Results of this study show that the effect of housing characteristics on selling price can be better explained by estimating quantile regressions across price categories. For example, previous studies that have examined the effect of characteristics such as square footage or age on selling price have found mixed results in terms of both the level and the direction of change. This study shows that some of those differences may be explained by differences in house prices. In particular, the regression coefficients of some variables behave differently across different house price levels, or quantiles. Buyers of higher-priced homes appear to price certain housing characteristics differently from buyers of lower-priced homes. For the given data set, it is shown that the quantile effects dominate any effects on coefficient size and statistical significance that arise from spatial autocorrelation. In fact, taking explicit account of spatial autocorrelation in the quantile regressions, adds very little information. Whether this is a general result or particular to the data set that is being used in this study is an open question that awaits further research. This study produces some interesting results. For example, square footage is often used to determine the appraised value of a home since it is expected to have a significant effect on the selling price. While previous studies bear this out, it is interesting to see how buyers in different pri
ce ranges value this variable. This is shown
by the significant difference between the coef
ficients at the lowest and the highest
quantiles where the additional price of a square foot for the highest priced homes is two
and a half times the additional price per square
foot for the lowest-priced homes. Clearly,
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traditional methodologies such as OLS or mode
ls that take into
account of spatial
autocorrelation can overstate the value of a
marginal square foot for lower-priced homes
but understate the effect
on higher-priced homes.
The quantile results provide some valuable
insights to the diffe
rent relationships
that the explanatory variables ha
ve with selling price. For
example, some variables such
as square footage, lot size, bathrooms, and
floor type have a greater impact as selling
price increases. Other variables have a rela
tively constant effect
on selling price across
different price ranges. These include gara
ge, exterior siding, sprinkler system, and
distance to city center. Some other variables such as bedrooms and percentage of
nonwhite population have a signif
icant effect on selling price
but there is no clear pattern
of the effect across different price ranges. Lastly, the quantile regressions confirm that
most variables showing no statistical si
gnificance under OLS or 2SLS remain not
significant across the different price ranges.
These results add to the body of research explaining house prices. Even though
variations in the value of
housing characteristics across di
fferent price ranges may have
been considered intuitive beforehand, quantil
e regression provides a way to confirm these
expectations.
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