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Loss aversion : the reference point matters Har, Neo Poh; Ong, Seow Eng; Somerville, Tsur Oct 25, 2006

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                                                                                                                                                                                                Centre for Urban Economics and Real Estate  Working Paper  2005 – 01       Loss Aversion: The Reference Point Matters  Neo Poh Har National University of Singapore  Ong Seow Eng National University of Singapore  Tsur Somerville University of British Columbia   Updated: October 25, 2006      Centre for Urban Economics and Real Estate Sauder School of Business University of British Columbia 2053 Main Mall Vancouver, BC  V6T 1Z2 Tel : 604 822 8399 or e-mail : cuer@sauder.ubc.ca Web: http://realestatecentre.ubc.ca/           Loss Aversion: The Reference Point Matters      Neo Poh Har*  Ong Seow Eng**  Tsur Somerville***   First draft: June 19, 2005 Current draft: October 18, 2006    * Department of Real Estate, School of Design and Environment, National University of Singapore, 4 Architecture Drive  117566, Singapore.  Email: rstnph@nus.edu.sg  ** Department of Real Estate, School of Design and Environment, National University of Singapore, 4 Architecture Drive  117566, Singapore.  Tel: (+65) 874-5161, Fax: (+65) 774-8684.  Email: rstongse@nus.edu.sg  *** Real Estate Foundation Professorship of Real Estate Finance, Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC, V6T1Z2, Canada.  Tel: (604) 822-8343, Fax: (604) 822-8477. Email: tsur.somerville@sauder.ubc.ca  We are grateful for comments from Jim Shilling, Robert Edelstein and Chris Downing, as well as participants at the ERES 2005, AsRES 2005 and AREUEA 2006 conferences. 1 Introduction  An often-noted characteristic of housing markets that sets them apart from other asset markets is the positive correlation between housing prices and transaction volume.  This relationship has been observed across continents and in many different housing markets.1  Stein (1995) argues that credit market imperfections that impose downpayment constraints on buyers can explain this phenomenon.  In contrast, Genesove and Mayer (2001) demonstrate that the data support prospect theory as an explanation for loss aversion.  In this paper we seek to increase our understanding of loss aversion behavior by taking advantage of the heterogeneity of housing market participants.  We examine two specific questions.  First, what is the relevant reference point for evaluating losses in a prospect theory framework?  Second, how does the sensitivity to loss vary across different types of sellers? Loss aversion is somewhat controversial.  While it is an outcome of prospect theory, there has been a challenge to demonstrate it empirically.  Most of the research to date relies on experiments.  The housing market is a fruitful place to test loss aversion because transaction data allows researchers to identify asset acquisition and disposition dates, which has been the challenge for other asset classes.  Unlike equities, housing is a search market, so loss aversion behavior will manifest itself through both price and time to sale measures.  We take loss aversion as a given, and instead focus on what is the relevant definition of loss for sellers.  In particular, is it the change in net wealth, the potential sales price relative to the purchase price, or is it more the loss of a gain they might have achieved, the potential sales price relative to the unit’s peak price over the                                                  1 See Stein (1995) and Ortalo-Magne and Rady (1998).    2 holding period or the more recent past.  Our second objective is to see how loss aversion behavior varies by seller type.  We assume that the Genesove and Mayer (2001) result holds in general and look at two sub-sets of sellers: highly motivated individual sellers and arms’ length, experienced institutional sellers.   Our data is of a sub-set of sellers in Singapore who put their houses up for auction.  One of the advantages in using data from Singapore is that we are able to construct high quality price indexes for the market, have a set of housing units with much less structural variation than is found in North America, and examine behavior over a severe market downturn.  The important advantage of using auction data is that it allows us to identify a sample of sellers who have self-selected themselves as motivated to sell.  Thus we would expect them to be less loss averse than the sample of all sellers used in existing studies.  Within the sample we have two groups, sales by individuals and by institutions, where the latter are sales of foreclosed properties.  This latter distinction allows us to also determine whether loss aversion is less likely to occur with more experienced sellers who do not have an emotional investment in a property. Our findings suggest that loss aversion is less acute among our group of “motivated” sellers than in the more general sample studied by Genesove and Mayer (2001).  