Bidding strategies and winner’s curse in auctions of non-distressed residential real estate
Rosane Hungria Gunnelin
Working Paper 2020:13
Division of Real Estate Economics and Finance Division of Real Estate Business and Financial Systems Department of Real Estate and Construction Management School of Architecture and the Built Environment KTH Royal Institute of Technology
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Bidding strategies and winner’s curse in auctions of non-distressed residential real estate
Rosane Hungria Gunnelin
Division of Real Estate Business and Financial Systems Department of Real Estate and Construction Management Royal Institute of Technology, Stockholm, Sweden
Email: [email protected]
Abstract: This paper analyzes how listing price and bidding strategies impact sales prices in non-distressed residential real estate auctions. Furthermore, the paper is the first that tries to explicitly quantify how these strategies affect the probability of a winner’s curse in such auctions. The findings support the results in the general auction literature that the winning bid and the probability of a winner’s curse is increasing in the number of bidders. The results further supports the notion of “auction fever” since high paced auctions (where unexperienced bidders may resort to emotional bidding) increases selling price and the probability of a winner’s curse. The results with respect to jump bidding and list price setting are mixed. Jump bidding has the intended effect of scaring off bidders, but not sufficiently to reduce the winning bid and the probability of a winner’s curse. Lowering the list price to market value ratio (the degree of underpricing) increases the number of bidders, but not sufficiently to counteract the anchoring effect of the list price leading to a reduction of the winning bid and the probability of a winner’s curse. In summary, the findings in this paper show that the unfolding of auctions of non- distressed residential real estate has a significant impact on selling price and the probability of a winner’s curse.
Keywords: Housing, auctions, list price, bidding strategies, winner’s curse
JEL-codes: D44, G41, R31
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1 Introduction
There is an abundant empirical literature studying the outcome of bidding strategies in auctions of (mostly low value) goods using data from various types of online auctions. An important factor facilitating such studies is the availability of large and detailed datasets containing micro-level information about the unfolding of the auctions. The empirical literature studying auctions of non- distressed residential real estate, representing a very high value durable good for most consumers, is on the other hand limited. Two main reasons may be behind this fact: firstly, in most countries, private negotiation is the dominant sales mechanism for non-distressed real estate and, hence, most studies focus on analyzing sales under such market conditions. Secondly, even in countries where auctions of non-distressed residential real estate are more common, there is a lack of recorded data from such auctions.1
The aim of this study is to reduce the knowledge gap with respect to the outcome of auction strategies in the setting of sales of non-distressed residential homes, which, for most people, represent the largest transaction they will ever make. The paper analyzes 802 single-family house transactions in the Stockholm region during the years 2010-2011. The study builds on and extends the modelling of Hungria-Gunnelin (2018), who analyzes list price and bidding strategies in auctions of non-distressed condominiums in the city of Stockholm during the same time period.
Overall, there are two main contributions in the present study. Firstly, the paper adds to the limited literature analyzing the effect of list price and bidding strategies on transaction price and number of bidders in auctions of residential real estate with non-professional bidders. Previous studies have mainly analyzed the relationship between underpricing, the number of bidders or bids and sales price (Haurin et al., 2013; Brown et al., 2013; Bucchianeri and Minson, 2013; Han and Strange, 2016). The present paper includes these variables and adds to the analysis variables measuring the speed of an auction (as a proxy for the degree of “auction fever”), jump bidding and late entry by the winning bidder. In relation to Hungria-Gunnelin (2018), the present paper extends the analysis by including a slightly different set of auction variables and a more thorough analysis of potential omitted variable bias including model specifications aiming at mitigating such bias. Furthermore, the results in this paper confirm the main results in Hungria-Gunnelin (2018), which studies auctions of condominiums. That is, the effect on sales price of list price and bidding strategies is similar between the condominium market and the market for single-family houses. While the results in these two papers may be specific for the housing markets in the Stockholm region and the Swedish auction sales mechanism, the fact that two different types of markets with different types of buyers and sellers generate similar results, increases the generalizability of the findings.
Secondly, the empirical literature on winner’s curse typically study this phenomenon only indirectly by estimating the effect on sales price or bidding strategies of variables associated with predictions from theoretical auction models.2 This paper, instead, tries to explicitly estimate how bidding strategies affect the probability of a winner’s curse. In a pure common value auction, the occurrence of winner’s
1 Examples of countries in which auctions of non-distressed homes are common are: Australia, New Zealand, Scotland, Ireland, Denmark, Norway, and Sweden. 2 See, for example, Easley et al. (2010), who find that increased uncertainty about the item’s value lowers auction participants’ bids, which is in line with predictions from auction theory. 3 curse can loosely be defined as the winning bidder paying more than the worth of the auctioned item.3 Residential real estate, however, has both common (resale) value and private value, making it more difficult to define and measure the occurrence of winner’s curse, since private valuations of bidders are usually not observable. Still, residential real estate represents a good for which worth, or “true” value, in terms of expected resale value, can be estimated with unusually good precision compared to many other illiquid goods. We, therefore, choose to relate the occurrence of winner’s curse to the market value/expected resale value (at the time of the auction) of the transacted properties in the auction database, estimated by a hedonic mass appraisal model.
Nevertheless, applying a heuristic definition of when a winner’s curse occurs, it is possible to analyze how the severity of a winner’s curse (how much the winning bid exceeds the market value) and the probability of a winner’s curse are affected by the way an auction unfolds. To analyze these questions, a probit model with winner’s curse as a binary dependent variable is estimated, where winner’s curse is (admittedly somewhat arbitrary) defined as the outcome of an auction, in which the winning bid is at least 10 percent higher than the market value estimated by a hedonic mass appraisal model.
Main findings in this study are that transaction price increases with number of bidders, degree of “auction fever” measured by the speed of the auction, degree of jump bidding in the opening and the winning bid, the ratio of list price to market value, while late entry by the winning bidder reduces transaction price. The results from the model estimating the probability of a winner’s curse are, as expected, qualitatively similar to the results from the price regressions with respect to the auction variables. The probability of winner’s curse increases with number of bidders, speed of the auction, degree of jump bidding in the opening and the winning bid, the ratio of list price to market value, while late entry by the winning bidder reduces the probability of a winner’s curse. Further findings are that the number of bidders increases in the speed of an auction and the degree of underpricing, supporting the common view that brokers may use underpricing as a strategy to attract many bidders to an auction with the aim of igniting fierce competition, so-called “auction fever” or “bidding frenzy”. Finally, jump bidding is found to reduce the number of bidders and, hence, has a deterring effect on competition.
The remainder of the paper is divided into six sections. Section 2 presents a literature review. Section 3 defines the local auction settings and its rules. Section 4 describes the data and the auction variables, while Section 5 introduces the models. Section 6 presents the results from the models introduced in Section 5. Section 7 concludes.
2 Literature review
The auction design, the level of list price, the number of bidders, and the behavior of auction participants have been the focus of many theoretical studies showing that these factors may have a significant impact on auction outcomes (Milgrom and Weber, 1982; Levin and Smith, 1996; Bajari and Hortacsu, 2003; Kamins et al., 2004; Dholakia and Simonson, 2005; Popkowski Leszczyc et al., 2009).
3 The literature on winner’s curse usually uses a more elaborate definition of winner’s curse, such as bidding more than equilibrium value or more than the expected value conditional on winning (see e.g. Kagel and Levin, 1986). But for the purpose of this study, we choose to relate winner’s curse to a more simple definition and equate “worth” with the estimated market value of the home for sale. 4
There are also numerous papers that empirically test theoretical hypotheses related to the unfolding and outcome of auctions such as the relationship between list price, bidding behavior and final sales price (see e.g. Haruvy and Popkowski Leszczyc, 2010; Chen, 2011; and He and Popkowski Leszczyc, 2013). The empirical auction literature has naturally benefitted from the event of online auctions, which has laid the ground for access to rich datasets. In comparison, there are only a limited number of empirical studies that analyze auctions of high value durable goods such as residential real estate, one reason being that detailed data from such auctions are usually not readily available. Moreover, empirical studies on seller and buyer behavior in real estate transactions are dominated by studies of markets in which private negotiation is the common sales mechanism.
Theoretical search-based models of list price setting normally assume that list price acts as an upper bound for the sales price (Haurin et al., 2013). The empirical literature examining this relationship has, on the other hand, found that there may be overpricing (expected sales price below list price), or underpricing, depending on the strength of the housing market. In particular, in hot markets and in markets where auctions is a common sales mechanism, underpricing is common. Stevenson et al. (2010) compares private treaty and auctioned property transactions in Dublin and finds that sellers/brokers consistently adjust guide prices for auctioned properties downwards. While they do not have information on the number of bidders, they draw the conclusion that underpricing is used to attract a higher number of bidders to the auctions. They find that, in the higher price range, auctioned properties sell for a higher price than properties sold through private treaty and that underpricing increases price, but in the lower price range, they do not find any significant difference in price between sales mechanisms, or underpricing strategy.
Haurin et al. (2013) analyze seller behavior and the relationship between list price and sales price in Belfast using data from both boom periods and down-turns. They show that unexpected demand shocks affect the ratio of list price to sales price, as well as time on market, and that the ratio of list price to sales price is persistently low during boom periods. They conclude that, during up-turns, the sales mechanism changes from that of the standard search model and becomes more auction-like where a low list price acts to encourage bidding, which generally leads to transaction prices above the list price. They further find evidence that the ratio of list price to sales price is persistently high during down-turns and explains this with loss aversion by sellers.
