111Equation Chapter 1 Section 1

Sorting in the Housing Market Surrounding Disamenities: The Case of Leaking

Underground Storage Tanks

By

Hans R. Isaksona*

And

Mark D. Eckerb

March 29, 2012

a Department of EconomicsUniversity of Northern Iowa

b Department of MathematicsUniversity of Northern Iowa

*Contact Author: Hans R. IsaksonProfessorDepartment of EconomicsUniversity of Northern IowaCedar Falls, Iowa 50614-0129Hans.isakson@uni.eduVoice: 319-273-2950Fax: 319-273-2922

Keywords: sorting, housing markets, disamenities, leaking underground storage tanks, spatial correlation, maximum likelihood

JEL Codes: Q51, Q53, R21

Running Title: Housing Market Sorting

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Abstract

This study examines the housing market surrounding sites with leaking underground

storage tanks (LUSTs) for the presence of sorting by the degree of households’ aversion

to living near a LUST. Using housing sales, Census, and LUST data, we estimate the

coefficients of a Rosen/Lancaster hedonic model, correcting for spatial correlation by

using a maximum likelihood regression technique. The results reveal that households

located within ¼ miles of a LUST have little or no aversion to living near a LUST, while

households located more than ¼ mile from a LUST are willing to pay a premium to live

further away from it.

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Sorting in the Housing Market Surrounding Disamenities: The Case of Leaking

Underground Storage Tanks

1. Introduction

The notion of sorting in housing markets was introduced by Tiebout (1956) in his well-

known answer to Samuelson’s (1954 and 1955) observation that, because people will not

reveal their true preferences for public goods (they would rather be “free-riders”), public

goods will be undersupplied by government. In the Tiebout model, households reveal

their preferences for local public goods by where they choose to live. Hamilton (1975)

extended the Tiebout model to include the use of zoning to solve a free-rider problem in

the Tiebout model when the local public goods are financed using a property tax

(households consuming low amounts of housing to lower their property taxes). Others

have presented similar models of sorting in which household locational decisions reveal

their preferences in markets for public education (Bogert and Cromwell (1997)), labor

(Wheeler (2001)), credit (Besanko and Thakor (1987), and insurance (Borenstein (1989).

Sorting happens in housing markets because when buyers purchase a house, they are also

buying into a particular location (school district, neighborhood, etc.).

Housing markets surrounding disamenities have been studied by many. In their

meta-analysis of 58 peer reviewed journal articles that focus on housing markets

surrounding disamenities, Simons and Saginor (2006) report that nearly all of these

studies find a positively sloped house-price gradient with increasing distance away from a

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disamenity. That is, house values, holding other things constant, increase with increasing

distance away from the disamenity. In locational equilibrium, households are indifferent

with respect to how far away they live from a particular disamenity, because they are

compensated for living near a disamenity with lower house prices, other things held

constant. These studies implicitly assume that the house-price gradient (change in price

per unit distance away from the disamenity) is the same for all households.

This study allows households’ tastes for living near a disamenity to vary.

Specifically, we hypothesize that some households may have a very low aversion, while

others have a high aversion, to living near a disamenity. If low aversion households are

sufficient in number, then the house-price-gradient will contain a break-point

corresponding to the point at which the high aversion households out-bid the low

aversion households for housing. In addition, the house-price-gradient for the low

aversion households will lie above the house-price gradient for the high aversion

households at locations near the disamenity. When these conditions are met, competition

sorts the households according to their aversion to living near the disamenity, with low

aversion households living closer to the disamenity, and households with high aversion

live further away from it.

We expect that sorting around relatively mild disamenities will be more evident

than around severe disamenities, because it is more likely to find a large number of

households willing to live near a mild disamenity than a severe one. Thus, the logical

place to look for sorting of the type described above is around relatively mild

disamenities. Simons, Bowen and Sementelli (1997 and 1999) and Simons and

Sementelli (1997) have previously reported finding mild disamenity effects near leaking

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underground storage tanks (LUST) sites, so LUST sites can represent the type of mild

disamenity around which sorting might occur1. In addition, LUST sites are typically not

found in clusters along with other types of commercial/industrial land uses. An

interesting feature of LUSTs in urban areas is that that they are almost always found

under aging, poorly maintained, commercial buildings, especially gasoline stations.

