to a shift in the quality supply curve,

say from a technological innovation in education making quality easier

to obtain.

However, if the Tiebout (1956) effect is allocating people

between districts optimally and/or the local election process is

forcing school administrators to optimize in order to hold their jobs,

this exercise has been strictly academic; districts are optimizing as

it is. Yet, if one accepts that in the short run districts may not be

behaving optimally, this demand curve could be used as a tool to

suggest possible change.

Appendix A

Characteristics by House

N = 621

21

Variable Mean S.D. Min Max

Pr ice $65> Lot Size ( s q . f t . ) 8,

078 635

Age (Years) 23.68 Bedrooms 3.17 Baths Garages

.61 1.82

F i r e p l a c e s 0.39 Living Room(sq.ft .) Kitchen ( s q . f t . ) Bedrooms ( s q . f t . ) Other ( s q . f t . ) [1] Blacks/1000 in town

241 153 433 275 104

Aver Income town 92*12 Distance (Minutes) [2] School Qual i ty [3] Brick (Dummy) [4] Aluminum (Dummy) [4] Frame (Dummy) [4] Fu l l Basemnt (Dmmy)[5] Crawl Space (Dummy)[5] P a r t i a l Bsmnt (Dmy)[5] Centra l Air (Dummy)[6] Window Air (Dummy) [6] Two Story (Dummy) [7] S p l i t Level (Dummy)[7] Mobile Home (Dmmy) [7] P o s i t i v e Qual i ty [8] Neighboring Q u a l i t y [ 9 ]

47 315 .59 .17 .20 • 3*1 .09 .13 .68 .11 .17 • 37 .003 624 288

Neighboring Income 9892

$33,150 7,115 12.72 0.68 0.61 0.83 0.56

55 46

133 196 158

2473 7

471 .49 • 37 .40 .47 .28 • 34 .47 • 32 .37 .48 .06 287 234

3231

$16,700 2,3^0

0.0 2.0 1.0 0.0 0.0

48 24

189 0 0

4719 30

-926 0 0 0 0 0 0 0 0 0 0 0

40 -528 5946

$455,000 99,792

80.0 5.0 6.0 4.0 3.0 610 416

1185 1012 932

19739 79

1450

1450 857

19739

[1] Other square footage is the sum of square footage of dining rooms and family rooms. It does not include area of things like screened-in porches.

22

[2] Distance to downtown Chicago is measured in minutes using the Illinois Central Gulf Railroad during Rush Hour plus an approximation of travel time to the nearest station at 20 miles per hour. I consider it to be a low estimate of true commuting time for most houses except for those that are so far from a train station that driving downtown is faster.

[3] Quality is a measure derived from percentile performance of third graders on a standardized test. For each school, I had data in the following form: % of students scoring in top quartile on state math test, % of students scoring in top quartile on state reading test, % of students scoring in bottom quartile on state math test, and % of students scoring in bottom quartile on state reading test. The quality number in the data set is

10*($TopMath + JfTopReading - ^BottomMath - ^BottomReading) Thus, for the "average" elementary school on a statewide basis,

one would get Quality=0 using this formula. This area tends to average above 0, partially since more houses are sold through realtors in good areas and partially because poor schools in downstate Illinois and in the inner city of Chicago assure most suburban schools of scoring above the state average.

[4] Default is "Other" exterior.

[5] Default is no basement.

[6] Default is no air conditioning.

[7] Default is one story.

[8] This is the quality measure used in the simultaneous equations section of the paper. It is

10*(% Top Math + % Top Reading) Obviously, it is less interesting than the other quality measure.

However, I have it for the simultaneous equations section because its nonnegativity allows the quality variable to be raised to arbitrary powers.

[9] Used in discussion of Wetzel hypothesis. See Table 2.