Hungria-Gunnelin (2013) analyses the impact of number of bidders on price of auctioned non- distressed condominium apartments in Stockholm and finds that the number of bidders has a strong positive impact on sales price. This result seems to support the argument asserted by brokers that the commonly used underpricing strategy in Stockholm attracts more potential buyers to the showing of a home for sale, resulting in more bidders in the following auction and a higher sales price. In a follow- up study, Hungria-Gunnelin (2018) extends the analysis to include, apart from the number of bidders, the level of list price and bidder aggressiveness in terms of speed of the auction and the level of jump bidding as factors affecting final sales prices. She concludes that although an increase in jump bidding on average reduces competition by reducing the number of bidders, the resulting effect is a higher selling price. Similarly, increased speed of an auction seems to amplify herd behavior/bidding frenzy by increasing the number of bidders, as well as selling price. Nonetheless, contrary to what brokers states (see Hungria-Gunnelin and Lind, 2008), and even though a low list price is found to increase the
5 number of bidders, underpricing affects selling price negatively. The same result is also found by Björklund et al. (2006) using transaction data for residential real estate in Stockholm, Sweden.
Brown et al. (2013) examine if the number of viewers, the number of bidders, and the number of bids explain differences between selling price and listing price during the period 2002 to 2009 in Belfast, Northern Ireland. They find a negative relationship between the degree of overpricing and sales price and a positive relationship between the number of bids and sales price. The number of viewers was, however, not significant.
Using a large dataset of residential real estate transactions, Bucchianeri and Minson (2013) also find that underpricing leads to a lower sales price. As part of their study, 35 local brokers were asked to recommend a list price for randomly selected homes for sale and also predict the final sales price, given the listing price they had recommended. Interestingly, while the participating brokers in general recommend underpricing, their private belief is in line with the results obtained from the statistical analysis of the transaction data. That is, a lower list price leads to a lower sales price and vice-versa. The authors conclude that their findings are consistent with anchoring behavior.
Notwithstanding, the result of Bucchianeri and Minson (2013) that brokers make recommendations against their private belief, several studies report that brokers commonly recommend underpricing in order to attract more bidders, the rationale being that more bidders leads to higher selling price (see e.g. Pryce, 2011). There is also empirical evidence that underpricing serves to attract more bidders (see Han and Strange, 2016, and Hungria-Gunnelin, 2018). Hence, there seems to be a discrepancy between the views of real estate agents, the fact that underpricing is common in certain markets, and the result in several studies that underpricing leads to lower selling prices. Pryce (2011) furthermore argue that underpricing is inefficient in that it mostly leads to irritation among visitors to showings of the objects for sale, and bidders with low valuations participating in the auctions.
As discussed in this paper, empirical studies analyzing list price strategies are susceptible to omitted variable bias in that under- or overpricing must be related to a reference value, commonly a market value estimate, that may suffer from omitted variable bias. Hence, the negative relationship between underpricing and selling price that is found in several studies may be the result of omitted variable bias. If the stated view among real estate agents that underpricing attracts more bidders and, as a consequence, a higher sales price, is correct, then rational buyers should exercise their bidding with caution in order to avoid a winner’s curse. Most models of common and affiliated value English auctions have assumed bidders to be almost exclusively rational investors. The general experimental literature, however, supports the claim that there is a positive correlation between the number of bidders and the likelihood of a winner’s curse (Dyer et al. 1989; Kagel and Levin, 1986; Kagel and Dyer, 1988; Thaler, 1988). In an experimental study, Thaler (1988) discusses how difficult it is to act rationally in a common value auction. He stresses that, in order to make rational and informed decisions, bidders must distinguish between the expected value of the object based on the information available, and the expected value restrained on winning the auction. Thaler concludes that in auctions with many bidders, one has to bid more aggressively in order to win the auction. However, this implies that the winning bidder will probably have overestimated the value of the object for sale, which suggests that bidders should bid less aggressively. Gonçalves (2008) introduces irrationality in the English auction model with two bidders, each of them assuming that their competitor always play a symmetric Nash
6 equilibrium game, allowing them to update their valuation as the price ticks up. Gonçalves concludes that, when only one bidder adopts irrational behavior, it is unclear whether final price is higher or lower than the price at the symmetric equilibrium. However, when both bidders embrace an irrational behavior of assuming that the competitor knows what he is doing, the final price always exceeds the equilibrium price.
The empirical literature studying winner’s curse in the context of real estate auctions is limited. Tse et al. (2011) analyze land auctions in Hong Kong in order to explain how valuation uncertainty, information pooling through joint bidding and competition affect bidding behavior. Their results show that bidders – who are real estate professionals – reduce their bids when valuation uncertainty increases, to lower the probability of a winner’s curse. Furthermore, joint bidding reduces the number of bidders and, consequently, the revenue for the seller. Shen et al. (2018) tests the effects of financial constraints of real estate developers on land auctions and analyze how capital budget constraints influences the bids and the auctions’ final prices. In relation to the winner’s curse phenomenon, their findings show that developers with high capital resources may decide to bid more than optimal to win the auctions. Another interesting empirical research on winner’s curse is Easley et al. (2010), who study the winner’s curse phenomenon in online auctions of rare coins that, similar to residential real estate, have components of both private and common value. They find that bidders generally lower their bids in anticipation of substantial competition and find strong evidence that bidders lower their bids in response to increased uncertainty concerning the item’s value.
Differently from Tse et al. and Shen et al., who study auctions with professional bidders, the present paper studies the outcome of auctions of non-distressed residential real estate with non-professional bidders with respect to selling price and the probability of winner’s curse. A few papers have studied auctions of residential real estate using data that, to a limited extent, describes the unfolding of the auctions (see e.g. Brown et al. (2013), who include number of viewers of the property for sale, number of bids and degree of overpricing as explanatory variables). To our knowledge, the only previous paper that has used a dataset sufficiently rich to allow more elaborate auction related variables for residential real estate auctions is Hungria-Gunnelin (2018). She studies how selling price is affected by underpricing, the number of bidders and bidding aggressiveness in terms of large bid increments4 and bidding frenzy.
Large bid increments and bidding frenzy are two concepts previously explored in the auction literature. A large bid increment is often referred to as jump bidding, while the term bidding frenzy is frequently exchanged with the term auction fever. Jump bidding is used by bidders to signal aggressiveness in order to limit competition by scaring off other bidders and, consequently, win the auction with a relatively low sales price (Avery, 1998). Easley and Tenorio (2004) analyze online auction data and their results show that jump bidding usually occurs early in an auction when it has a greater strategic weight to deter bidder entry. He and Popkowski Leszczyc (2013) conduct field studies of internet auctions and confirm Easley and Tenorio’s hypothesis that jump bidding deter bidders from entering the auction. Nevertheless, they also find that final prices increase with jump bidding and conclude that jump bidding is a costly strategy to exercise. Hungria-Gunnelin (2018) analyzes auctions of condominium apartments in Stockholm and her results confirm that jump bidding reduces the number of bidders, however, not enough to avoid a higher sales price. Another rationale for jump bidding can be found in
4 A large bid increment, also called jump bid, is generally defined as a bid that is larger than necessary to be a winning bid. 7
Ettinger and Michelucci (2016) who study Japanese auctions. They propose that jump bidding is used by bidders to hide drop out values of their competitors when the auction rule allows bidders to alter their valuations through the aggregation of information.
Bidding frenzy, or auction fever, has been directly associated with herding behavior in the behavioral economics literature. Ku et al. (2005) identify the phenomenon of bidding frenzy to be directly related to competitive arousal and emotional bidding, where competition and time pressure may lead bidders to behave irrationally, by placing bids past their limits. Adam et al. (2011, 2015) confirm that bidding frenzy is triggered by an emotional state that drives bidders to change the course of their initially chosen bidding strategy. They find that bidders’ arousal is positively correlated with time pressure and that this lead to higher bids in ascending auctions. Central to this phenomenon is rivalry and social competition, as their results show that the “joy of winning” is significantly stronger than the “frustration of losing”. In the context of residential real estate auctions, Hungria-Gunnelin (2018) finds that time pressure, in the form of a shorter time between bids, increases the probability of auction fever, as both the number of bidders and the final sales price are positively correlated with the speed of the auction. Han and Strange (2016) further suggests that sales of homes have the potential for emotional bidding. Directly related to the jump bidding strategy and the phenomenon of bidding frenzy is the notion of winner’s curse. Avery (1998) state that jump bidding increases the risk for the winning bidder to fall prey to the winner’s curse, partly because a jump bid signals that the bidder values the item for sale higher than other bidders, and partly because a drop out of the jump bidder may be a strong hint that the winning bidder has overpaid for the asset. In an experimental study, Avery and Kagel (1997) find that in a significant percentage of English auctions (around 30 percent), the winning bidder incurs monetary losses when bidders use aggressive bidding strategies.
3 The local auction setting
With the exception of sales of new developments, virtually all residential homes for sale in Sweden are sold through English auctions (The Association of Swedish Real Estate Agents, 2016). Differently from traditional real estate auctions that take place in an auction house with all bidders present, bidding is usually made over phone, where the broker calls the potential buyers, or potential buyers take the initiative to contact the broker to place a bid.5 The participating bidders register their cell phone number prior to the auction start, so that they can get live updates on newly incoming bids through text messages and have the opportunity to react to these bids. Most brokerage firms also display the incoming bids on their websites. The auction usually starts the day after the showing of a home and the duration of the auction is on average three days in the geographical region covered by this study.6
What makes the Swedish real estate auction unique is that there are no regulations for the bidding process. Swedish Contract Law says that all types of agreement, including oral agreements, are binding, with the exception of real estate transactions. According to the Swedish Land Law of 19707, for an agreement concerning a real estate transaction to be binding, it is required that the agreement is in written form, signed by both the seller and the buyer, and where the purpose of the property’s
5 A thorough description of the sales process is given in Hungria-Gunnelin (2018). 6 There is also the case when an incoming bid arrives before the showing of a property. If the seller accepts the bid, the showing is usually cancelled. This is a strategy from the buyer to avoid an auction. Although it is an interesting phenomenon, this strategy is not analyzed in this study. 7 Chapter 4, Section 1. 8 disposition, together with the price agreed, are included. Hence, since bids in the auctions are placed orally, they are not binding by the Law. Bidders can withdraw from the auction at any time without incurring any cost (Hungria-Gunnelin, 2018). This lack of regulation creates an environment that have implications for all the parties involved in the sales process, even after all bids have been placed: i) the seller does not know with certainty if the property is sold until the sales contract is signed; ii) because brokerage commission is only paid when (and if) the property is sold, the broker is also unsure about receiving her payment. Moreover, if the property is not sold after the broker has contacted all participating bidders, she usually needs to reschedule the showings for the coming weeks, which is costly for the broker; and iii) non-serious bidders may cross-bid in simultaneous auctions, inflating the price in these auctions for the remaining bidders.