Indeed, households might consider an aging, poorly maintained, commercial building a

disamenity all by itself. Although some types of commercial land uses cluster

(automobile dealerships, restaurants), gasoline stations (selling a convenience good) tend

not to cluster in particular locations. Because the observed condition of the building

might be a proxy for the unobservable condition of the LUST under it, a disamenity

affect might be due to the condition of the LUST or the condition of the building above it

or some combination of both. Separating these two effects would be difficult, at best.

But, for the purposes of this study, this separation is not necessary. We identify mild

disamenities (LUSTS) that are located in residential neighborhoods around which sorting

might occur. LUSTs, especially gasoline stations, represent an excellent type of

disamenity for testing the theory that households reveal the extent of their aversion to a

disamenity by the price they are willing to pay to live closer or farther from it.

2. Previous Studies of LUSTs

Others have found disamenity effects near LUSTs in housing sales data. Simons, Bowen

and Sementelli (1997 and 1999) provide insight into the impact of LUSTs (and non-

leaking USTs) on property values in Cuyahoga County, Ohio (Cleveland). Although they

do not look at the impact on nearby property values, Simons and Sementelli (1997) report

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that (commercial) LUST sites suffer in terms of salability and financing, making them

less than one-half as liquid (ability to convert into cash) than clean, comparable

commercial sites in Cleveland, Ohio. In another study, Simons, et al (1997) find about a

17% decline in the selling prices of 83 houses within 300 feet of a LUST site in

Cleveland, Ohio. Using the same data as their earlier study, Simons, et al (1999) report a

14% to 16% reduction in houses values within 300 feet of a gas station LUST site.

In a National Center for Environmental Economics (NCEE) study, Zabel and

Guignet (2010) test for a disamenity effect in houses that use well water near LUSTs and

report that proximity to a more publicized and more contaminated site can impact

surrounding home values by more than 10 percent. But, they also find that many LUSTs,

especially the less contaminated sites, have little (negative) impact on surrounding house

values.

Although they do not study LUSTs, Page and Rabinowitz (1993) study the effects

of groundwater contamination on property values. They compare rural residential

properties using well water with and without groundwater contamination and find no

difference in their prices. Dotzour (1997) examines the sales of houses near Wichita,

Kansas before and after the discovery of groundwater contamination and report no

significant differences in property values.

The findings from Zabel and Guignet, Page and Rabinowitz, and Dotzour suggest

that sometimes proximity to a disamenity may not be capitalized into lower house values,

while the Simon, et. al. studies suggest otherwise. Sorting can explain why an adverse

effect associated with proximity to a disamenity is not observed in areas close to it, yet an

adverse effect is found further away from it. If no allowances are made for the sorting,

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the influence of one group of households can weaken or even wash-out the influence of

another group of households.

3. The Theoretical Framework

Suppose that the households in a particular city (We focus on a single city to hold any

differences in preferences for local public goods and property tax rates constant.) are of

two types (1) those with an high aversion to living near a LUST, which we shall call High

Aversion Households (HAH) and (2) those with a low aversion to living near a LUST,

which we shall call Low Aversion Households (LAH). We will also assume that the

housing market in this city is competitive, so that houses sell to the highest bidder.

Now, consider the maximum price a household is willing to pay for a

standardized house2 located a particular distance from the nearest LUST. We shall call

the relationship between this maximum price and proximity to a LUST the house price-

bid function or HPBF. As long as proximity to a LUST is undesirable, we expect in

general that the HPBF will increase with distance away from a LUST. That is, in

general, households bid less on houses that are close to a LUST than houses that are

further away from a LUST. Virtually all studies of housing prices near a potential point

source disamenity employ this type of theoretical framework.

We refine this framework by postulating that LAHs will outbid HAHs for houses

located near a LUST. That is, near a LUST, the LAH HPBF lies above the HAH HPBF.

But, at some point, which we shall call d*, HAH will outbid LAH for housing. That is,

eventually all of the LAH will have purchased a house near a LUST, and HAH will start

to compete with each other for houses further away from the LUST. Thus, the HPBF for

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LAH will be flatter than the HPBF for LAH and the HPBFs will intersect at some

specific distance (d*) away from the nearest LUST.

Whether the HPBF intersect depends upon two factors: (1) the number of the

LAH and (2) the extent of the difference in the slopes of their HBPFs. Of course, the

second factor is driven by the difference in the aversion between the LAH and HAH.

The larger this difference, the greater the difference in their respective HBPF slopes.

