...sale data. The approach promoted and presented here, therefore, to provide an examination of housing sale dynamics using a step-by-step approach. We present three hypotheses about TOM: (i) there is nonmonotonic duration dependence in the hazard of sale, (ii) the hazard curve will vary both over time and across intraurban areas providing evidence of the existence of submarkets and (iii) institutional idiosyncrasies can have a profound effect on the shape and position of the hazard curve. We apply life tables, kernel-smoothed hazard functions and likelihood ratio tests for homogeneity to a large Scottish data set to investigate these hypotheses. Our findings have important implications for TOM analysis.

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In the past 30 years, there have been over 20 published studies of time on the market (TOM) for residential properties. The number of papers doubled in the 1980s, (1) compared with the 1970s. (2) The number doubled again in the 1990s, (3) and there is a good chance that the number of papers will double again by the end of the current decade. (4) This bourgeoning of the literature is partly driven by the increasing popularity of survival analysis techniques per se (assisted by their incorporation into popular statistical software packages) and partly because of the emerging availability of suitable housing data. With respect to the second cause, the present study is a case in point: this is the first large-sample published analysis of residential time to sale in the United Kingdom. The only previous United Kingdom-based paper was the very first in the literature (Cubbins (1974), based on 83 sales in Coventry, England). To our knowledge, all other published studies have used U.S. data.

We argue that the rush to apply multiple regression estimation to TOM may have led to important details and idiosyncrasies in local market dynamics being overlooked. What is needed is a more careful examination of the fundamental properties of time-to-sale data. The approach promoted and presented here, therefore, is to provide an examination of housing sale dynamics using a step-by-step approach. Kernel-smoothed nonparametric estimates of the aggregate hazard function (complemented by life table analysis and likelihood ratio tests) are applied to different subgroups of housing sales over different time periods. This anatomy of the selling process reveals insights and caveats previously unexamined in the housing literature--results that can inform future analysis of time to sale and related topics.

The starting point for our article is that time to sale cannot be analyzed in the same way as other continuous variables. This is because it is a "duration" variable and hence subject to two crucial characteristics: time dependency and censoring. The first of these relates to the fact that the probability of sale in any given period may itself be contingent on the length of time a property has already been on the market. As each day goes by, the probability of sale for a property on the market may change. Traditional approaches to estimating probability, such as logit and probit regression, assume that the probability of sale is independent of duration and so are unlikely to be applicable (note that this includes the application of Heckman correction of liquidity bias in hedonic regression, which relies on simple probit estimates of the probability of sale). The second effect arises because some properties will be withdrawn from the market before sale or remain unsold at the time of analysis. Ordinary least squares (OLS) and two-stage least squares (2SLS) techniques do not account for the effect of censoring, neither do they allow for the possibility of duration dependence (though both have been widely used in the housing literature; see, e.g., Miller (1978), Kang and Gardner (1989), Asabere, Huffman and Mehdian (1993) and Forgey, Rutherford and Springer (1996)).

Techniques (developed largely in the medical statistics literature) that explicitly account for both these phenomena have become known as duration (or "survival" or "time to event") models. Most of these techniques use the log of the relative hazard as the dependent variable. The meaning of "hazard" is similar to that of "probability," except that a hazard may vary between zero and infinity whereas probabilities vary between zero and one. So the "hazard of sale" can be thought of as simply a monotonic transformation of the probability of sale. The "relative" hazard accounts for the duration the property has already been on the market. In this article, we are particularly interested in how the (relative) hazard behaves over the duration of selling time (duration is also called "analysis time" and refers to the number of days a property has been on the market). That is, we want to know whether the hazard remains constant, rises or falls with TOM. We shall therefore be examining the "hazard function"--the hazard of sale as a function of analysis time. We also want to know whether (and how) the hazard function changes over time, across space and by marketing method.

The shape and stability of the hazard function is important because it will determine which empirical technique is most applicable. If the hazard function is flat (i.e., completely horizontal over the entire length of time a property is on the market), then we know that the hazard of sale is not duration dependent. This means that even the most basic duration technique--one that assumes exponentially distributed errors--could be applied, as could the more sophisticated approaches--those that assume Weibull, log-logistic, log-normal or Gompertz distributions, or those which adopt a semi parametric approach. If, however, the hazard function is not horizontal, but either continually rising or falling, then the exponential approach is inappropriate because it assumes duration independence in the hazard of sale. The choice of modeling technique is further limited if the hazard function is nonmonotonic because both the Weibull and the Gompertz duration models assume a monotonic hazard function. Further problems arise if the hazard function is not stable over time or across areas or institutional arrangements. Because nearly all existing studies are based on data aggregated for a particular city over a maximum of 2 years (Cubbins 1974, Miller 1978, Zuehlke 1987, Haurin 1988, Larsen and Park 1989, Kluger and Miller 1990, Yang and Yavas 1995, Yavas and Yang 1995), it is not clear whether their results are peculiar to the particular phase of the housing cycle considered. The literature has yet to reveal whether or how the hazard curve changes over time or across submarkets. Note also that, when there is only 1 year of data, and where these data only include properties put on the market in that year, then the right tail of the hazard function cannot be reliably estimated because some properties take much longer than a year to sell, and such properties are not always withdrawn from the market (i.e., there will be a large degree of censoring). Ideally, analysis should therefore be based on several years of data, employing statistical analysis that allows the hazard function to vary over both time and space. In permitting the hazard curve to vary across space, one has to make the prior assumption that submarkets exist and have some means of identifying where their boundaries are likely to lie.

