House Price Change and Highway Construction: Spatial
and Temporal Heterogeneity
(Presented at the American Real Estate Society conference, April 2008)
Michael Reibel 1 , Ekaterina Chernobai 2 and Michael Carney 3
Draft: March 31, 2008
Abstract
This paper studies the effect of a newly completed highway extension on home
values in the surrounding area. We analyze non-linearities in both the effect of
distance from the freeway and the effect of time relative to the completion of the
road segment. While previous studies of the effects of nearby amenities on
property and land values have focused on either cross-sectional spatial or
temporal patterns, the joint analysis of the two dimensions has not been
thoroughly investigated.
We use home sale data from a period of four years centered around the
completion of a new highway extension in metropolitan Los Angeles. We
combine a standard hedonic model with a spline regression technique to allow for
non-linear variations of the effect along the temporal and spatial dimensions.
Our empirical results show that the maximum home price appreciation caused by
the new freeway extension occurs at moderate distances from the freeway only
after it is completed. Lower price increases for this period are observed for
homes sold closer to the freeway or much further away. There is no statistically
significant distance dependency in the two years immediately prior to the
extension completion. This indicates that the housing market is not fully efficient
as the information about the impending completion of the freeway is not
immediately incorporated into sales prices.
Introduction
The effect of nearby amenities on home prices has been an important question in urban
economics since the late 1970s. At equilibrium, amenities (or disamenities) that are
1
2
3
Department of Geography and Anthropology, California State Polytechnic University, Pomona.
(E-mail: [email protected])
Department of Finance, Real Estate and Law, California State Polytechnic University, Pomona.
(E-mail: [email protected])
Department of Finance, Real Estate and Law, California State Polytechnic University, Pomona.
(E-mail: [email protected])
sufficiently close and sufficiently large as to affect homeowners’ utility will be
internalized into house values. This self-evident statement, however, does not resolve
which amenities have significant utility effects, the magnitude or even the direction of
those effects or of course, whether the system is in fact at equilibrium (i.e. whether utility
effects are fully internalized by the market pricing mechanism). More germane to our
current purposes, the phrase “sufficiently close and sufficiently large” is vague; moreover
there are further questions about the timing of the price changes corresponding to the
market internalization of new amenities.
This empirical paper investigates the spatial and temporal heterogeneity of house price
responses to new highway construction using the example of the Interstate 210 extension,
which opened November 2002 in Southern California. The case study is deliberately
modest in its scope, allowing us to focus in depth on the issues of spatial and temporal
heterogeneity in house price responses. Specifically, we focus on a single very large new
amenity (a ten mile stretch of ten-lane interstate highway), in the absence of other
important contemporaneous new amenities, thus effectively isolating its effect. Our
focus on observed price changes obviates the theoretical question of equilibrium while
imposing no assumptions about the direction or magnitude of actual price effects. Finally,
we estimate our models for a regular series of distances from the new road, and time
points both before and after the opening of the road, permitting us to track price effects
across various distances and over time.
We hypothesize that, first, the effect on home prices in the vicinity of the freeway
extension would be gradual over time since homeowners generally appear to be slow to
adjust home prices to changes in fundamentals. Second, we expect the price effect of the
freeway extension to be nonlinear and polytonic over distance. Specifically, for homes in
closest proximity to the freeway extension the negative externalities are expected to
dominate the positive externalities, exerting downward pressure on the prices of those
homes ceteris paribus. On the other hand, homes at moderate distance from the
extension, the transportation benefits of the freeway will dominate the inconveniences
caused by additional noise and air pollution resulting in higher home prices ceteris
paribus. At a certain distance threshold (to be empirically determined), the price effect of
the amenity is expected to fall asymptotically to zero. We also investigate how this
distance decay function may be changing over time prior to and after the freeway
extension completion.
The need for a new east-west freeway connection between Los Angeles and San
Bernardino counties was identified as early as in the middle of the 20th century. It was
needed for both travelers and commuters in order to relieve the traffic congestion on
other local freeways and streets between the cities of San Dimas and San Bernardino.
The construction of the main portion of the proposed 28-mile freeway extension,
stretching for 20 miles between San Dimas to Rialto, was started in early 1998 by the two
funding and construction partners of the project, SANBAG (San Bernardino Associated
2
Governments) and Caltrans (California Department of Transportation). It was completed
on November 24, 2002 4 .
The structure of the paper is as follows. The next section summarizes the theoretical
background and reviews related literature on the effects of local amenities on prices of
the surrounding properties. It is followed by the description of data and methodology
utilized for this paper. The results of the empirical analysis of the data are summarized
next. The last section concludes.