Given a sufficient number of LAH and a significant difference in their degree of

aversion to living near a LUST, we can portray their HPBFs as shown in Figure 1.

Because HAH are much more averse to living near a LUST, LAH outbid HAH for any

houses that are adjacent to a LUST and as far away as d* from the LUST. Beyond d*,

HAH outbid LAH for houses, because LAH are not willing to pay the premium that HAH

are willing to pay to live further away from a LUST. The result is that competition in the

housing market will sort households around LUSTs with the LAH living nearer to a

LUST than the HAH.

Unfortunately, the entire HPBFs of the LAH and HAH cannot be observed. All

we can observe is the house-price gradient created by the highest HPBFs. If the sorting

process described above is actually present, then we should find a break-point in this

house-price gradient at d*. So, the question of whether or not sorting occurs is an

empirical question. If sufficient LAH are present in the market, then the effects of

sorting should be observable in the house-price gradients around LUSTs. But, it turns out

that formally testing for the presence of a break-point in the house-price gradient around

LUSTs is not trivial. The challenges of testing for the presence of this break-point are

discussed in the Empirical Model section.

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4. The Study Area and Data

This study uses data from Cedar Falls, Iowa, a medium sized, Midwestern college town.

The college (University of Northern Iowa) has about 13,000 students, over 95% of which

live on or very near campus. The city has two junior high schools and several elementary

schools of nearly equivalent quality that feed students into the city’s only public high

school. The average commute time is only 14 minutes. The city is highly decentralized.

There is no dominant destination point, such as a central business district. Instead, jobs

and retail shops are disbursed throughout the city. Preliminary analysis of the data

reveals that premiums are not paid to gain proximity to any particular site in the city

(including the college), largely due, we suspect, to the short commute times from one

point to another within the city. Several small retail strip malls exist as well as a

downtown area containing several restaurants, retail shops, banks, a small hotel, and a

small theater. The downtown area is within a mile of the city’s sewage treatment plant

(STP), a source of occasional noxious odors depending on weather conditions. The city

has a newer (1995) industrial park containing primarily warehouses on its far south side

that is home to various, very low polluting industries.

4.1 Housing Sales and Census Data

Initially, the housing sales dataset contained every sale of a single-family house in the

city of Cedar Falls from January 2000 to November 20043; these sales were parsed by

using only those identified as “arm’s length transactions” by the county tax assessor’s

office. The time period (2000 to 2004) was selected in order to avoid the contamination

effects of the recent housing bubble and subsequent crash. Additional refinement

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consists of choosing only those sales with a selling price greater than $32,000 or less than

$400,000, houses with at least three but less than 12 rooms, at least 500 square feet of

living area, and a lot size less than 3 acres.4 Several homes were repeatedly sold in this

time frame; we use only the most recent sale because the house characteristics data

corresponds to the most recent sale.

The number and type of property specific variables included in previous studies

of proximity to externalities vary widely and are driven primarily by the character of the

urban area from which the sales data is drawn. Typically, these studies contain data, in

addition to the selling price of a house, on the characteristics of the house, the

characteristics of the neighborhood in which the house is located, and the distance of the

house to important points of influence. The sales data in this study include all of the

property characteristics information available from the public records, which include the

following information (variables) for each of the 2,078 transactions: selling price, date of

sale, state-plane coordinates of the centroid of the property, year built, lot size, living

area, and number of rooms. In addition to these variables, we calculate the Euclidian

distance from each property to the STP, the nearest highway, the Cedar River, and all 50

of the LUST sites in Cedar Falls. In addition, neighborhood data was collected from the

2000 census for all 21 census block groups in the city. The neighborhood data include

the following: median rent, median year that houses were built, percent of housing units

that are owner occupied, the number of housing units, and median household income.

Table 1 contains summary statistics of the variables in the model.

4.2 LUST Data

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Information for the 50 LUST sites in Cedar Falls was obtained from the Iowa Department

of Natural Resources (http://www.iowadnr.gov/land/ust/ustdbindex.html). Registration

of underground storage tanks (USTs) is required by federal (40 CFR parts 280 and 281)

and Iowa (Iowa Code 455.B.474) laws. In Iowa all USTs, except certain small,

residential USTs, must be registered with the Iowa DNR. These tanks must also be

inspected and assessed for their likelihood of contamination. If the site containing the

UST has evidence of contaminants that do not exceed certain delimited levels, then it is

classified as requiring no further action. If the onsite contaminants exceed the delimited

levels, but no receptors (water wells, aquifer, plastic water lines, basement, sewers, or

surface water) are within the transport plum of the contaminants, then it is rated as a low

risk LUST and must be tested annually. If receptors exist within the transport plum of

the contaminants, then it is classified as a high risk LUST and faces more intensive

monitoring, testing, and possible remediation. Figure 2 shows the location of all 2,078

sales together with the STP, the 50 LUST sites, the Cedar River, major highways, and

Census block group boundaries. The classification of each LUST is indicated in Figure 2

using different sized boxes.

