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Repair Expenses, Selling Contracts, and House Prices

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Abstract

This paper examines the impact of repair expenses on the selling price of a house. Using data from settlement statements, we investigate the frequency and extent to which performance of major repairs is part of the sales contract. We find that most homes are restored to a "normally maintained" state each time the home changes hands, and that the cost of bringing the home to this condition is included as part of house selling price. This implies it may be unnecessary to measure maintenance levels when using transaction data to study components of house price or to construct house price indexes.
JRER
Vol. 20
No. 3 2000
Repair Expenses, Selling Contracts and
House Prices
Authors
John R. Knight, Thomas Miceli and
C. F. Sirmans
Abstract
This article examines the impact of repair expenses on the selling
price of a house. Using data that include the actual dollar amount
of repairs stipulated in the settlement statement, we investigate
the frequency and extent to which the performance of major
repairs is part of the sales contract. We find that most homes are
restored to a ‘normally maintained’ state each time the home
changes hands, and that the cost of bringing the home to this
condition is included as part of the house selling price. This
implies that it may be unnecessary to measure maintenance
levels when using transaction data to study components of house
price or to construct house price indexes.
Introduction
Homeowners and landlords regularly perform maintenance and make minor
repairs to their properties in order to enjoy a normal level of housing services.
Major repairs, however, are often deferred until their need is obvious or until the
property is sold or prepared for sale. Existing homeowners logically put off repairs
as long as possible, but prospective buyers are aware of impending major repairs
and require that either the seller complete repairs prior to closing, discount the
price to allow the buyer to make needed repairs or provide the buyer with a repair
allowance as part of the settlement agreement. Roof repair or replacement, carpet
replacement, exterior painting, and heating, ventilation and air conditioning
replacement are major upkeep requirements that fall into this category.
Lack of data has been the major obstacle to studying the relationship between
homeowner maintenance activities and house price. As Reschovsky (1992) notes:
‘The factors influencing household decisions regarding home upkeep and
improvement remain one of the least studied aspects of housing economics. This
relative lack of attention most likely reflects the scarcity of good data rather than
the lack of importance.
The level of maintenance, because it is unobserved in most data, usually goes
unmeasured in hedonic house price regressions. This raises concerns about bias
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Knight, Miceli and Sirmans
in the estimates of other components of house prices as well as concerns about
bias in house price indexes constructed using transaction data. The data we use
in this study are very rich in information relating repair expenditures to the
associated home sales.
In this article, we look at the detail of house sales contracts. We have the dollar
amount of repairs and maintenance associated with under-maintained homes. This
sheds light not only on the frequency and cost of major repairs at point-of-sale,
but also on the nature of the transaction itself. We find evidence that a home’s
transaction price represents the value of a normally maintained home even when
the home has been substantially under-maintained prior to being marketed. As
a result, concern over omitting extraordinary maintenance as a variable in
transaction-based hedonic equations appears misplaced.
The article is organized as follows. In the next section, we briefly review the
theoretical and empirical literature surrounding property maintenance. Also
germane are studies of the capitalization of contract concessions and contingencies
into house selling price. The following section develops the theory describing
buyer and seller behavior with respect to under-maintained houses. Next, we
describe typical behavior of sellers and buyers with respect to repairs and
maintenance. The following sections describe the data and statistical model used
and the results. The final section is the conclusion.
Literature Review
Hedonic theory (Rosen, 1974) provides a framework for studying the contribution
of individual product characteristics to the value of differentiated products such
as houses. Marginal values of almost every conceivable amenity and disamenity,
ranging from physical characteristics such as living area and quality of
construction to locational attributes such as proximity to public transportation,
have been the subjects of previous research. Hedonic regressions have also been
used to estimate depreciation rates and the impact of noise and air pollution on
house value.
Relatively few empirical studies to date have focused on the details of the sales
contract itself, despite the direct impact of contractual agreements on the selling
price of a house. Allen, Shilling and Sirmans (1987), the first to employ the
hedonic framework to investigate the effect of differences in sales contracts on
house prices, found that the price premium exacted by the market for contract
contingencies is dependent on the number of contingencies and the manner of
their bundling within the contract. Similarly, Shilling, Sirmans, Turnbull and
Benjamin (1992) found that contingent contracts result in lower sales prices when
property and market characteristics are held constant. Seller concessions related
to financing costs and major repairs, proxied by a dummy variable for the
existence of such provisions, were found to have an insignificant impact on selling
price.
