JPTAA Foreclosures Bidanset

Journal of Property Tax Assessment & Administration • Volume 13, Issue 1 5
The accuracy of real estate valuations
suffers from foreclosures affecting
both the supply of and the demand
for residential housing. Arguably, the
influence of foreclosures is perceived
to dampen adjacent property prices
because foreclosed properties propa-
gate urban blight and associated crime
rates and increase the stock of avail-
able homes, potentially even serving
as cheaper alternatives or substitutes
to nonforeclosure sales once they are
released onto the market (Ellen, Lacoe,
and Sharygin 2013; Hartley 2014; Zhang
and McCord 2014). Pertinently, the
spillover effects of additional foreclo-
sures are not uniform and are expected
to behave differently according to the
socioeconomic characteristics of their
respective location (e.g., upscale neigh-
bourhoods, potentially having more
clout, get banks to respond quickly to
poorly maintained foreclosures). As a
result, models accounting for weighting
the proximal impacts must allow for co-
efficients to fluctuate across geographic
space. Consequently, the primary inten-
tion of this paper is not necessarily to
quantify impacts of foreclosures and/or
reintroductions of foreclosures onto the
market by way of interpretations of coef-
ficients. Rather, it proposes a method
for accurately accounting for, at least in
part, the spillover effects of such within
automated valuation models (AVMs)
to promote accuracy and uniformity
in mass appraisal valuations used for
ad valorem property tax purposes. By
employing a geographically weighted
regression (GWR) approach, this paper
finds that the inclusion of foreclosure
variables within AVMs improves the
Paul E. Bidanset is a doctoral student at Ulster University, School of the Built Environment,
Newtownabbey, Northern Ireland, United Kingdom, and Real Estate CAMA Modeler, Office
of the Real Estate Assessor, Norfolk, Virginia, United States.
Michael McCord, Ph.D., is Lecturer in Property Market Research, Ulster University, School
of the Built Environment.
Peadar Davis, Ph.D., MRICS, is Senior Lecturer in Property Appraisal and Management,
Ulster University, School of the Built Environment.
Spatially Accounting for Spillover Effects of Foreclosures
in Automated Valuation Models to Promote Accuracy
and Uniformity of Property Tax Assessments
BY PAUL E. BIDANSET; MICHAEL MCCORD, PH.D.;
AND PEADAR DAVIS, PH.D., MRICS
This research was conducted through a grant from the Academic Partnership Program of the
International Association of Assessing Officers (IAAO). The program, which is administered
by IAAO’s Research Committee, provides financial support to students and faculty for research
in the areas of property appraisal, assessment administration, and property tax policy.