These LUSTs are especially useful for this study, because they include mostly

neighborhood gasoline stations, and none of them are located near heavy industrial sites

(see Deaton and Hoehn (2004).

The potential effects of LUSTs clustering are managed using a count variable (the

number of nearby LUSTs), similar to what Ihlanfeldt and Taylor (2004) use in their

model. A distance of ¼ mile is chosen to represent “nearby.” That is, the count variable

is equal to the number of LUSTs within ¼ mile of the house (about three city blocks).

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This particular distance is somewhat arbitrary, but it is also reasonable. If clustered

LUSTs are going to have an influence on house prices, we would expect that the multiple

LUSTs would be relatively close to nearby houses as well as each other.

4.3 The LUSTs Variables

Previous studies (Simons, Bowen, and Sementelli (1997, 1990) and Simons and

Sementelli (1997) make use of a series of three dichotomous variables representing the

three classifications of LUSTs: (1) sale within 300 feet of a leaking, unregistered tank,

(2) sale within 300 feet of a registered UST, not leaking, and (3) sale within 300 feet of a

leaking and registered tank. Simon et al (1997) report that, although the extent of the

leaks in a LUST is important, information about the extent of the leaks were not available

to them.

The percent of LUST sites in close proximity (within 300 feet) of a house that

sold during the time period in this study is higher than in the Simon, et al (1997) study.

Simon, et al (1997) report 83 out of 16,990 (0.49%) sales occurring over a five year

period being within 300 feet of the nearest UST. In this study, we find 19 out of 2,079

(0.91%) of the sales within 300 feet of the nearest LUST. This study has a greater

percentage of sales in close proximity to a LUST site, because the LUST sites in this

study are predominately neighborhood gasoline stations. Unfortunately, 19 sales is far

too small a number to replicate the Simon, et al (1997) LUST binary variable definitions.

Therefore, we use a different approach to modeling the LUST effect. Specifically, we

use the Euclidian distance to the nearest LUST site, a version of the IDNR classification

of that LUST, and the number of LUSTs within ¼ mile of the house.

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Six of the LUST sites are classified by IDNR as High Risk (receptors exist within

the transport plum of the contaminants), four are classified as Low Risk (no receptors

within the transport plum of the contaminants), and the remaining 40 are classified as No

Further Action Required (contaminants do not exceed delimited levels). We create a

binary variable to capture the classification of the LUSTs as follows: Condition equals

one if the LUST is classified as low risk or high risk; zero if it is classified as no further

action required. We combine the low and high risk LUSTs because there are so few

(four) low risk LUSTs.

For each sale, we also include a LUST proximity variable (the Euclidian distance

to the nearest LUST). The coefficient of this variable represents the slope of the house-

price gradient and is the primary focus of this study.

In addition to the condition and the proximity variables, as mentioned above we

also include the count of the number of LUST sites within ¼ mile of each house in the

sales data set. Table 1 reveals that 597 of the 2,078 (28.7%) Cedar Falls sales have at

least one LUST site within a quarter mile and one home had eight LUST sites within a

quarter mile.

4.4 The Selection of d*

Finally, we select ¼ mile from the nearest LUST as our hypothetical value of d*.

Preliminary analysis of the data suggests that 1,320 feet, or about three city blocks,

provides a sample size of sold houses (597) sufficient to estimate the parameters of our

empirical model. Decreasing d* rapidly decreases our sample size of sold houses within

d* of a nearby LUST. Increasing d* may include so many HAH that any evidence of

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sorting gets washed-out. So, we hypothesize that if sorting occurs in our data, then the

LAH will out-bid the HAH for housing within ¼ mile of a nearby LUST, and HAH will

out-bid LAH for housing more than ¼ mile from a nearby LUST, holding other things

that affect house values constant.

