1

Chicago Area Housing Analysis

A Hedonic Price Study

By

Eric P. Morel

An MMSS Senior Thesis

Advisors

Michael Dacey

Edwin Mills

June 2000

2

ACKNOWLEDGMENTS

First and foremost, I would like to thank Ed Mills for his interest, support and

guidance. He gave me much needed direction and encouragement, as well as access to

his extensive knowledge of the subject. I would also like to thank Professor Dacey and

the rest of the MMSS faculty for facilitating such a wonderful program. Finally, I would

like to thank my family and friends for their love and support.

3

ABSTRACT

This study utilizes data provided by the Chicago Tribune Homes web site to

analyze the relationships between community home attributes and median home sale

prices in Chicago and surrounding counties for 1999. Based on the hedonic pricing

model that partitions complex commodities into variable quantities of uniform attributes,

the study shows that certain home related community attributes significantly and

predictably contribute to median home prices. The study examines attributes in four

categories including physical, community, inhabitant and location characteristics.

Regression analysis reveals that attributes in each of these categories affect home prices.

However, the feasibility of using least squares estimation to analyze this data is carefully

scrutinized. Beyond attribute pricing, this study also offers other interesting relational

findings among the community data.

4

INTRODUCTION

For years the housing market has captured the attention of professionals in both

academic and business arenas. The home as a commodity stands out for several reasons.

First, a home is the biggest purchase and investment many families will make in a

lifetime. Outside of extraordinary cases, whether renting or purchasing, every family

must devote some of their income towards a living environment. This makes supply and

demand analysis particularly interesting. Finally, a home is one of the best examples of

a truly heterogeneous good. Homes can vary by any number of factors including size,

material, age, design and location. As one of the most expensive and complex goods

available, homes and the housing market draw a great amount of analysis and speculation

from both commercial and private investors hoping to find trends or other insight to give

them a competitive edge. Study of housing data has also sparked as well as helped to

answer many sociological questions that have been the concern of many academics and

politicians as well as society as a whole.

Formalized by Rosen in the 1970’s, the hedonic pricing model has been regularly

applied to the housing market. The model asserts that any heterogeneous good is really a

bundle of fairly uniform, homogeneous goods or attributes that vary in quantity.

Therefore, the price or value of a complex commodity can be represented by a vector

containing the quantities of the underlying attributes. When applied to a utility function,

this attribute vector generates a value function. The addition of a composite good vector

and a budget constraint allow for the estimation of a housing demand function. Much of

the analysis of housing data is an attempt to identify and quantify these attribute goods

and estimate their value function within the context of the entire home. Other studies

5

focus on price indexing, studying national data in order to discover price discrepancies

among homes in different regions and at different time periods. There are many time

varying and regionally specific factors that affect the supply and demand for homes,

causing price variation. However, this broad longitudinal and regional analysis will not

be the focus of this work. This study will take the former approach in an attempt to

define and quantify the hedonic values of home attributes in a localized, cross sectional

study. According to the hedonic pricing model, the value of a home can be attributed to

the value of the bundle of homogeneous qualities that it contains. All other things equal,

a home containing more of one of these positively valued attributes will be worth more.

This study intends to show that these valued attributes are not only physical

characteristics of a home, but community characteristics as well. A home provides

membership in a community with benefits, obligations and sometimes problems. Some

of these factors, whether legally enforced or simply effects of proximity, can be measured

and compared across communities as commodities in the pricing model. This study

utilizes recent housing data from the city of Chicago and communities from seven

surrounding counties to analyze these commodities, both structural and neighborhood

attributes, to estimate a model for home values. The study also uncovers many

interesting sociological relationships worth mentioning.

6

DATA

The data for this study comes from the Homes section of the Chicago Tribune’s

web site, http://www.chicagotribune.com/homes. The site references sources including

the U.S. Census Bureau, Claritas Inc., MLS of Northern Illinois, Northeastern Planning

Commission, Illinois State Police, Chicago Police Department and the Illinois State

Board of Education. The site provides fairly uniform information for Chicago’s 77

community areas as well as an additional 296 suburban communities within Cook,

DuPage, Lake, McHenry and Will counties in Illinois and Lake and Porter counties in

Northwest Indiana. Most of the 77 Chicago communities, adopted by the Chicago

Association of Realtors, correspond with traditional Chicago neighborhoods such as

Lakeview or Hyde Park, while others are aggregates of neighborhoods that are seldom

referred to outside of the real estate community. The Chicago Tribune page for each

community includes a profile by a contracted writer, with access to a facts and figures

page as well as archived information. A wealth of information exists from the many

sources that are compiled into the facts page. The site includes location data, including

county designation, a measure of distance from the loop and area in square miles.

Community information reported from the 1990 census survey consists of percentages of

single-family units, number of housing units, population, percentages for the number of

people in a housing unit, the number of rooms in a housing unit, homes built in grouped

cohort years, as well as age, race, sex, marital status, education, employment and

occupation distributions. Important data also exists concerning standardized 1998 crime

data, 1998 educational data including average ACT scores by school district, and finally

7

1999 data on quarterly median home sales prices coupled with the number of homes sold

in that period and current figures for population and number of housing units. Archived

information for 1998 median home value also exists for some communities. Although

the available information is fairly consistent among the different communities, there is

some small variation in reporting depending on the given county. Missing information

also exists for a small number of communities. While most of the missing data exists for

the smallest and most outlying communities, there also appears to be some random holes

in the data that seem to be simple mistakes in data compilation. Treatment of missing

values will be discussed later.

When organized correctly and thoughtfully, this data contains valuable

information concerning the relationships between median community home sale prices

and community attributes. The 300 plus fairly uniform observations allow for adequate

statistical analysis. There have been a multitude of studies utilizing home sales data from

various sources. Home sale transactions and prices are traditionally well documented.