Theoretical Background
There have been hundreds of studies using hedonic models to estimate the effect of
nearby amenities on urban land and or home prices. The first works on hedonic
estimation are Rosen (1974) and Griliches (1971). In this approach, the price of an
individual property is modeled as a function of its physical, location and neighborhood
characteristics. Early studies applying hedonic methods to home prices and urban land
include Brown and Pollakowski, 1977; Goodman, 1978; Harrison and Rubinfeld, 1978;
Lafferty and Frech, 1978; and Nelson, 1978. A more recent important general study on a
very large Florida sample is Archer et al. (1996).
Subsequent work has often attempted to isolate the effects on home prices of particular
local factors of concern. Such factors include point source pollution (Brasington and
Hite, 2005), school quality (Leech and Campos, 2003; Haurin and Brasington, 1996), and
traffic externalities (Hughes and Sirmans, 1992). Particularly in the last few year such
studies have focused on the effects on house prices of such human-scale local amenities
as green space (Kong et al., 2007), bodies of water (Mahan et al., 2000; Larson and
Santelmann, 2007) and pedestrian-friendliness and new urbanist design (Kahn, 2007;
Matthews and Turnbull, 2007; Song and Knapp, 2003).
Another interesting development in the literature on hedonic estimation of the
determinants of house prices, and one with long-range theoretical relevance for studies of
the effects of transportation infrastructure investments, is research on the definition of
urban housing submarkets (Bourassa et al., 1999) and on the price gradients associated
with the multiple cores of multinodal cities (Plaut and Plaut, 1998; Waddell et al., 1993,
Dubin and Sung, 1987). Instead of seeking to use price differentials to reveal the implicit
price effects of household and/or local (dis)amenities, these studies treat the details of
urban morphology itself as amenities. Conceptually, they bridge the gap between
hedonic modeling of amenity effects and the seminal urban land rent theories of Alonso
(1964) and Muth (1969). These earlier studies were much simpler, relying as they did on
a conception of urban form dominated by a single central business district core. Further
developments of this sort in urban morphology may influence future studies of transport
infrastructure because of their potential implications for the value of accessibility to
secondary nodes in the urban system.
4
The remaining 8-mile eastern portion of the freeway extension was completed on July 24, 2007. It
stretches between Rialto and San Bernardino. Information source: www.sanbag.ca.gov
3
Of more immediate relevance to our analysis, many studies specifically address the
marginal effects of investment in the transportation infrastructure on affected home
prices. A number of these document the positive effects on home values of the addition
of nearby rail stations (Benjamin and Sirmans, 1996; Gatzlaff and Smith, 1993).
Debrezion et al. (2007) found a stronger positive impact of new rail station construction
on commercial property values at short distances and on residential values at slightly
longer distances. Gibbons and Machin (2005) employ a quasi-experimental design
comparing house price appreciation for a treatment group (homes for which new stations
made rail more accessible) and control group (otherwise similar nearby homes not
affected by new stations). Other rail station studies include Bowes and Ihlandfeldt (2001)
and McMillen and McDonald (2004). Both of these studies use a set of dummy variables
to code for distance from sample homes to rail stations. Bowes and Ihlandfeldt found the
most positive effects in richer, more peripheral neighborhoods, while McMillen and
McDonald found a steep negative price gradient with increasing distance from new
stations.
Studies examining the impact of new automobile oriented infrastructure on land values
are less common than studies of the impact of rail investment. Mikelbank (2004)
speculates that this is because of the more generally large, discrete and separable nature
of major rail infrastructure investments, which makes it easier to analyze their net effects
than those of road building. Kilpatrick et al. (2007) emphasize the negative impact on
house prices of nearby superhighways and tunnels when access points are more distant.
Mikelbank (2004, 2005) examines the effects of smaller, more numerous road
infrastructure investments in Ohio with mixed results. Smersh and Smith (2000) find
construction of a new bridge impacts positively on peripheral areas that subsequently
enjoy greater access but negatively on more central areas that experience greater
congestion.
In addition to the increasing range of causal factors examined, there has been
considerable methodological refinement in the hedonic estimation of house prices. A
number of studies incorporate spatial statistics or spatial interactions in the estimation of
models (Mikelbank, 2004; Fik et al., 2003; Can and Megbolugbe, 1997; Can 1992). By
contrast, Bourassa et al (2007) find that spatial econometrics do not improve the
estimation of house prices in their sample. Dubin (1998) provides an excellent overview
of the kriging technique and its applications in house price research. Case et al. (2004)
contrast several spatial econometric specifications and find evidence that such models
incorporating nearest neighbor information perform better than more typical local
regression models.
