1# RECORD 2e573f3384314fd1e0b0dd7c24f567743146abb72# TITLE: Selection Bias in Housing Price Indexes: The Characteristics Repeat Sales Approach*3# YEAR: 2022.0 VENUE: Oxford Bulletin of Economics and Statistics DOI: 10.1111/obes.125344# AUTHORS: Daniel Melser5# PAGES: 15 CANDIDATE TABLE PAGES (1-based): [8]6# ABSTRACT: nan789===== PAGE 1 (score 3, numeric-paren 0, table-words 0, var-words 3) =====1011OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 85, 3 (2023) 0305-904912doi: 10.1111/obes.1253413Selection Bias in Housing Price Indexes:14The Characteristics Repeat Sales Approach*15DANIEL MELSER16Department of Econometrics and Business Statistics, Monash University, 900 Dandenong Road17Clayton, 3800, Victoria, Australia (e-mail: danielmelser@gmail.com)18Abstract19The widely used repeat sales method for constructing house price indexes only uses20data for properties that sell twice or more. This makes it susceptible to selection bias as21price movements for these properties may not be representative of those for the stock of22homes. We outline a novel approach to modelling repeat sales, which allows for a home’s23characteristics to influence its price movement. This allows us to impute price changes24for the stock of homes and control for selection-on-observables. Using data for Florida25from 2002 to 2020 we find that selection effects significantly exaggerated the volatility of26Florida’s housing prices.27I.28Introduction29Since the global housing booms and busts of the 2000s housing price indexes (HPIs)30have taken an increasingly central role in the suite of macroeconomic indicators. They31are important in providing homeowners with information about the value of their32home – which for many households is their single largest asset. HPIs are also vital to33policymakers and those in industry given that housing prices influence a broad range of34social, economic and financial variables. Perhaps most importantly, as was seen during35the US subprime crisis, housing prices have an important impact on the stability of the36financial sector.37There have been consistent efforts across the years to improve the measurement of38housing price dynamics. This was stimulated by the important early work of Case and39Shiller (1989) in sourcing data and developing appropriate methods. The importance of40this work was reinforced by the housing market crisis across a number of countries in41the late 2000s. This emphasized the poor quality and comparability of housing price42statistics across countries (IMF, 2009).1 This led to a global consensus about the need to43JEL Classification numbers: C43, E31, R30.44*Open access publishing facilitated by Monash University, as part of the Wiley - Monash University agreement45via the Council of Australian University Librarians.461IMF (2009) writes, ‘Data on the stock of dwellings, the associated price levels and their changes over time47are critical ingredients for understanding household wealth, its evolution over time, and for the vulnerability of48households’ financial position. Similar information on commercial property is relevant not just for monitoring49the wealth of the corporate sector, but also for financial stability more generally, given that commercial property5062351© 2022 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.52This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and53reproduction in any medium, provided the original work is properly cited.545556===== PAGE 8 (score 22, numeric-paren 0, table-words 5, var-words 8) =====575863059Bulletin60TABLE 161Summary statistics for homes by number of sales62Number of sales630641652+66All67Number684,261,733692,373,035701,404,722718,039,49072Percent7353.07429.57517.576100.077Mean78SFR790.79800.71810.66820.7483Northwest840.05850.04860.05870.0588North Central890.05900.05910.05920.0593Northeast940.07950.06960.04970.0698East Central990.281000.211010.151020.24103West Central1040.251050.241060.221070.24108Southeast1090.071100.111110.131120.10113Southwest1140.081150.091160.091170.09118South1190.151200.191210.271220.18123Land area (sq. ft.)12413,48012510,2791268,32412711,634128Living area (sq. ft.)1291,8601301,8891311,8181321,861133Price ($000)134—135257.24136254.37137256.17138Standard deviation139Land area (sq. ft.)14024,45514119,34614215,25514321,735144Living area (sq. ft.)145861146881147857148867149Price ($000)150—151293.92152269.69153285.15154types, regions, lot sizes and living areas, as indicated in the table. This is important as it155means that this set of properties is likely to be sufficiently diverse to enable us to robustly156estimate the relationship between property characteristics and