6 Journal of Property Tax Assessment & Administration • Volume 13, Issue 1
coefficient of dispersion (COD) values
for 48 percent of the neighbourhoods
analyzed. Nonetheless, the findings also
highlight that the COD for many neigh-
bourhoods actually deteriorated, and
the implications are that exploration of
foreclosure variables should be included
at the model calibration phase and only
within certain submarket models that
benefit from their inclusion. Therefore,
a core finding pertains to how future
taxation methodologies can encompass
these variables and, perhaps more im-
portantly, at what stage and level within
the modelling process.
Since at least the late 1960s, foreclo-
sures of single-family homes have been
viewed as serious threats to neighbour-
hood stability and community well-being,
particularly in low-income neighbour-
hoods. These properties contribute to
physical disorder in a community, create
a haven for criminal activity, discourage
the formation of social capital, and lead
to further disinvestment, culminating in
lower property values in the immediate
area (Immergluck and Smith 2006) and
leaving vacant, boarded-up, or aban-
doned properties. In the past decade,
many U.S. cities have experienced sub-
stantial growth in foreclosures because
of the 2007 global financial crisis.
Although in a period of relative housing
market recovery, with forbearance and
mortgage arrears arguably continuing to
decline, the costs incurred by both prop-
erty owners and taxing jurisdictions due
to foreclosed properties continue to have
an impact on the market. The resulting
spillover effects of foreclosed properties
onto the market include shocks to both
the supply of and the demand for hous-
ing stock. Research has shown that each
foreclosure can create negative spillovers
onto neighbouring properties and reduce
a property’s sale price—quantified from
approximately 1 to 3 percent of a home’s
value (Immergluck and Smith 2006; Lin,
Rosenblatt, and Yao 2009; Biswas 2012;
Whitaker and Fitzpatrick 2013). Further,
when they are reintroduced into the
market, they command price discounts
ranging from 7 to 24 percent (Shilling,
Benjamin, and Sirmans 1990; Forgey,
Rutherford, and VanBuskirk 1994; Har-
din and Wolverton 1996; Daneshvary
and Clauretie 2012). As sale prices and
values are depressed, aggregated spill-
overs cause jurisdictions to forgo a larger
tax base. Immergluck and Smith (2006)
estimated that foreclosure spillover ef-
fects in Chicago reduced the overall tax
base by approximately $598 million from
1997 to 1998, with an average reduction
of $159,000 per foreclosure.
There are a number of viable reasons
why foreclosures have a negative impact
on the value of properties in the same
market. Two of the more prominent
reasons are that they reduce demand
(through blight and potentially associ-
ated crime rates) and increase the stock
of available homes, potentially even serv-
ing as cheaper alternatives or substitutes
to nonforeclosure sales once they are
released onto the market (Ellen, Lacoe,
and Sharygin 2013; Hartley 2014; Zhang
and McCord 2014). Additional impacts
on the market are introduced when
foreclosures are erroneously selected as
comparables in the determination of sale
prices or assessment values.
In this paper, a foreclosure is defined as
any mortgaged home that has been fully
seized by a lending institution because
of the owner’s failure to make contrac-
tual payments, and sale after foreclosure
is defined as the sale of a foreclosed
property on the open market immedi-
ately following the property’s respective
foreclosure. Pertinently, a sizeable volume
of foreclosure research does not dif-
ferentiate between foreclosure and sale
after foreclosure. Note that they do not
necessarily measure the same thing—a
foreclosure is not guaranteed to reenter
the market, and each foreclosure argu-
ably assumes a different role with respect
to spillovers. As mentioned earlier, sales
after foreclosure are expected to sell at

a discount compared to arm’s-length
sales (ceteris paribus). One reason is that
an increase in the supply of available
homes drives the market clearing price
downward. Hartley (2014) estimated that
for each foreclosure sale within 0.5 miles,
prices are reduced by approximately 1.2
percent.
In terms of market behaviour, an
increased supply of properties for sale re-
sults in more options for a buyer and thus
more potential substitutes. If a potential
homeowner desires to live in a specific
neighbourhood, an increased amount
of homes for sale there will result in
price competition, and if a foreclosure
is for sale, this introduces arbitrage ef-
fects whereby the buyer is more likely to
acquire a home in a desired neighbour-
hood at a price significantly less than
what he or she could have afforded or
have been willing and able to pay.
Whilst there is an abundance of real
estate literature evaluating and quan-
tifying the effects of foreclosures on
the market, there has yet to be a paper
(to our knowledge) that attempts to
improve mass appraisal models used for
ad valorem property tax assessments by
accounting for such effects. In addition,
limited research has incorporated lo-
cally weighted regression models, such
as GWR, to capture the spatial effects of
foreclosures on assessment uniformity
and equity. Because of the benefit of
such methodology to mainstream mass
appraisal modelling, that is, by correct-
ing for spatial heterogeneity (Borst and
McCluskey 2008; Moore 2009; Moore
and Myers 2010; Lockwood and Rossini
2011; McCluskey et al. 2013; Bidanset
and Lombard 2014a), it should be ap-
plied to foreclosure research as well. As
previous research has shown, coefficients
of automated valuation models behave
differently in various geographic submar-
kets; it should not be assumed that the
behaviour of foreclosure-based variables
is any exception. This paper uniquely
adds to the preceding literature base by
employing a GWR AVM, both with and
without foreclosure-based variables, and
examining potential improved equity
and uniformity attainment.
The next section discusses the cur-
rent literature on housing foreclosures
and the impact on pricing, followed by
presentation of the data, methodological
framework, the results, and discussion of
key findings. Conclusions are proffered
in the last section.
Literature Review
Foreclosures in the United States have
been of significant academic interest in
light of the global financial crisis, and
numerous studies have examined the
relationships among the wider (macro)
economy, monetary policy, mortgage
delinquency (default rate), and house-
hold foreclosures (Clauretie 1987; Case,
Shiller, and Weiss 1995; Ahearne et al.
2005; Gerardi, Shapiro, and Willen 2007;
Calomiris, Longhofer, and Miles 2008).
Other research studies have examined
legislative effects on foreclosure discount
rates. Mian, Sufi, and Trebbi (2011)
observed that states without a judicial
requirement for foreclosures are twice as
likely to foreclose on delinquent home-
owners. Comparison of zip codes close to
state borders with differing foreclosure
laws shows that foreclosure propensity
and housing inventory jump discretely
in the nonjudicial states.
Chatterjee and Eyigungor (2009)
constructed a quantitative equilibrium
model of the housing market. They
found that a decline in house prices
creates an incentive to increase the
consumption of housing space, but le-
verage makes it costly for homeowners
to sell their homes and buy bigger ones.
Pertinently, the authors explored the
effects of the government’s foreclosure
prevention policy in their model, finding
that the policy can temporarily reduce
foreclosures and shore up house prices.
There is a wealth of literature on the
spatial impact of foreclosures on sur-
rounding house prices, emanating from
the early 1990s. Shilling, Benjamin, and

