# RECORD 2e573f3384314fd1e0b0dd7c24f567743146abb7
# TITLE: Selection Bias in Housing Price Indexes: The Characteristics Repeat Sales Approach*
# YEAR: 2022.0  VENUE: Oxford Bulletin of Economics and Statistics  DOI: 10.1111/obes.12534
# AUTHORS: Daniel Melser
# PAGES: 15  CANDIDATE TABLE PAGES (1-based): [8]
# ABSTRACT: nan


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OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 85, 3 (2023) 0305-9049
doi: 10.1111/obes.12534
Selection Bias in Housing Price Indexes:
The Characteristics Repeat Sales Approach*
DANIEL MELSER
Department of Econometrics and Business Statistics, Monash University, 900 Dandenong Road
Clayton, 3800, Victoria, Australia (e-mail: danielmelser@gmail.com)
Abstract
The widely used repeat sales method for constructing house price indexes only uses
data for properties that sell twice or more. This makes it susceptible to selection bias as
price movements for these properties may not be representative of those for the stock of
homes. We outline a novel approach to modelling repeat sales, which allows for a home’s
characteristics to influence its price movement. This allows us to impute price changes
for the stock of homes and control for selection-on-observables. Using data for Florida
from 2002 to 2020 we find that selection effects significantly exaggerated the volatility of
Florida’s housing prices.
I.
Introduction
Since the global housing booms and busts of the 2000s housing price indexes (HPIs)
have taken an increasingly central role in the suite of macroeconomic indicators. They
are important in providing homeowners with information about the value of their
home – which for many households is their single largest asset. HPIs are also vital to
policymakers and those in industry given that housing prices influence a broad range of
social, economic and financial variables. Perhaps most importantly, as was seen during
the US subprime crisis, housing prices have an important impact on the stability of the
financial sector.
There have been consistent efforts across the years to improve the measurement of
housing price dynamics. This was stimulated by the important early work of Case and
Shiller (1989) in sourcing data and developing appropriate methods. The importance of
this work was reinforced by the housing market crisis across a number of countries in
the late 2000s. This emphasized the poor quality and comparability of housing price
statistics across countries (IMF, 2009).1 This led to a global consensus about the need to
JEL Classification numbers: C43, E31, R30.
*Open access publishing facilitated by Monash University, as part of the Wiley - Monash University agreement
via the Council of Australian University Librarians.
1IMF (2009) writes, ‘Data on the stock of dwellings, the associated price levels and their changes over time
are critical ingredients for understanding household wealth, its evolution over time, and for the vulnerability of
households’ financial position. Similar information on commercial property is relevant not just for monitoring
the wealth of the corporate sector, but also for financial stability more generally, given that commercial property
623
© 2022 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and
reproduction in any medium, provided the original work is properly cited.