Whether or not spatial statistics are applied, many of the studies of the effects of
transportation infrastructure on house prices are disaggregated by distance or otherwise
designed in such a way that they reveal major non-linearities in the effects of distance
from relevant new transportation amenities (Kilpatrick et al., 2007; Debrezion et al.,
2007; Waddell et al., 1993). In particular, effects are often found to be negative at very
short distances, because of noise, pollution, and (particularly in the case of rail stations)
excessive foot traffic and possibly crime. At the next functional range of distances, the
4
amenities are still close enough to be beneficial but the negative effects are diminished,
resulting in a positive overall effect on house prices. At greater distances the value of the
amenity gradually declines to zero.
Likewise, the effects of new transport amenities are not constant over time, and the effect
of the time variable is also non-linear. Several studies show effects anticipating transport
amenities that have been announced and/or are under construction but are not yet
available for use. Yiu and Wang (2005) found positive effects anticipating the opening
of a new tunnel in Hong Kong. McMillen an McDonald (2004) found similar positive
anticipation effects for the Midway rail line in Chicago. Conversely Mikelbank (2004)
found negative anticipation effects. Smersh and Smith (2000) found mixed effects that
were consistent both before and after the opening of the bridge in their study. Other
studies probe the question of price adjustments over time following the availability of a
new transportation amenity. Mikelbank (2005) shows negative effects one year after
availability, near zero effects at slightly more than two years after availability, peaking at
three years after, and followed by a slow decline. He speculates that the brief negative
effect might be due to temporary congestion resulting from the travel adjustment process.
Because these distance gradients and time lags in the effects of transportation
infrastructure investment are expected to be non-linear, a particularly promising
methodology for these purposes is spline regression (Bao and Wan, 2004; Smersh and
Smith, 2000). Splines are essentially piecewise regression models that are constrained in
such a way that there are no jumps (discontinuities) between segments, but rather changes
in slope at the segment junction points (called knots). The result is a continuous
estimation in which the changing slopes of the segments represent effects at successive
values of the spline variable.
By using spline regression models in our study we probe the non-linearities in the effects
of both distance and time from the initial availability of major transportation
infrastructure amenities, a freeway extension in metropolitan Los Angeles. Such nonlinearities have been demonstrated separately in previous studies but never jointly
analyzed; thus, we believe that our study would make a contribution to the literature on
the effects of distance from amenities on home values.
Data and methodology
The empirical data for the estimations was obtained from DataQuick Information
Systems and made available to the Real Estate Research Council of Southern California
at California State University, Pomona. Housing data for a total of 5,566 home sales in
San Dimas, La Verne, Pomona and Claremont was extracted for the period between
December 1, 2000 and December 1, 2004. This covers a four-year period, two years
before to two years after the freeway extension completion. The DataQuick dataset
provides information only for the most recent sale of each individual house that occurred
within the period. If a house was sold more than once within the period, then only the last
sale will be recorded in the sample.
5
The data provides information about the physical characteristics of each property which
included sales price, home and lot sizes, property age, number of bedrooms and
bathrooms, existence of heating and cooling systems, among others. The description of
the property characteristics obtained from the dataset, as well as other control variables
used in the estimations, is provided in Table 1. The descriptive statistics for them are
summarized in Table 2.
Value is the dollar assessed value of the house which is used as the dependent variable in
the hedonic regression estimations in this study. SqftHome and SqftLot are the total areas
of the house and of the lot, respectively, measured in square feet. The size of each is
expected to positively affect the Value. A related variable, PercentImprove, shows the
percentage of improvement on land, or the percentage of the lot used for the structure. A
lower percentage is expected to contribute to a higher property value since this would
indicate a higher amount of land that comes with the house. We expect that
multicollinearity between the percentage of improvement and the previous two variables
is not likely since the house structure may take different length and width dimensions as
well as occupy two or more floors. Thus there should be no clear relationship between the
size of the home, the size of the lot and the fraction of the lot that the structure occupies.
The age of the house, Age, measured in years, is one of the negative factors affecting
home value and we thus expect to see a negative coefficient for this independent variable.
Instead of using the number of bedrooms as an independent variable we decided to use
AllRooms which adds extra rooms in the house to the number of bedrooms. Our argument
is that each additional room in the house is viewed by households as an added value, and
in addition many extra rooms could be converted into additional bedrooms. Different
regression models that were attempted for data fitting in this study showed that this
variable gives statistically better results than for those in which the number of bedrooms
was used instead.
For a similar reason, we decided to not use the number of bathrooms directly in our
models but to use the number of bedrooms less the number of bathrooms, BedLessBath.