Sirmans (1990) estimated the discount
on distressed residential condominium
units that were foreclosed and sold in
Louisiana in 1985. They found a dis-
count of 24 percent attributed to the
sellers’ (lenders’) motivation to sell the
properties quickly to avoid carrying costs.
A similar study by Forgey, Rutherford,
and VanBuskirk (1994) estimated the
discount on 280 foreclosed single-family
properties in Arlington, Texas, between
1991 and 1993 out of a sample of 2,842
transactions. They found a foreclosure
discount of 23 percent, with cash sales
resulting in a discount of 16 percent.
In more recent research, Campbell,
Giglio, and Pathak (2009) analysed sales
data in the state of Massachusetts over
the period 1987 to 2008. They found
that houses sold after foreclosure sold
at lower prices than other houses and
that foreclosure discounts were par-
ticularly large, on average 28 percent of
the value of a house, and appeared to
be related to the threat of vandalism in
low-priced neighbourhoods. Moreover,
the econometric analysis clearly showed
that, at the local level, foreclosures oc-
curring within a quarter of a mile, and
particularly within a tenth of a mile, of a
house lowered the sale price. Pertinently,
the authors found that the foreclosure
effect at a distance of 0.05 miles lowered
the price of a house by about 1 percent.
Sumell (2009) estimated a 50 percent
foreclosure discount for property sales
in Cuyahoga County, Ohio, between
2004 and 2006.
A previous study by Pennington-Cross
(2006) evaluated the prices of 12,280
foreclosed single-family properties na-
tionwide and concluded that over their
life, whether sold by owner or lender, the
loan-foreclosed properties appreciated
22 percent less than the nonforeclosed
properties in the same metropolitan
area. However, the analysis failed to test
whether foreclosures caused a decrease
in sale price, and limitations in the
control variable subset neglected neigh-
bourhood characteristics. Therefore, the
findings mean only that the foreclosed
properties may have physical, neighbour-
hood, or location characteristics that
caused them to appreciate at a lower rate
than properties in the same area.
This is an important implication,
identified by Clauretie and Danesh-
vary (2009). When they estimated the
house foreclosure discount corrected
for spatial price interdependence and
endogeneity of marketing time, they
questioned the issue of omitted variable
bias and foreclosure per se as discount
stigma effects within some studies.
This point was incorporated into
the research of Rogers and Winter
(2009), who, controlling for a variety
of neighbourhood features and spatial
econometric techniques, measured the
impact of foreclosures on housing sales
using a unique data set from St. Louis
County, Missouri. Their results not only
revealed an expected decline in the sale
price of neighbouring properties but
also demonstrated that the marginal
impact of foreclosures declines with an
increase in the number of foreclosures.
In a slightly different vein, Leonard
and Murdoch (2009) investigated the
relationship between neighbourhood
quality and house prices, controlling
for both spatial dependence and er-
rors in housing prices. Their findings
highlighted the fact that changes in
nearby foreclosures reveal changes in
neighbourhood quality, thereby signal-
ling that estimates of the hedonic price
of nearby foreclosures provide a glimpse
of values that people hold for local
neighbourhood quality. Their model
estimates suggested that nearby fore-
closures produce externalities that are
capitalized into house prices, whereby an
additional foreclosure within 250 feet of
a sale has a negative impact on sale price
of approximately $1,666 ceteris paribus,
suggesting that changes in nearby fore-
closures foreshadow (negative) changes
in neighbourhood quality leading to an
expectations effect (Frame 2010).

