房地产英文文献

Home Price, Time-on-Market, and Seller Heterogeneity Under Changing Market Conditions Ping Cheng & Zhenguo Lin & Yingchun Liu # Springer Science + Business Media, LLC 2009 Abstract This paper develops a formal model to examine the effect of changing market conditions and individuals’ selling constraints on selling price and time-on- market. Using the concept of Relative Liquidity Constraint (RLC)—a stochastic variable that captures the randomness of future individual constraints and market conditions—the study presents the first ex ante analysis that extends the investigation of the issue of seller heterogeneity to the point of the buying decision, that is, from the perspective of the buyer’s (future seller’s) point of view. We show that seller constraint, as well as the uncertainty of such a constraint, significantly depresses the expected selling price and increases risk. Our closed-form formulas provide a set of simple quantitative tools that enable buyers and sellers to adjust the “market average” to their ex ante “individual expectations”. Keywords Home price . Time-on-market . Seller heterogeneity . Market conditions J Real Estate Finance Econ DOI 10.1007/s11146-009-9167-1 P. Cheng Department of Industry Study, College of Business, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA e-mail: pcheng@fau.edu Z. Lin (*) : Y. Liu Fannie Mae, 3900 Wisconsin Avenue, Washington, DC 20016, USA e-mail: len_lin@fanniemae.com Y. Liu e-mail: yingchun_liu@fanniemae.com “Happy families are all alike; every unhappy family is unhappy in its own way”. Leo Tolstoy (Anna Karenina, Chapter 1) When it comes to real estate, there are two kinds of sellers—those who can afford to wait for as long as it is necessary to sell at fair market values, and those who cannot wait but have to sell more quickly due to various constraints. While every constrained seller employs a selling strategy according to his unique situation, the unconstrained sellers share one common aspect in their strategies—to wait as long as it normally takes to sell at their desired price under the current market conditions. Since selling under constraint is more often than not due to unpleasant circumstances (death of a family member, divorce, unemployment, foreclosure, double mortgage payments, and so on), the absence of these circumstances characterizes unconstrained sellers. To borrow from Leo Tolstoy’s famous words, the unconstrained sellers are all alike; every constrained seller is constrained in his own way. The distinction between constrained and unconstrained sellers, however, is relative rather than absolute. In a booming market when properties are selling quickly, most sellers can afford to wait comfortably long enough to sell at their desired prices. But when the market turns, many previously unconstrained sellers may find themselves suddenly pinched—either they have to wait much longer and incur more holding costs in order to obtain their desired price, or they have to sell in less time and receive a less-than-desirable price. Simply put, market conditions determine asset liquidity in general, individuals’ specific conditions determine the degree to which they are constrained under given market conditions, which in turn determines sellers’ expected time-on-market (TOM), reservation prices, and expected transaction prices. While the impact of seller constraints on price–TOM relationship has been frequently researched in the literature, few studies have attempted to examine the impact under changing market conditions. This study intends to add to the discussion by examining how changing market conditions and their interaction with individuals’ selling constraints impact the selling price. Why is this issue important? After all, at the time of listing a property for sale, the seller faces known market conditions and known personal constraints. Since neither is expected to change dramatically in the near term (a few weeks or a few months of the marketing period), should anyone care about the impact of uncertain market conditions? The answer is yes: the buyers (future sellers) should care. All knowledge about value and risk ultimately helps buyers (future sellers) make better investment decisions. The obvious difference between current and future sellers is that the current condition is known but the future is uncertain. At the time of selling, the current sellers’ personal constraints and market conditions are known. But at the time of the buying decision, both of these are uncertain ex ante. These uncertainties imply ex ante risk to the buyers (future sellers) and, moreover, they tend to compound each other (i.e., poor market conditions accompanied by a higher job-loss probability and stringent credit conditions that significantly reduce the seller’s ability to wait). Rational buyers, therefore, need to understand the expected return as well as the risk associated with these uncertainties in order to form a realistic valuation of the property. If the risk is too high, it may not be justifiable to enter the market in the first place. Arguably, an ex ante understanding of value and P. Cheng et al. risk is a more valuable piece of knowledge because it may help prevent buyers from turning into constrained future sellers. The purpose of this paper, therefore, is to provide a formal analysis of the complex interaction among property price, time-on-market, seller heterogeneity, and market conditions, from both the ex post (current seller) and ex ante (future seller) perspectives. We attempt to make these contributions to the literature: First, based on the micro market structure of the real estate transaction process, we develop a formal model that quantifies the impact of seller constraints on expected selling price. The model reveals that a higher degree of seller constraint associates with shorter expected time-on-market and lower selling price or returns. Second, and