Under these conditions, and especially in the big cities where new objects are listed every week8, brokers may act rationally by trying to speed up the bidding process and get the winning bidder9 to sign the sales contract as soon as possible to assure the transaction. The time pressure imposed on potential buyers may have a direct impact on bidders’ behavior, who may engage in a bidding war by responding quickly to previous bids. As discussed in Section 1, this behavior may trigger an auction fever that leads bidders to make irrational decisions. Hungria-Gunnelin and Lind’s (2008) findings show that there has been a willingness from some brokers to solve the problem of underpricing – which has been considered by the media to be a deceiving method to attract potential buyers – by changing the bidding regulation and making bids binding.
With today’s technology, it would be fully possible to make bids binding without making large alterations of the existing Swedish Land Law on real estate transactions, as bidders can electronically identify themselves and digitally sign every bid they place through an identification application.10 In Norway, for example, written digital bids are common in real estate auctions, where bids are binding (The Norwegian Association of Estate Agents, 2013). Such auctions attract only genuine bidders (Ong, 2006). In a study of online auctions, Anwar et al. (2006) show that auction participants tend to cross- bid when similar items are sold in auctions that start and end approximately at the same time, which is the case of single-family house auctions in Stockholm (bidding usually starts on Monday after the weekend showings). The problem with the participation of non-serious bidders is that, in an ascending auction context, it contributes to increase the gap between list and sales prices, enlarging the effect of the underpricing strategy (Hungria-Gunnelin, 2018). Moreover, it is believed that regulated participation11 would diminish the pressure on brokers that try to speed up the sales process in order to guarantee a sale. That would, in turn, imply less time pressure on bidders leading to more rational decisions under less stressful conditions.
8 An average of 1,009 single-family houses and 1,973 condominium apartments were listed on a weekly basis during 2016 in Sweden (Hemnet, 2017). 9 There are some exceptional cases where the winner is not the one who placed the highest bid. Because the broker only checks the financial status of the winner after the auction is over, it may happen that the winner have not arranged sufficient financing. In those cases, the broker normally contacts the bidder that placed the second highest bid to see if he still is interested in buying the house (Hungria- Gunnelin, 2018). 10 BankID is, for example, an electronic identification application widely used in Sweden by individuals and organizations for login authentication or to sign electronic documents of government authorities, banks and other firms. 11 In the form of binding bids and households with approved loan commitments from their banks. 9
4 The data and the constructed auction variables
4.1 The data The main dataset in this study consists of 802 transactions of non-distressed single-family houses during the years 2010 and 2011. This data was gathered from eBud12 and contains information on property attributes such as Municipality, address, living area, extra area13, plot size, list price, sales price, as well as auction variables concerning the size and time of each bid and an identification code for each bidder in the auction.
A secondary dataset was acquired from the Swedish Mapping, Cadastral and Land Registration Authority (hereafter, the SMCLR-dataset) containing all the sales of single-family houses in Stockholm County (a total of 196,744 transactions) during the period 1996 – 2016. Differently from the eBud dataset, this official property register contains very detailed data on the properties’ quantitative attributes such as living area, extra area, plot area, sales price, assessed value, standard points14, geo coordinates, the land value area15 (VO), as well as on its qualitative characteristics, such as construction type16, land use rights (leasehold or freehold), reasons for extra adjustment of assessed value (if any), construction year, value year17, sea/lake view and the transaction registration date18.
To this data, a third dataset from the Swedish Tax Authority was acquired containing a classification of the land into slightly larger areas than the VOs, but where locational factors affecting property values are still very similar.19 These areas, called PVOs, are very useful as geographical dummies when, as in the case of the auction database used in this study, the number of observations is not sufficient to use the smaller VOs as geographical dummies. The VO and PVO variables have, to my knowledge, not been previously used in any empirical study of the Swedish housing market.
The eBud-dataset containing unique information on the auction unfolding of each object was matched with the SMCLR-dataset, as well as with the Swedish Tax Authority’s PVO data in order to create a dataset that is as extensive as possible. Table 1 shows the descriptive statistics of the main dataset.
12 eBud was a Swedish online service owned by Handelsbanken where data on ongoing auctions of residential properties were displayed. 13 Extra area is the area of a house that is not planned as main living area. Examples of such area are a basement, an attic or a garage. In Sweden, there is also a rule to differentiate the living area from the extra area when part of the house is built underground due to a sloped terrain. In this case, all the area that exceeds 6 meters from the stand-alone wall (i.e. not underground) is considered extra area. A sloped roof in a floor that is less than 1.90 meters in height can also create a space that is considered difficult for usage and, thus, be included in the calculation of the extra area of a house. 14 One of the variables used to calculate the assessed value of a house is the standard points. Standard points grades the quality of construction materials and equipment in a property and are calculated based on a questionnaire made by the Tax Authority that the property owner answers, covering five areas: exterior (roof and façade), energy, kitchen, sanitation, and other interior (For more information, see: https://www4.skatteverket.se/rattsligvagledning/edition/2014.6/3450.html#h-Standardpoang). 15 The Swedish Tax Authority constructs, for all municipalities in Sweden, land value areas (VOs), which are homogeneous geographical areas for which the tax authority deem the land value per square meter to be very similar. It is important to note that these classifications are made by experts at the tax authority with local knowledge about the property market in each municipality. 16 Divided into three categories: detached house, semi-detached (normally separated from the neighboring house by a garage or carport), and row house (sharing at least one sidewall with a neighboring house). 17 The value year differs from the construction year only if the whole or part of the house has been considerably renovated, or if new constructions are made after the original construction year. For such alterations made before 1929, the value year equals 1929. For alterations made after this date, the value year is adjusted according to a weighted formula. The value year is used for taxation purposes and is considered a better representation of the life-span of the property than the original construction year. 18 The registration date usually occurs with a couple of months delay from the date the sales contract is signed. 19 When determining the geographical area of each VO, the tax authorities use a slightly larger geographical area than a typical VO, a so called PVO (a test valuation area), as the base for collecting comparable sales that are analyzed statistically as part of the process of assessing separate land and construction values for each residential property. A PVO typically consists of about three adjacent VOs.