Overall, the literature highlights that
spillover effects and foreclosure dis-
counts exist, although the magnitude
varies by location and axiomatically by
time period, given the housing market
cyclic effects. Nonetheless, whilst the
literature is rich from both a pricing
effect and financial integration perspec-
tive, more limited insights have been
garnered for property tax assessment
purposes.
Model Specification
Hedonic modelling is the orthodox
technique applied in property analysis to
ascertain the marginal effects of property
attributes. The essence of hedonic price
modelling is to capture the relationship
between house prices and housing at-
tributes. Typically, as identified in the
seminal writings of Rosen (1974), the
basic form of the house price model is
the functional relationship between the
price, P, of a heterogeneous good, i, and
its quality characteristics represented by
a vector xi
:
(1)
Pi
= f(xi
;ß) + ui
where
Pi
= a property with a price P
xi
= structural attributes of size and
quality and also attributes of the
neighbourhood in which the property
is located (indicators of the adjacent
environment and accessibility)
ß = the vector of coefficients simu-
lated for the characteristics
ui
= the error term.
GWR is an extension of the ordinary
least squares regression model and is
represented by the formula:
(2)
yi
= ß0
(xi
,yi
) + ∑ ßk
(xi
,yi
)xik
+ εi
where
yi
= i-th sale
ß0
= model intercept
ßk
= k-th coefficient
xik
= k-th variable for the i-th sale
εi
= the error term of the i-th sale
(xi,
yi
) = the x and y coordinates of
the i-th regression point.
Within GWR, a separate regression is
estimated at each observation (for this
paper, the xy coordinate of each sale),
allowing model coefficients to vary
across geographic space (Fotheringham,
Brunsdon, and Charlton 2002). The
bandwidth of each regression point
refers to the encompassing distance of
observations to be included and how
the spatial kernel assigns weights. This
bandwidth value can be either fixed
(including all properties within some
predetermined distance) or adaptive
(including some predetermined value
of nearest neighbours), where the spatial
kernel calculates and assigns weights
to other observations. The models
employed in this paper apply a spatial
kernel with a Gaussian weight—with sales
nearer to the regression point receiving
a higher weight than those further away
(visually depicted in figure 1)—and an
adaptive bandwidth. (Bidanset and Lom-
bard [2014b] demonstrated that kernel
and bandwidth combinations do have
statistically significant varying impacts
on model performance and specifically
attainment of the COD. During model
specification and calibration, additional
kernel and bandwidth combinations
were tested.) The Gaussian weight is
expressed as follows:
(3)
wij
= exp [−1/2(dij
÷ b)2
]
where
wi
= the weight applied to the j-th
property at regression point i
b = the bandwidth