When losses are measured relative to the purchase price , we do not find that transaction prices, either from an auction or a subsequent negotiated sales in the event the unit failed to sell at auction, are statistically higher with more severe loss aversion.  The same holds true for time to sale, it does not increase with loss aversion.  These results would suggest that not all individuals are equally affected by loss aversion, as our self- 3 selected motivated sellers are less sensitive to losses relative to their original purchase price. However, we find that the choice of reference point matters.  Instead of using the purchase price (actual change in nominal wealth), we use either the highest price achieved over the holding period, or the highest achieved over the last two years (maximum potential gain).  For both, we find that for some types of units the sales price, and for all units time to sale, rise with loss aversion.  Also, the probability of an auction sale declines.   Of interest, “experienced sellers” who should have no emotional link to the property, in our data sales by financial institutions, display less loss aversion than do individuals.  Relative to sales by individuals, as loss aversion grows, units sold by institutions are more likely to be sold, shorter time to sale, and are more likely to be successfully sold at auction.  This is despite no robust evidence that overall, that is independent of the loss aversion behavior, sales by institutions occur more quickly than do those of individuals.   Overall our findings suggest that loss aversion is not a uniform aspect of participants in housing markets.  Motivated sellers are less sensitive to loss aversion.  For institutions, they are less sensitive to loss aversion than are individuals, but we cannot distinguish if this is because the institutional sellers are more experienced or less emotionally connected to the unit.  However, there is no statistical difference in the price they receive upon sale, and Singapore law gives them an incentive to achieve the highest price, so it is not because they are only sensitive to the value of the outstanding loan on the property.  We find compelling evidence that the choice of reference point matters. It is the perception of loss because of some missed opportunity to sell that matters more for  4 loss aversion in our data than does the purchase price and the change in actual wealth.  At least in our data, people focus especially on what they could have had, rather than what they actually have gained. This paper makes two primary contributions to the literature.  First, we examine whether there are differences in the extent of loss aversion across types of sellers.  Genesove and Mayer (2001) compare owner-occupiers and investors; we extend this dichotomy to look at the difference between individual (owners) sellers and institutional sellers.  This distinction is important as we expect it to shed light on the question of whether market experience weakens the endowment effect that is a foundation of loss aversion.   Second, we provide empirical evidence on the relevant reference point for prospect theory, specifically are losses evaluated relative to acquisition prices or the highest possible price the owner could have received over the holding period/recent past.  If the latter, it would offer more evidence that it is loss aversion rather than equity constraint concerns that underlay the price volume relationship in housing.   The remainder of the paper is structured as follows.  We next provide context for this paper, providing a discussion of and survey of the relevant literature on loss aversion and auctions.  We follow this with a brief overview of auctions in Singapore and then a presentation of our data.  We cover a small number of methodological issues and then present our results.      5 Loss Aversion  Kahneman and Tversky (1979) present prospect theory as a way to explain the asymmetry in people’s responses to gain versus losses, loss aversion. In this framework, the gains and losses are evaluated relative to some reference point.  In Tversky and Kahneman (1991) they highlight three features of an individual’s value function that must hold for prospect theory to explain loss aversion.  First, the magnitude of all gains and losses are evaluated relative to a given reference point, typically assumed to be the acquisition price or an initial endowment.  Second, value changes, for given changes in wealth, are asymmetric; the value function declines more for a given loss than it rises for a gain of the same amount.  Third, for both gains and losses the marginal value of a change in wealth declines with the magnitude of the change.   This and other work by Kahneman and Tversky has been subject to considerable analysis, especially experimental studies.  The theory and evidence on this class of “anomaly” to the neo-classical model of preferences is presented in Kahneman, Knestsch, and Thaler (1991).  