Unfortunately, the quality and quantity of existing information on the attributes of those

homes is much lower. The AHS (American Housing Survey), is one heavily studied

source, along with NAR (National Association of Realtors) data. These data sets differ

from the Tribune data, however, because the observations deal with individual homes and

sales. Although these provide an accurate source of pricing information and physical

home properties, they can be inadequate for deciphering community attributes. The

American Housing Survey polls for the adequacy of some community amenities, and

comparisons between communities are the product of home owner opinion. The response

is based on the individual home owner’s values rather than any standardized measure of

8

performance. This data may become biased when compared across communities. For

instance, a suburban family might be overly critical of a great school that might not quite

measure up to the one in the next neighborhood, although they are both in the top few

percent of schools. Also, a homeowner might respond with incomplete information. A

single professional’s response to the adequacy of education might be completely arbitrary

due to lack of concern. Ultimately, these survey questions do provide valuable insight

towards qualities of attributes in a neighborhood, but may not be as accurate as

standardized statistical measurements. This is a great feature of the Tribune data.

Measurements for many community commodities are uniform and standardized. Mean

ACT scores of high school seniors are available for each community, as well as crime

rates per 1000 residents. While these are still only proxies for the quality of education

and safety in a community, they at least insure a standardized comparison across

communities. Another main motivation for using the Chicago Tribune Homes data to

study attribute contributions toward housing prices involves the assumption that there is a

great deal more variance in home values between communities than within communities.

Homes within a community share many of the same resources that affect value. Also,

homes should be expected to share more physical characteristics then present for a larger

sample. The Tribune data is conveniently aggregated at this level, facilitating the

exploration of variance causation between communities. The aggregated observations

are also interesting from a modeling standpoint. In this study, a model will be formulated

using home attribute variation to account for variance in median home values. The

residual errors of this model will be particularly valuable because they will show which

communities are undervalued and overvalued by the regression analysis. The largest

9

outlying communities can be studied to look for any explanation of the deviance between

the actual and expected home prices. This may lead to the identification of significant

home and community attributes that might have been over looked by the model. This

residual analysis would be much more difficult from an individual home perspective, as it

would be very difficult to uncover additional information for each home.

The benefits of the Chicago Tribune data are coupled with some weak points.

First, the data is a collection of information from a variety of sources. Although all the

sources seem reputable and the data appears to be accurate, the actual conditions and

integrity of the data collection will never be known. The population data from the

different years are most likely sophisticated estimates of actual population. While the

Census Bureau provides the 1990 data, Claritas provides the 1999 population

information. It is possible that these two sources have different estimation methods that

might cause a bias in the information.

Another problem that may lead to the misspecification of median home price

variance in the model stems from levels of data aggregation for certain variables that

differ from the community levels. For instance, the 1999 sales data provided by the MLS

couples some of the smaller outlying suburbs with a larger neighboring suburb. Since the

observations are represented per community, any sales data that bundles several

communities will result in a replication of the exogenous variables. The model losses

some freedom as the medians may have differed if the data had been partitioned by

community. If a difference does exist, some of the explanatory power of the endogenous

variables for those communities will be lost through the overly aggregated data.

10

An interesting problem of aggregation is present in the descriptive properties of

the Tribune data. Some community variables are displayed as averages of individual

statistics while others are median values. One relevant example includes quarterly home

sale prices and number of rooms which are represented as median values and gross

percentages respectively. For modeling purposes, these percentages were used as

weights to derive the average number of rooms. When data is not distributed

symmetrically, means can differ significantly from medians. It is possible to

misrepresent the data when regressing means against medians. Using the median home

price and average number of rooms as an example, imagine that the true value of a home

is exactly $50,000 times the number of rooms. Community A has 10 home sales; all four

room homes for $200,000. Community B also has 10 home sales; six two room homes

for $100,000 and four seven room homes for $350,000. For each community, there is an

average of four rooms per home and the average home price is $200,000. However, the

median home price for community B is only $100,000. The comparison of the mean of

one variable to the median of another fails to uncover the true relationship between the

number of rooms and home price. This phenomenon is particularly threatening to any

future model because the median home prices are certainly not normally or symmetrically

distributed among communities (see Appendix 1.1), although individual home prices

within a community may more closely subscribe to these distributions.

While the previous problems are more subtle, the time lag between the 1990

census attribute variables and the 1999 median price data may be the most recognizable

problem with the data. Crime and educational data are lagged by one year. This is ideal

under the assumption that these are the most current statistics that would be realized by a

11

potential buyer and are good proxies for the level of these attributes. However, many of

the attribute variables that will be used in the hedonic model were calculated from census

information that is nine years removed from the home sales data. Luckily, most of these

attributes should not vary greatly over a decade for communities within reasonable

growth and construction limitations. These include the average number of rooms per

home, average number of people per housing unit and the percent of single family

structures. Two other community attribute variables raise concern, however. One

attribute that could change significantly over a decade is the racial composition of a

community. Particularly in Chicago, many traditionally ethnic and minority

neighborhoods have been experiencing gentrification and an influx white urban

professionals within recent years. The census data cannot account for any of these recent

changes and may cause a bias for some neighborhoods. Another disturbing shortcoming

of the census data involves average home age. All average community home ages have

been calculated as of the year 1990. This data is right censored and does not factor any

new homes built after 1990. With the Tribune data, there is a lack of information

concerning the percentage of the sales of new homes as opposed to old structures. Many

outlying suburbs are rapidly growing under new construction. Even some of the most run

down neighborhoods in Chicago are experiencing home restoration and construction as

investors attempt to take advantage of low property values within minutes of the Loop. It

seems logical that the median home price within a community would increase as the

percentage of new home sales increases. Unfortunately, the Tribune data offers little to

account for this median price variance. For communities with a stable population, the

lack of accountability for the last ten years of average home age should make little

12

difference in median price. However, for rapidly growing communities, particularly

those outside of Cook County, the average home age as of 1990 could greatly

misrepresent the true average age of homes as reflected in the median home prices for

1999.

As entered directly from the Tribune Homes site, the data contained 374

observations of 63 variables. Certain cases were missing data. Some of this was

systematic by county; some appeared to be more frequent in smaller outlying

communities, while other missing values seemed completely random. It became

immediately apparent that too much information was missing from the two Indiana

counties. These observations could not be included in any model of median home prices

due to missing values. Therefore the 32 Indiana observations were discarded from all

further data analysis for consistency, leaving the total number of observations at 342.

