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Property delisting, housing cycle and pricing bias

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Property delisting, housing cycle and pricing bias d p Glades 62, US Canad R31 a for rices roper ct su down S ho not g Even out a g. Si price may be a biased indicator of the real market condi- tions. The degree of such bias is dependent on the fre- quency of delisting. In hot market where sales are quic...

Property delisting, housing cycle and pricing bias
d p Glades 62, US Canad R31 a for rices roper ct su down S ho not g Even out a g. Si price may be a biased indicator of the real market condi- tions. The degree of such bias is dependent on the fre- quency of delisting. In hot market where sales are quick 1051-1377/$ - see front matter � 2011 Elsevier Inc. All rights reserved. ⇑ Corresponding author. E-mail addresses: pcheng@fau.edu (P. Cheng), llin@cobilan.msstate. edu (Z. Lin), yingchun.Liu@fsa.ulaval.ca (Y. Liu). 1 Obviously, the implicit assumption is that all listed properties are reasonably priced. In practice, this is ensured to a large extent by brokers who presumably tend to refuse to list any properties with unrealistic price expectations in the first place, especially in cold market. Therefore, properties listed and then delisted represent true (shadow) supply, while properties whose owners have unrealistic high price expectations are not considered as true supply. Journal of Housing Economics 20 (2011) 152–157 Contents lists available at ScienceDirect Journal of Housing Economics journal homepage: www.elsevier .com/locate / jhec doi:10.1016/j.jhe.2011.02.002 houses are part of the true supply (or shadow supply) in the market, given demand, the true equilibrium price (or the shadow price) may be significantly lower than the ob- served market prices based on the sold houses. Intuitively, if all the houses listed for sale must remain on the market to be sold, competition among sellers will likely be inten- sified, thus the eventual prices on average will be even lower, and the expected time-on-market (the shadow time-on-market) will be longer than those observed only from successful sales. In other words, the observed market typically based on only transaction prices, they are likely to suffer from such a bias. Simply put, transaction-based housing indices tend to overstate the true equilibrium price and understate the price decline from previous periods, thus making the housing market appear to be in better condition than it really is during down cycles. This problem is intuitively well understood. But how can we correct such pricing bias and find out the true mar- ket condition? Theoretical and empirical solutions to this problem have significant policy implications because the Keywords: Property delisting Housing cycle House prices A wide-spread phenomenon in a estate market (such as the recent U that houses listed for sale often do tended period of time-on-market. them are pulled off the market with This is known as property delistin cycle of the real using market) is et sold after ex- tually, many of cceptable offers. nce the delisted and delisting is rare, the bias is negligible. But in cold mar- ket, like in the recent years, the bias can be severe in the face of rampant property delisting.1 An important implica- tion of such bias is that it may cause biased housing price indices. Since major housing market indices, such as the widely watched S&P/Case-Shiller Home Price Indices, are JEL classifications: G11 G12 makers to form less biased views of the true state of the housing market, especially during the down cycles. � 2011 Elsevier Inc. All rights reserved. Property delisting, housing cycle an Ping Cheng a, Zhenguo Lin b,⇑, Yingchun Liu c aDepartment of Finance, College of Business, Florida Atlantic University, 777 bDepartment of Finance and Economics, Mississippi State University, MS 397 cDepartment of Finance, Insurance and Real Estate, Laval University, Quebec, a r t i c l e i n f o Article history: Received 27 July 2010 Available online 19 February 2011 a b s t r a c t This paper provides vable transaction p numbers of listed p to identify and corre ricing bias Road, Boca Raton, FL 33431, USA A a G1V 0A6 mal analysis on a well-known issue of the housing market – obser- are a biased indication of the true market condition if significant ties are delisted without sale. We provide a closed-form formula ch pricing bias. The model can help market participants and policy degree of the index bias, besides causing potential mis- judgment among market participants, is likely to be most severe during the worst market times, when accurate assessment of the true market condition is most needed for appropriate policy responses. The purpose of this study, therefore, is to seek general understanding of the impact of property delisting on property price, and to develop an for such a successful bid to arrive (i.e., time-on-market) should follow an exponential distribution with parameter of gk.6 This has recently been empirically confirmed by the findings of Bond et al. (2007), in which UK data are used A tP * tp O Observable B Unobservable tP 4 In fact, our essential results would hold under a wide variety of more complex distribution function assumptions. 