5. The Empirical Model

Ideally, an empirical test of the sorting model would consist of testing the hypotheses that

the LAH HPBF lies above and is flatter than the HAH HPBF within a distance of d* to

the nearest disamenity. A similar test could be constructed for sales beyond d*, where

the HAH HPBF should lie above and be steeper than the LAH HPBF. Unfortunately,

these ideal tests are not possible, because we cannot observe the lower HPBFs. We can

only observe the house-price gradient illustrated by the bold line in Figure 3.

Recall that the model is predicated on households between a disamenity and d*

having different tastes for living near the disamenity than households living beyond d*.

Consequently, these two distinct groups of households could also have different tastes for

the characteristics of houses, the characteristics of neighborhoods, and the distance to

points of influence. So, the statistical estimates of the coefficients of a standard

Rosen/Lancaster type model of house prices could differ for the two types of households.

Consequently, applying a simple binary variable to the proximity to a disamenity variable

will yield unreliable results, because the binary variable should have been applied to

additional or even all of the independent variables in the model.

To formally test for differences in the coefficients of the independent variables

(including the coefficient of proximity to a LUST) for LAH and HAH households, we

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conduct an Analysis of Covariance.5 The results of this analysis demonstrate that we

must not pool the two data sets (LAH and HAH) into a single data set. Therefore, we

estimate the coefficients of the model using two separate analyses. We test whether the

proximity-to-a-LUST coefficient within each data set is greater than zero (meaning

proximity to a LUST is a disamenity) and we compare the signs and statistical

significance of the proximity-to-a-LUST coefficients from each regression to see if they

are consistent with the sorting model.

We use the popular Lancaster/Rosen hedonic type of empirical model to estimate

the coefficients of our model within the two data sets. Three key aspects of the hedonic

model used to examine housing sales data for sorting near LUSTs must be addressed,

namely, (1) the set of variables (dependent and independent) used in the model, (2) the

functional relationship among these variables, and (3) the structure of the error term of

the model. Each of these aspects of the empirical model is discussed below.

We select the selling price of a house as the dependent variable in our empirical

model. Selling price is a popular choice in hedonic models, but selling price per unit area

(dollars per square foot) is also common. The only difference between these two choices

is the role that area plays in the set of independent variables. Using selling price per

square foot of living area, for example, is equivalent to using selling price as the

dependent variable and then multiplying every independent variable by the square

footage of living area. We cannot justify using a set of independent variables implicitly

or explicitly weighted by living area. Therefore, we choose to use the selling price of the

house as our dependent variable.

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We select independent variables that reflect the (1) structural characteristics of the

property, (2) proximity of the property to points of influence (other than a LUST), (3)

characteristics of the neighborhood in which the property is located, (4) date at which the

sale occurred, and, of course, and (5) LUST specific data. The specific independent

variables included in the model are discussed in greater detail in the next section.

Various functional forms for hedonic models are possible. The log-linear

specification is popular, in which the log of selling price is the dependent variable and the

independent variables are entered in a linear fashion. In the log-log form, all of the

variables are entered in the log form. We use a combination of the log-log form for some

independent variables and the log-linear form for the rest of the independent variables.

The manner in which the distance to the nearest LUST is entered into the model is

not a trivial matter. The functional form of this important variable must be such that it

diminishes with increasing distance from a LUST. The shape of the curves in Figure 1

can be achieved using the square root of distance to the nearest LUST (d1/2), or in general

for 0 < x < 1, using d x. The point estimate of x, together with its associated statistical

inference, will indicate the strength of aversion to living near a LUST.

The mean structure of the empirical model contains several types of explanatory

variables typically thought to explain house prices. Most broadly, these variables include

(1) site level non-spatial characteristics of the home (house size characteristics including

living area, number of rooms, parcel size, year built, and time of sale), (2) spatial

characteristics (distance to a sewage treatment plant (STP), a river, and the nearest

highway), (3) LUST level factors (such as distance to the nearest LUST; classification of

the nearest LUST, and number of LUSTs within ¼ mile), and (4) neighborhood data

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(median rent, median year that houses were built, percent of housing units that are owner

occupied, the number of housing units, and median household income). Specifically, let

P = the selling price of the house,

S = lot size in acres,

H = the living area of the house,

t = the time of the sale,

C = number of rooms in the house,

D = a vector of variables measuring distance to points of influence,

N = a vector of neighborhood level variables,

d = distance to the nearest LUST, and

L = a vector of other LUST level variables (the classification of the nearest LUST, and

the number of LUSTSs within 0.25 miles of the sale).