In order to effectively describe, interpret and model relationships in the data, new

variables were derived from the original input, and for some important variables, missing

values were estimated using available data from surrounding communities. Any

respecifications or extrapolations of data were conducted in a uniform manner. Much of

the data from the 1990 Census contained percentages from categorized survey responses.

In all cases, these percentages were used as weights to compute average values. For the

case of home age, dummy variables indicating the decade of median home age were also

derived. Other variables appeared as a single percentage, such as the racial and

occupational data. Dummy variables were also created for these figures, provided that

the use of percentages in OLS regression creates a bounding problem. In general,

percentage bounds for the dummy variables were assigned close to one standard

13

deviation from the mean. Several variables required considerably more attention.

Excluding the Indiana data, 27 missing values for crime existed, all for communities

outside of Cook and DuPage Counties. Three variables were created to deal with the

missing values. The first variable leaves the missing values as missing, the second

replaces the missing values with reported county averages, while the third estimates the

crime statistic by averaging crime rates from surrounding communities. Equal care was

given to the education variable of ACT scores. The mean ACT scores were supplied by

school district, not by community. Fortunately, in the suburbs, one school district

typically corresponds to one community. However, when a suburban community was

served by more than one school district, the mean ACT scores of the relevant districts

were averaged to arrive at the community statistic. The situation becomes more complex

for the 77 Chicago communities. One school district, including over 60 high schools,

encompasses the entire city. Unlike the suburbs, children are not forced to attend the

closest public school. In fact, there exist a number of magnet schools like Young that

encourage the enrollment of promising students from all over the city. Complicating

matters further, many parents who can afford private schools avoid the Chicago Public

School system. As a result, schools are filled with a much higher percentage of

underprivileged minorities than the surrounding population. Despite the overall

complexity and diminished significance of public education in Chicago, ACT statistics

were retrieved and recorded for each individual school. Under the loose assumption that

families might locate themselves closest to the school in which they intend to enroll their

children, ACT scores were matched with Chicago communities by high school. ACT

values were estimated for communities without a high school by averaging the scores

14

from nearby communities. Therefore, two versions of the ACT proxy variable for quality

of education exist. The first records the school district mean ACT score of 17.3 for all of

the Chicago communities, while the second lists individual high school results with

extrapolation for surrounding community values. For the second variable, ACT statistics

were estimated for 28 out of the 77 communities.

The lack of distance measures for the Chicago communities also merits a final

procedural mention. Within the Tribune data for the suburbs surrounding Chicago,

community measures of area in square miles and distance to the Loop in miles were

listed. These statistics were not included for the Chicago communities. Anticipating

their importance for descriptive and modeling purposes, these values were measured

manually from the Census Tract Reference Maps distributed by the Chicago Association

of Realtors. Other transformations of existing data occurred in order to arrive at

noteworthy statistics or regression friendly data. Any procedures of importance not

previously covered will be mentioned in later sections of this study.

After a good amount of data analysis, any observations containing less than ten

1999 home sales and or less than 2500 population were eliminated to create a new subset

of the data, hereafter entitled adjusted data. This subset was created for several reasons.

First, by eliminating the smallest communities with few home sales, the chance of the

median house data being unrepresentative of true median community home value is

reduced. As mentioned earlier, some of the more sparsely populated outlying suburbs

were combined with bigger suburbs to aggregate sales data. By placing a minimum

constraint on population, and eliminating some of these outlying suburbs, the presence of

duplicated exogenous variables under individually specified community attributes can be

15

reduced for more accurate explanation of variance between communities. Another

rationale involves the reduction of both endogenous and exogenous outlying statistics.

Some community attribute variables are population sensitive, such as the number of

crimes per 1000 residents or the estimate for average lot size, which varies with the

number of housing units. With small populations figured in the denominator of a

statistic, values can become unreasonably large. For instance, the community of Bedford

Park has a population of 535 and a large industrial park. In 1998, the town recorded

approximately 600 crimes, mostly nonviolent property crimes occurring in the park. The

computed statistic of 1127, several standard deviations above the mean, presumably

overestimates the danger placed on the average home owner in this neighborhood. These

problems arise from the misspecification of variables, and can be magnified in small

communities. In that example, the data did not distinguish between violent crime and

industrial crime outside of residential areas. A similar phenomenon can occur for median

home prices in a small residential area. The smaller the community, the more likely the

majority of homes sold can contain a common attribute not contained in or explained by

the data. For analytical and regression purposes, both the complete and adjusted data sets

will be utilized, insuring two perspectives on the Tribune data.

16

DESCRIPTIVES

This section highlights and describes the variables collected from the Tribune

data, as well as studies relationships between variables prior to regression analysis.

Descriptive statistics are displayed for variables from both the complete and adjusted data

set. In order to avoid large ranges created by outlying data points, scatter plots will be

limited to the adjusted data set. In order to achieve consistency, any further graphs,

simple regressions or Pearson correlation statistics will also be derived from the adjusted

data set. Pearson correlation statistics with a significance of .05 or better will be

designated by one asterisk, while .01 or better will be given two asterisks.

Exogenous Variable

Median community home sales prices are at the focus of this study. Actually, the

finalized statistics are the average and weighted average of the quarterly sales prices.

These statistics would differ from true yearly medians. The first computation, not

weighted by quarterly home sales, highlights the fact the quarterly prices are not

averages, and that any quarterly median could be closest to the true median with equal

probability. This variable will be labeled Price1. The weighted average assumes that a

quarter with more home sales is more likely to represent the true yearly median statistic.

When the means of these two variables are compared, the weighted average registers

slightly higher. This is because the quarter with the highest mean number of home sales

also has the highest mean quarterly price figure. This third quarter phenomenon could be

the result of seasonality or supply and demand issues. Descriptive statistics are listed

below.