Experimental work by Knestch (1989) and Bateman, et. al (1997) show that individuals are more likely to keep their endowed good than engage in a trade for a higher value good.2   One issue that has emerged is the difference between the behavior of experienced and inexperienced market participants.  Knez, Smith and Williams (1985) and Coursey, Hovis, and Schulze (1987) argue that the endowment effect phenomenon is just the result of inexperienced market participants, and that as they learn “true” values over time, their behavior would come to better resemble neo-classical                                                  2 Thaler (1980) presents the term “endowment effect,” but this is functionally equivalent to prospect theory.  In our case the endowment will be the reference point for evaluating gains and losses in house value.  6 theory.  Work best associated with List (2003, 2004) and in trying to explain myopic loss aversion in Haigh and List (2005) demonstrates that loss aversion type behavior diminishes with market experience.  However, the results are sensitive to experiment design: Knetsch, Tang, and Thaler (2001) find that the endowment effect (loss aversion) decline with experience using a Vickrey auction framework vary depending on the context of the valuation.   Even if one accepts loss aversion, there remains the question of the appropriate reference point for identifying losses.  The theoretical work cited above and the empirical work described below use the initial endowment as the reference point.  In this paper, we compare this choice with two others: the change from the highest price achieved over the holding period and changes over the recent past.  The former reflects the maximum possible notion of a loss.  The latter is in response to theoretical work by Barberis, Huang, and Santos (2001), who suggest that if investors experience loss aversion and if the degree of loss aversion is sensitive to their recent changes in asset values, this can explain why asset returns that are more volatile and have a low correlations with changes in consumption. Studies of loss aversion using actual market behavior have been quite few in number, mostly limited to housing markets.  Housing markets offer a unique opportunity to study loss aversion behavior because we are able to identify acquisition prices, market prices, and market liquidity.  Genesove and Mayer (2001) provide the first non-experimental evidence on loss aversion using data on Boston, Massachusetts condominium sales.  They find that owners for whom the expected sales price is below  7 their nominal purchase price set higher asking prices, receive higher prices when they sell, and that their hazard for selling is lower than for other sellers not facing these losses.   Engelhardt (2003) uses a study of household mobility to evaluate the extent to which the price-volume pattern in housing markets is driven by equity constraints (Stein 1995 and Ortalo-Mage and Rady 1998) or the loss-aversion treatment developed in Genesove and Mayer (2001).  Earlier work on this topic by Genesove and Mayer (1997) and Chan (2001) looked only at equity constraints and found that declines in equity below downpayment thresholds resulted in fewer sales and longer time on the market.  Engelhardt’s contribution is to distinguish between the competing theories.  He finds that nominal loss aversion resulting from declines in house prices for financially constrained owners has a much greater effect on mobility than does a decline in house equity below financing constraints.    Auctions  The auction mechanism is gaining acceptance as an effective method of disposal for commodities in general and real estate in particular. Recent research tends to focus on two main thrusts: comparing revenues from different auction formats to revenues from private negotiations (Lusht, 1996; Mayer 1998; Dotzour, Moorhead and Winkler, 1998; Allen and Swisher, 2000), and evaluating the probability of a positive auction outcome (Maher 1989; DeBoer, Conrad and McNamara, 1992; Mayer, 1995; Anglin, 2003; Ong, et al., 2005).  8 There is no clear consensus on whether prices determined at auctions should be higher or lower than that obtained from private searches. Mayer (1995) developed a search model with a monopolistic seller to show that a quick sale under the auction mechanism results in a poorer “match” between the buyer and the house, thus resulting in a discount compared to a private negotiated sale that would allow more time for the buyer to search for his ideal home. Empirical work by Mayer (1998) using repeat sales to control for quality differences shows that the auction discount increases in market downturns. In contrast, using data for 309 single-family detached houses offered for sale in the Australian housing market from 1988 to 1989, Lusht (1996) finds that privately negotiated sales prices are 5.6% less than auction prices.  Quan (2002) develops a theoretical model that allowed for interaction between multiple sellers and the number of bidders, yielding the result that prices determined at auctions will be higher than private negotiated sales. His empirical analysis using data from Texas supports this prediction.  