This reflects how many bedrooms come without a bathroom and is thus viewed by
households as a disadvantage. For example, having not three but only two bathrooms in a
house will not necessarily decrease home value if there are a total of only two bedrooms
in the house; having too much space in the house allocated for bathrooms may be viewed
as a space inefficiency and may thus lower the house value. Heat and Cool dummy
variables reflect the presence of heating and cooling systems in the house which are
expected to affect positively the value of the house.
To control for market conditions, LastMonth30r and Change30r are used to indicate the
level of the 30-year fixed rate mortgage rate. LastMonth30r is the daily average mortgage
rate for the previous calendar month. We believe that using the recent average rate is
more accurate than the one on the property sale day since homeowners selling their
homes consider a recent trend in the rate at the time they put their properties for sale.
Change30r is the change in LastMonth30r between the last two calendar months. This
6
Table 1. Description of variables used in estimations
___________________________________________________________________________________________________________
Variable
Description
Units
______________________________________________________________________________
Value:
SqftHome:
SqftLot:
Age:
AllRooms:
BedLessBath:
Heat:
Cool:
LastMonth30r:
Change30r:
PercentImprove:
Miles
m2
m3
m4
m5
m6
m7
Open-i
Open+i
Time
Assessed value of the house
Total area of the house
Total area of the lot
Age of house calculated by subtracting the year built from the year of
sale date
Total number of rooms in the house (bedrooms and extra rooms)
Number of bedrooms less number of bathrooms
Dummy variable: 1 if heating exists, 0 otherwise
Dummy variable: 1 if cooling exists, 0 otherwise
Average 30-year fixed mortgage rate for the previous calendar month
Difference in the average 30-year fixed mortgage rate between two
previous calendar months
Percentage of the improvement on the property
Distance from the freeway extension
Distance from the freeway extension less 0.4 miles
Distance from the freeway extension less 0.8 miles
Distance from the freeway extension less 1.2 miles
Distance from the freeway extension less 1.6 miles
Distance from the freeway extension less 2.0 miles
Distance from the freeway extension less 2.4 miles
Dummy for i-th year preceding the freeway extension opening
date, i = 1, 2
Dummy for i-th year following the freeway extension opening
date, i = 1, 2
Number of days between 12/1/2000 and sale date of the house
dollars
square feet
square feet
years
percent
percent
percent
miles
miles
miles
miles
miles
miles
miles
days
____________________________________________________________________________________________________________
Table 2. Summary statistics of variables used in estimations (N = 2,259)
Variable
Mean
St. Dev.
Minimum
Maximum
Range
Value
SqftHome
SqftLot
Age
AllRooms
BedLessBath
Heat
Cool
LastMonth30r
Change30r
PercentImprove
Miles
Time
316,070.3
1,575.22
10,359.9
44
8.31
1.25
0.99
0.24
5.15
-0.003
38.26
1.37
851.32
140,168.2
504.99
23,745.06
16
1.99
0.68
0.11
0.43
0.35
0.21
13.7
0.9
402.8
8,400
480
126
0
3
-1
0
0
4.37
-0.37
0
0
0
1,700,000
5,695
757,900
114
19
5
1
1
5.78
0.55
93
3
1,460
1,691,600
5,215
757,774
114
16
6
1
1
1.4
0.92
93
3
1,460
Note: The means for Heat and Cool indicate the percentage of homes that have heating or cooling, respectively.
7
variable is expected to proxy for the expectation about the direction of the mortgage rates
prevailing in the market.
The data was used to estimate the change in the effect of the proximity to the freeway
extension on property values over the four-year period. The distance to the freeway for
each property was obtained using geo-coding techniques of geoprocessing tools in
ArcGIS Geographic Information Systems (GIS) software. The distance is measured in
miles and is labeled Miles in our estimations.
To obtain the change over time in the effect of the distance to the freeway extension we
split the dataset into four subsets – two before and two after the extension opening date –
that contain data for a year-long period in each. For example, the first subset contains
data for the period between December 1, 2000 and November 23, 2001. The remaining
three subsets cover consecutive years with the last one being November 24, 2003 through
December 1, 2004. The hedonic regressions are then run for all respective subsets
simultaneously as a system. We restrict the non-varying coefficients of the independent
variables, other than those controlling for the distance effects, to be the same across the
individual regressions. This way only the distance effects may vary over time. While
obtaining a continuous distance effect path is impossible, we believe that this regression
technique becomes a good approximation of the time path of the distance effect on
property values.