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630
Bulletin
TABLE 1
Summary statistics for homes by number of sales
Number of sales
0
1
2+
All
Number
4,261,733
2,373,035
1,404,722
8,039,490
Percent
53.0
29.5
17.5
100.0
Mean
SFR
0.79
0.71
0.66
0.74
Northwest
0.05
0.04
0.05
0.05
North Central
0.05
0.05
0.05
0.05
Northeast
0.07
0.06
0.04
0.06
East Central
0.28
0.21
0.15
0.24
West Central
0.25
0.24
0.22
0.24
Southeast
0.07
0.11
0.13
0.10
Southwest
0.08
0.09
0.09
0.09
South
0.15
0.19
0.27
0.18
Land area (sq. ft.)
13,480
10,279
8,324
11,634
Living area (sq. ft.)
1,860
1,889
1,818
1,861
Price ($000)
—
257.24
254.37
256.17
Standard deviation
Land area (sq. ft.)
24,455
19,346
15,255
21,735
Living area (sq. ft.)
861
881
857
867
Price ($000)
—
293.92
269.69
285.15
types, regions, lot sizes and living areas, as indicated in the table. This is important as it
means that this set of properties is likely to be sufficiently diverse to enable us to robustly
estimate the relationship between property characteristics and price change.
Table 1 also illustrates the variation in the characteristics of the homes which are sold
once, twice or more, or not at all. We report the mean of SFR – a dummy variable equal
to one if a home is a single family residence – for each sales frequency. SFRs are around
74% of all homes in our data. However, they are only 66% of properties that sold twice or
more. This indicates a significant dwelling type selection bias in the repeat sales sample.
We also report the mean of a dummy variable indicating which region in Florida a home
came from for the different sales frequencies.9 There are significant changes in sample
composition across the regions. For example, the South region, containing the counties
of Broward, Miami-Dade and Monroe – make up around 18% of the stock of homes but
around 27% of homes that sold twice or more. The table also illustrates that properties
which sold more often are smaller – in terms of both lot size and living area – than those
that sold less frequently. They also tend to have lower prices on average. These findings
9In our main CRS model we will include effects for each of Florida’s 67 counties. But there are too many of these
to include in the table so we break the counties up into eight regions: (1) Northwest (Bay, Calhoun, Escambia,
Franklin, Gulf, Holmes, Jackson, Liberty, Okaloosa, Santa Rosa, Walton, Washington), (2) North Central (Alachua,
Bradford, Citrus, Columbia, Dixie, Gadsden, Gilchrist, Hamilton, Jefferson, Lafayette, Leon, Levy, Madison,
Marion, Suwannee, Taylor, Union, Wakulla), (3) Northeast (Baker, Clay, Duval, Nassau, Putnam, Saint Johns),
(4) East Central (Brevard, Flagler, Lake, Orange, Osceola, Seminole, Sumter, Volusia), (5) West Central (DeSoto,
Hardee, Hernando, Highlands, Hillsborough, Manatee, Pasco, Pinellas, Polk, Sarasota), (6) Southeast (Indian River,
Martin, Okeechobee, Palm Beach, Saint Lucie), (7) Southwest (Charlotte, Collier, Glades, Hendry, Lee), (8) South
(Broward, Miami-Dade, Monroe). These regions are mapped in Figure A.1 of Appendix S1.
© 2022 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.
 14680084, 2023, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/obes.12534 by Monash University, Wiley Online Library on [04/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License


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Selection bias in housing price indexes
631
2002
2004
2006
2008
2010
2012
2014
2016
2018
2020
Years
0.8 
1.0 
1.2 
1.4 
1.6 
1.8 
2.0 
2.2 
2.4 
2.6 
Index (2002Q1 = 1)
SRS
SRS (Using Spline)
Figure 1. Standard repeat sales indexes [Colour figure can be viewed at wileyonlinelibrary.com]
are consistent with what others have found in the literature (Case et al., 1997; Hwang &
Quigley, 2004). This is important because it indicates that different homes sell at different
frequencies. If different homes also exhibit heterogeneous price trends then this is likely
to lead to biased estimates of housing price change from the SRS model.
IV.
Results
We start by discussing the CRS model and examine how well it fits the data. Then we
turn to examining the impact of selection bias on the SRS index by comparing it with our
CRS index.
The CRS model outlined in section II includes two main innovations. First, the use
of a spline in time, rather than time fixed effects. Second, the inclusion of the effects of
characteristics price changes in modelling price trends. We consider each of these issues
in turn.
First, to the estimation of the repeat sales model using penalized regression spline
methods. We examine this by looking at the simplest possible case; where we include only
a spline effect for time in the model and no housing characteristics. In terms of model (3)
we set δtc = 0 for all c > 0. We estimated such a model and compared this with the SRS
model. The index results are shown in Figure 1. The two indexes are indistinguishable.
This indicates that the spline approach closely approximates the SRS model, at least on
large data sets such as ours.10
Second, the primary innovation of the CRS model is the inclusion of effects for the
evolution of shadow characteristics prices over time. A key question then is, does the
10We note that a benefit of the spline approach is that it can be useful when applied to smaller data sets or where the
price effects of certain characteristic-time combinations are not well identified. In cases where there is less data the
results using a spline are likely to be more robust.
© 2022 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.
 14680084, 2023, 3, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/obes.12534 by Monash University, Wiley Online Library on [04/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License