A second area of research on auctions addresses the probability a unit will sell at auction.  Mayer (1995) and Anglin (2003) explicitly focus on changes in market conditions and Maher (1989) evaluates the impact of intermediaries on sale probability. Ong, et al, (2005) extend prior work by estimating a model that includes controls not only for location and structure characteristics, but also variables that measure the impact of “turnout” – a proxy for the number of bidders at an auction – and the impact of the auctioning house.   Units unsold at auction are the subject of studies by Ashenfelter and Genesove (1992), who show that the prices for identical units were 13% higher than for units subsequently sold in private negotiations. Ong (2005) focuses on properties that were sold through private negotiations after unsuccessfully put up for auction.   9 A final area of research on auctions that is relevant for this paper is the study of what causes owners to decide whether to bring units to auction.  Mayer (1995) explicitly addresses the role of seller search cost.  Bulow and Klemperer (1996), focuses on the seller’s bargaining power. Quan (2002) in contrast, addresses the potential buyers, choosing to model their search cost. As Dehring, Dunse, and Munneke (2006) demonstrate, this topic is extremely sensitive to the housing market institutions in a particular location.  .   Auctions in Singapore   The dominant auction format in Singapore is the English ascending bid auction with a secret reserve price. Auctions have generally been regarded as a last resort method of disposal. The local sentiment toward auctions is similar to that of the US, where auctions are associated with distress properties – foreclosure or mortgagee sales (Asabere and Huffman, 1992). Distress sales are typically put up by the mortgagee, usually a bank or financial institution. Only private properties are put up for auction.3  There was a surge in auction sales 1998-199 following the Asian financial crisis.  Although a good proportion comprises mortgagee sales, there has been a discernible increase in owner auctions.  Local commentators have suggested that this is due to a diminution of the stigma associated with auctions.  This is along with a growing perception among potential buyers that auctions of distress properties provide a good                                                  3 Over the sample period, all public housing flats are financed by mortgages from the Housing Development Board (HDB). As a statutory body responsible for providing affordable housing, HDB often adopts a benign work-out policy regarding delinquency. Foreigners may own private housing only in development is more than 4-storey high. All low-rise housing are hence not available for foreign ownership. Expatriates typically rent rather than own.  10 05000100001500020000250003rd & 4th Qtr 1995 1996 1997 1998 1999 1st Qtr 2000FrequencyTotal Units Sold Auction Attemptsavenue to acquire properties at bargain prices. Buyers and sellers have a better understanding and awareness of the efficiency of the auction system as a method of sale, and auction companies in Singapore have substantially increased the frequency of auctions held each month to meet the growing demand.  Even so, the number of properties put up for auction is very low.  As Figure 1 shows, auctions comprised only 3.5% of the total number of property transactions in 1998 and 1999.   Figure 1: Total Number of Property Transactions and Auction Attempts by Year            Bidders in Singapore are generally not aggressive. Among the 608 properties that are not sold at the auction, about 78% of them did not receive any bid.  The success rate  11 for each bidding session varies from 10% to 50%.  The low success rate has been attributed to the flagging performance of property over this period, rather than the appeal of auctions themselves. There my also be a market discovery process at work, where owners use the auction process as a gauge of market interest in their properties and some buyers withhold from biding during an auction in the hope of securing lower transaction prices in post-auction private negotiations. The expectation that private negotiations are more likely to secure a sale will also create an incentive for sellers to set unrealistically high reserve prices for the auctions.  In Singapore reserve prices are disclosed to the auctioneer only on the day of the auction itself, and auctioneers have to rely on appraisals and identify interested buyers during the open-house viewings prior to the auction.  Since auctioneers only know the reserve price for a property literally hours before the auction, they usually set a realistic opening bid that would convey useful information to interested bidders identified prior to the auction. Auctioneers have anecdotally verified that opening bids are usually good indications of the reserve prices. This is particularly so over the sample period when the real estate market was “soft”.  