We model the mean structure using the following non-linear functional form,

P=α S β 1 H β 2 dβ 3 eδt+ λC +κD+ωL+θN (1)

where the Greek letters represent parameters of the model which will be estimated using

the sales, distances, census and LUSTs data. On the natural log scale, the empirical

model (1) becomes:6

ln P=ln α+β 1 ln S+ β 2 ln H+β 3d+δt+ λC+κD+ωL+θCT (2)

The lot size (S) and house size (H) parameters, β1 and β2, represents the (constant)

elasticity of price with respect to lot size and house size, respectively (see Isakson and

Ecker (2001) and Ecker and Isakson (2005) for discussion). The key parameter, β3,

represents the slope of the house-price gradient on the log-log scale. The parameters of

the rest of the explanatory variables represent the percentage change in price given a one

unit change in the variable. Based upon our preliminary Analysis of Covariance, we

estimate the parameters of (2) for the LAH and HAH separately.

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To estimate the parameters of (2), we must include an error or disturbance term

(ε) in it. Standard Ordinary Least Squares (OLS) regressions assume that ε ~ N (0 , τ 2)

where normality and constant variance (τ2

is a variability parameter, after accounting for

all values of the covariates) is assumed. When dealing with spatial data, such as housing

sales, the potential exists for the OLS parameter estimates to be biased, especially any

spatial distance parameter estimates in the mean structure, such as distance to the STP

and distance to the nearest LUST site. Visual examination of an empirical variogram

(Cressie, 1993) of the OLS residuals in (2) reveals the presence of spatial correlations

(see Figure 4). Therefore, efforts to remove this source of bias could be beneficial.

Spatial linear models assume that the errors are not independent, that is, two

comparable homes that are closer in space sell for a more similar price than two

comparable homes farther apart. For example, houses located near each other are also

near the same neighborhood amenities/disamenities. In this case, the selling prices of

nearby, comparable houses tend to be more highly correlated than comparable houses

further apart. We build this spatial correlation into our model by assuming that

ε ~ N (0 , τ 2+σ2 ) (3)

where τ2

is called the “nugget” , i.e. a micro-scale or measurement error variability, in

the geostatistical literature (Cressie, 1993). The sum τ2+σ2

in equation (3) is termed

the spatial variability of the spatial process or “sill” (the variability of the home prices

after adjusting for individual home characteristics). Finally, for two home sales with

errors ε i and ε j , their spatial correlation is modeled as a function of their Euclidean

distance apart, d ij . Specifically, we adopt the exponential correlation structure, i.e,

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. (4)

The parameter φ directly controls the spatial correlation in the dataset and is termed the

“range” (technically 3φ is the exact value of the range in equation (4) (see Ecker, 2003)

for the exponential correlation structure). Thus, any two homes that are separated by a

distance of more than the range, have selling prices that are essentially uncorrelated.7

We make use of a Simultaneously-fitted Spatial Linear model (SFSL) by

combining the traditional hedonic model, (2), together with a spatial correlation

disturbance term, (3) and (4). All parameters of the SFSL model are jointly estimated via

SAS. The spatial correlation terms (3) and (4) are random effects models designed to

capture extra spatial variability not explained in the mean structure of the model. Spatial

correlation models can also help mitigate the impact of missing variables, such as

proximity to neighborhood amenities/disamenities, and incorrectly specified variables in

the model (Brasington and Hite. 2005).

6 Model Fitting and Results

Any OLS parameter estimates might be biased due to potential spatial correlation in the

data. To determine if the model given by equations (2), (3), and (4) is appropriate for the

Cedar Falls home sales data, we generate an empirical variogram from the residuals of

the OLS regression for HAHs and for LAHs. The sharp drop-off near the origin in both

empirical variograms in Figure 4 indicate that houses are more similar (less variability) as

separation distances between a pair of houses decreases, i.e., spatial correlation is present

in the data. Thus, the OLS model is inferior to the SFSL model because the SFSL model

directly incorporates the spatial correlation.

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To fit the model given by equations (3) and (4) simultaneously with the mean

structure coefficients in equation (2), seed values are required for the range, sill and

nugget spatial parameters. We use S-Plus to fit a theoretical variogram to the empirical

variogram from the residuals from the OLS regression to obtain these seed values. The

coefficients of the model are then simultaneously estimated using Proc Mixed in SAS,

and the results are reported in Table 2.