17

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Price1 168,338 106,282 142,563 15,900 1,011,500 336

Price2 169,006 106,278 143,484 15,900 963,945 336

Adjusted

Price1

163,046 89,085 141,730 24,750 694,125 286

Price2 163,512 89,464 142,178 24,654 700,754 286

Price1 = Average of Quarterly Median Home Sale Prices

Price2 = Average of Quarterly Median Home Sale Prices Weighted by Quarterly Number of Homes Sold

As the dependent variable, the price data is highly correlated with many variables

assumed to affect the price. Price is also correlated with other factors that direct

individual demand levels for home attributes. These include income, years of education,

age, and marital status. The distributions of the price variables are also important to

consider. Statistics for skewness and kurtosis are both well over two, suggesting that

there is little chance that the distribution is normal. A histogram of the non-weighted

average variable (Appendix 1.1) shows that the distribution is skewed to the right. This

identifies the presence of several elite communities where the average of quarterly

median home values is several times the mean average.

Endogenous Variables

For classification purposes, expected hedonic attributes have been placed in four

groups: home attributes, community attributes, inhabitant attributes and indicator

attributes. These groups will resurface in the choice of regression models. The first

group encompasses physical properties of the house. Using all available Tribune data,

four basic variables were created within this category, along with logical derivations.

They include average number of rooms per home, home age, percent of single family

homes and a calculation for number of square feet per housing unit.

18

The first variable of the group, average number of rooms per home, is an obvious

valued home attribute. Unfortunately, the data for this variable is lagged, as derived from

the 1990 census data. Fortunately, the average home structure of a community should not

change much over a decade. The variable still shares a strong correlation with Price1 of

(0.617)**. Descriptive statistics are shown below.

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Rooms In Home 5.70 0.94 5.58 3.36 8.55 337

Rooms Per Person 2.02 0.31 2.02 0.94 2.94 330

Adjusted

Rooms In Home

5.64 0.91 5.53 3.36 8.55 287

Rooms Per Person 2.01 0.30 2.00 0.94 2.84 280

Notice that the descriptive statistics for rooms per person are included in the table above.

Although this variable should not have a direct causal relationship with room prices, it is

highly correlated (0.760)** with median family income, since high income homeowners

demand more space per person. It would be interesting to compare the mean number of

rooms per person with means from different geographical areas.

The transformation of Tribune data for home age to a set of analyzable variables

was much more complicated than for average number of rooms. Again, the data

originated from the 1990 census. Already this presents a problem of censoring. Ideally,

if no homes were built in the ten years since the survey, average home age would just

increase by ten. However, new homes have been built. This provides the freedom for

average home age to increase by less than ten or even decrease in a rapidly expanding

community. The question for determining whether the lagged values for home age are

adequate is whether or not home construction and has been fairly uniform across

communities. The answer is no. Another problem lies at the other end of the home age

19

spectrum. In order to display home age, the census survey lists period ranges, usually by

decade, along with the percent of homes built within that period. The earliest period is

listed as 1939 or earlier. This introduces a problem of left censoring. While the other

periods have a ten year range, the range for the earliest period is much greater. The

statistic for home age was calculated by the weighted average of the upper bounds of

these periods. Clearly this could underestimate the average home age in a community

with a number of homes built in the early 20th

century, or even the 1800's. In order to

correct for this left censoring, a series of dummy variables indicating median period of

home construction as of 1990 was created and will be considered in regression models.

Overall the variables for home age leave much to be desired and contain a possible bias

for comminutes with large quantities of home construction in the past 10 years.

Considering the available data, however, they are the best approximations of true

community home age. Descriptive statistics for the average home age as of 1990, using

upper decade bounds of the census, are listed below.

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Average Home Age 25.78 10.08 25.60 6.02 48.05 337

Adjusted

Average Home Age 25.64 10.09 25.60 6.02 48.05 287

Average home age is slightly yet significantly negatively correlated (-0.172)** with

Price1. This supports the reasonable assumption that newer homes are worth more.

Hedonic analysis will determine whether the age of the home itself or other attributes that

are correlated with the age of the home contribute to the variance in home price. This

appears interesting because several variables, including education (-0.601)**, average

20

number of rooms (-0.43)** and percent minority (0.474)** are all more highly correlated

with home age than price. Another correlation (-0.585)** suggests that average home

age decreases as communities move further from the loop. This supports the claim that

new home construction is most likely not uniform across communities.

The percentage of single family units in a community is an interesting variable to

study because of its high correlation with many other variables. Logically, this variable

is positively correlated with Price1 (0.361)**. However, there is a much stronger

correlation between this variable and the average number of rooms in a housing unit

(0.789)**. A scatter plot of these two variables can be found in Appendix 1.2. Basically,

the average home size in a community closely approximates the percentage of single

family units. This could present problems if both variables are included in a model of

price estimation. Descriptive statistics are found below.

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Percentage of Single

Family Units

.692 .210 .739 .019 .993 337

Adjusted

Percentage of Single

Family Units

.686 .206 .730 .019 .990 287

The final physical attribute variable was computed using two of the Tribune

variables in an attempt to approximate lot size. Unfortunately, no lot size data was

directly available. The statistic was derived by dividing the data for the area of the

community by the number of housing units in the community as of 1999. The area,

which had been provided in square miles, was converted to square feet. This statistic is

inferior to an actual measure of average lot size because the percentage of land devoted to

21

residential zoning is unknown among the communities. Even if this percentage is fairly

constant among communities, space unoccupied by homes is generally unaccounted for.

Certainly a large space containing a park will have a different effect on home values

when compared to a space devoted to a garbage dump or a chemical plant. Despite its

shortcomings, this variable does contain some explanatory power. As expected, the

number of square feet per housing unit is positively correlated with Price1 (0.236)**.

There is also a positive correlation with the distance to the Loop (0.387)**, suggesting

that housing density decreases as communities get further from the city. Descriptive

statistics are displayed below.

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Number of Square

Feet Per Housing

Unit

87,507 470,485 22,026 1,754 8,131,200 330

Adjusted

Number of Square

Feet Per Housing

Unit

34,131 62,238 20,063 1,754 612,419 280

The next group of attributes provided by the Tribune data, entitled community

attributes, differs from the previous set because the attributes are independent of the

physical characteristics of properties within the community. However, this study intends

to show that these attributes still significantly contribute to median home values among

communities. Each of the four major variables in this group represent a community

characteristic. ACT scores are studied to estimate the quality of public education within

a community, while crime rates should measure safety. Distance to the Loop represents

the ease of access to all the benefits of downtown Chicago, including employment and

social opportunities. Finally, a measure for the number of places of worship per thousand

22

residents may provide a loose estimate for family values and family structure as well as

camaraderie within a community.

