DICK NETZER, MICHAEL SCHILL, AND SCOTT SUSIN
4. Quantile regression was developed by Koenker and Basset
(1978). For an example of an application of quantile re-
gression methods, see Friedlander and Robins (1997).
5. The predicted values from OLS regressions are predicted
means. Quantile regression allows us to predict not only
what the mean water bill will be in the future, but also the
10th percentile water bill, the median water bill, etc. Use of
this estimator allows predictions of the future distribu-
tion of water bills without requiring any a priori assump-
tions about the shape of the distribution.
6. Box-Cox tests suggest that measuring the dependent vari-
able in logarithms improves the fit of the equation. In ad-
dition, the use of logarithms greatly reduces the hetero-
skedasticity of the data.
7. Because the dependent variable is measured in loga-
rithms, our predicted means are geometric means, rather
than the more common arithmetic means. The geometric
mean is the anti-logarithm of the arithmetic mean of the
logarithm of water charges. The advantage of geometric
means is that because they put less weight on extremely
high water charges, they are a better measure of central
tendency, in this case the water bill received by the “typi-
cal” customer.
1000 vs. about 4000 for the M-O-M buildings) and be-
cause there are few high-poverty tracts where the Jamaica
buildings are located.
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