The size variables of Living Area, Number of Rooms and Parcel Size are all

positive and strongly significant for both LAH and HAH sales. As expected, bigger

houses sell at higher prices. Year built is positive and significant for both LAH and HAH

homes showing that newer houses sell for higher prices than older houses. Date sold is

positive and significant, indicating a 5.2% annual rate of appreciation over the 4 years of

sales for HAH sales and 4.9% for LAH homes.

Distance to the STP is positive and significant at the 0.05 significance level, for

both LAH and HAH homes, suggesting that no one wants to live near the sewage

treatment plant. Distance to the nearest school is significant and negative for LAH homes

only, indicating that only LAH are willing to pay a premium to live closer to a school.

Distance to the nearest highway is marginally significant (p-value=0.0808) for LAH sales

and moderately significant (p-value=0.0323) for HAH homes. Neither group desires to

live very close to a highway. Also, HAH homes are willing to pay a premium to be close

to the river.

For the census block variables, household income is positive and statistically

significant for both LAH and HAH, but very weak in magnitude.  Prices and incomes are,

not surprisingly, highly correlated. People with higher incomes tend to buy slightly more

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expensive houses.  The number of occupied units and median rent are not significant for

any of the households.  Median year built is strongly significant only for HAH,

suggesting that HAH prefer newer houses, while LAH do not.

Overall, the parameter estimates for the LUST variables are consistent with the

sorting model presented earlier. The positive but non-significant distance to the nearest

LUST variable for LAH sales suggests that these buyers do not have an aversion to living

close to a LUST. The positive and strongly significant distance to the nearest LUST

variable for HAH indicates that these households are willing to pay a premium to farther

away from the nearest LUST. In particular, the coefficient for distance to the nearest

LUST for HAH sales are about three times the size of that for the LAH sales.

Specifically, HAH are willing to pay 1.037% more for a house that is 10% further away

from the nearest LUST.

In addition, the count and condition LUST variables reveal an interesting pattern.

The count variable is only relevant to the LAH, because all of the HAH are more than ¼

away from the nearest LUST. But, the LAH do not seem to mind if they live near one or

multiple LUSTs. This finding is consistent with the statistical insignificance of the

proximity-to-LUST parameter. The condition of a LUST does not seem to matter to

either group of households. Nothing about LUSTs seems to matter to LAH, while all that

matters to the HAH is their proximity to a LUST.

The spatial association parameters for the simultaneously fit mean structure in

equation (2) and spatial components in equations (3) and (4) are also reported in Table 2.

Notice that the nugget and sill estimates for the LAH and HAH sales are close while

21

range parameter is 189 feet (0.0189 times ten thousand feet) for LAH sales, compared to

330 feet for HAH sales.

7. Summary and Conclusions

This study presents the theoretical framework for a model of household sorting around

mild disamenities (LUSTs). It estimates the parameters of a Rosen/Lancaster type

hedonic model modified to include spatial correlation in the error term. Using housing

sales data from a medium sized, Midwestern city, the parameters (mean structure and

error terms) are estimated simultaneously using a maximum likelihood regression

technique. We find evidence that households within ¼ of a mile of a LUST do not have a

statistically significant aversion to living near the LUST, in sharp contrast to a significant

aversion for households living more than ¼ mile from a LUST. Neither the number of

LUSTs nearby, nor the condition of the nearest LUST seems to impact either LAH or

HAH households.

Researchers should be cautious not to pool housing sales data near disamenities,

because doing so may very well wash out any sorting effects. For example, pooling the

LAH and HAH sales together in this study yields the erroneous conclusion that proximity

to a LUST matters for all households, when in fact, it matters only for a fraction of them.

Opportunities for additional research in this area abound. For example, the

sorting process presented in this study may also be found around mild amenities. The

intensity of the disamenity also deserves attention. For example, stronger disamenities

may not show signs of sorting. Lastly, more direct statistical tests to directly compare the

proximity-to-disamenity parameters also deserve additional attention.

22

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Figure 1: The Conceptual Model

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Figure 2 : Cedar Falls sales (o) and LUSTs (■) locations.