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Financing concessions have been the subject of most of the literature relating the
details of the sales contract to house selling price. Of particular interest in these
studies is the degree to which creative financing and seller financing concessions
are capitalized into the transaction price. Brueckner (1984) provides the theoretical
foundation for this area of study. Generally, empirical investigation of this issue
(Sirmans, Smith and Sirmans, 1983; Smith, Sirmans and Sirmans, 1984; and
Ferreira and Sirmans, 1986) has revealed that seller concessions are partially, but
not fully, capitalized into the transaction price. This implies that buyers and sellers
share the benefit and cost of such an arrangement. Ferreira and Sirmans (1989)
extend this inquiry by looking not only at the impact on selling price, but also at
the effect on selling period. They discover that, in certain markets, the financing
concessions may manifest their benefits in terms of a reduced time-on-market
rather than in a higher selling price.
While the value of maintenance and repairs has been the subject of a number of
theoretical (e.g., Dildine and Massey, 1974; Sweeney, 1974; and Arnott, Davidson
and Pines, 1983) and empirical (e.g., Chinloy, 1980; Malpezzi, Ozanne and
Thibodeau, 1987; and Knight and Sirmans, 1996) housing studies, we know of
only one (Shilling, Sirmans, Turnbull and Benjamin, 1992) that looks at the
provision for maintenance and repair costs within the sales contract. In this latter
study, major repairs are combined with financing concessions as a single dummy
variable in a hedonic regression that controls for other property characteristics. In
contrast, we have data that include the dollar amount of major repairs stipulated
in the settlement statement and are therefore able to isolate these concessions from
others that may appear in the contract for sale.
An understandable preconception may be that repair allowances, much like
financing concessions, would be capitalized, at least partially, into the transaction
price of a house. We elaborate the ways that a buyer wishing to acquire a
‘normally maintained’ home might approach a purchase. We also develop a
theory that relates the unobserved willingness to pay and the cost of needed repairs
to the observable selling price and repair allowances.
Theory
We assume that buyers wish to purchase a ‘normally maintained’ home. Four
possible situations cover the range of methods by which the buyer might acquire
such a home:
Case 1: The buyer might purchase a home that has received a normal level
of maintenance and repairs over the holding period of the current
owner. In this case, no special arrangements are included in the sales
contract, and the transaction price represents the value of the home.
Case 2: The buyer might require the seller to make the repairs necessary to
bring the house to a normal level of maintenance as part of the
purchase agreement. The selling price represents the value of a
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Knight, Miceli and Sirmans
normally maintained home, the repairs are accomplished before
closing and repair expenditures appear in the closing statement as a
reduction in the proceeds available to the seller at closing.
Case 3: The buyer might receive a repair allowance as part of the closing
settlement. Once again, the selling price represents the value of a
normally maintained home. Although the house is undermaintained
at closing, it is presumed that the buyer makes the needed repairs
soon thereafter.
Case 4: The buyer might purchase, without contingencies or allowances, a
home that does not fall into the category of a normally maintained
home. In this case, the selling price represents the value of a
normally maintained home plus or minus the difference in value
associated with the home’s repair level.
To formalize these cases, let W
N
be the amount that a household is willing to pay
for a normally maintained house, and let R
0 be the cost of repairs needed to
bring the house up to the normal level. Assume that a fraction
(0
1) of
this amount is to be paid by the buyer, while the seller pays the remaining fraction,
1
. The household’s net willingness to pay for the house is therefore:
W
R. (1)
N
Note that neither W
N
nor
R is generally observable. Instead, we observe the
quoted price of the house, P, and either the repair expense of the seller or the
repair allowance to the buyer at closing (if any), A. The household’s net payment
for the house is therefore P
A. In equilibrium, it must be true that:
P A W
R. (2)
N
Equation (2) should hold for all houses if the hypothesis that the housing market
correctly capitalizes repair expenses is true.
Consider how this equation relates to the above cases. In Case 1, a normally
maintained house is sold, so R
A 0. That is, no repairs are needed and no
repair allowance is given at closing. It follows from (2) that the sale price should
equal the value of a normally maintained house, or P
W
N
. In Case 2, the house
has not received normal maintenance, but the seller agrees to make all necessary
repairs prior to closing. Thus, R
0, but A
0, implying that P W
N
. That
is, the sale price should also equal the value of a normally maintained house
regardless of the value of R.