First, we run a “global” hedonic linear regression model over the entire dataset covering
the four-year period:
“Global” model:
Value = f (const, SqftHome, SqftHome2, SqftLot, SqftLot2,
Age, Age2, AllRooms, AllRooms2, BedLessBath,
BedLessBath2, Heat, Cool, PercentImprove,
PercentImprove2, LastMonth30r, Change30r, Open -2 ,
Open +1 , Open +2 )
This regression model includes the physical characteristics and the market conditions
variables described earlier. It also contains dummy variables that control for the year of
sale. The dummies are denoted by Open -i and Open +i and represent i-th year preceding or
following the freeway extension opening date, respectively, where i = 1, 2. The squared
values in the constructed model are expected to detect the presence of convexities in the
effect of the variables on the property value.
Next, we remove the time dummies from the “global” regression model and fit the
resulting “local” model to the data in each of the subsets in a system, as was explained
earlier. We use three forms of the “local” model. In “local” model (a), no distance
variable is included. Thus, it ignores any potential effect of the distance from the freeway
extension on property value completely.
A “local” model (b) includes all independent variables that model (a) contains and an
additional Miles variable which will detect the linear relationship between the proximity
to the freeway extension and the property value. The further from the freeway the lower
8
the home value is expected to get due to the inconvenience caused by longer time
required to drive to the freeway. Thus we expect to see a negative regression coefficient.
A “local” model (c) includes all independent variables that model (b) does plus additional
distance spline variables that will detect any nonlinearities in the dependence of the
property values on their distance away from the freeway extension. For consistency
between the data subsets, we fixed the distance cutoffs used for the spline knots in each
subset. The cutoffs are in 0.4 mile increments: 0.4 miles, 0.8 miles, 1.2 miles, 1.6 miles,
2.0 miles and 2.4 miles away from the freeway. 0.4 mile distance increments appear to be
optimal. Larger increments appeared to be not good enough to catch short distance
nonlinearities especially for homes lying in relatively close proximity to the freeway. On
the other hand, smaller increments weaken the regression results by making the number
of observations between any two adjacent distance cutoffs too small.
Following the spline technique methodology of Marsh and Cormier (2001) we construct
the spline adjustment variables in “local” regression model (c) in the following way. The
six distance cutoffs explained earlier require us to first create six dummy variables D 1M ,
D 2M , D 3M , D 4M , D 5M , and D 6M . Here, D 1M = 1 when the distance to the freeway is more
than the first distance cutoff of 0.4 miles, and D 1M = 0 when the distance is less than 0.4
miles. Similarly, D 2M = 1 when the distance to the freeway is more than the second
distance cutoff of 0.8 miles, and D 2M = 0 when the distance is less than 0.8 miles, and so
on.
These dummy variables are then used to construct the spline adjustment variables m2,
m3, m4, m5, m6, m7, corresponding to the second, third, fourth, fifth, sixth and seventh
0.4 mile distance segments, respectively. Here, m2 = D 1M (Miles – 0.4), m3 = D 2M (Miles
– 0.8), and so on.
The coefficients of these six spline adjustment variables thus indicate the additional
effects of the distance on home value relative to that in the distance segment next closest
to the freeway. For example, to determine the effect of the distance on home value for
homes located 0.8 to 1.2 miles away from the freeway extension, one needs to sum the
regression coefficients for Miles, m2 and m3 spline regression variables.
In summary, the three “local” regression models are:
“Local” model (a):
“Local” model (b):
“Local” model (c):
“Global” model without the time dummy variables
“Local” model (a) with the additional variable Miles
“Local” model (b) with the additional distance spline
adjustment variables m2, m3, m4, m5, m6, m7
Our hypothesis is that, first, there may be statistically significant non-linear effects of the
distance on sales values of the properties. This should get reflected in a better fit of the
regression model with the distance spline variables producing an R-squared higher in
“local” model (c) than in “local” models (a) and (b). Second, we hypothesize that the
spline variable coefficients will indicate an initial increase in the total distance effect
9
followed by a decrease as homes get more distant from the freeway extension. We
believe this effect would become more noticeable for later time periods of the dataset as
households take time to readjust their home prices in response to the changes in the local
amenities.
For an additional testing of our hypothesis of a time-varying effect of the distance from
the freeway extension on property values, we split the entire data set into seven subsets.
Each contains homes lying in different distance intervals on both sides of the freeway
extension. For example, in the first subset we only left those homes that lie within 0.4
miles away from the extension, the second subset contains homes that lie 0.4 to 0.8 miles
away from the extension, and so on.
Since we no longer need to control for the distance in each subset, using the same system
estimation technique we run for each subset a “local” model (a) that also contains two
additional variables. The first variable Time shows the number of days between
December 1, 2000 and the sale date of the house. The second variable Complete is a time
spline adjustment variable created following the same method that was used to create the
distance spline adjustment variables explained earlier. It shows the number of days
between the freeway extension completion date, November 24, 2002, and sale date if
house was sold after this date, and 0 otherwise.