Note: Plot is in State Plane Coordinates

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Figure 3: The Empirical Model

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Table 1 Summary Statistics of Sales Data

ALL SALES LAH HAH N=2,078 N=597 N=1481

Variable Mean Std Dev Mean Std Dev Mean Std Dev

Sale Price $144,995 71,415 $104,831 36,481 $161,142 75,575

Structural VariablesLiving Area 1332.8 489.5 1138.6 382.2 1411.1 506.1Year Built 1960.6 28.5 1940.5 25.2 1968.7 25.6Number of Rooms 5.9 1.4 5.7 1.3 5.9 1.5Lot Size (acres) 0.27 0.16 0.22 0.12 0.28 0.16Date of Sale (0=1/1/2000)

2.56 1.39 2.55 1.42 2.57 1.37

Distances (miles)Distance to STP 3.43 1.17 3.10 0.78 3.56 1.27Distance to River 1.20 0.72 0.84 0.36 1.35 0.77Distance to School 0.44 0.27 0.36 0.16 0.47 0.43Distance to Highway 0.73 0.46 0.65 0.50 0.75 0.43

LUST VariablesDistance to LUST (miles)

0.48 0.31 0.17 0.06 0.61 0.28

Count 0.64 1.29 2.23 1.50 0 0Condition 0.11 0.31 0.16 0.37 0.09 0.28

Census Block VariablesMedian Household Income

40,817 12,015 38,152 9,718 41,892 12,670

Number Occupied Units

695.3 423.3 487.9 304.4 778.9 435.6

Percent Owner Occupied

59.3 22.4 58.0 23.9 59.8 21.7

Median Year Build 1962.3 12.8 1953.9 10.5 1965.7 12.1Median Rent 474.3 189.9 464.9 164.1 478.0 199.2Difference Median Year

-1.7 20.9 -13.4 21.7 3.0 18.5

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Table 2: SAS results for Cedar Falls sales data including Parameter Estimate (P-value).

Note: Numbers in parentheses are p- values.

Figure 4 : Empirical Variograms created from the OLS residuals for the Cedar Falls LAH sales in a) and HAH sales in b). Note that distance is measured in 10,000’s feet.

32

LAH HAHIntercept 7.7291

(0.0001)-4.9447(0.0076)

Proximity to LUST 0.0387 (0.2527)

0.1037 (0.0086)

Count 0.0117 (0.2498)

N/A

Condition 0.0182 (0.6416)

-0.0037 (0.9425)

Distance to STP 0.1050 (0.0376)

0.09007 (.0001)

Distance to School -0.00004(0.0265)

.0000008(0.4371)

Distance to Highway .00002(0.0808)

0.00002(0.0323)

Distance to River .00001(0.4457)

-0.00002(0.0144)

Ln Living Area 0.4043 (0.0001)

0.3027 (0.0001)

Date Sold .05162 (0.0001)

0.0489 (0.0001)

Number of Rooms 0.0726 (0.0001)

0.0632 (0.0001)

Ln Parcel Size 0.1417 (0.0001)

0.1195 (0.0001)

Yr Blt – Median Yr Blt .0044(.0001)

0.0060(0.0001)

Median HH Income .00000050.0301

.0000008(0.0001)

Num Occ Units 0.0001(0.0578)

.00002(0.6349)

Pct Owner Occ -0771(0.4519)

-0.2805(0.0050)

Median Yr Blt .0001(0.9628)

0.0071(0.0005)

Median Rent -0.00005(0.6425)

0.00003(0.6786)

Nugget 0.0133 0.0086Sill 0.0346 0.0431Range 0.0189 0.0330

33

1 LUSTs can also be severe disamenities. In July, 2011, a Maryland jury awarded 154 property owners $1.495 billion for MTBE contamination of their drinking water from a nearby LUST (Allison v. Exxon).

2 A standardized house is one with a given set of characteristics, such as lot size, living area, number of bedrooms, etc. The term house in the remainder of this study will refer to a standardized house.

3 The authors thank the Black Hawk County Board of Supervisors for providing the housing sales data used in this study. Of course, any opinions expressed in this study are strictly those of the authors.

4 Because the original data set contained all transactions of houses, it included a few very small structures (as small as 100 square feet) that sold for very low prices (as low as $7,500) as well as a few very large houses with large amounts of land that sold for as much as $2.5 million. These outliers were excluded because they were not representative of the typical house in Cedar Falls, Iowa.

5 The results of this analysis of covariance are available from the authors upon request.

6 Equations 1 and 2 do not yet contain an error term. The structure of the error term is discussed later in this section.

7 Ihlanfeldt and Taylor (2004) use a SAR for the error term in their model.