The derivation of the ACT statistics was explained in the previous section. For

this study, ACT scores are a great measure of public education because they are

standardized across communities. However, it must be noted that public education is not

the only factor attributed to the level of ACT achievement. Parental influence is critical

for a child's success at school. The significant correlation between ACT scores and

median years of school completed within a community shows this (0.606)** Just as

public education cannot account for all of the results on ACT tests, the tests cannot reveal

the entire level of educational quality at any school. Mean ACT scores are negatively

correlated with the percentage of minorities in a community (-0.644)**, even though

educational spending per student is not dictated by race. Lower percentages of two

parent homes and lower parental education levels contribute to the decreased

performance of minorities on ACT tests as much as inadequate schools. Despite this, the

ACT scores provide good insight into a parent's perception of the quality of education in

a community. This will ultimately affect median home values. The correlation between

ACT scores and Price1 shows a significant relationship between the two variables

(0.557)**. Descriptive statistics can be found below.

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

ACT1 20.87 2.57 21.6 16.7 26.2 338

ACT2 20.65 2.98 21.6 14.0 26.2 342

Adjusted

ACT1 20.69 2.60 21.3 16.7 26.2 287

ACT2 20.45 3.02 21.3 14.0 26.2 288

ACT1 = Mean ACT Composite Score (Chicago Communities Treated as One District)

ACT2 = Mean ACT Composite Score (Chicago Communities By Individual Schools - Extrapolated Data)

23

Just as consumers are concerned with education levels, they are also interested in

safety levels. As mentioned earlier, the Tribune crime data measures total crimes

committed in 1998 per 1000 residents. Although reported crime is clearly a measure of

safety, the data does not distinguish between violent crime and property crime. There is

also no distinction between crime in residential areas, opposed to industrial or

commercial areas. These different types of crime might affect a resident's perception of

safety in different ways that cannot be accounted for in the data. Interestingly, crime is

not nearly as correlated with Price1 as many of the endogenous variables (-0.193)**.

There are much higher correlation statistics between crime and percent minority

(0.513)** and average number of rooms per housing unit (-0.503)**. This relationship is

of particular interest and is shown in a scatter plot in Appendix 1.3. There are many

speculative reasons why this relationship might exist. Communities with large homes

may be more likely to have a higher percentage of residential zoning, limiting crime

against industrial and commercial properties. Also larger homes tend to have bigger

yards and better security, inhibiting stealthy movement. The descriptive statistics for the

crime variables can be found below.

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Crime1 54.88 79.82 39 0 1127 315

Crime2 53.05 76.88 36 0 1127 342

Crime3 52.57 77.04 35 0 1127 342

Adjusted

Crime1 51.11 49.55 40 4 615 280

Crime2 50.55 48.97 39 4 615 288

Crime3 50.46 49.04 39 4 615 288

Crime1 = Crimes Per 1000 Residents (Missing Values)

Crime2 = Crimes Per 1000 Residents (Missing Values Filled With County Averages)

Crime3 = Crimes Per 1000 Residents (Missing Values Filled With Extrapolated Values)

24

The variable for the distance to the Loop is of particular interest because there is

no significant correlation between it and Price1. However, it seems logical that all other

attributes equal, median home prices should decrease as communities distance

themselves from downtown Chicago. It will be interesting to discover the attribute price

assigned to this variable in the hedonic model. Not surprisingly, distance to the Loop is

highly correlated with average home age (-0.585)**. Descriptive statistics are listed

below.

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Distance to Loop 26.18 16.24 23 0 73 342

Adjusted

Distance to Loop 23.76 14.73 21.5 0 70 288

Finally, the number of parks per 1000 residents and places of worship per 1000

residents were measured in order to estimate the 'family atmosphere' of a community.

The Tribune data listed information on parks and worship areas for each community.

These were tallied and divided by the 1999 population and multiplied by 1000.

Unfortunately, parks were only listed for Chicago communities and the variable could not

be utilized in subsequent models. The parks variable is positively correlated with Price1

(0.251)*. After reviewing the data for places of worship in a community, their effect

home prices is not quite clear. It seems that many places of worship per capita should be

considered a positive attribute. However, many of the most poverty stricken

communities have an abundance of churches. Obviously they are not the cause of this

despair, but the result of it. As a result, there seems to be no clear linear relationship

25

between the places of worship variable and Price1. A scatter plot found in appendix 1.4

displays this. Descriptive statistics are listed below.

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Parks per 1000

Population (1999)

.2294 .1496 .1935 .00 .83 72

Places of Worship

Per 1000 Population

(1999)

.8360 .9685 .5650 .00 7.63 332

Adjusted

Parks per 1000

Population (1999)

.2114 .1237 .1831 .00 .62 68

Places of Worship

Per 1000 Population

(1999)

.7372 .5680 .5980 .00 3.63 282

The third set of variables was grouped as inhabitant attributes. This group of

variables differs from the first two because the direct bearings of these attributes on home

values are questionable. Included in this group are race and occupation. The rationale

behind the inclusion of this group of variables in this study and ensuing hedonic models

relies on the assumption that home owners choose to locate themselves in communities

containing residents of similar background, occupation and race in order to feel

comfortable and sociable. Out of several listed occupations, managerial positions were

chosen to most likely represent white collar lifestyle, while factory positions were to

represent blue collar lifestyle. The descriptive statistics for both race and occupation

variables are listed below.

26

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Percent African Amer .1459 .2900 .0100 .0000 .9940 337

Percent Hispanic .0722 .1199 .0280 .0000 .8780 337

Percent Other .0283 .0436 .0160 .0000 .0521 337

Percent Minority .2463 .3024 .1010 .0000 .9990 337

Adjusted

Percent African Amer .1520 .2893 .0140 .0000 .9910 287

Percent Hispanic .0787 .1266 .0310 .0000 .8780 287

Percent Other .0295 .0356 .0180 .0000 .2410 287

Percent Minority .2601 .3002 .1110 .0020 .9990 287

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Managerial Positions .2823 .1308 .2530 .0440 .6690 337

Factory Positions .0615 .0438 .0530 .0000 .2660 337

Adjusted

Managerial Positions .2851 .1264 .2590 .0740 .6290 287

Factory Positions .0614 .0436 .0530 .0010 .2660 287

27

THE MODEL

The main objective of this hedonic pricing model is to estimate what attributes are

actually incorporated into home values, and to what extent they explain the variation in

median home prices by community. This model differs from most previous analyses as it

only attempts to explain variance of home prices between communities, not within them.