Data   Our sample comprises 938 private residential auction attempts from 1995Q3 to 2000Q1. This period corresponds to an intense run-up in property prices followed by the 1997 downturn in the real estate market precipitated by the Asian Financial Crisis.  Figure 2 shows Singapore house prices with a conventional repeat sales index and using  12 the Fourier transformation smoothing technique (McMillen and Dombrow, 2001).4 Our period has two price peaks and two troughs, allowing for more variation in loss aversion across properties than was the case with Genesove and Mayer’s (2001) single peaked Boston data.5.   Figure 2: Singapore House Price Indexes  7580859095100105110115120125Q1Y92 Q1Y93 Q1Y94 Q1Y95 Q1Y96 Q1Y97 Q1Y98 Q1Y99 Q1Y00 Q1Y01 Q1Y02 Q1Y03 Q1Y04Quarter:YearIndex Value (Q2:1999=100)OLS Repeat Sales Fourier Repeat Sales    In Figure 3 we show the distribution of auction attempts.  Most of the auctions occurred between mid-1998 and the end of-1999, during the trough of the first downturn.                                                    4 The index is calculated from 28,790 high-rise property repeat sales transaction pairs from 1985 to 2004 compiled using SISV sales database. 5 Low rise properties constitute only an average of 5% (from year 1990 to 2004) of the total housing stock (both private and public housing) in Singapore. Hence, using a standard repeat sales index with the low rise data introduces excessive volatility that results in a noisy measure of loss aversion.  Deleted:  and 8,561 low-rise properties repeat sales transactions from 1989 to 2004, 13 01020304050607080901003Q 954Q 951Q 962Q 963Q 964Q 962Q 973Q 974Q 971Q 982Q 983Q 984Q 981Q 992Q 993Q 994Q 991Q 00Auction Date (Qtr/Year)FrequencyThe data set includes variables on the unit location, date of auction, auction attendance (turnout), auctioneer, sale by individual or foreclosure sale by a financial institution, type of property, whether the land title is fee-simple or leased, opening bid, last bid, and number of bid increments during the auction.   Figure 3: Auctions Attempts by Year             Residential properties in Singapore are typically classified into high-rise (apartment and condominium) and low-rise (terrace, semi-detached, detached houses). The later comprise about 5 percent of the total housing stock in Singapore.  Because the number of low rise units is relatively small, we choose to use the Fourier transformation repeat sales index as it is best suited for relatively sparse data sets such as low rise  14 0200040006000800010000120001400016000180001995 1996 1997 1998 1999 2000 2001 2002 2003 2004FrequencyLow Rise High Riseproperties in Singapore (see Figure 4).  Figures 5 and 6 show the differences by location and property type for the Fourier transformation repeat sales indexes.   While properties in different locations appear to move together, there are differences by type.   We use property type specific indexes in the analysis.   Figure 4: Transaction Sale Volumes by Year and Property Types            15 707580859095100105110115120Q1Y90Q4Y90Q3Y91Q2Y92Q1Y93Q4Y93Q3Y94Q2Y95Q1Y96Q4Y96Q3Y97Q2Y98Q1Y99Q4Y99Q3Y00Q2Y01Q1Y02Q4Y02Q3Y03Q2Y04Year/QtrProperty Price IndexSingapore Wide Central East North/North East West60708090100110120Q1Y90Q4Y90Q3Y91Q2Y92Q1Y93Q4Y93Q3Y94Q2Y95Q1Y96Q4Y96Q3Y97Q2Y98Q1Y99Q4Y99Q3Y00Q2Y01Q1Y02Q4Y02Q3Y03Q2Y04Qtr/YearProperty Price IndexSingapore Wide High Rise Low RiseFigure 5:  - Singapore Wide vs. Regional Residential Price Indexes            Figure 6 - Singapore Wide Low Rise and High Rise Price Indexes           16  The auction attempt data include a number of properties that were re-auctioned.  Thus our 938 attempts cover 751 distinct properties.  143 properties were sold at the auction, and of the remaining 608 properties, 488 were subsequently sold through private negotiations while 120 remained unsold at the censored date, the end of 2004.  The time to sale numbers are quite sensitive to whether a unit is sold at the first auction attempt or is right censored in our data.  Figure 7 shows the time to sale for units that are sold in the sample period.  The largest mass is for the 143 sold at the first auction attempt (days to sale equal to 0).  The distribution drops off very quickly from the <100 days cell, but there is a very long tail.  Figure 8 shows the distribution of “time on the market” defined as the time between their first auction date and the end of our transaction data period in 2004.  For the 120 units brought to auction, but not sold, the bulk of the observations are those brought to auction between the 2nd quarter of 1998 and the 1st quarter of 2000, giving censored “time on the market” values in excess of 5 years.  We estimate time to sale as the number of days from the first-auction attempt until sale or the right-censoring date.  These data are quite skewed as the mean number, 615 days, greatly exceeds the median, 124 days, because of the 120 units that remain as unsold, censored units (see Figure 8).  The auctions are concentrated in 1999, in the price downturn following the 1997 Asian financial crisis.  