dij
= the geographic distance between
regression point i and property j.
This weighting scheme is visually de-
picted in figure 1,
where
X = regression point (in an AVM, this
would be the subject property)
● = a data point (in an AVM, this could
be a sale).
Figure 1. Spatial kernel used in
geographically weighted regression
IAAO Equity and Uniformity
Standards
The analysis is measured by employ-
ing standardised tests for fairness and
equity taxation approaches, namely, the
coefficient of dispersion (COD) and the
price-related differential (PRD) as fur-
nished in equations 4 and 5, respectively.
The International Association of Assessing
Officers (IAAO) has established statistical
standards by which assessments may be
inspected with respect to accuracy, eq-
uity, and uniformity. The COD measures
the uniformity of an assessment stratum
and provides a measure of the variation
of individual assessment ratios around
the median. If the individual ratios are
clustered closely around the median, the
COD will be low, which implies the assess-
ments are relatively uniform. However, if
the individual ratios vary widely from the
median, the COD will be high, which indi-
cates that the property was not uniformly
assessed. Statistically, the COD expresses
the average absolute deviation of the in-
dividual ratios from the median ratio as a
percentage of that median. The Standard
on Ratio Studies (IAAO 2013) indicates
that the COD for non-new, single-family
homes should be less than or equal to
15.0. Values below 5.0 indicate potential
sampling error or sales-chasing.
The formula for COD is given as
(4)
COD =
100

N |Ri
− Rm
|
Rm
N1
where
COD = the average percentage of
dispersion around the median as-
sessment ratio
Rm
= the median assessment ratio
Ri
= the observed assessment ratio
for each parcel
N = the number of properties
sampled.
In addition to the COD, the intra-
area PRD is used to indicate assessment
uniformity and to quantify the degree of re-
gressivity, in which the low-value properties
are over-assessed relative to the high-value
properties, or progressivity, in which the
low-value properties are under-assessed
relative to the high-value properties. The
benchmark range for the PRD is 0.98 to
1.03. If there is a tendency for the assess-
ment ratios of high-value properties to be
lower than those of low-value properties,
the PRD will be greater than 1.03. If, on
the other hand, high-value properties have
higher assessment ratios than low-valued
properties, the PRD will be less than 0.98.
In this regard, the PRD measures the pat-
tern of inequity in assessments that has a
correlation with the value of the property.
Calculating the PRD assesses the mean
assessment ratio as the sum of all ratios
divided by the number of ratios. The for-
mula for calculating the PRD is

(5)
PRD =
i



Yˆ
i


Yi
n
i

 Yi

æ
ç
è
Yˆ
i
ö
÷
ø

/i
YiYi
Data and Variables
The final data set used in the analysis
consisted of 2,109 valid sales (a density
plot is shown in figure 2) and comprised
detached, single-family homes that
transferred between the period January
1, 2010, and December 31, 2012, in
Norfolk, Virginia. The data observa-
tions were inspected for potential data
entry errors (e.g., negative square feet),
missing values (e.g., no condition or
grade), and outliers (e.g., sale prices
statistically significantly above or below
the interquartile range), and these were
subsequently cleansed. This process
removed approximately 3 percent of
all observations, which were purged
from further analysis. A second data set
comprising 1,630 foreclosures (figure 3)
and 1,332 sales after foreclosure (figure
4) was prepared in order to create the
foreclosure-based variables.
The final useable variable data set and
an accompanying description of each
variable, with associated descriptive sta-
tistics, are presented in table 1. Where
appropriate, the variables have been
transformed into binary state. The area
of finished living space (in square feet)
of each home is represented by TLA.
This value does not take into account, for
example, unfinished attic space, garage,
or basement area. TLA2
is included to
capture any nonlinear relationship be-
tween finished area and sale price due
to diminishing marginal returns to value.
EffAgeRatio is an index calculated by
dividing a property’s effective age by its
actual age; this is a previously unused
modelling technique (to the authors’
knowledge). An EffAgeRatio value of 1 oc-
curs when a home’s effective age is equal
to its actual age; that is, there have been
Figure 2. Density plot of 2,109 valid sales in
Norfolk, Virginia (January 1, 2010–December
31, 2012)
Figure 3. Density plot of 1,630 foreclosures in
Norfolk, Virginia (January 1, 2010–December
31, 2012)
Figure 4. Density plot of 1,332 sales after
foreclosure in Norfolk, Virginia (January 1,
2010–December 31, 2012)

