Introduction
Council officials in Dane County, Wisconsin have noticed an
increase in foreclosures between the years 2011 – 2012 – where a mortgagor
fails to keep up with their payments, resulting in their property being
repossessed. The aim of this report is to look for spatial patterns in the
foreclosures, as well as predict whether or not there will be a further
increase in foreclosures in 2013.
Figure 1 - Numbered Census Tracts in Dane County,
Wisconsin, with test tracts outlined in red
Methodology
Using data showing the number of foreclosures per census
tract within Dan County in 2011 and 2012, a map was created to show the areas
of the county in which the number of foreclosures either increased or
decreased. Preexisting data showing foreclosure numbers in both 2011 and 2012
was used to figure out how 2012 numbers differed from those observed in 2011.
Three test tracts were randomly chosen, from which the
Z-scores of the number of foreclosures in both 2011 and 2012 were measured. The
chosen tracts (122.01, 31 and 114.01) are highlighted above in figure 1.
A Z-score is used to locate the exact position of an
observation on a standard deviation curve relative to the mean, so that exactly
how many standard deviations away from the mean it lies can be known. This is
useful, as from this probability can be derived of how likely this result was
to occur. Z-score calculations can also be utilized to answer questions that
help make predictions for the future: for instance, what number of foreclosures
will be exceeded 50% of the time?
Results
Figure 2 - Changes in foreclosures, from 2011 to 2012, in Dane County census tracts.
Figure 2 shows the changes in foreclosure numbers between 2011 and 2012 in Dane County. We can see that while there was a total of 1219 foreclosures in 2011, and 1316 in 2012, the number of foreclosures actually fell in many census tracts, particularly in Tract 113.02 in the north of the county, and Tract 5.04 in the center. Areas where the number of foreclosures fell are illustrated in blue on this map. There are however, many tracts where the number of foreclosures increased in this time, notably in the large Tract 129 in the north west and 119 in the east.
Figure 3 - 2011 Foreclosures by census tracts, Dane County, Wisconsin
If we compare these changes to the map in Figure 3, which
shows the number of foreclosures by census tract in 2011, we can see that while
some tracts that experienced a lot of foreclosures in 2011 saw an increase in
2012, this is not the case for all tracts – some of those, such as Tract 132 in
the north of the county, has a high number of foreclosures in 2011 but saw a
decrease in 2012. Furthermore, just to the east of Tract 132 is Tract 129,
which in 2011 had a low number of foreclosures that rose sharply in 2012. These
instances do seem to be anomalies, however, as the majority of tracts with
higher numbers of foreclosures in 2011 saw an increase in 2012, as can be seen
by comparing the smaller tracts in the center of the state from both Figure 2
and 3. Likewise, most of the tracts that had low numbers of foreclosures in
2011 saw a decrease in 2012, as illustrated by the tracts in the south west of
the county.
Part 2 – Z-Score Results
2011
|
2012
|
|
Tract 122.01
|
-0.614
|
-0.636
|
Tract 31
|
1.437
|
0.576
|
Tract 114.01
|
2.384
|
2.695
|
Table 1 – Z-Score
results for selected census tracts, for 2011 and 2012.
From the results above, we can see that for these three
tracts, despite the overall rise in foreclosures within the county as a whole,
the relative position on the standard deviation curve of these tracts has not
changed drastically. The results for Tract 31 emphasis the fact that the rising
number of foreclosures hasn’t affected all tracts in the county equally, as
here the 2012 value of 24 the previous year dropped to 2012.
Based on the mean for 2012 across all of the census tracts
of 9. 906 foreclosures, and the standard deviation of 8.776, there is a 70%
probability that there will be over 16 foreclosures in any given county. There
is a 20% chance that the number of foreclosures will be above 19. If this
occurs, it is likely to do so in the tracts such as 120.01, just west of test
tracts 31 and 114.01 (see figure 1). This tract can be seen to have a recorded
a high number of foreclosures in 2011 from figure 3, and then proceeded to
experience a large increase on this in 2012, as can be seen in figure 2. If
this pattern of growth is to continue, it is likely that it would do so in this
location.
Conclusion
From the data, we can see that growth in foreclosure numbers
was not consistent across the county, but limited to certain tracts. The
spatial pattern therefore seems weak, however if growing foreclosure numbers is
to continue past 2012 there is a 70% chance of foreclosure numbers above 16
will be observed in the census tracts. It is clear from figures 2 and 3 the
number of foreclosures in tracts are variable in most circumstances, however
notable areas such as tract 120.01 have experienced high growth on already relatively
high numbers of foreclosures. This could be due to changing economic
circumstances after the 2008 financial crash, which has caused many redundancies
and wage cuts which could explain why the numbers of foreclosures are so
variable and not confined to one area of the county – perhaps a more deprived
area, for instance.