In Case 3, the house has again received sub-normal maintenance, but here the
buyer agrees to pay a share
of the required repairs. That is, R, A and
are all
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positive. Suppose that the repair allowance at closing exactly equals the buyer’s
share of repairs, or A
R. Then (2) implies that in equilibrium the price should
be P
W
N
; the price again equals the value of a normally maintained house.
Alternatively, suppose that A
R, or the repair allowance is less than the buyer’s
share of repairs. In the extreme, suppose that the buyer receives no allowance for
maintenance (A
0) and plans to finance all repairs himself. This is the scenario
in Case 4. Equation (2) implies that in equilibrium, P
W
N
R, or the sale
price should equal the value of a normally maintained house discounted by the
buyer’s expected maintenance costs.
The preceding analysis implies that in all but Case 4, the sale price should equal
the value of a normally maintained house; that is, it should be independent of any
repair expenses needed to bring the house up to a normal level of maintenance.
Only in Case 4 do we predict that the price will be negatively related to the
required repairs. Unfortunately, we can not separate Case 4 homes from Case 1
homes. Therefore, the extent to which our theory holds empirically depends on
the prevalence of Case 4 homes for the sample in question.
Before turning to the empirical analysis, it is interesting to speculate on why at
least some buyers and sellers transact at a gross sale price that includes repairs
rather than just a net price equal to W
N
R (Case 4). One possibility has to do
with the financing of the repairs. Note that by obtaining a mortgage for W
N
rather
than W
N
R, the buyer is in effect financing the required repairs via the
mortgage, which may be the cheapest source of funds given the lower interest
rate on mortgages compared to personal loans and the tax deductibility of
mortgage interest. At the same time, the lender is willing to finance repairs because
it brings the house up to the normal level of repair, at which time it is worth W
N
.
Repairs and Maintenance
Homeowners differ in the extent they engage in repairs and maintenance during
their period of ownership. Some of this relates to behavioral differences, such as
the tolerance levels for house imperfections, or even differences in perception of
what constitutes an imperfection. Some differences in repair and maintenance
levels may be caused by income constraints that prevent an owner’s maintaining
the home in the desired condition. Thus, for whatever reason, some homes are
maintained continuously in a ‘like new’ condition, while some houses proceed
during the course of ownership to a ‘needs work’’ state.
Most home buyers are quite fussy about the condition of the house they buy. They
typically insist that all plumbing and electrical equipment work properly and they
are concerned as well about faded or chipping paint and worn or damaged carpet.
Many buyers go to the expense of hiring an inspector to check the condition of
house components and to diagnose structural problems that may not be apparent
to the layman.
Regardless of differences in homeowner behavior with respect to repairs and
maintenance during tenancy, the attitudes and actions of home buyers toward the
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Knight, Miceli and Sirmans
condition of the house at point of purchase bring most homes to a ‘normal’ level
of maintenance by the time the transaction reaches close of escrow. This result
may be reached by the continuous attention of homeowners, or it may occur by
stipulation of the buyer as a condition of sale.
Data and Model
To investigate the effect of maintenance level on the quoted selling price of homes,
we examined the details of all the closed sales of Coldwell Banker Grupe, a large
brokerage firm in Stockton, California. This firm participates, as either listing or
selling broker, in about 20% of all residential transactions in the area. In all, 342
sales contracts were examined, with particular focus on the dollar amount of
repairs stipulated in the settlement statement. Stockton is a medium sized city in
the San Joaquin Valley located about forty miles south of Sacramento and about
eighty miles east of San Francisco.
We filtered the data to reduce the impact of outliers, eliminating those properties
that sold for less than $50,000 or more than $325,000, properties with less than
700 or more than 5,000 square feet of living area, and properties on less than
one-tenth acre or more than five acres of land. The remaining data set consists of
264 transactions occurring between July, 1997 and December, 1998, a period
during which home prices were generally rising.
Summary statistics for the data appear in Exhibit 1. The average home had about
1,725 square feet of living area with three bedrooms, was about twenty-three years
old and sat on a quarter-acre lot. The average home sold for about $138,000. The
dollar amount of the repairs enumerated in the settlement statement ranged from
zero to $25,000, and on average constituted about 1% of the selling price, or about
$1,380.