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Table 1 Descriptive statistics. The sample is constructed from the eBud data containing sales of 802 single-family houses in Stockholm County during the years 2010-2011. The sample consists of transactions with a minimum of 2 bidders and excludes PVO areas with less than 5 sales. Descriptives for the VOs and PVOs are omitted due to the large number of areas. Variable Variable name Unit Average Std. Dev. Min. Max. Sales price PRICE Swedish crowns, SEK 4,195,623 1,796,976 1,470,000 27,500,000 Living area AREA Square meters 131.97 29.82 50 238 Extra area EXTRA_AREA Square meters 25.25 37.06 0 222 Lot size LOT_SIZE Square meters 686.80 547.45 86 6,540 Ground lease GROUNDLEASE Binary, 1 if the lot is a leasehold 0.015 0.12 0 1 Value year VAL_YEAR Year 1975.09 17.83 1929 2008 Age AGE Number of years since value_yr to sales date 35.50 17.88 2 83 Standard points STD_PTS Points that represent quality, for taxation purposes 29.29 3.41 16 51 Detached house DETACHED Binary, 1 if construction type is detached house 0.52 0.50 0 1 Semi-detached CHAINED Binary, 1 if construction type semi-detached 0.28 0.45 0 1 Row house ROW HOUSE Binary, 1 if construction type is row house 0.20 0.40 0 1 Lot near beach NEAR_BEACH Binary, 1 if plot located up to 150 m from waterline, without private-owned 0.01 0.07 0 1 beach Lot no beach NO_BEACH Binary, 1 if plot located at least 151 m from waterline 0.99 0.07 0 1 Number of bidders NR_BIDDERS Number of bidders 3.69 1.71 2 11 Number of bids NR_BIDS Number of bids 12.10 7.59 2 49 Average reaction time AVG_TIME Average time between bids in the auction in days 0.77 2.44 0 35.06 Jump bid (first bid) JUMPBID_FIRST Average percentage bid increment of first bid in relation to list price 0.002 0.06 -0.73 0.25 Jump bid (winning bid) JUMPBID_WIN Average percentage bid increment of last bid in relation to next last bid 0.02 0.04 0 0.90
Single bid from winner LATE_ENTRY Binary, 1 if the winner placed only one bid 0.06 0.24 0 1 Underpricing UNDERPRICE Log difference between predicted market value and list price 0.11 0.15 -0.74 0.55 Parish 1 (Vallentuna) KF_1501 Binary, 1 if plot located in Vallentuna parish 0.19 0.39 0 1 Parish 2 (Österåker-Östra Ryd) KF_1702 Binary, 1 if plot located in Österåker-Östra Ryd parish 0.08 0.27 0 1
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Table 1 Continued. Variable Variable name Unit Average Std. Dev. Min. Max. Parish 3 (Järfälla) KF_2304 Binary, 1 if plot located in Järfälla parish 0.03 0.16 0 1 Parish 4 (Täby) KF_6001 Binary, 1 if plot located in Täby parish 0.46 0.50 0 1 Parish 5 (Danderyd) KF_6201 Binary, 1 if plot located in Danderyd parish 0.006 0.08 0 1 Parish 6 (Sollentuna) KF_6301 Binary, 1 if plot located in Sollentuna parish 0.006 0.08 0 1 Parish 7 (Vantör) KF_8023 Binary, 1 if plot located in Vantör parish 0.03 0.16 0 1 Parish 8 (Vällingby) KF_8031 Binary, 1 if plot located in Vällingby parish 0.02 0.15 0 1 Parish 9 (Hässelby) KF_8038 Binary, 1 if plot located in Hässelby parish 0.03 0.18 0 1 Parish 10 (Hägersten) KF_8039 Binary, 1 if plot located in Hägersten parish 0.03 0.18 0 1 Parish 11 (Spånga-Kista) KF_8041 Binary, 1 if plot located in Spånga-Kista parish 0.06 0.08 0 1 Parish 12 (Lidingö) KF_8601 Binary, 1 if plot located in Lidingö parish 0.03 0.16 0 1 Quarter 1 Q1 Binary, 1 if sale occurred between January-March 2010 0.12 0.33 0 1 Quarter 2 Q2 Binary, 1 if sale occurred between April-June 2010 0.20 0.40 0 1 Quarter 3 Q3 Binary, 1 if sale occurred between July-September 2010 0.11 0.32 0 1 Quarter 4 Q4 Binary, 1 if sale occurred between October-December 2010 0.14 0.34 0 1 Quarter 5 Q5 Binary, 1 if sale occurred between January-March 2011 0.12 0.33 0 1 Quarter 6 Q6 Binary, 1 if sale occurred between April-June 2011 0.16 0.37 0 1 Quarter 7 Q7 Binary, 1 if sale occurred between July-September 2011 0.08 0.27 0 1 Quarter 8 Q8 Binary, 1 if sale occurred between October-December 2011 0.06 0.24 0 1
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4.2 Auction Variables Empirical studies of real estate auctions that quantify the effects of different auction strategies are scarce, mainly due to data limitation concerning both the number of observations and the level of detail of auction data. Examples of empirical studies, albeit with fewer auction related variables than in the current study, are: Chow and Ooi, 2014, Ong et al., 2005, Ong, 2006, and Shen et al., 2018. While the dataset available for this study is quite detailed in the context of real estate auctions, the variables constructed to describe the unfolding of the auctions are simplistic compared to, for example, variables used in papers analyzing online auctions with larger datasets (see e.g. Anwar et al., 2006, Bajari and Hortaçsu, 2003, and Bapna et al., 2009). Nevertheless, the present study develops further the auction variables used in Hungria-Gunnelin (2018) and also studies bidding behavior in auctions of single-family houses instead of condominium apartments.
Seven auction-related variables are used in this study. Since the construction of some of the variables requires at least two bidders, all transactions with one single bidder were excluded from the analysis. The first variable, BIDDER_RES, is the residual from Model I, the model estimating the number of bidders in an auction, and it is the same variable as is used in Hungria-Gunnelin (2018). Using the residual, i.e. the unexpected number of bidders and not the total number of bidders as explanatory variable in the price and winner’s curse models, is motivated by the fact that all variables explaining the total number of bidders in Model I are included in the price and winner’s curse equations. Removing the expected part of the total number of bidders makes it possible to analyze, explicitly, the effect of different list price and bidding strategies. For example, different strategies may lead to the same expected number of bidders, but they may affect selling price differently. Hence, when including the residual from the bidder equation (and not the total number of bidders), the effect of a certain strategy is measured directly by the coefficients of the variables describing that strategy, while the coefficient on the residual represents the effect of random variation of the number of bidders in an auction.20
The second variable, UNDERPRICE, measures the seller’s list price strategy and is calculated as the difference between the natural log of the estimated market value of the house and the natural log of its list price. The variable is constructed as follows:
UNDERPRICEiln MV i ln LP i
where MVi is the estimated market value of object i and LPi is the list price for the same object. The MV variable is estimated from a mass valuation model that is identical to the benchmark model (Model II), with the exception that the time dummy variables are expressed in months, instead of quarters.
The remaining variables are related to the bidding aggressiveness in the auctions and they measure both the size of bid increments and the speed at which bids are placed. As discussed in the literature
20 Since the auction variables only controls for a subset of possible auction strategies, the residual from the bidder equation partly represents variation that originates from bidding strategies that are not controlled for, and partly represents true random variation in the number of bidders in an auction. 13 review, these variables are an attempt to quantify the economic effect of bidding aggressiveness in the form of jump bids and bidding frenzy.
The third variable, AVG_TIME, measures the average time span between the bids in the auction:
N ti AVG_ TIME i2 , i N 1
where ti equals the time span between bid i and bid i 1 and 푁 equals the number of bidders.
The fourth variable, JUMPBID_FIRST, measures the percentage difference between the first incoming bid and the announced list price:
BID1 JUMPBID_1 FIRSTi , LPi
where BID1 represents the first bid placed at the beginning of the auction of the object i and LPi equals the list price of the same object.
The fifth variable, JUMPBID_WIN, measures the percentage difference between the winning bid and the next-to-last bid:
BIDN JUMPBID_1 WINi , BIDN 1
where BIDN equals the winning bid for the object i and BIDN-1 represents the second-highest bid.
The sixth variable, LATE_ENTRY, is a dummy variable that is equal to one if the winning bidder only bids one time, i.e. the winning bid. The hypothesis is that a late entry by the winner increases the probability of winning the auction at a low price by not being a part of bidding up the price through multiple bids (see Bajari and Hortacsu (2003) for a discussion on late entry in eBay auctions).
14
5 The Models
5.1 Number of bidders model The seller of a home may strategically set a low list price in order to attract many bidders to the following auction, the rationale being that the winning bid is an increasing function of the number of bidders (see e.g. Han and Strange, 2016; Stevenson et al., 2010; and Bucchianeri and Minson, 2013, for discussions). Yet, the only previous papers that have tested empirically this assertion are Han and Strange (2016) and Hungria-Gunnelin (2018). Similar to Hungria-Gunnelin (2018), the model in this paper is richer than the one in Han and Strange (2016) in that it includes both underpricing (the seller’s strategy) and auction participants’ bidding strategies as explanatory variables in the regression. The model includes all variables defined in Table 1, except the variable LATE_ENTRY since it is difficult to motivate why this variable should affect the number of bidders at an auction. Model I is specified as follows:
푁푅_퐵퐼퐷퐷퐸푅푆푖 = 훼 + 훽[푃푅푂푃퐸푅푇푌]푖 + 훾[퐿푂퐶퐴푇퐼푂푁]푖 + 훿[푄푈퐴푅푇퐸푅]푖 (1) + 휆(푈푁퐷퐸푅푃푅퐼퐶퐸)푖 + 휂[퐴푈퐶푇퐼푂푁]푖 + 휀푖
where the dependent variable NR_BIDDERSi is the number of bidders in auction i. PROPERTY represents the variables related to the characteristics of the property such as living area, extra area, plot size, age, construction type, and so on. LOCATION represents the geographical dummy variables controlling for the parish in which a house is located, as well as its micro-location, the PVO dummy variables. QUARTER is the time dummy variable indicating the quarter in which the house was sold. UNDERPRICE is the measure of the seller’s list price strategy and AUCTION represents variables defining buyers’ bidding strategies defined in Section 4.2, except for LATE_ENTRY.
5.2 House price models Two hedonic price models are estimated, starting with a benchmark model in form of a standard hedonic price regression with property attributes and geographical and time dummy variables as explanatory variables. The benchmark model, Model II, is specified as follows:
퐿푁(푃푅퐼퐶퐸)푖 = 훼 + 훽[푃푅푂푃퐸푅푇푌]푖 + 훾[퐿푂퐶퐴푇퐼푂푁]푖 + 훿[푄푈퐴푅푇퐸푅]푖 + 휀푖 (2)
where LN(PRICE) is the natural log of the transaction price. PROPERTY, LOCATION and QUARTER are defined as in Model I.
In order to analyze the effect of list price and bidding strategies, Model III augments Model II with the auction related variables:
15
퐿푁(푃푅퐼퐶퐸)푖 = 훼 + 훽[푃푅푂푃퐸푅푇푌]푖 + 훾[퐿푂퐶퐴푇퐼푂푁]푖 + 훿[푄푈퐴푅푇퐸푅]푖 (3) + 휆(푈푁퐷퐸푅푃푅퐼퐶퐸)푖 + 휂[퐴푈퐶푇퐼푂푁]푖 + 휀푖
AUCTION represents all bidding strategy variables, including LATE_ENTRY.
5.3 Controlling for Omitted Variable Bias Empirical modeling of residential real estate prices tend to suffer from omitted variable bias (OVB) due to e.g. unobserved quality (see Clapp et al. (2018) for a recent discussion of omitted variable bias in housing price models). In the context of the current study, omitted variable bias may distort the coefficient estimates of interest, i.e. the coefficients of the auction-related variables. For example, errors in the estimation of the variable UNDERPRICE may be correlated with the error term of Model III, since the estimated market value from a hedonic mass appraisal model is used as reference point for calculation the underpricing variable and the mass appraisal model uses the same set of control variables as Model III. This paper attempts to control for OVB in a number of ways as discussed in the remaining of this section.21
5.3.1 Inclusion of repeat-sales residuals Genesove and Mayer (2001), Bokhari and Geltner (2011), Bucchianeri and Minson (2013) and Clapp et al. (2018) include as explanatory variable in their price regressions the residuals from a price regression of previous sales, in order to control for omitted variable bias. One reason for including this variable is that the effect on price of unobserved quality ends up in the regression residuals. That is, a positive repeat-sales residual may partly be caused by positive unobserved qualities, and vice-versa. Hence, the repeat-sales residual serves as a noisy proxy for omitted variables. Another reason is that loss- aversion makes the previous sale of the property a reference point for the current owner (Genesove and Mayer, 2001).