5 In certain circumstances, it is well recognized that potential buyers can get into a ‘‘bidding war’’ in which they bid a price above the asking price; however, this happens rarely and only when the market is exceptionally ‘‘hot’’ or a property is dramatically underpriced. Based on the data from the National Association of Realtors, Green and Vandell (1998) find that such a situation occurs in about five percent of transactions. 6 Statistics principles state that the exponential distribution occurs naturally when describing the lengths of the inter-arrival times in a homogeneous Poisson process. P. Cheng et al. / Journal of Housing Economics 20 (2011) 152–157 153 analytical framework that enables us to determine the sha- dow price and the shadow time-on-market with observed transaction and delisting information. Using empirical data, we demonstrate that, when there is rampant prop- erty delisting (as reported in the media),2 the true market condition is likely to be significantly worse than the major housing indices suggest. 1. A model of the real estate transaction process In this section, we examine the matching process of the real estate transaction. This process is characterized by sequential search and bargaining. During the search pro- cess, a seller receives offers over time from a stream of buyers whose offer prices and timing of arrival are stochas- tic in nature. The buyers make bids based on the informa- tion acquired from their search. Each time a buyer makes an offer; the seller evaluates the costs and benefits of wait- ing for a potentially better offer, and decides whether to accept the current bid. If the bid is rejected, the search con- tinues. A common stopping rule for this process is to as- sume that the seller will accept the first bid above the reservation price, and to reject all bids below it.3 The reser- vation price is affected by the seller’s holding costs due to his/her unique personal and financial constraints. Generally speaking, sellers who are more constrained tend to set lower reservation prices in order to increase the probability of sale within a planned or expected time frame. To formally model such a process, we make the following assumptions: a) The distribution of buyers’ arrivals. We assume the buyers’ stochastic arrival follows a Poisson process with rate k. This assumption is widely adopted by previous studies including Sirmans et al. (1995), Arnold (1999), Glower et al. (1998), Miceli (1989), Cheng et al. (2008), among others. It is also widely used in standard search models in labor economics. b) The distribution of bidding prices. Consider a seller who places a property on the market at time 0 and sells it at time t. As shown in Fig. 1, assume the dis- tribution of bidding prices is uniformly distributed over ½P; P� with density function f(Pbid), where P and P are the minimum and maximum bid prices, respectively, and p�t is the seller’s reservation price. By the stopping rule, a seller only accepts an offer that is at least as high as the reservation price. That 2 See, for example, The New York Times report: ‘‘Home Sales Put Shares In a Tailspin’’, Jul 25, 2008, Page 1, By Michael M Grynbaum and Eric Dash 3 Early studies in labor economics literature often rely on this assump- tion (e.g. Stigler (1962), Whipple (1973) and Barron (1975)), and it has been extensively applied to the real estate market since the 1980s (e.g. Yinger (1981), Read (1988), Quan and Quigley (1991), Yavas (1992), Arnold (1999), Lin and Vandell (2007), Lin and Liu (2008)). is, the distribution of transaction prices is a trun- cated distribution of bidding prices. The degree of the truncation depends on the reservation price. The higher the reservation price, the higher the likely transaction price, but the smaller the range of transaction price variations. The assumption of bidding prices being uniformly dis- tributed is another widely adopted assumption in early studies including Read (1988), Yavas (1992), Sirmans et al. (1995), Arnold (1999), and Cheng et al. (2008). For technical simplicity, we adopt the same assumption.4 Since no buyer will normally bids above the listing price, P can be regarded as the listing price.5 In addition, we should point out that the underlying value of the property is closely re- lated to both holding period and market conditions. To sim- plify notation, we intentionally omit the subscripts denoting market state and holding period. Hence, the buyers’ bid price is distributed as f ðPbidÞ ¼ 1 ðP�PÞ ; P bid 2 ½P; P� 0; otherwise ( ð1Þ Given the two assumptions above, it is obvious that there are two random processes in the determination of the probability of a real estate sale. The first is the potential buyers’ stochastic arrival, which is assumed to follow a Poisson distribution with constant rate k. The second is the probability of the offering price being above the seller’s reservation