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
P r i c e $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 i n town
241 153 433 275 104
Aver Income town 92*12 D i s t a n c e (Minutes) [2]
School Q u a l i t y [ 3 ]
Brick (Dummy) [4]
Aluminum (Dummy) [4]
Frame (Dummy) [4]
F u l l Basemnt (Dmmy)[5]
Crawl Space (Dummy)[5]
P a r t i a l Bsmnt (Dmy)[5]
C e n t r a l Air (Dummy)[6]
Window Air (Dummy) [6]
Two S t o r y (Dummy) [7]
S p l i t Level (Dummy)[7]
Mobile Home (Dmmy) [7]
P o s i t i v e Q u a l i t y [ 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 F u n c t i o n a l Form A n a l y s i s
P"K = a + bx[1] + c x [ 2 ] + . . . + z x [ n ]
k R e s u l t a n t Box-Cox S t a t i s t i c
- 2 . 0 0 -1698.44 - 1 . 8 0 -1625.96 - 1 . 6 0 -1583.66 - 1 . 4 0 -1513-30 - 1 . 2 0 -1458.64 - 1 . 0 0 -1412.44 - 0 . 8 0 -1372.71 - 0 . 6 0 -13110.35 - 0 . 4 0 -1316.80 - 0 . 3 5 -1312.57 - 0 . 3 0 -1309.08 - 0 . 2 5 -1306.40 - 0 . 2 0 -1304.60 - 0 . 1 9 -1304.35 - 0 . 1 8 -1304.13 - 0 . 1 7 -1303.96 - 0 . 1 6 -1303-82 - 0 . 1 5 -1303.72 - 0 . 1 4 -1303.67 - 0 . 1 3 -1303.65 - 0 . 1 2 -1303.68 - 0 . 1 1 -1303.75 - 0 . 1 0 -1303.86 - 0 . 0 5 -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 F u n c t i o n a l Form A n a l y s i s
P J = a + bY + cE + dF
iS R e s u l t a n t B o x - C o x S t a t i s t i c
-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 . 7 9 - 4 . 6 4-7.64
- 1 0 . 7 9 - 1 4 . 0 8
O
>
O O
J C
-X.
25 -
20 -
15 -
1 0
0 -
- 5 -
10 - - 1 5 -
Box — Cox Functional Form Plot
Appendix D
- 2
27
Appendix E
Box-Cox F u n c t i o n a l Form A n a l y s i s
Q~K = e + f P " ( - . 2 3 ) + gY + hE
- R e s u l t a n t Box-Cox S t a t i s t i c
- 2 . 0 0 -463.67 - 1 . 8 0 -442.13 - 1 . 6 0 -420.61 - 1 . 4 0 - 4 0 0 . 2 3 - 1 . 2 0 -380.40 - 1 . 0 0 -361.89 - 0 . 8 0 -344.98 - 0 . 6 0 -330.06 - 0 . 4 0 -317-55 - 0 . 2 0 - 3 0 7 . 7 3 +0.00 -300.65 +0.20 -296.04 +0.40 -293.51 +0.41 - 2 9 3 . 4 3 +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 - 2 9 2 . 8 5 +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 - 2 9 2 . 6 3 +0.61 - 2 9 2 . 6 3 +0.62 -292.6224192 +0.63 -292.6212738 +0.64 -292.6232104 +0.65 - 2 9 2 . 6 3 +0.66 -292.64 +0.67 - 2 9 2 . 6 5
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 - 2 9 2 . 7 5 -292.77 -292.80 -292.84 -2 92.87 -292.91 - 2 9 2 . 9 5 -293-00 -293-04 -294.47 -296.71 - 2 9 9 . 6 3 -303-13 -307.15 -311.62
>
O O . C
- 2 9 0 - 3 0 0 - 3 10 - 3 2 0 - 3 3 0 - 3 40 - 3 50 - 3 6 0 - 3 7 0 - 3 8 0 - 3 9 0 - 4 0 0
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 Q u a l i t y 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.
3 2 0 - 3 0 0 - 2 8 0 - 2 6 0 - 2 4 0 - 2 2 0 • 2 0 0
180 1 6 0 - 1 4 0 - 1 2 0 - 1 0 0 - 8 0 - 6 0 - 4 0 - 2 0 •
0
0 0.2 0.4 0.6
( T h o u s a n d s ) Quality Units
0.8
Quality Demand Curve
CO 1 -D O O
CD O
X CL
0.4 0.6 ( T h o u s a n d s )
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 ( T h o u s a n d s )
Quality Units
O.S
Q u a 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 . 3 8 2 -1 - 0 . 3 8 3 - - 0 . 3 8 4 - -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
T0.4 0.6 (Thousands)
Quality Units
0.8
33
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