Further evidence of the importance of repairs in negotiations between buyers and
sellers is provided by Exhibit 2, which shows the frequency distribution of repairs
by dollar amount. Fully 75% of the contracts provided for the performance of
repairs. Over half of the homes in the sample had repairs of at least $500, and
about 38% of the transactions included amounts of over $1,000. The
preponderance of contracts involving such repairs implies that a large percentage
of home sales fall into the category of either Case 2 or Case 3, situations wherein
the homes are restored to a normal level of maintenance at the time of sale. Only
25% of the home sales involved no repairs; these transactions would meet the
criteria of Case 1, in which no repairs are needed, or Case 4, where premiums
(discounts) apply for over- or under-maintained homes.
1
We employ hedonic pricing theory (Rosen, 1974) to construct the statistical model.
The theory holds that the composite price of a multi-attribute product is simply
the sum of the marginal prices of the individual attributes. Attribute prices can be
obtained statistically by regressing the sales price of homes on the characteristics
of the homes thought to influence price. Hedonic pricing has been widely used in
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Exhibit 1 Summary Characteristics of Data
Variable Description Mean Std. Dev. Min. Max.
Percentage
of Sample Observations
SPRICE Selling price 137,996 57,726 56,000 320,000
LIVAREA Square feet of living area (100’s) 17.24 5.17 8 41
BEDS Number of bedrooms 3.22 0.67 2 6
TREND Market trend variable for time of sale 10.49 3.74 2 18
ACRES Lot size in acres 0.25 0.34 0.11 2.92
AGE Age of dwelling in years 22.78 17.76 1 80
MR Dollar amount of repairs in closing statement 1,379 2,553 0 25,000
PMR Repair expense as a percentage of selling price 1.1 1.8 0 14.1
MRDY Repair expense part of closing statement 75.4 199
SCD2 House in school district 2 33.0 87
SCD3 House in school district 3 25.4 67
SCD4 House in school district 4 12.9 34
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Knight, Miceli and Sirmans
Exhibit 2 Frequency Distribution of Repairs
0
10
20
30
40
50
60
70
None
1 - 500
501 - 1000
1001 - 2000
2001 - 3000
3001 - 4000
4001 - 5000
5001 - 6000
6001 - 7000
> 7000
$ Amount of Repairs
Frequency
.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
Frequency Cumulative %
the house price and house price index literature to measure the effect of various
characteristics on house price and to measure the change in house prices over
time.
The statistical model is:
y x
, (3)
where y is a vector of selling prices for the homes in the sample, x a matrix of
the physical characteristics explaining the selling price,
a vector of coefcients
representing the marginal contribution of each characteristic on composite house
price and
a homoskedastic error term with mean zero.
The matrix of explanatory variables in our study includes the number of square
feet of living area, the number of bedrooms, the size of the lot on which the house
sits, and the age of the home at the time of sale. We also include a trend variable
to control for the fact that market prices were rising during the study period,
2
and
a dummy variable for the school district associated with the home. In addition to
valuing the educational differences among the school districts, this latter dummy
variable proxies for many of the unmeasurable but value-laden amenities
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associated with a homes location. We augment this basic hedonic model with
information regarding the repair expenditures included as part of the sales
agreement. The augmented model:
y x
z
, (4)
includes a vector z of house repairs, with the coefcient
measuring the
contribution of repairs to the selling price of the home. We operationalize the
repair characteristic in two ways: rst, as a dollar amount of repairs itemized in
the closing statement; and second, as a dummy variable, one if any repairs were
stipulated in the selling agreement and zero otherwise. In accordance with our
theory, we hypothesize that the coefcient,
, will be statistically insignicant.
This hypothesis of insignicance differs from the positive and signicant
coefcient encountered in the literature surrounding the capitalization of nancing
concessions into selling price. The difference is in the ability to distinguish
between subsets of comparison. Homes with nancing concessions are clearly
distinct from those without, and the cash equivalence of concessions imparts value
only to the homes with concessions.
In our case, except for Case 4 homes, the values of homes with point-of-sale
repairs are no different from the values of homes that have been maintained and
repaired throughout the duration of the sellers occupancy. Homes with time-of-
sale repairs sell for no more or less than homes without, because the repairs merely
bring the value of the house to the norm at one discrete point rather than
continuously over time.