The results of these additional regressions are expected to show whether there existed any
differences in the speed of home value increases over the four-year period for homes sold
in different distance rings on both sides of the freeway extension. We expect to see the
slowest increase in value for properties in the closest and longest proximity to the
freeway, and the fastest increase in value for properties at moderate distances from the
freeway.
Results
Elimination of observations with missing value variables left 2,262 out of the original
2,575 observations for homes sold within the four-year period and located within 3 miles
from the freeway extension. The regression results for the “global” model with year
dummies are summarized in Table 1.
About 67 percent of the variations in home values are explained by the variations in the
chosen independent variables as is indicated by the R2. The majority of the independent
variables are statistically significant at the 1 percent level, and some other are significant
at 5 or 10 percent. As expected, both SqftHome and SqftLot positively affect home value
although the absolute magnitude of the effect appears to be rather small. When the size of
the house is measured in the number of rooms the magnitude of the effect on home value
appears much larger with an additional room in the house raising the value by $29,050.
Each bedroom that comes without a bathroom decreases the value of the house by
$16,680. As was discussed in the earlier section, this supports our suggested argument
that the advantage of having an extra bedroom is weakened if the house does not provide
10
an additional bathroom. The significance of the coefficients for the squared variables
suggests the presence of strong convexities or concavities in the effects.
The percentage of improvement on land, PercentImprove, statistically significantly raises
the property value by about $6,963 per each percentage point with a slight concavity in
the effect. Age decreases home value with the marginal coefficient equal to $2,623. The
significance of the coefficient for Age2 indicates the weakening of the effect as the house
becomes much older. The presence of cooling in the house raises house value by almost
$34,346. The effect of Heat is also positive although not statistically significant. A
percent increase in the 30-year fixed mortgage rates increases home values by $17,705.
The positive statistically significant coefficients for the dummy variables used to control
for the year of sale confirm that over the four years home prices have been increasing.
Moreover, they have been doing so at an increasing rate as can be seen from the
increasing differences between the year dummy coefficients.
The same “global” model, excluding the dummy variables, was used to fit the data in the
system consisting of the four one-year subsets. As was explained in the earlier section,
we include additional variables that control for the distance of each house from the 210
freeway extension. The linear effect of the distance on home values in each subset is
measured in a “local” regression model (b), and the non-linear effect in a “local” model
(c). Model (a) does not control for the distance. The regression results for the three
“local” models for each subset are shown in Table 2. As the coefficients for the majority
of the independent variables remain statistically significant at least at the 10 percent level,
the table only presents the results for the goodness-of-fit and the distance variable
coefficients. Those for the “global” model, with and without the distance variables, are
also included in the table for comparison.
First, the results in Table 2 indicate that for the entire dataset and for the four subsets the
goodness-of-fit of the hedonic regression model increases when property values are
controlled for the distance from the 210 freeway extension. In each case the value of R2 is
higher in model (b), which contains the linear distance variable, Miles, relative to model
(a). The expected negative sign of the Miles coefficient and the 1 percent significance
level in all but the first year of the four-year period of interest suggest that the further
from the freeway the lower the house value. Based on our regression models, an
additional mile away from the freeway decreases home value by $18,276, $23,119, and
$29,962, for the year preceding and the two years following the freeway completion,
respectively. The negative distance effect thus gets stronger over time.
Second, regression model (c) results indicate that for all subsets the model fits the data at
least as well when one controls for non-linear effects of the distance using the spline
technique described in the earlier section. The distance spline variable coefficients
reflecting marginal effects of the distance on property values appear to be statistically
significant for close distances to the 210 freeway extension after the extension was
completed. The fact that the effects of distance on home values do not appear significant
before the freeway completion may imply that households were slow to change their
11
Table 1. Hedonic regression results for the “global” model with year dummies.
Variable
Coefficient
t-statistic
Constant
-179,578.4
-3.2325
SqftHome
28.0263
1.6362
SqftHome2
0.0284
7.0634
***
SqftLot
3.9098
14.7414
***
SqftLot2
-0.0001
-14.2357
***
Age
-2,622.735
-5.0429
***
29.8186
6.8126
***
29,049.66
4.8527
***
AllRooms
-1,421.071
-4.3854
***
BedLessBath
-16,680
-2.7668
***
BedLessBath2
3,351.763
1.6918
*
Heat
11,211.55
0.7485
Cool
34,345.59
6.5249
***
6,963.42
12.7474
***
PercentImprove
-113.0195
-19.3086
***
LastMonth30r
17,705.4
2.1433
**
Change30r
-7,218.281
-0.768
Open -1
30,309.89
4.988
***
Open +1
69,902.07
8.9312
***
Open +2
136.434.5
20.3681
***
2
Age
AllRooms
2
PercentImprove
2
R
2
0.6736
Number of observations = 2,262
The dependent variable is Value.