Adopting this strategy for mitigating possible OVB and anchoring effects, a mass valuation model is estimated using the SMCLR-dataset in order to retrieve the residual of each repeat-sale. Since the time period of the dataset is quite long (20 years), the regressions are broken down into moving windows of 5 years each, where the first window covers the sales in years 1996-2000, the second window, the sales in 1997-2001, and so forth. In total, 17 windows are estimated.
Model IV adds the repeat-sales residual to Model III:
퐿푁(푃푅퐼퐶퐸)푖 = 훼 + 훽[푃푅푂푃퐸푅푇푌]푖 + 훾[퐿푂퐶퐴푇퐼푂푁]푖 + 훿[푄푈퐴푅푇퐸푅]푖 (4) + 휆(푈푁퐷퐸푅푃푅퐼퐶퐸)푖 + 휂[퐴푈퐶푇퐼푂푁]푖 + 휈(푅퐸푃퐸퐴푇_푅퐸푆)푖 + 휀푖
21 The models may also suffer from bias due to measurement errors in the variable AVG_TIME, since there is no way to control that the broker immediately registered an incoming bid. However, in general, brokers aim at updating the bids very quickly. 16 where REPEAT_RES is the repeat-sales residual. Many of the 802 transactions in the eBud-dataset, have more than one repeat-sale identified in the SMCLR-dataset and, for those transactions, REPEAT_RES is calculated as the average of the residuals of the two repeat-sales transactions that are closest in time to the transaction date of the observation in the eBud-dataset. Furthermore, since a five year moving window is used in the mass appraisal model, each identified repeat-sale becomes an observation in five different estimates of the mass appraisal model, with the exception of repeat-sales occurring during the first and last four years in the dataset. The REPEAT_RES variable in Model IV is, therefore, calculated as the average of five residuals22, except when occurring the first or last four years in the dataset.23
5.3.2 Inclusion of list price residuals Xie (2018) uses the degree of overpricing (DOP) as a control for OVB. DOP is calculated as the residual of a list price regression. The argument is that a deviation of list price from the predicted value is partly caused by unobserved (for the researcher and perhaps the buyer) home characteristics. Hence, adding the list price residual to the price equation will, in a similar manner as the repeat-sales residual, serve as a proxy for omitted variables. It can further be argued that the variable UNDERPRICE (the ratio of estimated market value to list price), in a similar way as the DOP, partially captures the effect on price of omitted variables (see discussion in Pryce (2011), where the variable measuring overpricing is identical to UNDERPRICE in this paper). That is, if the market value estimate from the mass appraisal model suffers from OVB, this error will be captured by the UNDERPRICE variable.
As an alternative model specification, DOP is included as an explanatory variable in the price model. DOP is calculated as the residual from a regression of the log of the list price on the same explanatory variables as in Model II. Model V replaces UNDERPRICE in Model III with the DOP variable:
퐿푁(푃푅퐼퐶퐸)푖 = 훼 + 훽[푃푅푂푃퐸푅푇푌]푖 + 훾[퐿푂퐶퐴푇퐼푂푁]푖 + 훿[푄푈퐴푅푇퐸푅]푖 (5) + 휂[퐴푈퐶푇퐼푂푁]푖 + 휈(퐷푂푃)푖 + 휀푖
5.3.3 Robust regression Because the eBud-dataset covers transactions within different municipalities in Stockholm County, it is expected that the data on the different local markets may diverge quite a lot from each other. For example, the Danderyd and Lidingö municipalities are known to have exclusive residential properties that may overweight the prices in the regression for the rest of the sample, while Spånga-Kista and Österåker-Östra Ryd may underweight prices, if the factors that affect prices are not controlled for in the model. Although geographical heterogeneity is controlled for, there may be large outliers within each area that potentially distort coefficient estimates due to the overweighting of outliers. A robust regression is, therefore, estimated to mitigate this potential problem.
Model VI is identical to Model III except that it is estimated as a robust regression applying the robust regression method presented in Li (1985). Although the robust regression method is not a direct
22 Each of the five residuals is the average of two residuals when there is more than one repeat-sale. 23 An implicit assumption in this method to control for OVB is that attributes have not changed between the time of the repeat-sale and the time of the transaction in the auction dataset (eBud). The motivation for using the average of the two closest repeat-sales residuals when available is that the averaging reduces the effect of the true random component of the residuals (which we do not want to capture), since the expected value of that component equals zero. 17 attempt to solve the OVB problem, it indirectly does so as large residuals due to omitted variables or random noise are down-weighted in the calculation.
5.3.4 Spatial autoregressive and spatial error models Given the influence of spatial characteristics of real estate on house prices, one cannot ignore the effects of spatial dependency and heterogeneity that may cause bias, inefficient coefficient estimates and inference problems in the regression estimations (Anselin, 1988; Dubin, 1998; Wilhelmsson, 2002). The standard OLS model of property prices does not account for these influential factors. LeSage and Pace (2008) argue for the use of spatial regression models that accounts for spatial dependency, as such may cause coefficients to become inefficient and inconsistent. They give two econometric reasons why spatial models should be applied in those cases: “The first motivation comes from viewing spatial dependence as a long-run equilibrium of an underlying spatiotemporal process and the second motivation shows that omitted variables that exhibit spatial dependence leads to a model with spatial lags of both the explanatory and dependent variables.”
Real estate pricing models usually suffer from spatial dependence caused by omitted variables. Wilhelmsson (2002) clarifies that spatial dependence (or spillover effect) may result, among other reasons, from spatially correlated variables that have been omitted. For example, it is difficult to have access to all data in a sample that correctly reflects the property’s spatial location in terms of neighborhood characteristics, socioeconomic characteristics of residents, service quality (such as schools, banks, shops, restaurants, and other amenities), the perceived safety in the neighborhood, and so forth. In other words, spatial dependence means that an observation at one location depends on other observations from a number of other locations. On the other hand, because real estate is a durable good fixed in space and its supply is basically inelastic (Malpezzi, 2003), functional disequilibria arise as a result of the impact of socioeconomic and demographic conditions of households on spatial variation in housing demand. These disequilibria are manifested in the form of heterogeneous market structures (Sheppard, 1997). Thus, spatial heterogeneity should be considered in hedonic models (Helbich et al., 2014).
LeSage and Pace (2008) emphasize, thus, the importance of using a spatial lag model (SAR) as a protection against bias caused by possible omitted variables that are correlated with the included explanatory variables in the model. When such correlation is absent, a spatial error model (SEM) is preferred. Differently from the spatial lag model, the spatial error model assumes that the errors of a model are spatially correlated (Ward and Gleditsch, 2008). If only spatial autocorrelation of the errors (residuals) are correlated, OLS estimates become unbiased, but inefficient, as the standard errors would be wrong. Because it is difficult to tell if the presence of spatial autocorrelation is caused by dependency or heterogeneity, a Lagrange multiplier test is usually run to decide which of these two models to apply (Helbich et al., 2014). In this study, we run the Lagrange diagnostic test with and without fixed effects. The reason that both variants are tested is that the well-known trade-off between increased control for geographical heterogeneity and loss of degrees of freedom due to a large number of control dummy variables. Hence, two models are estimated: Model VII and Model VIII which are based on the same equation as Model III, but Model VII is estimated as a SAR model and Model VIII as a SEM model.
18
5.3.5 Detailed geographical control Xie (2018) includes subdivision as a geographical control variable and argues that this variable controls for unobservable home characteristics, which are homogeneous within subdivisions. The variable PVO used in this paper serves the same purpose, since PVOs represent geographical areas that valuers from the tax authorities with local knowledge deem as homogeneous geographical areas with respect to characteristics affecting land value. Han and Strange (2016) use property tax assessments based on assessed values as a control for unobserved housing attributes and argue that the tax assessments are not only based on reported housing attributes, but also on valuers’ actual inspection of houses and neighborhoods. Property tax could be included as a control variable also in the current study, but since all variables that the tax authorities use to determine assessed value are included in the models (both house characteristics and geographical variables), adding property tax as control is unnecessary.
5.4 The winner’s curse model As discussed in Section 1, it is not obvious how to define and measure the occurrence of a winner’s curse in the setting of residential real estate auctions since a home possesses both common and private value. We sidestep this problem by adopting an admittedly heuristic approach when estimating the effect of the auction variables on the probability of a winner’s curse.