Hopefully, this unique level of aggregation will provide a new and interesting twist to an

old and popular subject of analysis.

It is also important to realize that this regression analysis is an approximation to

an ideal hedonic model. A hedonic model as described by Sheppard (1999) allows for

freedom in individual consumers' preferences and their corresponding utility functions.

The hedonic model also estimates housing demand and equates it with supply before

arriving at price estimation. Although this model should reveal home and community

attributes that significantly affect median community housing prices, it is considerably

constrained from a perfect hedonic model. There are two important assumptions that

should hold true for the success of this model:

1. Sales events are randomly distributed throughout homes in a community

2. Home values are summations of attribute values. There exists no declining

marginal utility of attributes.

The first assumption is important because the sales data that generate the median home

sale prices for the communities are not directly paired with the data that generate the

explanatory variables. The sample of homes for the sales data is different from the

sample of homes that represent the attribute data within a community. Therefore it is

28

imperative that one sample is representative of the other. For instance, if a new housing

division within a community represents 60 percent of the home sales but only 15 percent

of the homes, there is likely to be error. The relationship between variables in the model

and the true community relationship between home price and attribute quantity may

differ because community attributes are not representative of the sample of homes sold.

The second assumption addresses the constraints of linear regression.. For this OLS

model to be effective, consumers' utilities must closely follow a simple summation of

attributes. It is possible to apply a functional form to a variable, but unlikely that a linear

function can closely approximate a complex utility function.

During the actual regression process, over fifty models were analyzed. These

models varied between several factors:

1. The use of both the complete and adjusted data sets.

2. The use of average median price, weighted average median price, and the

natural log of these prices.

3. The inclusion and removal of different variables.

4. The use of different specifications of the same variable, as in crime and

ACT variables.

5. The use of different functional forms

6. The use of weighted least squares estimation

Two variables were removed in order to avoid colinearity. A threshold correlation of .75

was established and the home attribute variable for single family housing had a

correlation statistic of (0.789)** with the average number of rooms, while the dummy

variable for Chicago community was too negatively correlated (-0.79)** with the variable

29

for average ACT score. The majority of models were fairly consistent concerning the

variables of significance and directional effect. A set of models was chosen from the

others because of its simple, straightforward nature, and powerful results. The set of

models regresses an incrementally increasing group of variables against Price1. The

models placed variables in the groups previously introduced. The group of Home

Attributes contains Average Number of Rooms in Housing Unit, Average Home Age as

of 1990 (Using upper Decade Bounds of Census), and Number of Square Feet per

Community Housing Unit (1999), with dummy variables for level of Single Family

Units omitted. The second group, entitled Community Attributes, contains the variables

ACT1 (Chicago communities counted as one district), Distance from Loop, Crime

3

(Extrapolated Missing Values) and Places of Worship per 1000 Population. The next

group contains Inhabitant Attribute Variables, all of which are dummy variables

calculated from percentages. This group includes both occupational and racial attributes.

There is a dummy for Percent Managerial Occupation <= 15% and Percent Managerial

Occupation >= 40%, with >15% < 40% as control values. Another occupational dummy

accounts for the percent of factory workers in a community; Percent of Factory Workers

>= 15% with < 15% as the control. Racial dummies include Percent African American

>= 10% < 90%, Percent African American >= 90% with < 10% as a control and Percent

Hispanic >= 10% with < 10% as a control. The final group contains an indicator variable

called North Shore Effect. This is a dummy variable that incorporates four North Shore

communities that feed into New Trier High School. Median home prices for these

communities are extremely high. Without this indicator variable, the model cannot really

30

account for the large deviation in the prices of these homes. The regression results are

listed below.

31

Variable Coefficients and T Statistics of Regressions Against Price1

MODEL 1 2 3 4

Constant -291,350.3 584,021.3 -325,507.5 -140,233.7

(-7.561)** (-11.6)** (-5.458)** (-2.484)*

Hom

e

Att

ribute

s

Rooms 74,007.592 50,890.765 31,464.323 26,124.75

(13.426)** (8.425)** (4.910)** (4.582)**

Home Age 1,528.101 2,313.218 2,160.187 800.597

(2.99)** (4.283)** (3.985)** (1.596)

Square Feet 0.002877 0.007671 0.0002837 0.004787

(0.279) (0.825) (0.033) (0.624)

Com

munit

y

Att

ribute

s

Distance to Loop - -1,906.069 -1,208.848 -878.804

(-5.218)** (-3.248)** (-2.652)**

Crime - 2.167 5.092 15.079

(0.037) (0.093) (.0.312)

ACT - 21,946.031 13,771.243 7,383.63

(8.876)** (5.238)** (3.042)**

Places of Worship - -6,382.023 -2.068.652 -1,287.826

(-1.253) (-0.4) (-0.281)

Inhab

itan

t

Att

ribute

s

Low Managerial - - -41,590.288 -42,781.206

(-2.714)** (-3.154)**

High Managerial - - 85,878.798 87,171.531

(6.768)** (7.761)**

High Factory - - 2,556.501 4,234.95

(0.177) (0.331)

Middle African Amer - - -33,835.188 -40,537.345

(-2.900)** (-3.915)**

High African American - - -28,771.233 -38,292.485

(-1.454) (-2.183)*

High Hispanic - - 1,065.53 5,057.242

(0.080) (0.427)

North Shore Effect - - - 320,167.46

(9.266)**

Adjusted R Square 0.371 0.513 0.587 0.676

F Statistic (64.011)** (49.211)** (35.951)** (48.742)**

Incremental F - (24.111)** (10.274)** (85.852)**

32

Results of a regression of the same set of models against Ln(Price1) can be found in

Appendix 2.1.