* indicates 10 percent statistical significance
** indicates 5 percent statistical significance
*** indicates 1 percent statistical significance
12
***
Table 2. Results of hedonic regression models (a), (b), and (c) for full dataset and four
one-year subsets.
Full
dataset
One-year subsets
Open -2
Open -1
Open +1
Open +2
2,262 obs.
381 obs.
381 obs.
760 obs.
740 obs.
(a) R2
0.691
0.325
0.582
0.656
0.656
(b) R2
0.706
0.373
0.612
0.674
0.672
-18,276.45 ***
-23,118.78 ***
-29,961.71 ***
0.618
0.685
0.678
95,630.61 **
101,976.3 **
-142,657.7 *
-129,130.3 *
Miles
2
(c) R
-21,980 ***
0.711
0.373
Miles
m2
m3
m4
m5
m6
m7
NOTES:
Regression models (a), (b), and (c) for the full sample include year dummy variables.
The dependent variable in each hedonic regression model is Value.
Model (a) contains no distance variables.
Model (b) contains linear distance variable, Miles.
Model (c) contains distance spline variables.
* indicates 10 percent statistical significance.
** indicates 5 percent statistical significance.
*** indicates 1 percent statistical significance.
Distance spline variable coefficients not statistically significant at the above levels were omitted.
13
pricing in response to the change in surrounding amenities despite the fact that the
information about the new freeway extension under construction was already publicly
available. In our econometric model this may also be due to a smaller sample size for the
earlier subsets of data making them not large enough to detect the distance effects on
home values.
The marginal distance effects for the two years following the freeway opening can be
converted into total effects of the distance on home values for each 0.4 mile distance
segment. For example, within 0.4 miles from the freeway the value of homes that were
sold within one year from the freeway completion rises by $95,631 per each mile as the
distance from the freeway rises, as indicated in Table 2. For the second 0.4 mile distance
segment in that time period home prices fall by $47,027 per each mile – this number
comes from taking the sum of Miles and m2 coefficients 95,631 and -142,658,
respectively. The results for the two-year period, when split into two year-long periods,
are summarized in Table 3. From the resulting total distance effects one can also infer the
difference in home values between the beginning and the end of 0.4 mile segments,
summarized in the table in the last column for each time period.
The numbers in Table 3 support our hypothesis that there exist non-linearities in the
effects of the distance to the freeway on property values. According to our hypothesis,
home values should first increase and then gradually decrease as the distance rises. We
also hypothesized that these distance effects would not be immediately incorporated in
home values when the information regarding the freeway construction was already
publicly available, thus creating a delay in the occurrence of the effects. Table 3 shows
that homes that were sold in the first year after the extension was completed and that lie
0.4 miles from the freeway are $38,252 more expensive than homes sold right next to the
freeway, when physical characteristics are controlled for. According to our hypothesis,
this may reflect the presence of negative externalities caused by the noise generated by
the freeway traffic. The corresponding number for homes sold in the second year is
slightly higher at $40,790. The price of homes sold 0.8 miles from the freeway is $18,811
and $10,862 lower than for those that lie 0.4 miles from the freeway for the two
respective years. This may reflect the increasing disadvantage of being located further
away from the freeway.
Table 4 summarizes the results of the hedonic regressions performed in a system for the
seven 0.4 mile distance subsets and aimed at identifying any differences in the time path
of the house value appreciation. The first system of regressions does not control for the
time when a house was sold. The second one contains the Time variable and identifies the
linear effect of time, measured in days, on the house value. The third model is expected
to produce a more accurate time trend as it contains an additional time spline variable
Complete. This model aims at identifying additional differences in the time effects
following the freeway extension completion date, November 24, 2002.
The inclusion of variables that control for the time of sale improve the goodness-of-fit of
the hedonic regression model as is indicated by the higher R2 for model (a) with Time
variable, and an even higher R2 for model (a) with time spline variables. This is true for
14
Table 3.
Non-linear effects of the distance to the freeway extension on home values.
0~0.4 miles
0.4-0.8 miles
Table 4.
Homes sold within the 1st year
following freeway completion
Homes sold within the 2nd year
following freeway completion
Marginal
effect,
$ per mile
Total
effect,
$ per mile
Price change
over 0.4 miles,
$
Marginal
effect,
$ per mile
Total
effect,
$ per mile
Price change
over 0.4 miles,
$
95,631
-142,658
95,631
-47,027
38,252
-18,811
101,976
-129,130
101,976
-27,154
40,790
-10,862
Results of hedonic regressions with and without time variables for full dataset
and seven distance subsets.