price, P�p � P�P ; given k. Let g ¼ P�p� P�P , the arrival rate of a successful bid is then the joint probability of the two stochastic processes, i.e. gk. Therefore, the time it takes t Fig. 1. Real estate bidding prices and transaction prices. TDL ¼ gkð1� dÞ ð3Þ transactions (T) rather than the shadow time-on-market (TDL), the sellers have to compete harder. Under the assumption of homogeneous property and market partici- pants, the implication is that sellers will have to lower 154 P. Cheng et al. / Journal of Housing Economics 20 (2011) 152–157 Eqs. (2) and (3) suggest TDL ¼ T1� d ð4Þ Since T is observable from transactions, the true (or sha- dow) time-on-market TDL can be computed given delisting percentage d. Also, since (0 6 d 6 1), Eq. (4) suggests that, in the presence of delisting, the shadow TOM is always longer than what can be observed solely from the sold properties, and that a higher percentage of delisting (often occurs in weak real estate market) implies a bigger differ- ence between the two. From the price perspective, if all the properties were to be sold within the same time frame as those observed to investigate a number of possible assumptions about the distribution of times to sale, such as the normal, chi-square, gamma and Weibull distributions. Bond et al. (2007) finds that the exponential distribution explains the data better than the others. For exponentially distributed time-on-mar- ket, the mean, or the expected TOM of the sale, is simply T ¼ EðTOMÞ ¼ 1 gk ð2Þ It is important to notice that, given the bidding price distri- bution, g is determined by the seller’s reservation price p⁄, which in turn is affected by the seller’s constraint. In other words, g can be considered as an indicator of the seller’s constraint. 2. Correction of pricing bias in the homogeneous market Based on the model above, we now study the effect of property delisting on real estate price/return and volatility. We begin with a simple setting of a homogeneous real es- tate market, in which we assume there is only one type of properties and all market participants have homogeneous expectations. This is a useful simplification if one agrees with that the heterogeneous real estate market can be con- sidered as to consist of many relatively homogeneous seg- ments. In this section we focus on the within-segment analysis. In the later section, we will extend the model to inter-segments analysis in the context of heterogeneous housing market. As previously discussed, if the supposedly delisted properties were to remain on the market until a successful sale, the observed average time-on-market of all sold prop- erties would be longer. This notion can be demonstrated formally. Suppose that there is a pool of housing supply in the market, let d (0 6 d 6 1) denote the percentage of properties to be delisted in the pool, so the percentage of the properties remaining on the market is (1 � d). The probability of a successful sale now can be viewed as the joint probability of the buyer’s arrival (k), the offering price being above the reservation price (g), and the house’s remaining on the market (1 � d). Similar to Eq. (2), the ex- pected TOM upon a successful sale should be, 1 their reservation price to P⁄ < p⁄ in order to increase their chance of successful sale to g� ¼ P�P� P�P . From Eq. (2) and (3), let TDL ¼ 1g�kð1�dÞ ¼ T ¼ 1gk, we can conclude that (g⁄) must satisfy: g� ¼ g 1� d ð5Þ It is obvious that, since g < g⁄, g indicated by the suc- cessful sales will overstate the reservation price (thus the expected sales price) if more properties are likely to be delisted (i.e. d > 0).7 The degree of the overestimation is pos- itively related to d – from negligible in hot market when all properties are sold quickly to very high in cold market when a significant number of properties are pulled off the market. Now we move to examine the impact of delisting on real estate return and risk. As illustrated in Fig. 1, each bid- ding price ~Pbid received by the seller implies a total return ~Rbid over a holding period s, which can be expressed as ~Rbid ¼ ~Pbid � P0 P0 ð6Þ where ~Pbid is uniformly distributed over ½P; P� and P0 is the original purchase price.8 Similarly, the total return upon sale for a seller with reservation price p⁄ or g can be ex- pressed as ~Rg ¼ ~Pg � P0 P0 ; ð7Þ where ~Pg is uniformly distributed over ½p�; P�.From Eq. (6), the expected total return of bidding prices is uM;s ¼ E ~Pbid � P0 P0 " # ¼ ðP þ PÞ 2P0 � 1 ð8Þ And the volatility (or risk) of such return is r2M;s ¼ Var ~Pbid � P0 P0 " # ¼ ðP � PÞ 2 12P20 ; ð9Þ where (uM;s;r2M;s) characterize the distribution of bidding prices from potential buyers (or buyers’ valuation). Simi- larly, the expected total return and volatility upon a suc- cessful sale in the absence of delisting can be computed as, us ¼ E ~Pg � P0 P0 ~P P p� ��� i " ¼ p � þ P 2P0 � 1 ð10Þ r2s ¼ Var ~Pg � P0 P0 ~P P p� ��� i " ¼ ðP � p �Þ2 12P20 ð11Þ Since g ¼ P�p� P�P , we have 1 g � 1 ¼ p � � P P � p� ð12Þ 7 This can also be seen by noting g� ¼ P�P� P�P and g ¼ P�p� P�P , where P ⁄ < p⁄. 