no efforts to cure depreciation. Eco-
nomic theory would expect that as this
value moves from 0 to 1, the associated
impact on price becomes more negative.
Age is the age of the home in years
(year of sale minus year of construc-
tion). With condition and effective age
accounted for, this variable is expected
to capture any premiums associated with,
for example, desirable historic proper-
ties and/or vintage architectural styles.
A squared age variable (Age 2
) is included
for potential nonlinear returns to value.
A dummy variable for each level of con-
dition (Condition) and grade (Grade) is
included, with average being the model
default for each.
Reverse month of sale time splines
offer a more accurate method of ac-
counting for seasonality and other
time-related fluctuations in the market
than reverse month of sale dummy vari-
ables (Borst 2013). Three-month time
spline variables were constructed based
each sale’s respective reverse month of
sale (RMOS) value.(RMOS variables are
categorical variables that indicate the
number of months between the observa-
tion and the month after the most recent
sale. For example, data comprising three
years of consecutive month sales would
have 36 RMOS variables, with the earli-
est month being RMOS36 and the most
recent month being RMOS1.) Only
splines for RMOS12 and RMOS24 have
statistically significant impacts on these
models and are included.
SAFDist is designed to measure the im-
pact of the proximity of the nearest sale
after foreclosure. Specifically, SAFDist
measures the straight-line distance to
the nearest sale after foreclosure. SAFDist
is expected to be positively correlated
with price; as distance between a valid
subject sale and a sale after foreclosure
increases, the likelihood of that sale after
foreclosure being a market substitute for
a potential buyer should decrease (the
Table 1. Explanatory variables and descriptive statistics
Variable Description Minimum Maximum Mean
Standard
Deviation
TLA Totallivingarea(sqft) 570 5262 1726 613
TLA2
TLAsquared 324900 27688640 3355276 2749428
EffAgeRatio Effectiveage÷age 0 1.00 0.84 0.27
Age Age(years) 0 123 56 26
Age2
Agesquared 0 15129 3848 2642
TGA Totalgaragearea(detached+attached)(sqft) 0 1564 240 211
TGA2
TGAsquared 0 2446096 102263 149059
RMOS12 Three-monthtimespline,12threversemonth
ofsale 0 24.00 6.57 7.14
RMOS24 Three-monthtimespline,24threversemonth
ofsale 0 12.00 1.30 2.70
Grade Gradecategoricalvariables(averageisdefault) – – – –
Condition Conditioncategoricalvariables(averageisdefault) – – – –
Foreclosure
Ratio
Foreclosures/validsalesforrespective
neighbourhoodandmonth 0 1.00 0.29 0.21
SAFDist Straight-linedistance(meters)tonearestprior
saleafterforeclosure 10 3672 280 406
SAFDist2
SAFDistsquared 94 13482930 243057 915838
Note
All values are rounded to the nearest whole number with the exception of those for RMOS12,
RMOS24, EffAgeRatio, and ForeclosureRatio; therefore, squared values may appear to be incorrect.