Firstly, the amount of overpaying by the winner of an auction, the log difference between the sales price and the market value of the home (as estimated by the mass appraisal model), WIN_PREMIUM, is calculated:
푊퐼푁_푃푅퐸푀퐼푈푀푖 = 퐿푁(푃푅퐼퐶퐸)푖 − 퐿푁(푀푉)푖 (6)
Secondly, a binary variable measuring the occurrence of a winner’s curse is calculated as follows:
WIN_CURSEi = 1 if WIN_PREMIUMi > 0.1 (7) WIN_CURSEi = 0 if WIN_PREMIUMi ≤ 0.1
Recognizing that a home is a mixed value good and that a winner may overpay compared to the market value simply because his/her private valuation is high, a winner’s curse is (somewhat arbitrary) defined to occur if the winning bid exceeds the market value with an amount given by Equation 7. That is, we assume that a winner’s curse occur if the winning bid is approximately 10 percent higher than the estimated market value.24
24 Another possible way to analyze the occurrence of a winner’s curse is to look at the ration between the winning bid and the second highest bid and see how much the winning bid exceeds the second bid, as discussed in Thaler (1988). However, in the context of the present study, where bidders are amateurs and where houses also have a private value component, it becomes difficult to infer that anyone is behaving irrationally and overpaying for the property. Therefore, it is much more plausible to compare the winning bid to the estimated market value of the property to be able to make any inference about the winner’s curse. 19
Thirdly, the probability of a winner’s curse is estimated by a probit model as follows, where the explanatory variables are the same as in Model III, although the auction related variables, for simplicity of interpretation, enters the model only in linear terms. Hence, Model IX is as follows:
푊퐼푁_퐶푈푅푆퐸푖 = 훼 + 훽[푃푅푂푃퐸푅푇푌]푖 + 훾[퐿푂퐶퐴푇퐼푂푁]푖 + 훿[푄푈퐴푅푇퐸푅]푖 (8) + 휆(푈푁퐷퐸푅푃푅퐼퐶퐸)푖 + 휂[퐴푈퐶푇퐼푂푁]푖 + 휀푖
6 Results
6.1 Number of bidders model The results from Model I are displayed in Table 2. Confirming the results of both Han and Strange (2016) and Hungria-Gunnelin (2018), UNDERPRICE increases the number of bidders. Han and Strange (2016) finds that a reduction of the asking price by 10 percent increases the number of bidders by 2.2 percent. Han and Strange uses the log of the number of bidders as dependent variable, while Hungria- Gunnelin (2018) and this paper use the number of bidders. The effect of underpricing in Hungria- Gunnelin (2018) is approximately 0.05 more bidders when list price is reduced by 10 percent. The combined effect of the linear and quadratic term of underpricing in Model I in the current paper corresponds to approximately 0.15 more bidders for the same list price reduction. While the result is not directly comparable to the result in Han and Strange, since they use a log-linear specification, the effect in a typical auction with the average number of bidders (3.8 bidders) is about twice of that in Han and Strange. One possible explanation for the stronger effect in the Swedish data may be related to the fact that bidding in Sweden is non-committing and a low list price may entice an increased amount of bidders with low valuations who, without risk, place bids in hope of making a bargain.
Table 2 Number of Bidders regression. OLS estimation with heteroscedasticity-consistent standard errors. Minimum number of bidders equals 2. The variables related to property attributes, construction type, as well as fixed geographical and time effects are included in the regression. The numbers in parentheses are t statistics. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. Model I Number of bidders Coef. t-stat. Auction Variables: AVG_TIME -0.2796 (-6.26)*** AVG_TIME (squared) 0.0077 (4.16)*** JUMPBID_FIRST -4.9548 (-4.93)*** JUMPBID_FIRST (squared) -4.3521 (-2.28)** JUMPBID_WIN -10.1336 (-3.07)*** JUMPBID_WIN (squared) 9.6795 (2.65)*** UNDERPRICE 1.3476 (2.91)*** UNDERPRICE (squared) 1.5324 (1.18)
R-squared 0.2995 Observations 802
20
The variable JUMPBID_FIRST has a strong negative effect on the number of bidders, a result that is in line with the hypothesis that jump bidding deters competition. An opening bid that is 10 percent higher than the list price results in approximately 0.5 less bidders compared to an opening bid that is equal to the list price.
A similar effect is obtained for JUMPBID_WIN, again in line with the hypothesis that jump bidding deters competition. The effect is, in fact, stronger than that for jump bidding in the first bid. If the winning bid is 10 percent higher than the second highest bid, the jump bidding reduces the number of bidders by 0.9 compared to the case in which the winning bid is only marginally higher. The result that the deterring effect is stronger than for jump bidding in the first bid is expected, since bids in the end of an auction are higher compared to the market value of the home, and the risk of a winner’s curse should, therefore, be higher than in the beginning of an auction, which likely makes competitors wary of placing more bids after a large jump bid late in the auction.
The negative sign on AVG_TIME supports the hypothesis that fast auctions may lead to auction fever, where potential buyers interpret fierce bidding as a signal that the home is attractive and become lured into bidding themselves. A fast auction, in which bids are placed every hour or faster, will, on average, have about 0.27 more bidders than an auction with one bid per day, and about 0.88 more bidder compared to a slow auction in which there are two bids per week (the average in the dataset is 0.77 days between bids).
The variables AVG_TIME and JUMPBID_WIN may pose a potential simultaneity problem since the causality between the number of bidders and the average time between bids as well as jump bidding in the winning bid may go in both directions. As a robustness test Model I was also estimated excluding these variables and the exclusion did not significantly alter the coefficients or significance of the remaining variables.
6.2 Price models Two models are presented in Table 3. Model II is a classical hedonic price equation containing property attributes and spatial and time fixed effects. Model III is an extension of Model II in which the auction- related variables are added.
The results from the hedonic price regression in Model II, Table 3, show that all variables controlling for house attributes, construction type, and spatial characteristics are significant with expected sign, except for the squared terms for extra area and plot size. The variable STD_PTS, measuring the quality of a home, is only included in a linear fashion since this produces a significantly better fit than when including a quadratic term. Due to the detailed set of control variables, the explanatory power of the model is quite high with an R-squared of 0.87. Hedonic models of sales price typically have an R- squared close to 0.80 or above when using explanatory variables such as physical property attributes and fixed geographical and time effects (see e.g. Brown, 2012; Bucchianeri and Minson, 2013; and Shen et al., 2018).
Model III shows the effect of adding the auction variables, as well as the variable measuring underpricing to Model II. The R-squared increases to 0.95, implying that a sizeable part of the
21 unexplained variation in house prices in the standard hedonic pricing model, Model II, is in fact explained by the unfolding of the auctions and the sellers’ list price strategies.25
Table 3 Log of Sales Price regressions. OLS estimations with heteroscedasticity-consistent standard errors. Minimum number of bidders equals 2. Fixed geographical and time effects are included in both regressions. The numbers in parentheses are t statistics. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. Model II Model III LN(PRICE) without auction LN(PRICE) with auction variables variables Coef. t-stat. Coef. t-stat. Property Attributes: AREA 0.00661 (4.30)*** 0.00699 (6.58)*** AREA (squared) -0.00001 (-2.55)** -0.00001 (-3.86)*** EXTRA_AREA 0.00103 (2.51)** 0.00114 (4.33)*** EXTRA_AREA (squared) -6.43e-07 (-0.24) -7.44e-07 (-0.44) LOT_SIZE 0.00018 (5.67)*** 0.00015 (7.74)*** LOT_SIZE (squared) -2.29e-08 (-4.39)*** -1.80e-08 (-4.64)*** AGE -0.00764 (-6.22)*** -0.00961 (-12.46)*** AGE (squared) 0.00008 (5.15)*** 0.00010 (9.86)*** STD_PTS 0.00978 (5.88)*** 0.00903 (7.63)*** GROUNDLEASE -0.12693 (-2.93)*** 0.06489 (1.69)*
Construction Type: DETACHED (omitted) (omitted) CHAINED -0.02111 (-0.94) -0.04957 (-3.79)*** ROW HOUSE -0.12486 (-4.44)*** -0.14180 (-7.93)***
Spatial Characteristics: NO_BEACH (omitted) (omitted) NEAR_BEACH 0.11704 (1.30) 0.04156 (0.99)
Auction Variables: BIDDER_RES - - 0.02559 (10.02)*** BIDDER_RES (squared) - - -0.00190 (-2.40)*** AVG_TIME - - -0.01979 (-5.53)*** AVG_TIME (squared) - - 0.00055 (2.86)*** JUMPBID_FIRST - - 0.55984 (9.25)*** JUMPBID_FIRST (squared) - - 0.79210 (3.75)*** JUMPBID_WIN - - 0.05824 (0.30) JUMPBID_WIN (squared) - - 2.60393 (11.57)*** LATE_ENTRY - - -0.00904 (-0.69) UNDERPRICE - - -0.51688 (-14.98)*** UNDERPRICE (squared) - - -0.36464 (-3.60)***
R-squared 0.8664 0.9549 Observations 802 802
25 Model III was also run using the Rogers procedure, i.e. OLS with the cluster-robust standard error option (Rogers, 1993). This test relaxes the assumption that the observations are independent and adjusts the standard error for the correlation within a cluster (i.e. within parishes across sales quarters). In order to do that, an interaction between the PARISH and QUARTER variables was created to check if errors correlate in time and space. The results showed standard errors to be a bit lower than the ones obtained through the OLS with heteroscedasticity- consistent standard errors, implying that the statistical significance of the results displayed for Model III in Table 3 are robust. 22
All auction variables are significant with the expected sign, except for the linear terms of jump bidding in the winning bid and the dummy variable controlling for a single bid by the winner of the auction. Starting with BIDDER_RES, the residual from the bidder equation, we can see that, initially, one extra unexpected bidder increases the selling price with approximately 2.6 percent. The negative squared term implies that the marginal effect of an extra bidder is decreasing, which makes sense; increasing the number of bidders from nine to ten does not represent the same increase in competition as when going from one to two bidders. The estimated coefficients are quite similar to the coefficients reported in Hungria-Gunnelin (2018), who estimate a similar equation for condominium apartments in Stockholm.
Continuing with the AVG_TIME, that is, the average time between bids in the auction, the effect on selling price is also strong. In a fast auction, in which bids are placed with just hours or minutes in- between, the price is on average almost 1.4 percent higher than a slower auction in which the average time between bids is a day. In a decidedly slow auction for the Stockholm market with one bid per week, the selling price is, on average, about 13 percent lower compared to the fast auction. This result is supportive of the bidding frenzy/auction fever hypothesis in the general auction literature stating that speedy auctions with many bidders lure unexperienced bidders into emotional bidding, with the result that they may overpay for the object. Again, a similarly strong effect was found in Hungria- Gunnelin (2018) for auctions of condominium apartments.