more importantly, we extend the model to the buyer’s perspective, and present the first ex ante analysis on the issue of seller heterogeneity and selling price. Third, unlike previous theoretical analysis that aimed at revealing directional relationships between variables, the results of our analysis are in closed-form formulas, which provide a set of quantitative tools for buyers or sellers to evaluate (as opposed to generally understand) their ex ante expected return and risk. The rest of the paper is structured as follows. We begin in the next section with a brief review of some recent literature development in this area. In the “Model of Real Estate Transaction Process” section we present a model for the real estate transaction process and elaborate in detail key assumptions and concepts. In the “Analytical Results” section we present a formal analysis leading to two theorems, each represents the main results of our ex post and ex ante analysis. The “Numerical Example” section provides a numerical example to demonstrate the application of the two theorems using empirical data. The “Conclusions” section concludes. Recent Research Development Research on the impact of seller motivation on the price–TOM relationship is an evolving body of literature in housing economics. Early studies focus on examining the issue in the context of specific seller motivations such as relocation (Turnbull et al. 1990), high holding costs (Sirmans et al. 1995), double mortgage payment (Glower et al. 1998), foreclosure (Shilling et al. 1990; Forgey et al. 1994; Springer 1996), and vacant property (Zuehlke 1987). Genesove and Mayer (1997) shows that a seller’s equity position affects their desired selling price and the time they are willing to wait to obtain that price. Glower et al. (1998) analyzes a survey of homeowners that contains explicit measures of multiple seller motivations. They find that most sellers set a planned selling time when they list a property, and that longer planned selling time is correlated with higher selling prices. Collectively, these studies support the consensus that seller motivation has significant impact on the price–TOM relationship. Other things being equal, motivated (or constrained) sellers tend to set shorter expected time- on-market and realize lower prices relative to the unconstrained normal sellers. But of course, this conclusion cannot be simply extended to imply that longer TOM necessarily leads to higher prices. For example, Lazear (1986) and Taylor (1999) provide theories indicating there is a negative relationship between selling price and TOM. Recent work by Knight (2002), and Merlo and Ortalo-Magne (2004) shows that one way sellers respond to constraints is by lowering listing prices Home Price, Time-on-Market, and Seller Heterogeneity… during the selling period, and Huang and Palmquist (2001) suggest that the negative price–TOM relationship is simply a result of lowering reservation prices as the house remains unsold. Sirmans et al. (2005) enumerate the results of 27 papers using TOM, Total Days on Market, or Ln(TOM) to explain selling price. These 27 empirical tests find two positive relationships, 12 negative relationships, and 13 instances of non- significance. Even among studies that have found a positive price–TOM relation- ship, (Rutherford et al. 2005, among many others) some have shown that the relationship is non-linear. (Forgey et al. 1996; Cheng et al. 2008) The benefit of patiently waiting has a diminishing effect and prolonged time-on-market may sends negative signals about the quality of the property.1 Far fewer studies have examined the interaction between seller constraints and price in the background of dynamic market conditions. Ferreira and Sirmans (1989) examines the effect of changing market conditions on the seller’s ability to capture a premium on favorable assumable loan in a transaction. They find that such a premium can be captured in good market conditions without a sacrifice in time-on- market, but it largely disappears in poor market conditions when a seller gives away such a premium in order to limit the marketing time. Krainer (2001) shows that both price and the probability of sale are affected by the changing market demand, as indicated by the flow of buyers. Anglin (2006) takes a theoretical approach in analyzing the effect of changing market conditions. He uses a locus of feasible combinations of the expected sale price and of the probability of sale to describe the trade-off created by a given set of market conditions. However, he does not provide a closed-form solution that quantifies the impact of market conditions on price or the probability of sale. Lin (2004) and Lin and Vandell (2007) provide a closed-form solution to the task of quantifying illiquidity risk and integrating it with price volatility. Their model considers two types of sellers—those who can always await a desirable bid for as long as necessary, and those who are forced to sell immediately when a liquidity shock occurs. The fact that most sellers are found in between these two extremes, with different degrees of constraint, is not considered in their model. This fact is formally incorporated in a recent study by Lin and Liu (2008), in which they develop a theoretical model and formulate a unified risk metric for integrating real estate price risk and marketing period risk. Their model includes an explicit parameter capturing the degree of seller constraint under certain market conditions. The current paper extends and complements Lin and Liu (2008) in three aspects. First, Lin and Liu (2008) assumes that the seller’s circumstances at listing time is known with certainty. In reality, the degree of seller constraint in the future is likely to be uncertain ex ante. In other words, constraint should be a stochastic variable and follow a certain distribution. Second, they assume that an investor’s listing price increases during the marketing period, while a more realistic observation in the real estate market is that the listing price remains fixed during the marketing period.2 In 1 We thank an anonymous referee for his knowledgeable insight that directed our attention to the studies cited in this paragraph. 