The possibility of Case 4 homes in the sample causes us to modify our hypothesis
somewhat. Insignicance of the repair coefcient is consistent with three possible
situations. First, all transactions are categorized as Case 1, 2 or 3. That is, all
homes are normally maintained, either over time or by repairs performed at point-
of-sale. Second, there are Case 4 homes in the sample, but the degree of over-
and under-maintenance is mild. Finally, there are Case 4 homes, and some may
be substantially over- or under-maintained, but the extreme outcomes offset the
effects of each other.
In a practical sense, it matters little which of the above situations produces an
unimportant repair variable. The fact that, on average, homes are at a normal level
of maintenance and repairs when sold would be sufcient to allay concerns about
omitting the variable when using transaction-based data.
Results
Exhibit 3 provides the model estimation results. We report the results of the semi-
log model, ln(Y)
X, the most common specication for hedonic regressions of
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Knight, Miceli and Sirmans
Exhibit 3 Parameter Estimates for Hedonic Models of House Value
Model 1 Model 2 Model 3
Variable Estimate Std. Error Estimate Std. Error Estimate Std. Error
Constant 11.003 0.076 10.997 0.077 10.998 0.077
145.4 143.7 143.0
Sq. ft. of living area (100’s) 0.058 0.003 0.059 0.003 0.058 0.003
20.3 20.0 20.1
Number of bedrooms 0.062 0.022 0.062 0.022 0.061 0.022
2.8 2.8 2.8
School district 1 0.184 0.030 0.183 0.030 0.184 0.030
6.1 6.1 6.1
School district 2 0.193 0.033 0.192 0.033 0.191 0.033
5.9 5.9 5.8
School district 3 0.159 0.040 0.159 0.040 0.160 0.040
3.9 3.9 4.0
Time trend (monthly) 0.010 0.003 0.010 0.003 0.010 0.003
3.3 3.4 3.3
Acreage 0.163 0.036 0.166 0.037 0.162 0.036
4.5 4.5 4.4
Age 0.003 0.001 0.003 0.001 0.003 0.001
4.4 4.0 4.4
Dollar repairs 0.003 0.005
0.59
Repairs dummy 0.012 0.028
0.42
Adj. R
2
.758 .757 .757
Notes: All models take the functional form ln(Y) X. Model 1 contains no information regarding the
performance of maintenance and repairs as part of the sales agreement. Model 2 adds the dollar
amount of repairs contained in the sales contract. Model 3 is a repair dummy that is one if repairs
exceeded $500 and zero otherwise. t-Statistics appear beneath the standard errors.
house price on house characteristics. Analysis was also performed using linear
and log-log functional forms. The results of those analyses are nearly identical to
those reported here.
Model 1 estimates house attribute values without any information regarding
repairs. This relatively parsimonious model explains 76% of the variation in the
selling price of homes in the sample. All coefcients are signicant at the 1%
level, and all are of the expected sign.
3
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Exhibit 4 Data Collinearity Diagnostics
Model 2 Model 3
Collinearity Test Dollar Amount of Repairs Dummy Variable for Repairs
Simple correlations Highest correlation was 0.28
with the age variable.
Highest correlation was 0.16
with the age variable.
Variance inflation factor
a
1.2 1.1
Auxiliary R
2b
0.16 0.07
Highest condition number
c
20.1 21.0
Variance proportions No two variables had a high
proportion of variance
associated with the same
characteristic root.
No two variables had a high
proportion of variance
associated with the same
characteristic root.
a
A variance inflation factor of 10 or higher would indicate a collinearity problem.
b
R
2
from regressing the maintenance and repair variable on the other explanatory variables in the
model. A high R
2
would reveal a problem.
c
Pertains to normalized data. A condition number greater than 30 denotes ill-conditioned data.
Model 2 imposes additional information regarding the dollar amount of any repairs
listed in the settlement statement. As hypothesized, the coefcient on this variable
is insignicant. Note also that adding this variable has negligible impact on the
house characteristic parameter estimates. The model in fact has a lower adjusted
R
2
and a lower F-value than the model that excludes repair information.
In Model 3, we represent repair information as a binary variable, distinguishing
transactions that involved repairs of any magnitude from those that had no repairs.