Turning to jump bidding strategies, the result is qualitatively the same as in Hungria-Gunnelin (2018), as well as in other papers examining jump bidding in the setting of online auction (see e.g. Easley and Tenorio, 2004; He and Popkowski Leszczyc, 2013). Jump bidding does not seem to pay off by scaring off enough bidders to reduce the level of the winning bid. On the contrary, jump bidding, in particular in the first bid, has a strong positive effect on selling price. The combined effect of the linear and the quadratic term on JUMPBID_FIRST corresponds to an increase in selling price of about two thirds of the percentage difference between the first bid and the list price. That is, comparing an auction where the first bidder place a bid equal to the list price with an auction in which the first bid is 10 percent above the list price, the selling price is, on average, 6.4 percent higher.
The effect of jump bidding by the winner of the auction, represented by the variable JUMPBID_WIN, is in the same direction, albeit not as strong. Comparing the case in which the winning bid is only marginally higher than the second highest bid with an auction in which the winning bid is 10 percent higher, the selling price is, on average, 3.2 percent higher.
The binary variable LATE_ENTRY controls for auctions in which the winning bid is the only bid by the winner. The aim of the variable is to capture, in a simplified way, late entry in the auction. Motives for deliberate late entry would be to minimize your contribution to bidding up the price during the unfolding of the auction and to reveal as little as possible about your reservation price and your valuation of the object for sale. The coefficient on LATE_ENTRY is, however, insignificant. A caveat here is that that the variable is measured ex post. A bidder that enters the auction late does not know ex- ante if the late bid will become the winning bid. It is, however, difficult to construct a variable that measures an ex ante strategy to enter the auction late, and we simply posit that an ex post observation that the winner placed only one bid is a noisy proxy for deliberate late entry (the average number of bids per bidder in the data is 3.29).
23
Confirming the result of several previous studies, UNDERPRICE is negatively correlated with selling price and the effect is strong. Going from a list price that is equal to the estimated market value to an underpricing of 10 percent reduces selling price with approximately 5.5 percent. This is a rather large effect on price, but the size of the coefficient is similar to other studies. As discussed in the following section, caution is, however, warranted with respect to the magnitude of the effect.
6.2.1 Analysis of omitted variable bias In order to analyze possible problems due to omitted variable bias, Model III was re-estimated according to the model specifications described in Section 5.3. Model IV in Table 4.1 is an extension of Model III, where the variable REPEAT_RES, i.e. the residuals from repeat-sales transactions in the mass appraisal model, is included as a proxy for omitted variables. In a similar manner, Model V extends Model III by including, instead, the residual from a list price regression (DOP). As the list price residual is a measure of underpricing similar to the variable UNDERPRICE, the latter was excluded in Model V. Model VI has the same explanatory variables as Model III, but is a robust regression that weights down observations with large residuals. Model VII and Model VIII, in Table 4.2, control for potential omitted spatially dependent characteristics that are not captured by the geographical dummy variable PVO.
The coefficient on the linear term of the repeat-sales residual in Model IV is significant with the expected sign. That is, a positive (negative) residual for a repeat sale transaction in the mass appraisal model increases (reduces) the transaction price of the same object in the auction dataset. The effect on price is, however, moderate. A residual corresponding to 10 percent of the predicted price in the mass appraisal model has an impact of approximately 0.6 percent on the price.
Similarly, DOP yields a significant coefficient on the linear term with expected sign in Model V. The effect here is much stronger than for the repeat-sales residual, with an impact of almost one to one. A list price residual of 10 percent affects the price with about 9 percent. It is difficult to sort out how much of the effect that is due to the residuals acting as a proxy for omitted variables and how much that is due to deliberate list price strategies.26
The coefficients in Model IV and Model V of the variables of interest in this study, the auction variables, changes little from those obtained in Model III except for the coefficient on LATE_ENTRY, that becomes negative and significant when including DOP in the regression. We interpret these results as an indication that the coefficients on the auction variables are not suffering from severe omitted variable bias. A further indication that possible omitted variable bias is limited is that the coefficient estimates in Model VI, the robust regression, also changes little compared to Model III.
26 When running Model V also including the variable UNDERPRICE, it becomes insignificant, while the coefficients on the list price residual remains largely the same, indicating that the DOP and UNDERPRICE to a large degree measure the same thing. 24
Table 4.1 Mitigating possible OVB in Model III: Regression methods. Minimum number of bidders equals 2. Models IV and V display OLS estimations with heteroscedasticity- consistent standard errors. Model IV includes the residual of repeat-sales, while Model V includes the list price residual (DOP) instead. Model VI exhibits the results obtained by a robust regression. Fixed geographical and time effects are included in all regressions. The numbers in parentheses are t statistics. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. Model IV Model V Model VI Repeat-sales residual DOP Robust regression Coef. t-stat. Coef. t-stat. Coef. t-stat. Property Attributes: AREA 0.00630 (4.89)*** 0.00722 (11.16)*** 0.00754 (10.63)*** AREA (squared) -0.00001 (-2.69)*** -0.00001 (-6.89)*** -0.00002 (-6.59)*** EXTRA_AREA 0.00067 (1.99)** 0.00107 (6.43)*** 0.00078 (3.20)*** EXTRA_AREA (squared) 2.12e-06 (0.88) -5.67e-07 (-0.47) 1.11e-06 (0.64) LOT_SIZE 0.00018 (4.90)*** 0.00018 (13.93)*** 0.00017 (9.07)*** LOT_SIZE (squared) -1.02e-08 (-0.73) -2.26e-08 (-11.05)*** -2.22e-08 (-6.25)*** AGE -0.00929 (-9.35)*** -0.00837 (-16.41)*** -0.00982 (-12.70)*** AGE (squared) 0.00011 (8.50)*** 0.00009 (14.64)*** 0.00011 (12.72)*** STD_PTS 0.00784 (6.17)*** 0.00976 (13.05)*** 0.00882 (8.78)*** GROUNDLEASE 0.07950 (1.88)* -0.12354 (-6.02)*** 0.04449 (1.60)
Construction Type: DETACHED (omitted) (omitted) (omitted) CHAINED -0.02381 (-1.52) -0.03281 (-3.76)*** -0.04350 (-3.50)*** ROW HOUSE -0.12001 (-5.46)*** -0.12216 (-11.40)*** -0.13608 (-8.48)***
Spatial Characteristics: NO_BEACH (omitted) (omitted) (omitted) NEAR_BEACH 0.05631 (1.45) 0.10220 (4.94)*** 0.02480 (0.58)
Auction Variables: BIDDER_RES 0.02446 (7.41)*** 0.02678 (15.47)*** 0.02530 (10.84)*** BIDDER_RES (squared) -0.00170 (-1.71)* -0.00202 (-3.88)*** -0.00184 (-2.15)** AVG_TIME -0.03016 (-6.92)*** -0.02012 (-9.74)*** -0.02288 (-7.77)*** AVG_TIME (squared) 0.00129 (5.20)*** 0.00054 (6.48)*** 0.00087 (7.30)*** JUMPBID_FIRST 0.48534 (6.55)*** 0.53917 (13.19)*** 0.59384 (9.45)*** JUMPBID_FIRST (squared) 0.94917 (2.79)*** 0.95539 (9.64)*** 0.51892 (3.81)*** JUMPBID_WIN -0.09031 (-0.16) -0.02206 (-0.16) -0.59168 (-1.36)
25
JUMPBID_WIN (squared) 2.76005 (0.56) 2.69100 (17.31)*** 7.21932 (1.87)* LATE_ENTRY -0.00518 (-0.30) -0.02156 (-2.66)*** -0.00459 (-0.37) UNDERPRICE -0.45764 (-12.84)*** - - -0.52770 (-22.13)*** UNDERPRICE (squared) -0.53689 (-5.56)*** - - -0.36686 (-5.27)***
OVB Correction Variables: REPEAT_RES 0.05469 (2.54)** - - - - REPEAT_RES (squared) 0.01053 (0.47) - - - - DOP - - 0.85678 (44.48)*** - - DOP (squared) - - 0.12871 (0.94) - -
R-squared 0.9682 0.9812 - Observations 496 802 800
26
Table 4.2 Mitigating possible OVB in Model III (continued): Spatial regressions. Minimum number of bidders equals 2. Model VII displays the results from the Spatial Lag Model (SAR), while Model VIII shows the results for the Spatial Error Model. Although both models control for omitted geographical factors, fixed geographical and time effects are included in both regressions. The numbers in parentheses are t statistics. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. Model VII Model VIII SAR SEM Coef. t-stat. Coef. t-stat. Property Attributes: AREA 0.00705 (10.13)*** 0.00716 (10.21)*** AREA (squared) -0.00001 (-5.87)*** -0.00001 (-5.95)*** EXTRA_AREA 0.00102 (4.27)*** 0.00107 (4.49)*** EXTRA_AREA (squared) -8.09e-08 (-0.05) -4.01e-07 (-0.24) LOT_SIZE 0.00029 (9.77)*** 0.00029 (9.71)*** LOT_SIZE (squared) -7.44e-08 (-7.10)*** -7.43e-08 (-7.00)*** AGE -0.00991 (-12.76)*** -0.01007 (-13.24)*** AGE (squared) 0.00011 (12.29)*** 0.00011 (12.73)*** STD_PTS 0.00911 (9.34)*** 0.00931 (9.51)*** GROUNDLEASE 0.06791 (2.52)** 0.07610 (2.72)***
Construction Type: DETACHED (omitted) (omitted) CHAINED -0.02670 (-2.11)** -0.02676 (-2.16)** ROW HOUSE -0.10206 (-6.01)*** -0.10251 (-6.14)***
Spatial Characteristics: NO_BEACH (omitted) (omitted) NEAR_BEACH 0.04580 (1.11) 0.04681 (1.17)
Auction Variables: BIDDER_RES 0.02418 (10.64)*** 0.02478 (10.86)*** BIDDER_RES (squared) -0.00177 (-2.15)** -0.00181 (-2.18)** AVG_TIME -0.02560 (-8.36)*** -0.02516 (-8.15)*** AVG_TIME (squared) 0.00096 (6.85)*** 0.00094 (6.58)*** JUMPBID_FIRST 0.57978 (9.51)*** 0.59248 (9.67)*** JUMPBID_FIRST (squared) 0.82254 (6.27)*** 0.82411 (6.28)*** JUMPBID_WIN 0.01970 (0.10) -0.00254 (-0.01) JUMPBID_WIN (squared) 2.64076 (10.68)*** 2.66854 (10.77)*** LATE_ENTRY -0.00361 (-0.30) -0.00306 (-0.25) UNDERPRICE -0.51312 (-21.92)*** -0.51901 (-21.94)*** UNDERPRICE (squared) -0.35785 (-5.27)*** -0.35682 (-5.21)***
Squared correlation 0.957 0.957 Number of observations 792 792
Final evidence that the model do not suffer from severe omitted variable bias is that the two different spatial models, Model VII and Model VIII, also yields similar results as those found in Model III. Table 5 displays the diagnostic tests for spatial dependence to determine which spatial model should be chosen. According to the results in Diagnostic Test 1 (with identical specification as in Model III), the SAR model is preferred as its robust Lagrange multiplier is much greater for the spatial lag model.