price change.157Table 1 also illustrates the variation in the characteristics of the homes which are sold158once, twice or more, or not at all. We report the mean of SFR – a dummy variable equal159to one if a home is a single family residence – for each sales frequency. SFRs are around16074% of all homes in our data. However, they are only 66% of properties that sold twice or161more. This indicates a significant dwelling type selection bias in the repeat sales sample.162We also report the mean of a dummy variable indicating which region in Florida a home163came from for the different sales frequencies.9 There are significant changes in sample164composition across the regions. For example, the South region, containing the counties165of Broward, Miami-Dade and Monroe – make up around 18% of the stock of homes but166around 27% of homes that sold twice or more. The table also illustrates that properties167which sold more often are smaller – in terms of both lot size and living area – than those168that sold less frequently. They also tend to have lower prices on average. These findings1699In our main CRS model we will include effects for each of Florida’s 67 counties. But there are too many of these170to include in the table so we break the counties up into eight regions: (1) Northwest (Bay, Calhoun, Escambia,171Franklin, Gulf, Holmes, Jackson, Liberty, Okaloosa, Santa Rosa, Walton, Washington), (2) North Central (Alachua,172Bradford, Citrus, Columbia, Dixie, Gadsden, Gilchrist, Hamilton, Jefferson, Lafayette, Leon, Levy, Madison,173Marion, Suwannee, Taylor, Union, Wakulla), (3) Northeast (Baker, Clay, Duval, Nassau, Putnam, Saint Johns),174(4) East Central (Brevard, Flagler, Lake, Orange, Osceola, Seminole, Sumter, Volusia), (5) West Central (DeSoto,175Hardee, Hernando, Highlands, Hillsborough, Manatee, Pasco, Pinellas, Polk, Sarasota), (6) Southeast (Indian River,176Martin, Okeechobee, Palm Beach, Saint Lucie), (7) Southwest (Charlotte, Collier, Glades, Hendry, Lee), (8) South177(Broward, Miami-Dade, Monroe). These regions are mapped in Figure A.1 of Appendix S1.178© 2022 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.179 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 License180181182===== PAGE 9 (score 5, numeric-paren 0, table-words 0, var-words 5) =====183184Selection bias in housing price indexes1856311862002187200418820061892008190201019120121922014193201619420181952020196Years1970.8 1981.0 1991.2 2001.4 2011.6 2021.8 2032.0 2042.2 2052.4 2062.6 207Index (2002Q1 = 1)208SRS209SRS (Using Spline)210Figure 1. Standard repeat sales indexes [Colour figure can be viewed at wileyonlinelibrary.com]211are consistent with what others have found in the literature (Case et al., 1997; Hwang &212Quigley, 2004). This is important because it indicates that different homes sell at different213frequencies. If different homes also exhibit heterogeneous price trends then this is likely214to lead to biased estimates of housing price change from the SRS model.215IV.216Results217We start by discussing the CRS model and examine how well it fits the data. Then we218turn to examining the impact of selection bias on the SRS index by comparing it with our219CRS index.220The CRS model outlined in section II includes two main innovations. First, the use221of a spline in time, rather than time fixed effects. Second, the inclusion of the effects of222characteristics price changes in modelling price trends. We consider each of these issues223in turn.224First, to the estimation of the repeat sales model using penalized regression spline225methods. We examine this by looking at the simplest possible case; where we include only226a spline effect for time in the model and no housing characteristics. In terms of model (3)227we set δtc = 0 for all c > 0. We estimated such a model and compared this with the SRS228model. The index results are shown in Figure 1. The two indexes are indistinguishable.229This indicates that the spline approach closely approximates the SRS model, at least on230large data sets such as ours.10231Second, the primary innovation of the CRS model is the inclusion of effects for the232evolution of shadow characteristics prices over time. A key question then is, does the23310We note that a benefit of the spline approach is that it can be useful when applied to smaller data sets or where the234price effects of certain characteristic-time combinations are not well identified. In cases where there is less data the235results using a spline are likely to be more robust.236© 2022 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.237 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 License238