time a buyer spends looking for a house
is, after all, restricted to a finite window).
SAFDist looks only at the nearest sale after
foreclosure that occurred before the sale
of the observation; foreclosure sales that
occur after a sale have no ability to act as
a substitute or comparable. A squared
transformation (SAFDist2
) is included
for potentially nonlinear relationships
between distance and price. This ap-
proach helps account for both distance
and time of a sale after foreclosure.
ForeclosureRatio is included to exam-
ine the effect of foreclosures as they
occur on the local market; it is the ratio
of foreclosures to valid, arm’s-length
transactions of each observation’s respec-
tive neighbourhood and respective sale
month (Bidanset and Lombard 2014b).
This variable provides a relative view of
the density of foreclosures in a particular
area and is expected to have a negative
relationship with price; as foreclosures
increase relative to valid sales, there are
more opportunities for blight, crime,
and potential overall undesirability
(among other effects). The dependent
variable of the model is Ln.ImpSalePrice,
the natural logarithm of the sale price
less market land value. This method of
subtracting the land value from the total
value is often used in the assessment in-
dustry to help isolate and model impacts
on improvements only (Moore and My-
ers 2010; Bidanset and Lombard 2014b).
Results and Discussion
A GWR model that contained no variables
to account for effects of foreclosures
served as a baseline (model 1); the vari-
ables SAFDist, SAFDist2
, and ForeclosureRatio
were added to a second model (model 2)
(see table 2). The Akaike information
criterion (AIC) is a goodness-of-fit mea-
surement used to evaluate models applied
to the same sample, with lower scores
corresponding to a better goodness-of-fit.
A reduction of 2 or more is considered
statistically significant. Model 1 achieved
an AIC of −551.37, a COD of 9.02, and a
PRD of 1.01 (table 2 and figure 5). Model
2 achieved a better AIC, reducing it from
−551.37 to −559.97. While the COD of
model 2 improved the baseline model
by only 0.06, disaggregated COD values
showed that its improvements resonated
much more at the neighbourhood level
where model 2 reduced the COD for 74
out of the 130 neighbourhoods (57 per-
cent), with a maximum reduction of 33.8
percent (see figure 6). Note that accord-
ing to the Standard on Automated Valuation
Models (AVMs) (IAAO 2003), only neigh-
bourhoods with at least 5 sales are used
for computing ratio tests. Interestingly,
reductions appear to be concentrated in
areas with higher densities of foreclosures
and in areas with high densities of sales
proximate to these foreclosures. The PRD
remained unaffected across all models
at the citywide level (1.01), with little to
no fluctuation across all models at the
neighbourhood level. Whilst the baseline
model did not exhibit any indications
of progressivity or regressivity, it would
be worthwhile to evaluate the impact of
these foreclosure-based variables on a
model that does.
Table 2. Model results
Variable Model1 Model2
TLA * *
TLA2
* *
EffAgeRatio * *
Age * *
Age2
* *
TGA * *
TGA2
* *
RMOS12 * *
RMOS24 * *
Grade * *
Condition * *
ForeclosureRatio *
SAFDist *
SAFDist2
*
AIC −551.37 −559.97
COD 9.02 8.96
PRD 1.01 1.01

SAFDist coefficient values that are
statistically significant are illustrated in
figure 7. Interestingly, with respect to
SAFDist, there are not many statistically
significant coefficient values, probably
because as ForeclosureRatio increases, the
chances that one of the foreclosures will
be sold increases. Nevertheless, there
was no indication of multicollinearity
between SAFDist and ForeclosureRatio, and
SAFDist still statistically significantly im-
proved the model.
Statistically significant coefficient val-
ues of ForeclosureRatio are displayed in
figure 8; values range from 0 to −40 per-
cent as the ratio of foreclosures to valid
sales increases from 0 to 1. The results
suggest that areas with higher relative
amounts of foreclosure are expected to
have lower prices. Where such activity is
Figure 5. AIC and COD performance for models 1 and 2
Figure 6. Neighbourhood COD reduction in model 2

most dense, values for ForeclosureRatio are
much more negative, on average, than
areas where such activity is less dense.
Whilst the analysis shows that foreclo-
sure variables improved COD values for
57 percent of the neighbourhoods in the
data, the COD of many neighbourhoods
actually deteriorated, in all likelihood
because irrelevant variables created es-
timation errors. Pertinently, 47 percent
of neighbourhoods actually achieved
higher COD values once ForeclosureRatio
and SAFDist were added. In this regard,
for property tax assessment purposes,
it is recommended that practitioners
disaggregate COD results by neighbour-
hood during the calibration phase of
the modelling process, and only include
such variables in submarket models for
areas that benefit from their inclusion.
Figure 7. Statistically significant SAFDist coefficients
Figure 8. Statistically significant ForeclosureRatio coefficients