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Table 5 Diagnostic tests for spatial dependence in the OLS regressions. Diagnostic Test 1 Diagnostic Test 2 Diagnostic Test 3 With PARISH and PVO With PARISH only No geo VARS Test Statistic p-value Statistic p- Statistic p- value value Spatial error: Moran’s I 9.736 0.000 20.276 0.000 31.464 0.000 Lagrange multiplier 26.097 0.000 310.111 0.000 920.401 0.000 Robust Lagrange 2.130 0.144 134.757 0.000 359.275 0.000 multiplier
Spatial lag: Lagrange multiplier 69.729 0.000 253.558 0.000 693.163 0.000 Robust Lagrange 45.762 0.000 78.204 0.000 132.037 0.000 multiplier
As observed in Table 5, PVO and PARISH are good controls for unobserved geographical elements. When PVO is removed from the model, Moran’s I increase by 10.54 and the SEM Model becomes preferable in explaining geographical omitted variables. When PARISH is also removed, Moran’s I increase by 21.728 when looking at the original model that includes both PARISH and PVO, and SEM becomes the preferable spatial model, which confirms that these two geographical explanatory variables are good controls of spatial fixed effects.
6.3 The winner’s curse model Table 6 displays the results from the model estimating the probability of a winner’s curse, Model IX, as a function of the sellers’ list price strategy and the auction participants bidding strategies. For simplicity of interpretation, the auction-related variables only enter the model in linear terms. The occurrence of winner’s curse is defined by a binary variable that equals one when the winning bid is at least 10 percent higher than the market value estimated by the mass appraisal model, and zero otherwise.
As in the price models, the residual from the bidder regression (Model I), is used as explanatory variable instead of the total number of bidders, since the purpose is to analyze how the probability of a winner’s curse is affected by strategic seller and bidder behavior. If, for example, we want to analyze the effect of jump bidding with the intent to deter competition, the expected response in the number of bidders of jump bidding should be included in this strategy and the residual from the bidder equation measures the effect of deviations from the expected response.
The coefficients on all variables in Table 6 have, as expected, the same sign as the corresponding coefficients in the price model. The coefficients on BIDDER_RES, AVG_TIME, JUMPBID_FIRST, and UNDERPRICE are significant on the 1 percent level while JUMPBID_WIN and LATE_ENTRY are significant only on the 10 percent level.
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Table 6 Probit Regression. Minimum number of bidders equals 2. Model IX displays the estimates for the average marginal effects of a winner’s curse. The variables related to property attributes, construction type, as well as fixed geographical and time effects are included in the regression. The numbers in parentheses are z values. ***, **, and * denote statistical significance at the 1%, 5%, and 10% levels, respectively. Model IX Winner’s curse Average marginal effects Coef. z-value dy/dx z-value Auction variables: BIDDER_RES 0.53195 (7.43)*** 0.04899 (9.05)*** AVG_TIME -0.24891 (-2.96)*** -0.02293 (-3.04)*** JUMPBID_FIRST 20.21874 (7.18)*** 1.86222 (8.81)*** JUMPBID_WIN 9.83338 (1.83)* 0.90569 (1.84)* LATE_ENTRY -0.74659 (-1.69)* -0.06876 (-1.70)* UNDERPRICE -23.59863 (-10.63)*** -2.17352 (-19.53)***
Pseudo R-squared 0.7100 - Observations 758 758
Looking at the average marginal effect for BIDDER_RES, one extra unexpected bidder increases the probability of a winner’s curse with almost 4.9 percent. The coefficient on AVG_TIME shows that prolonging the time between bids with one day reduces the probability of a winner’s curse with 2.3 percent. The marginal effect on jump bidding is large, one percent increase in a jump bid increases the probability of a winner’s curse with 1.9 percent for the first bid (JUMPBID_FIRST) and 0.9 percent for the winning bid (JUMPBID_WIN). The latter coefficient is, however, only significant at the 10 percent level. Similarly, the average marginal effect for LATE_ENTRY is only significant at the 10 percent level, but the effect is negative. The probability of a winner’s curse for a winner that only bid once is 6.9 percent lower than that of a winner who place more than one bid. Finally, the coefficient on the average marginal effect for UNDERPRICE is big. Lowering the list price with 1 percent reduces the probability of a winner’s curse with 2.2 percent.
The overall result of list price, the unexpected number of bidders, and bidding strategies on final sales price and the probability of winner’s curse empirically confirm Kagel and Levin’s (1986) experimental findings on a first-price auction, where the winner’s curse emerged in larger groups as bidders bid more aggressively when competition is high.
7 Discussion and conclusions
The findings in this paper contribute to the empirical literature studying auctions of residential homes, since very few papers have analyzed micro-level auction data in the setting of non-distressed residential real estate auctions. The dataset used in this study is rich enough to construct a number of variables describing list price and bidding strategies and to estimate their effect on transaction price and the probability of a winner’s curse.
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Three models are estimated: a model of the number of bidders in an auction, a hedonic price model, and a model of the probability of a winner’s curse. While several papers in the empirical literature have estimated the impact on price of the number of bidders in an auction (albeit applications to real estate are rare), the estimation of the probability of a winner’s curse as a function of the seller’s list price strategy and auction participants bidding strategies is novel. Furthermore, the effect on the number of bidders and sales price of variables describing list price strategies, as well as bidding strategies in residential auctions, has previously only been modeled by Hungria-Gunnelin (2018).
Confirming the results in several studies, an increase in the number of bidders in an English auction increases the winning bid, holding constant the other variables of the model. However, the inclusion of variables describing list price and bidding strategies in the bidder and price equations, show that the reason why the number of bidders is high or low matters for the resulting effect on price. By including the residual from the model of the number of bidders in the price equation, instead of the total number of bidders, the coefficients on the variables describing list price and bidding strategies can be interpreted as marginal effects given the expected number of bidders. That is, conditional on the particular list price and bidding strategies employed including the effect on the expected number of bidders. For example, jump bidding in the opening and the winning bid are negatively correlated with number of bidders in the bidder model, but they are positively correlated with price in the price model. Hence, on average, such strategies seem unrewarding. Similarly, increased underpricing increases the number of bidders, but the coefficient on underpricing is negative in the price equation. That is, underpricing is an unrewarding strategy for the seller. The speed of an auction, measured as the average time between bids, on the other hand, is negatively correlated with both price and the number of bidders. Hence, a fast auction unequivocally increases transaction price.
Similar to the analysis of the price regression, when analyzing the probability of a winner’s curse as a function of list price and bidding strategies, one must consider the effect of a particular strategy on the number of bidders since the number of bidders, in turn, affects the probability of a winner’s curse. Hence, as in the price model, the residual from the bidder equation – rather than the total number of bidders – is included as an explanatory variable. For example, the purpose of a jump bidding strategy is to deter competition. Hence, when calculating the marginal change of the probability of a winner’s curse from an increase in jump bidding we do not want to hold the number of bidders constant. Using the residual from the bidder equation (that is, the unexpected number of bidders given the particular bidding strategy), instead of the total number of bidders as explanatory variable, allows analysis of the effect of bidding strategies including their effect on the number of bidders, as well as the effect of the unexpected number of bidders in isolation.
The results from estimating the winner’s curse model show, not surprisingly, that the sign of the coefficients of underpricing and the auction variables are the same as in the price model. Underpricing reduces the probability of a winner’s curse, while jump bidding and a fast pace of the auction, as well as more bidders than predicted by the bidder equation, increases the probability.
The ratio of winning bid to market value that defines the lower bound for the occurrence of a winner’s curse in this paper is admittedly chosen somewhat arbitrary. However, adopting a pragmatic view on this problem suggests that the model can be useful in several applications and where the researcher can choose a ratio that is suitable for the purpose of the analysis. For instance, one may simply see the winner’s curse model as akin to value-at-risk models commonly applied in financial management.
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Mortgage lending institutions may, for example, be interested in estimating how different factors surrounding a sale of a home affects the probability that a potential lender overpaid for the home.
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