8 To simplify notation, we intentionally omit the subscript denoting the holding period in prices. ffi Application of the formulas in Eq. (21) and (22) requires knowledge of the percentage of delisting (d). Empirically, d narios and shows the impact of delisting on the average P. Cheng et al. / Journal of Housing Economics 20 (2011) 152–157 155 Given ðP þ PÞ 2P0 � 1 ¼ ðP þ p �Þ 2P0 � 1� ffiffiffi 3 p p� � P P � p� � � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðP � p�Þ2 12P20 s ð13Þ and ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðP � PÞ2 12P20 s ¼ 1þ p � � P P � p� � � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðP � p�Þ2 12P20 s ð14Þ using Eqs. (8)–(12), we can therefore rewrite Eqs. (13) and (14) as uM;s ¼ us � ffiffiffi 3 p ð1 g � 1Þrs ð15Þ rM;s ¼ 1grs ð16Þ Eqs. (15) and (16) illustrate how the buyers’ valuation can be inferred from the observed transaction if there are no properties to be delisted. At the presence of delisting, in order to achieve the observed TOM in Eq. (2), the seller needs to set lower reservation prices P⁄ where g⁄ should satisfy Eq. (5) and P⁄ < p⁄. Suppose uDL;s and rDL;s are the ex- pected return and volatility when g⁄ satisfies Eq. (5). The buyer’s valuation of the same property (uM;s;r2M;s) can be inferred in the similar fashion: uM;s ¼ uDL;s � ffiffiffi 3 p ð 1 g� � 1ÞrDL;s ð17Þ rM;s ¼ 1g� rDL;s ð18Þ From Eqs. (15)–(18), we can have us � ffiffiffi 3 p ð1 g � 1Þrs ¼ uDL;s � ffiffiffi 3 p ð 1 g� � 1ÞrDL;s ð19Þ 1 g rs ¼ 1g� rDL;s ð20Þ Simplifying Eqs. (19) and (20) by using Eq. (5) yields the relationship between the observed transactions indicated by (us, rs) and the shadow return and volatility described by (uDL,s, rDL,s): uDL;s ¼ us � ffiffiffi 3 p d 1� drs ð21Þ rDL;s ¼ 11� drs ð22Þ Note that if d = 0, that is, no property is delisted, there will be no pricing bias and the observed return and volatil- ity are in fact unbiased estimates of the expected return and volatility. But if d > 0, it can be easily shown that, uDL;s � us < 0 and @ðuDL;s � usÞ @d < 0 ð23Þ rDL;s � rs > 0 and @ðrDL;s � rsÞ @d > 0 ð24Þ Eqs. (23) and (24) suggest that, in the presence of delist- ing, the observed return based on transacted properties is upward biased, while the observed volatility (risk) is downward biased. Such biases are greater if a larger per- centage of properties on the market are delisted. index return and volatility during down market periods. The shadow return and volatility are computed based on Eqs. (21) and (22) for each assumed delisting percent- age. As shown above, if the shadow return and volatility indicate the true market conditions, it is clear that the ob- served return significantly overstates the true market re- turn and understates its volatility when delisting is not negligible (i.e. 5% or more). If one accepts that property delisting is widespread in down markets such as the one we are currently experiencing, the shadow return and 9 In comparison, during the up market periods, the average annual (year- over-year) index return and volatility are 5.63% and 3.61%, respectively. for a particular time period (i.e. a quarter) can be estimated from the total number of properties listed for sale at the beginning of the quarter and then pulled off the market without sale during that quarter. For residential properties, this information, though not often reported, can be ex- tracted from the Multiple Listing Service (MLS). This study highlights the usefulness of the delisting information and calls for systematic tracking and recording delisting per- centage over time, since this information is so critical to understand the true housing market conditions. 3. Numerical example Now we present a numerical example to demonstrate the application of Eqs. (21) and (22) to provide some prac- tical sense as to the magnitudes of the pricing biases due to property delisting. To begin with, it is necessary to stress that the formulas can be applied to any relevant data in specific markets, as long as the delisting information is available. For convenience, we use the data from one con- venient source: the OFHEO Repeat-transaction Home Price Index for the period from 1975 to 2008. We use the OFHEO index to compute the quarterly US home price growth for the period of analysis. Fig. 2 presents a historic perspective of the US housing market via the OFHEO Home price indices. During the past 33 years or so, the housing market exhibits clear cyclical patterns. In nominal terms, the housing market never experienced negative year-over-year growth rate until very recently. In real terms (inflation-adjusted), negative growth rate happened during the early 1980s, the early 1990s, and, of course, the most recent two years of 2007 and 2008. During these down market periods, it is ex- pected that sales are slow and time-on-market is relatively long. Property delisting, therefore, is more likely during these periods. From the index data, we can observe the average annual (year-over-year) index return and standard deviation (volatility) over these down market periods
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