Comparing Model 1 with Model 3 in Exhibit 3, we see once again that repair
information is insignicant in explaining variation in transaction price. Parameter
estimates of house characteristics are virtually unaffected, and again model
performance as measured by adjusted R
2
and the F-Statistic is degraded.
Support for our proposition that the transaction price represents the value of a
normally maintained home is provided by the insignificance of the maintenance
and repair estimates in Models 2 and 3 as presented in Exhibit 3. One possible
source of insignicance is the high variance of parameter estimates associated
with multicollinearity, a data problem known to exist in hedonic models. For this
reason, we subjected the data to a barrage of tests for ill-conditioned data. We
examined simple correlations, variance ination factors, auxiliary regressions,
condition numbers of the normalized data and a collinearity diagnostic table
showing the proportion of variance for each explanatory variable associated with
each characteristic root of the data. As summarized in Exhibit 4, none of these
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Knight, Miceli and Sirmans
tests reveals a collinearity problem associated with the maintenance and repair
variables.
Conclusion
This article contains important information about the performance of repairs at
point-of-sale. We nd evidence in our sample that about three-fourths of
residential transactions provide for repairs within the contract, and that many of
these repairs entail signicant dollar amounts. According to local residential
brokers, requiring that the repairs be accomplished prior to closing (Case 2) is the
usual manner by which the buyer acquires the desired normally maintained home;
the occurrence of repair allowances to the buyer (Case 3) is less frequent. From
this, in a large majority of transactions, we are able to infer the buyers willingness
to pay for such normally maintained home, a value that is not directly observable
in the data. The 25% of transactions that did not involve repairs would be split
in unknown proportions among homes that needed no repairs (Case 1), and homes
that were over- or under-maintained and were sold as such (Case 4). Only in the
latter case would the selling price represent other than the value of a normally
maintained home. Moreover, if the number of over- and under-maintained homes
were roughly equal in a sample, as seems reasonable, the effects of these
observations would be likely to statistically counterbalance each other.
As hypothesized, the variables used to represent the existence and level of repairs
called for in the contract were insignicant. This gives further support to the notion
that the selling price measured in transaction-based data is representative of the
value of a normally maintained home. We further note that the hedonic model we
choose is relatively parsimonious in the number of explanatory variables, allowing
ample opportunity for the repair variables to explain variation in selling prices if
they were capable of doing so. Collinearity diagnostics are fully supportive of this
assertion.
The major implication of our study is that maintenance, repair and upkeep data,
notoriously difcult to measure in transaction-based data, may be unnecessary in
hedonic price regressions. Inasmuch as the measured selling price represents the
value of a normally maintained home in the vast majority of cases, unbiased
estimates of the value of house characteristics, and accurate estimation of hedonic
house price indexes may be accomplished without such information. Of course,
our conclusions pertain only to the sample we studied, and in general would
depend on the preponderance of Case 4 homes in any given sample. Replication
of our results in other data scenarios would be needed to generalize the
conclusions.
Endnotes
1
Unobserved in our study is the bargaining process between buyer and seller. Some sellers
may resist the concessions required by prospective buyers and wait for a less demanding
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buyer. This creates sample selection bias if the population of interest is both sold and
unsold homes. Our focus is on the homes that culminate in a transaction, and our results
pertain only to this censored sample.
2
The trend variable summarizes the price effect of the various components of the real
economy during the study period. The practice is common in house price and house price
index literature. A trend variable was chosen over periodic dummy variables because the
time effect was steadily upward during the study period as indicated by a house price
index for the Stockton area using dummy variables and a much larger data set.
3
The bedroom coefcient is negative because it represents the marginal value of an
additional bedroom while holding square feet of living area constant. The result is
common in hedonic regressions of price on house characteristics.
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The authors thank Larry Vivian and Jerry Abbott of Coldwell Banker Grupe in
Stockton, California, and Cindy Scheublein, Liina Veidemann and Zhilan Feng for
their assistance in collecting and developing the data for this study.
John R. Knight, University of the Pacific, Stockton, CA 95211 or jknight@UOP.edu.
Thomas Miceli, University of Connecticut, Storrs, CT 06269 or
thomas.miceli@uconn.edu.
C. F. Sirmans, University of Connecticut, Storrs, CT 06269 or cf@sba.uconn.edu.
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