Full
Distance subsets
dataset
0-0.4 0.4-0.8 0.8-1.2 1.2-1.6 1.6-2.0 2.0-2.4
miles miles miles
miles
miles
miles
2.4-3.0
miles
2,262
obs.
391
obs.
369
obs.
348
obs.
317
obs.
134
obs.
259
obs.
444
obs.
R2
0.585
0.415
0.577
0.55
0.527
0.725
0.620
0.575
(a) with R2
Time
0.684
0.603
0.725
0.661
0.613
0.809
0.700
0.690
140
***
164
***
149
***
172
***
140
***
145
***
109
***
123
***
0.690
0.608
0.734
0.668
0.617
0.812
0.706
0.711
54
***
137
***
86
***
126
***
61
**
146
***
78
***
154
***
62
**
119
***
79
**
54
*
80
*
179
***
(a)
Time
(a) with R2
time
spline
Time
Complete
NOTES:
Regression model (a) for the full sample is the “global” model that excludes time period dummy
variables.
The dependent variable in each hedonic regression model is Value.
* indicates 10 percent statistical significance.
** indicates 5 percent statistical significance.
*** indicates 1 percent statistical significance.
Time spline variable coefficients not statistically significant at the above levels were omitted.
15
all seven distance subsets as well as for the entire dataset. In the “local” models that show
a linear relationship between sale time and home value the Time coefficients indicate an
increase in home prices at the speed of $109 to $172 per day depending on the subset,
and they are all statistically significant at 1 percent level.
For all distance subsets the results of the hedonic model containing time spline variables
indicate a faster increase in house values following the freeway extension opening date.
The regression coefficients for the variable Complete indicate that the price appreciation,
caused by the freeway extension opening, is slow in the closest proximity to the freeway
(within 0.4 miles), faster in the next two distance intervals, followed by slower
appreciations at the subsequent distances. Interestingly, the price appreciation is even
faster at the highest distance from the 210 freeway extension (the coefficient of 179) –
this can potentially be explained by the relieved traffic congestion in the area of the
former only east-west Interstate highway (FWY10), which lies about 3 miles south from
Interstate 210, causing local home prices in that region to rise faster.
These differences in the time paths of home value appreciation for the later two years of
our sample produce a pattern of non-linear effects on home values of the distance from
the freeway. In particular, the additional speed of price appreciation following the
extension opening is the slowest for homes in the closest proximity to the freeway (within
0.4 miles), a lot faster at moderate distances, and slower again as the distance further
increases. This produced pattern is consistent with that obtained from the systems of
regressions for different time periods presented earlier.
Discussion
The object of our study has been to use spline regression models to probe the nonlinearities in the effects of both distance and time from the initial availability of major
transportation infrastructure amenities – in our case, a freeway extension in metropolitan
Los Angeles. Such non-linearities have been demonstrated separately in previous studies
but never jointly analyzed as is done in our empirical case study. In our incremental
approach, we first modeled a standard hedonic regression of house prices on housing
characteristics and contextual variables including dummy variables for year of sale (to
control for the global effect of a rapidly appreciating metropolitan housing market).
These results are consistent with those from many earlier studies in the same vein.
Our next step was to disaggregate data along the time dimension and analyze them
separately for two years before and two years after the opening of the freeway extension.
For each of the four years we estimated separate models without any variable capturing
distance to the freeway extension, then with linear distance, and finally with distance
splines. The linear distance model shows the expected consistent decline with increasing
distance from the freeway extension. When the spline model for distance ranges is fitted
we find no statistically significant distance effect anticipating the freeway opening, and
the expected pattern of positive effects at shorter distances followed by mildly negative
effects at moderate distances. The latter is interpreted as reflecting a decline in the
16
competitive advantage of these properties relative to those closer to the freeway
extension. At longer distances, as expected, the effects fade into insignificance.
Our final step was to reverse the relationship of time and distance in our models. In other
words, we disaggregated the sample by 0.4 mile distance intervals and modeled the
effects of time. Once again, time effects were modeled first as continuous and linear and
subsequently as a spline. The time analysis reflects the distance effects already
discussed; in other words, after the freeway extension completion homes at the closest
and more distant regions appreciated less rapidly than homes in the intermediate distance
intervals.
More generally, our analysis adds to a growing literature on the use of splines to examine
specific time and distance non-linearities in the effects of local amenities on house prices.
We maintain that while spatial regression models may be a beneficial refinement of
standard hedonic price models of housing amenities they do not provide concrete
information on the form of time and distance decay functions. Splines, on the other hand,
serve this purpose.
17
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