23

Appendix B Box-Cox Funct ional Form Analysis

P"K = a + bx[1] + cx[2] + . . . + zx[n]

k Resul tant Box-Cox S t a t i s t i c

-2 .00 -1698.44 -1 .80 -1625.96 -1 .60 -1583.66 -1 .40 -1513-30 -1 .20 -1458.64 -1 .00 -1412.44 -0 .80 -1372.71 -0 .60 -13110.35 -0 .40 -1316.80 -0 .35 -1312.57 -0 .30 -1309.08 -0 .25 -1306.40 -0 .20 -1304.60 -0 .19 -1304.35 -0 .18 -1304.13 -0 .17 -1303.96 -0 .16 -1303-82 -0 .15 -1303.72 -0 .14 -1303.67 -0 .13 -1303.65 -0 .12 -1303.68 -0 .11 -1303.75 -0 .10 -1303.86 -0 .05 -1305.08 +0.00 -1307.48 +0.20 -1330.57 +0.40 -1379.69 +0.60 _1n59.no +0.80 -1570.68 +1.00 -1710.15 +1.20 -1871-79 +1.40 -2049.30 +1.60 -2237.65 +1.80 -2433-33 +2.00 -2634.12

Box —Cox Functionol Form Plot Appendix B

24

Appendix C Characteristics by District

N = 53

Variable

Willingness Income Education Quality-Fixed Cost/Pupil

Mean

4222 9030 1519 601 1862

S.D.

1464 2349 951 273 436

Min

2253 5946 392 40 728

Max

11114 17674 4369 1450 3108

25

Appendix D Box-Cox Funct ional Form Analysis

P J = a + bY + cE + dF

iS Resultant Box-Cox Statistic

-2.00 12.28 -1.90 13.04 -1.80 13.76 -1.70 14.46 -1.60 15.14 -1.50 15.78 -1.40 16.39 -1.30 16.97 -1.20 17.51 -1.10 18.02 -1.00 18.49 -0.90 18.91 -0.80 19.29 -0.70 19.62 -0.60 19.90 -0.50 20.13 -0.40 20.29 -0.30 20.38 -0.29 20.38 -0.28 20.39 -0.27 20.39 -0.26 20.39 -0.25 20.39 -0.24 20.39567790 -0.23 20.39614410 -0.22 20.39580220 -0.21 20.39 -0.20 20.39 -0.19 20.39 -0.18 20.39 -0.17 20.38 -0.16 20.38 -0.15 20.37 -0.14 20.36 -0.13 20.36 -0.12 20.35 -0.11 20.34 -0.10 20.33 +0.00 20.17 +0.10 19.91

26

+0.20 +0.30 +0.40 +0.50 +0.60 +0.70 +0.80 +0.90 + 1.00 + 1.10 + 1.20 + 1.30 + 1.40 + 1.50 + 1.60 + 1.70 + 1.80 + 1.90 +2.00

19.55 19.07 18.46 17.71 16.81 15.76 14.53 13.14 11.56 9.80 7.85 5.71 3-39

.89 -1 .79 -4 .64 -7.64

-10.79 -14.08

O >

O O

J C

-X.

25 -

20 -

15 -

1 0

0 -

- 5 -

10 -

-15 -

Box — Cox Functional Form Plot Appendix D

- 2

27

Appendix E Box-Cox Funct ional Form Analysis

Q~K = e + fP" ( - .23) + gY + hE

- Resul tan t Box-Cox S t a t i s t i c

-2 .00 -463.67 -1 .80 -442.13 -1 .60 -420.61 -1 .40 -400.23 -1 .20 -380.40 -1 .00 -361.89 -0 .80 -344.98 -0 .60 -330.06 -0 .40 -317-55 -0 .20 -307.73 +0.00 -300.65 +0.20 -296.04 +0.40 -293.51 +0.41 -293.43 +0.42 -293.36 +0.43 -293-28 +0.44 -293.22 +0.45 -293.15 +0.46 -293.09 +0.47 -293-04 +0.48 -292.98 +0.49 -292.94 +0.50 -292.89 +0.51 -292.85 +0.52 -292.81 +0.53 -292.78 +0.54 -292.75 +0.55 -292.72 +0.56 -292.70 +0.57 -292.68 +0.58 -292.66 +0.59 -292.64 +0.60 -292.63 +0.61 -292.63 +0.62 -292.6224192 +0.63 -292.6212738 +0.64 -292.6232104 +0.65 -292.63 +0.66 -292.64 +0.67 -292.65

28

+0.68 +0.69 +0.70 +0.71 +0.72 +0.73 +0.74 +0.75 +0.76 +0.77 +0.78 +0.79 +0.80 + 1.00 + 1.20 + 1.40 + 1.60 + 1.80 +2.00