Conclusions
This paper set out to evaluate the impact
of GWR models that account for vari-
ous spatial foreclosure spillovers on the
equity and uniformity of mass appraisal
AVMs. By using a set of 2,109 valid sales
and a set of 1,630 foreclosures and 1,332
sales after foreclosure that occurred in
Norfolk, Virginia, between 2010 and
2012, variables were constructed to ac-
count for each observation’s straight-line
distance to the nearest sale after foreclo-
sure that occurred before the sale of the
observation (SAFDist), as well as the ratio
of foreclosures to valid sales (Foreclosure-
Ratio) for each observation’s respective
neighbourhood and sale month. Over-
all, the findings show increased model
accuracy and prediction using this type
of methodological approach. The find-
ings illustrate that reductions appear to
be the most drastic in areas with higher
densities of foreclosures. Pertinently,
the analysis indicates that the PRD re-
mains unaffected across all models at
the citywide level (1.01), with little to
no fluctuation across all models at the
neighbourhood level. In this regard,
whilst the baseline model did not exhibit
any indications of progressivity or regres-
sivity, it would be worthwhile to evaluate
the impact of these foreclosure-based
variables on a model that does.
Moreover, the findings indicate that
the inclusion of foreclosure variables
improves the COD values for 57 per-
cent of the neighbourhoods in the
data; nonetheless, the COD of many
neighbourhoods actually deteriorated.
Therefore, a core finding pertains to
how future taxation methodologies can
encompass these variables and, perhaps
more importantly, at what stage and level
within the modelling process.
Indeed, whilst the findings of this
research offer great implications for im-
proving mass appraisal AVMs with spatial
foreclosure variables, it appears to be the
first of its kind and there is much room
for improvement in methodology and
variable creation and implementation.
The current issue with GWR bandwidths
is that they may cross over multiple
neighbourhood boundaries simultane-
ously. The bandwidths employed were
not so small that errors were created
within their estimation, but further re-
search should be undertaken to compare
additional spatial variables techniques
(e.g., the ratio of foreclosures and sales
after foreclosure to valid sales within x
miles and y months). Furthermore, note
that because GWR controls for much of
the effect of location, the use of foreclo-
sure variables would likely have a much
more significant impact on, for example,
a spatially unaware global model.
It is also very important to continue
to evaluate foreclosure spillovers by
both time and space. There are many
multidimensional questions that should
be considered: for example, What is the
impact of a foreclosure that is physically
close but temporally far away (and vice
versa)? How does the impact differ from
a foreclosure that occurs next door to a
subject property one year before, and a
foreclosure that occurs a half-mile away
just two months before?
While straight-line distances measure
how far a sale after foreclosure is from a
subject property, this method of quanti-
fication is arguably not without potential
shortcomings. Although a foreclosure
may, at first hand, seem to be in proxim-
ity based on straight-line distance, this
neglects a wealth of potential physical
barriers that may prevent it from actu-
ally lying in the same effective market
as a subject property. A programmed
computer script designed to find the
nearest sale after foreclosure from the
subject property, based on straight-line
distance, may discover one on the other
side of some boundary, when that prop-
erty is actually much further away when
evaluated in terms of accessibility.
A proposed method for improving
distance variables would be to examine
a drive-time coefficient (i.e., the time
it takes to drive). Moreover, other vari-
ables, such as school zones, should also

be evaluated. A discounted sale after
foreclosure in proximity to a subject
property but perhaps just across a zoning
line and belonging to an inferior school
district may not be a viable alternative for
parents; the risk on their children’s edu-
cation may not be worth the discount on
the home. The rates of owner occupancy
should also be evaluated. Areas where
owners are less likely to live and more
likely to lease may not be as affected by
the potential blight of foreclosures be-
cause the owners themselves do not have
to experience it as frequently as those
to whom they are leasing. In addition,
potential owners of income property
and other investment-based buyers may
be more attracted to areas of high fore-
closures, because lower costs offer the
potential for higher profits. Nonethe-
less, our intent in this paper has been
to set the stage for the development of
assessment industry AVMs that possess
foreclosure awareness to attain superior
uniformity levels.
Acknowledgments
The authors’ sincere gratitude goes to
IAAO, sponsor of the Academic Part-
nership Program; the IAAO Research
Committee, namely, Margie Cusack,
Ken Uhrich, Daniel Fasteen, Patrick
Alesandrini, and Ruel Williamson; grant
facilitator and research librarian Mary
Odom; and Norfolk, Virginia’s Office
of the Real Estate Assessor, namely, Bill
Marchand (Deputy Assessor) and Debo-
rah Bunn (Assessor).
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