2 Of course, in some cases, once a property is placed on the market and an investor has received insufficient interest given her motivation to sell, she may revise her listing price downward based upon a revised perspective of the underlying bid distribution. In addition, in a recent paper Cheng, Lin and Liu (2008) also adopt this assumption to study a model of time-on-market and real estate price under sequential search with recall. P. Cheng et al. this paper, we assume that listing price remains constant throughout the marketing period. Third, Lin and Liu (2008) examines seller heterogeneity by assuming there is only one state of market conditions, while we adopt a more realistic assumption that future market conditions are uncertain. A Model of Real Estate Transaction Process The real estate selling process is characterized by sequential search and bargaining. During the search process, a seller receives offers over time from a stream of buyers whose offer prices and timing of arrival are stochastic in nature. The buyers make bids based on the information acquired from their search. Each time a buyer makes an offer, the seller evaluates the costs and benefits of waiting for a potentially better offer, and decides whether to accept the current bid. If the bid is rejected, the search continues. A common stopping rule for this process is to assume that the seller will accept the first bid above the reservation price, and to reject all bids below.3 And the reservation 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: 1. The distribution of buyers’ arrivals. We assume the buyers’ stochastic arrival follows a Poisson process with rate l. 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. 2. The distribution of bidding price. 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 distribution of bidding prices is uniformly distributed over P t;Pt � � with density function f(Pbid), where P t and Pt 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 is, the distribution of transaction prices is a truncated 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 distributed is another widely adopted assumption in early studies including Read (1988), Yavas (1992), Sirmans et al. (1995), and Arnold (1999), as well as a more recent study by Cheng et al. (2008). For technical simplicity, we adopt the same assumption.4 Note that we 3 Early studies in labor economics literature often rely on this assumption (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)). 4 In fact, our essential results would hold under a wide variety of more complex distribution function assumptions. Home Price, Time-on-Market, and Seller Heterogeneity… assume the bidding price distribution is unchanged during the selling period. Since no buyer will normally bid above the listing price, P can be regarded as the listing price.5 Therefore, in this paper we assume that the listing price remains unchanged during the marketing period. In addition, we should point out that the underlying value of the property is closely related to both holding period and market conditions. To simplify notation, we intentionally omit the subscripts denoting market state and holding period. Hence, the buyers’ bid price is distributed as: f Pbid � � ¼ 1P�Pð Þ ; Pbid 2 P;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 l. The second is the probability of a successful sale upon the arrival of a potential buyer, P�p* P�P . Let h ¼ P�p* P�P , the arrival rate of a successful bid is then the joint probability of the two stochastic processes, i.e. ηl. Therefore, the time it takes for such a successful bid to arrive (i.e., time-on-market) should follow an exponential distribution with parameter of ηl.6 This has recently been empirically confirmed by the findings of Bond et al. (2007), in which UK data are used 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 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. A tP Observable * tp O B Unobservable tP t Fig. 1 Real estate bidding prices and transaction prices P. Cheng et al. exponentially distributed time-on-market, the mean, or the expected TOM of the sale, is simply: Th ¼ E TOMhð Þ ¼ 1hl : ð2Þ It is important to notice that, given the bidding price distribution, η is determined by the seller’s reservation price p*. Generally speaking, sellers under higher constraints are likely to set lower p* to increase the probability of sale. Thus, η essentially captures the degree of seller’s liquidity constraint. In contrast, unconstrained sellers are likely to set higher reservation prices in order to give their properties adequate market exposure and sell at desirable prices.7 Theoretically, such seller influence on the expected time-on-market should be exercised according to the seller’s optimal policy or plan, subject to his unique constraints. Glower et al. (1998) reports a survey which indicates that sellers do set planned time-on-market. To the extent that the planed time-on-market is optimally set, Th satisfies the liquidity definition by Lippman and McCall (1986)—the necessary expected time required to sell assets under optimal policy. As for the actual time-on-market, it may be longer or shorter than the planned time-on-market due to matters such as luck. Suppose that P* is the reservation price for an unconstrained seller. Since P � p* < P*, thus we have h* < h � 1, where h* ¼ P�P* P�P . Similarly, the expected TOM for the unconstrained seller is: T* ¼ E TOM h* � � ¼ 1 h*l : ð3Þ T* can be defined as the normal selling time (NST), which represents the expected necessary time-on-market for typical prop