Overall, these models appear to be successful and informative. The F statistic is

significant at the .000 level for each model, indicating that there is less than a one in

10,000 chance that these models explain none of the variance in Price1. The incremental

F statistics for the last three models are also significant at the .000 level, indicating that

there is less than a one in 10,000 chance that each additional model explains no more

variance than the model preceding it. The adjusted R squared statistic for each successive

model increases as more explanatory variables are added. In the final model, over 65

percent of the total variance Price1 is accounted for.

Overview of Regression Coefficients

The directional effect of significant variables on Price1 are as expected other than

the fact that the first three models show Price1 increasing with home age. This might be

explained by the fact that some of the priciest communities contain refurbished vintage

homes and are often located on expensive land. This theory is supported when the

variable for home age losses significance in the fourth model when the North Shore effect

is introduced. The North Shore effect 'steals' explanatory value from the average home

age variable. These communities all contain older homes that have been upgraded over

the years. This model lacks a variable for amount of home quality improvements within

a community. This is an attribute that may not be well recorded or hard to standardize.

Also, due to a suspiciously high correlation statistics among most of the explanatory

variables, multicollinearity may be at hand for any deviations from expected results.

33

As expected, the variable for number of rooms is significant and positive,

although it losses explanatory power in each new model as more variables are introduced.

The variable for community square feet per housing unit, which is supposed to be a proxy

for lot size, is not significant. This could be the cause of poor variable specification. The

variable fails to account for zoning within a community. It is possible and probable for

communities with similar square feet per housing unit estimates to have completely

different lot sizes.

For the community attributes, the ACT and distance to loop variables are

significant as expected. The insignificance of the crime variable is puzzling. It seems

obvious that home values should be lower in crime prevalent communities. Possibly the

measurement of crime is too inadequate and the true crime induced variance in home

prices is explained by other correlated variables, such as race or even home size. The

crime variable also fails to distinguish between violent and property crime, although they

have different impacts on a home owner's estimation of safety. A final problem with the

crime variable might be underreporting of crime in the worst neighborhoods .

For the inhabitant attributes, the percent of residents with a managerial occupation

seems to be very significant in explaining variance in community home prices. The

occupational variables assume that home owners will choose to locate in a community

that provides access to their job type and other people sharing similar occupational and

lifestyle interests. However, the cause/effect relationship between home prices and

managerial occupation may be somewhat unclear. Perhaps a managerial occupation is

just a proxy for income and the model is displaying the fact that families with higher

income will buy homes in more expensive communities. The negative effects of a high

34

percentage of African American inhabitants coupled with insignificant effects of

Hispanic inhabitants is another interesting phenomenon. Perhaps the actual effects of

racial prejudice are really insignificant and a high percentage of African American

inhabitants is just a proxy for truly significant community attributes such as

unemployment, education, income, crime, or even redlining. Finally the significance of

the North Shore effect is apparent in the fourth model. This variable eliminates a large

amount of the unexplained residual error present in the previous model from the four

outlying communities of Wilmette, Winnetka, Glencoe and Kenilworth. These

communities must possess high quantities of some attribute that has not been specified or

was not adequately measured by the Tribune data.

35

PROBLEMS WITH HETEROSCEDASTICITY AND MODEL SPECIFICATIONS

Simple histograms and scatter plots of variables provide suspicion that many of

the variables in this study are not normally distributed, and there are not many clearly

linear relationships between variables. Many variables have outlying data that are

difficult to account for. Sets of variables are highly correlated, questioning a hierarchy of

dependency. In general, the Tribune data and this model draw attention to several of the

assumptions of least-squares regression. Problems of this nature are not uncommon

when dealing with pricing models. This excerpt comes from Sheppard:

Estimation of hedonic prices confronts the economist with a rich sampling

of the standard difficulties that arise in estimation using cross-section data.

These include choices of the proper parametric specification--both of

functional form and of variables to be included--coping with collinearity

and ill-conditioned data, potential heteroscedastic and nonnormal errors,

regressors subject to measurement error, and maximum likelihood

estimation of relationships that are nonlinear. (Sheppard 1614)

One major concern is the presence of heteroscedasticity in the model. By simply

graphing the squared residuals against each explanatory variable, it is difficult to discern

a definite linear relationship. An example is given in Appendix 1.5. However, several

outlying points are a cause for concern. Tests for heteroscedasticity were performed for

several of the models. Using the Breush-Pagan Test, Chi-squared statistics were

generated. Of all the models, the lowest Chi-square value was 65, still highly significant

with the degrees of freedom allowed by the model. After trying the adjusted data,

logarithmic relationships and even least squares weighted by housing units, the presence

of heteroscedasticity seems likely. This presents problems for the regression estimates.

Heteroscedasticity affects models in several ways. First, the OLS estimates are still

36

unbiased and consistent, but they are no longer efficient. This means that another

unbiased linear estimate that has lower variance than the OLS estimate may exist. Also,

variance estimates of the coefficients are no longer valid. They are biased and

inconsistent. This renders hypothesis tests such as F and T tests invalid. Although the

presence of heteroscedasticity should not nullify the findings of this study, it does raise

larger questions of a linear model's overall ability to estimate hedonic functions.

37

CONCLUSION

This study attempts to quantitatively explain median community home prices in

the Chicago area using hedonic analysis. It evaluates whether median community home

prices can be expressed as composite prices of values assigned to varying quantities of

underlying attributes. A linear model was constructed in order to value attributes’

expected to influence home prices. These attributes were derived from aggregated

community data available through the Chicago Tribune Homes web site. Attributes were

divided into home, community and inhabitant groups and a seemingly successful model

was generated using least squares regression. The Adjusted R-squared statistic for the

full model is (0.676), suggesting that the majority of the variance in median home prices

can be explained by the model. However, the success of the model is threatened by the

assumptions that were used to generate it. The marginal utility and corresponding impact

on overall price is unlikely to remain constant as the quantity varies for some attributes

analyzed in the study.