Consequently, the auction sales are either by institutions, foreclosed properties, or what we believe to sellers motivated to sell because of financial difficulties brought on by the financial crisis.  Unfortunately we have no wealth, debt, or income data on the sellers.   17 050100150200250100200300400500600700800900100011001200130014001600170018001900>1901DaysFrequency0246810121416181900 2000 2100 2200 2300 2400 2500 2600 2700 3000 3200 3300 3400 3500DaysFrequencyFigure 7: Number of Days from 1st Auction Date to Date of Sale (Excluding properties that remain unsold at censored date)           Figure 8: Number of Days from 1st Auction Date to Censored Date (Only for  properties that remain unsold at censored date)    18 Table 1 provides the summary statistics for the 751 unique properties. Since we are interested in the difference in loss aversion behavior in pricing and sales strategy based on seller type, we also present descriptive statistics for two sub-samples (sales by institution and by owners).   Table 1: Descriptive Statistics by Property   All Units Sales by institutions (foreclosure sales) Sales by individuals Observations 751 430 321  Mean Std.Dev. Mean Std.Dev. Mean Std.Dev. Days from 1st auction date to date of unit sale 615 840 486 759 787 911 Dummy: =1 if unit is vacant 0.89 0.32 0.93 0.26 0.83 0.38 Dummy: =1 if title is freehold 0.76 0.43 0.71 0.46 0.83 0.37 Dummy: =1 if market prices have fallen for 2 successive quarters 0.64 0.48 0.67 0.47 0.61 0.49 Price index at auction date 155 45.5 157 45.3 152 45.7 Price index at eventual sale 152 44.3 155 44.1 148 44.3 Days from purchase to 1st auction date 1257 579 1305 564 1192 594 Days from highest price over holding period to 1st auction date 763 367 857 309 638 400 Days from highest price over  past 2 years to 1st  auction date 482 244 515 213 439 274 Dummy: =1 if unit is low rise structure 0.46 0.50 0.42 0.49 0.52 0.50 Dummy: =1 if unit is being sold by institution (foreclosure sale) 0.57 0.50 - - - - Dummy: =1 if unit is sold at auction 0.19 0.39 0.30 0.46 0.04 0.19 Dummy: =1 if unit is sold at 1st auction 0.16 0.37 0.25 0.44 0.04 0.19 Change in housing price index from1st auction to eventual sale dates -0.02 0.04 -0.01 0.03 -0.02 0.05 Loss aversion (relative to price index at purchase date) 0.04 0.05 0.05 0.04 0.04 0.04 Loss aversion (relative to highest price index over holding period) 0.10 0.06 0.10 0.05 0.09 0.06 Loss aversion (relative to highest price index over 2 years prior to sale) 0.07 0.05 0.07 0.05 0.07 0.06  Notes: Loss aversion is censored at zero for those units for whom the price index at time of sale or censoring is greater than the value at the reference point.  We then use the absolute value of the loss.   19 Table 2: Descriptive statistics by Auction Attempt (938 Observations)  Mean Std.Dev. Minimum MaximumDummy: =1 if unit is sold at auction 0.15 0.36 0 1.00Dummy: =1 if unit is vacant 0.90 0.30 0 1.00Dummy: =1 if title is freehold 0.74 0.44 0 1.00Auction attendance 191 87.5 15.0 450# of previous auction attempts 0.28 0.64 0 5.00Dummy: =1 if no bids made at auction 0.67 0.47 0 1.00# of steps in auction bidding 1.24 3.28 0 30.00Dummy: =1 if market prices have fallen for 2 successive quarters 0.67 0.47 0 1.00Price index at auction date 103 4.54 99.4 119Days from purchase to 1st auction date 1248 573 21.0 2754Days from highest price over holding period to 1st auction date 751 355 0 1331Days from highest price over past 2 years to 1st auction date 490 235 0 685Dummy: =1 if unit is low rise structure 0.49 0.50 0 1.00Dummy: =1 if unit is being sold by institution (foreclosure sale) 0.61 0.49 0 1.00Loss aversion (relative to price index at purchase date) 0.05 0.05 0 0.16Loss aversion (relative to highest price index over holding period) 0.10 0.06 0 0.24Loss aversion (relative to highest price index over 2 years prior to sale) 0.07 0.05 0 0.23  The properties put up for auction are mainly located in the central and east regions of Singapore. Close to 90% of the properties are vacant, and freehold properties make up the bulk of the sample. The auction attempts are fairly evenly divided between low and high rise properties. Approximately 57 percent of the properties are offered for sale by institutions, but they constitute 60 percent of the auction attempts as they are more likely to attempt to auction again if the first attempt ended in failure.   The state of the market variable suggests that 64% of properties were first put up for auction during a down market. The average holding period from purchase to first  20 auction attempt is about 1,257 days.  Only 16 percent of the properties are sold at first auction On the average, owners suffered a 4% loss from their original purchase price and 10% from the highest peak observed during their holding period. If we take the most recent losses (past 2 years prior to sale), owners suffered an average loss of 7%. The highest loss is about 24% over the holding period and 23% over the 2 years prior to sale.  It is important to note that because the bulk of our auctions are 1998 to 1999 and the market index peaked in 1996, there is a very high correlation between these loss aversion measures for the two peak price measures.   