-292.66 -292.68 -292.70 -292.72 -292.75 -292.77 -292.80 -292.84 -2 92.87 -292.91 -292.95 -293-00 -293-04 -294.47 -296.71 -299.63 -303-13 -307.15 -311.62

>

O O

.C

-290 -300 - 3 10 -320 -330 - 3 40 -3 50 -360 -370 -380 -390

-400

Box —Cox Functional Form Plot A p p e n d i x E

• 4 1 0

• 4 2 0

• 4 3 0

• 4 4 0

• 4 5 0

• 4 6 0

• 4 7 0

- 2

29

Appendix F Qual i ty Demand Curve

Income, Education held constant at mean levels,

Quality 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510

Price 3T9.82 255.08 207.17 170.87 142.81 120.74 103.12 88.86 77.19 67.53 59.46 52.67 46.90 41.96 37.72 34.04 30.84 28.04 25.58 23.40 21.48 19.76 18.23 16.85 15.62 14.50 13.50 12.58 11.75 10.99 10.30 9.67 9-09 8.55 8.06 7.61 7.19 6.80 6.44 6.11 5.79 5.50

30

520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000

5.23 4.98 4.75 4.52 4.32 4.12 3.94 3.77 3.61 3-46 3-31 3.18 3.05 2.93 2.81 2.71 2.60 2.51 2.41 2.32 2.24 2.16 2.09 2.01 1.94 1.88 1.82 1.76 1.70 1.65 1.59 1.54 1.50 1.45 1.41 1.36 1.32 1.28 1.25 1.21 1.18 1.14 1.11 1.08 1.05 1.02 1.00 0.97 0.94

Quality Demand Curve

V)

o 6 a a> o

a.

320 -

300 -

280 -

260 -

240 -

220 •

200

180

1 60 -

1 40 -

1 20 -

100 -

80 -

60 -

40 -

20 •

0 0 0.2 0.4 0.6

(Thousands) Quality Units

0.8

Quality Demand Curve

CO 1 -D O

O

CD O

X CL

0.4 0.6 (Thousands) Quality Units

31

Appendix G Quality Demand Elasticities

Income, Education held constant at mean levels,

Quality 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510

Elasticity -0.423 -0.420 -0.417 -0.414 -0.412 -0.410 -0.408 -0.407 -0.405 -0.404 -0.403 -0.401 -0.400 -0.399 -0.398 -0.398 -0.397 -0.396 -0.395 -0.395 -0. 394 -0. 394 -0.393 -0.392 -0.392 -0.391 -0.391 -0.391 -0. 390 -0.390 -0.389 -0.389 -0.389 -0.388 -0.388 -0.388 -0.387 -0.387 -0.387 -O.386 -0.386 -0.386

32

520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000

-0.386 -0.385 -0.385 -0.385 -0.385 -0.384 -0.384 -0.384 -0.384 -0.384 -0.383 -0.383 -0.383 -0.383 -0.383 -0.383 -0.382 -0. 382 -0. 382 -0. 382 -0. 382 -0.382 -0. 382 -0.381 -0.381 -0.381 -0.381 -0.381 -0.381 -0.381 -0.380 -0.380 -0.380 -0.380 -0.380 -0.380 -0.380 -0.380 -0.380 -0.380 -0.379 -0.379 -0.379 -0.379 -0.379 -0.379 -0.379 -0.379 -0.379

-t~>

• — o V)

o UJ

- 0 . 3 7 5

- 0 . 3 8

- 0 . 3 8 5 •

- 0 . 3 9 H

- 0 . 3 9 5 -

- 0 . 4 H

- 0 . 4 0 5 •

- 0 . 4 1

- 0 . 4 1 5 •

- 0 . 4 2 -

- 0 . 4 2 5 -0

Quality Demand Elasticity

0.2 T

0.4 0.6 (Thousands) Quality Units

O.S

Qua l i t y D e m a n d E l a s t i c i t y -0.378 --0.379 --0.38 -

-0.381 --0.382 -1 -0.383 --0.384 --0.385 --0.386 -

rg-0.387 -"1-0.388 -.2-0.389 -LJJ

-0.39 --0.391 --0.392 --0.393 --0.394 --0.395 --0.396 --0.397 --0.398 -

O 0.2 7 r T

0.4 0.6 (Thousands) Quality Units

0.8

33

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