Case-Shiller for
The City of Cleveland
PAIRED-SALE METHODOLOGY
The “Premier” Methodology
June, 2004: $225,000
June, 2014: $250,000
Sale of same house
10 years apart (120 months)
Sale price change: +$25,000
Percent price change: 11.11
Annualized percent price change: 1.06
Data Restrictions – Part 1
* Single-family only
* Sales at Least 6
months apart
* Sale prices of at
least $20,000
City of Cleveland request
Data Restrictions – Part 2
Remove non arm’s-length transfers
Data Restrictions – Part 3
* Limit to standard
deed types
ADM, AFF, EXC, FID, GDN, LIM, SUR, TOD,
TRS, WAR
* No sheriff sales,
and no sales if
within one year of a
sheriff sale
David Stiff of CoreLogic Case-Shiller:
“Outlier control can be very difficult for
Cleveland, because during the crash
there were really two distributions of
price changes -- one for bank resales of
foreclosed properties and another for
resales of non-foreclosed properties. If
repeat pairs from these two
distributions are mixed (either
deliberately or inadvertently), then
estimates of the mean and/or standard
deviation of price changes can be
unstable.”
* Weights and
unrealistic changes
in price
Some parts are proprietary – will be
discussed later
The Base Period: 1989 to January, 2000
Unrealistic changes in value, and Weighting
For each second year of paired data, calculate z-scores for all observations,
based on annualized rates of change.
IF zscore LE .5 THEN mwgt=1;
ELSE IF zscore LE 1 THEN mwgt=1 - ((zscore-.5)/2); * goes down to .75; * at .5=1, at 1=.75;
ELSE IF zscore LE 1.5 THEN mwgt=.75 - ((zscore-1)/2); * goes down to .1667; * at 1=.75,
at 1.5=.5;
ELSE IF zscore LE 2 THEN mwgt=.5 - ((zscore-1.5)/2); * goes down to .1667; * at 1.5=.5, at
2=.25;
ELSE mwgt = .25 - ((zscore-2)/2); * goes way down could go negative; * at 2=.25, at 3=0;
IF mwgt LE .001 THEN mwgt=.001;
Creating matrices for the analysis of the base period, 1989 – January, 2000
Example 1: First sale in January, 1989
Example 2: First sale not in January, 1989
Basic Matrix Form of the Regression
β = (X’X)-1 (X’Y)
Matrix Form when Using Instrumental Variables
β = (Z’X)-1 (Z’Y)
Matrix Form when Adjusting for Heteroskedasticity
β = (Z’ Ω-1X)-1 (Z’ Ω-1Y)
Basic Index Pattern for the Base Period 1989 – January, 2000
Calculating Index Values for Months Beyond the Base Period: Chain Weighting
Sale 1
Jan-92
(mo=37)
$64,500
Beta for mo 37:
0.78580619
Sale 1
Estimated price at
time 0:
$50,684
Sale 2
Jan-00
(mo=133)
$94,000
Comparison of Case-Shiller and Median Value Index