The remainder of the article is structured as follows. First, we provide background information on the Scottish house-selling system and summarize the relevant literature. A description of our methodology and a summary of three intuitive hypotheses about the time to sale follow. We then briefly describe the data and consider each of the stated hypotheses in turn. The article concludes with a brief summary and discussion of the implications of our analysis for future research.

Background on the Scottish Selling System

Three in five Scots now own their homes and periodically confront the stresses of attempting to both sell and purchase potentially illiquid, expensive properties. To achieve this, households employ housing market professionals to wade through legal and other transactions procedures. In Scotland, the buyer and seller agree on a price through a sealed bid auction where a potential purchaser works up a bid on the basis of both a professional valuation and an "Offers Over" price set by the seller. The uncertainties and opportunities created by a system that can allow the seller to capture economic rent in this way (see Gibb 1992) and in which housing market professionals such as estate agents, lawyers and valuation surveyors prosper, means that house purchase and the housing market are always topical and contentious economic phenomena.

In the Scottish sealed bid system, the chances that a property will still be on the market at a given point in time can be thought of as being determined by the cumulative probability, up to that point, of the seller having received a suitable offer, where "suitable" is defined as an offer at least equal to the seller's reservation price. Sellers may hold out for a higher bid by asking for a second closing date, but this is extremely rare; the Offers Over price is typically set so that the auction will produce a successful outcome. This does not mean that the Offers Over price will necessarily equal the seller's reservation price--the seller will be advised by the estate agent as to the Offers Over price that would attract the most interest, and so the advertised price may actually be below the seller's reservation price; however, potential buyers who express an interest in bidding are often given clues to the minimum price the seller would accept as well as some indication of the typical bid--offer spread of recent auctions in the area. Because there is a significant cost to bidding--the price of obtaining a survey--spuriously low bids are rare, and the auction nearly always results in a sale. Thus, the probability of selling will depend not only on how long the property has been on the market, but also on the range of offers and the seller's reservation price (Zuehlke 1987, Haurin 1988, Yavas and Yang 1995).

What determines the seller's reservation price? It is likely that the seller will at least want to cover the outstanding mortgage and transactions costs to avoid negative equity but may also have some other minimum driven by external constraints, such as the equity required by the seller to purchase a desired destination dwelling (Stein 1995, Genesove and Mayer 1997). To some extent, however, one might argue that there is a degree of endogeneity about the reservation price that may cause it to change during the period of time the dwelling is on the market. For example, if there is little interest from buyers and negative news about the general state of the market, then the seller may revise his or her reservation price downward.

Current Scottish legislation aims both to reduce the transactions costs facing potential purchasers of private housing and to make objective property valuation information publicly available at zero cost. While increasing efficiency in the system, these reforms do nothing to alter the basic vendor benefits (in terms of economic rent maximization) associated with the sealed bid system.

In our study, the dynamics of the selling process are complicated further by a particular idiosyncrasy of the Scottish system. Most dwellings are sold on an Offers Over basis, where bids are not revealed to the seller until the closing date (the day of the auction). A closing date is set as soon as one or more buyers commission a survey and/or sufficient notes of interest are lodged with the selling agent. The seller usually takes the highest offer (though the move-in date set by the bidder may also be a deciding factor). As we have noted, it is unusual for the seller to reject all offers revealed on the closing date, though this is an option (typically discouraged by the estate agent or solicitor who is usually keen not to delay the sale). A seller can, however, switch the terms of sale to "Fixed Price" at any point in the marketing process. This alternative selling mechanism entails the seller revealing his or her true reservation price and marketing the property on a first come, first served basis (this precludes bargaining or bidding). It therefore bypasses the auction process and is used as a means of achieving a speedy sale. It is always within the rights of the seller to negotiate a price directly with the first interested party and thereby bypass the sealed bid system. In practice, this is the exception rather than the rule, and in our data such transactions would still be recorded as Offers Over sales.

Differences Between the Scottish Sealed Bid Auction and Traditional Property Auctions

Note that the auction used in the Scottish selling system is different than those commonly used in Australia and elsewhere in a number of important respects. Crucially, the closing date for the Scottish auction is dependent on the seller receiving notification of an intention to bid from a second prospective buyer. Because an auction cannot occur with a single bidder, and because the number of bidders usually consists only of those who have viewed and commissioned a survey of the property, the auction date is entirely dependent on the emergence of buyers willing and able to purchase. As such, the auction date is fully endogenous. The consequence of this is to make TOM contingent on market demand and supply conditions in very much the same way as it is in the English and American list price selling systems.

This contrasts with the more typical format of a property auction, such as those commonly conducted in Australia or in the sale of repossessed properties (see Eklof and Lunander (2003) for an example from Sweden), where the date of the auction is predetermined, and potential buyers are invited to bid on that date. In Sweden, for example, forced sales of properties following debt default occur through the Enforcement Administrator's office in Stockholm, which holds open outcry auctions every second week of the month: "Several apartments of various types, located everywhere in the Stockholm metropolitan area, were usually...

NOTE: All illustrations and photos have been removed from this article.



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