38

Appendix 1.1

Histogram of Price1

AVGPRICE

3325000275000 .0

225000 .0

175000.0

125000 .0

75000 .0

25000.0

675000 .0

625000.0

575000 .0

525000.0

475000 .0

425000 .0

375000 .00 .0

70

60

50

40

30

20

10

0

Std. Dev = 89085 .16

Mean = 163046.4

N = 286.00

39

Appendix 1.2

Average Number of Rooms in Housing Unit

9876543

Percentage of Single Family Units

1.0

.8

.6

.4

.2

0.0

Park City

Lake Forest

South Barrington

West Garfield Park

Uptown

Near South side

40

Appendix 1.3

Average Number of Rooms in Housing Unit

9876543

Cri

me with Extrapolated Values

700

600

500

400

300

200

100

0

-100

Oak Brook

MattesonBroadv iew

O'Hare

Near West Side

Loop

41

Appendix 1.4

Places of Worship per 1000 Population (1999)

43210-1

AVGPRICE

700000

600000

500000

400000

300000

200000

100000

0

Riverwoods

Barrington

Robbins

Glencoe

Englewood

42

Appendix 1.5

Residuals taken from featured regression Model 4

Average Number of Rooms

9876543

Squared

Residuals

39999999000

0

29999999000

0

19999999000

0

9999999700

0

0

-

99999990000

Lake Forest

Bannockburn

Kenilworth

43

Appendix 2.1

Variable Coefficients and T Statistics of Regressions Against Ln(Price1)

MODEL 1 2 3 4

Constant 10.108 8.659 10.530 10.882

(54.221)** (36.042)** (42.787)** (42.275)**

Hom

e

Att

ribute

s

Rooms 0.313 0.180 0.08957 0.07942

(11.754)** (6.256)** (3.387)** (3.055)**

Home Age 4.144E-04 6.955E-03 5.112E-03 2.529E-03

(0.167) (2.699)** (2.285)* (1.105)

Square Feet 3.493E-08 4.518E-08 8.400E-09 1.696E-08

(0.701) (1.018) (0.235) (0.485)

Com

munit

y

Att

ribute

s

Distance to Loop - -6.800E-03 -4.667E-03 -4.040E-03

(-3.900)** (-3.036)** (-2.674)**

Crime - -2.467E-04 -5.139E-05 -3.242E-05

(-0.884) (-0.228) (-0.147)

ACT - 0.110 0.04371 0.03158

(9.283)** (4.029)** (2.853)**

Places of Worship - -0.07237 -0.01106 -9.574E-03

(-2.977)** (-0.518) (-0.459)

Inhab

itan

t

Att

ribute

s

Low Managerial - - -0.424 -0.426

(-6.704)** (-6.890)**

High Managerial - - 0.431 0.434

(8.239)** (8.471)**

High Factory - - 0.06613 0.06932

(1.109) (1.189)

Middle Black - - -0.334 -0.346

(-6.926)** (-7.334)**

High Black - - -0.531 -0.549

(-6.496)** (-6.857)**

High Hispanic - - -6.527E-06 7.578E-03

(0.000) (0.140)

North Shore Effect - - - 0.608

(3.860)**

Adjusted R Square 0.338 0.501 0.683 0.697

F Statistic (55.431)** (46.941)** (54.109)** (53.584)**

Incremental F - (26.956)** (30.989)** (14.902)**

44

Appendix 3.1

OTHER INTERESTING VARIABLES

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Households 1999 7,685.66 8,263.60 4983 24 54,935 330

Population 1999 21,297.48 21,908.49 14,124 71 124,321 330

Increase1 .1649 .3276 .0716 -.3499 3.0857 251

Increase2 .1674 .3246 .0713 -.293 3.028 250

People per Household 2.85 .39 2.81 1.69 5.33 330

Adjusted

Households 1999 8,933.93 8,370.02 6586 864 54,935 280

Population 1999 24,743.63 22,047.62 18,119 2,705 124,321 280

Increase1 .1723 .3458 .0753 -.3499 3.0857 207

Increase2 .1766 .3416 .0764 -.293 3.028 206

People per Household 2.84 .39 2.80 1.69 5.33 280

Increase1 = Percent Increase in Households From 1990 to 1999

Increase2 = Percent Increase in Population From 1990 to 1999

Mean Standard

Deviation

Median Minimum Maximum Valid N

Complete

Family Income 75,841.12 42,579.82 64,313.50 8,944.00 256,359.00 330

Never Married .2735 .0822 .2520 .1370 .5550 337

Median Age 36.21 4.78 36.10 21.30 49.50 330

Adjusted

Family Income

75,862.20 40,409.22 65,894.50 11,189.00 256,359.00 280

Never Married .2767 .0797 .2560 .1600 .5550 287

Median Age 36.22 4.57 36.10 21.30 49.50 280

45

REFERENCES

Cited

Chicago Tribune. http://cgi.chicago.tribune.com/homes. 2000.

Sheppard, Stephen. "Hedonic Analysis of Housing Markets." Handbook of Regional

and Urban Economics. Elsevier Science B.V., 1999. 1595-1635.

Not Cited

Asabere, Paul K., and Forrest E. Huffman. "Price Determinants of Foreclosed Urban

Land." Urban Studies 29 (1992): 701-707.

Bednarz, Robert S. The Effect of Air pollution on Property Value in Chicago. Chicago:

The University of Chicago, 1975.

Bloom, George F., and Henry S. Harrison. Appraising the Single Family Residence.

Chicago: American Institute of Real Estate Appraisers, 1978.

Carn, Neil, et al. Real Estate Market Analysis: Techniques & Applications. New Jersey:

Prentice Hall, 1988.

Lawrence, Roderick J. "Housing Quality: An Agenda for Research." Urban Studies 32

(1995): 1655-1664.

Mills, Edwin S. "New Hedonic Estimates of Regional Constant Quality House Prices."

Journal of Urban Economics 39 (1996): 209-215.

46

Paris, Chris. "Demographic Aspects of Social Change: Implications for Strategic

Housing Policy." Urban Studies 32 (1995): 1623-1643.

Peek, J., and J. Wilcox. "The measurement and determinants of single-family house

prices." AREUEA Journal 19 (1991):353-382.

Ring, Alfred A. The Valuation of Real Estate: Second Edition. New Jersey: Prentice

Hall, 1970.