In Table 1 we also compare properties put up for auction by institutions with those offered by individual owners. For nearly all of the variables the differences in the means are statistically different from zero.  The differences are greatest in magnitude for the days from first auction date to sale, principally because of the large difference in the probability that a unit is sold at auction. On average, institutions sell their units in 486 days to sell their properties, while it takes 787 days for individual owners. This provides some anecdotal evidence of difference in behavior between financial institution and individual owners.  Methodology  Prospect theory suggests that when faced with choices involving simple two and three outcome lotteries, people behave as if maximizing an S-shaped value function. Hence critical to this value function is the reference point from which gains and losses are measured. As Kahneman and Tversky (pp, 286 – 287) put it, “In most cases, the  21 status quo is taken as the reference point, but there are situations in which gains and losses are coded relative to an expectation or aspiration level that differs from the status quo.” The reference point used for the past studies of loss aversion using housing market data is the purchase value. Given that property is usually held for a long time over a wide range of prices, the purchase date may be only one determinant of the reference point. The price path may also affect the level of the reference point.  For measuring the magnitude of loss aversion we use the change in the market price index.  Our defense of this approach is presented in Appendix A. This study uses three reference points – price at purchase, the peak property price over the owner’s holding period and the peak property price over the recent past, which we define as the past two years. To take account of the same market peak that we observed for part of our samples, the loss aversion relative to the highest price over the holding period is measured as a function of purchase value, that is, it is taken to beprice purchasepricecurrent price purchasepricehighest ? .  In addition, we examine the reaction of the owners to the most recent losses.  The purchase date in our sample is traced using the Singapore Institute of Surveyors and Valuers (SISV) sales database, which encompasses all residential real estate transactions in Singapore since 1988.    We use three approaches to measure the effect of loss aversion on auction sales. First we test for the effect of loss aversion on a unit’s sales price, either the price that the properties are sold either at the auction itself or via private negotiated sales after failure to sell at the auction. We recognize that there may be a sample selection issue in that we are focusing on properties that are put up for auction, as well as those that sell. We applied a Heckman correction for sample selection.  However, the coefficients on the inverse mills  22 ratio in the 2nd stage OLS regressions on sales price and time to sale were consistently statistically not different from zero, so we reject any problems of bias.6  In this and the subsequent two tests we control for seller type and introduce an interaction between seller type and the measures of loss aversion to see if there is any evidence of variation in sensitivity to loss across seller types.   Housing markets clear via both price adjustment and time on the market.  Our second approach is to test for an effect of our different loss aversion measures on the number of days from the first auction where the property has been put up for auction to the point where it is sold, either at the auction itself or via private negotiated sales. This is similar to the research on time on market and we hypothesize that owners who are loss averse should have a higher reserve prices and be less likely to sell their properties if they were to incur a loss, hence their units should remain a longer time on the market. We employ a proportional hazard model of duration for this test. Our third approach takes advantage of our auction data to test a variant of the probability of sale analysis, whether a unit is sold at auction or not.  Since most successful auction sales occur at the first auction this is analogous to testing whether time to sale equals zero.   To control for market condition, we specify a state-of-the-market variable that indirectly affects the sentiment of property buyers and hence affects the probability of a sale (Mayer, 1995).  The state-of-the-market variable is a dummy variable that takes on a value of zero if the auction occurred in a quarter following two previous successive                                                  6 We used Lee’s (1982) 2-stage procedure by estimating a first stage probit regression on a data set of 13,225 properties, of which 12,408 properties that are sold via private negotiated sales (does not include those that are sold via private negotiated sales after failure to sell at the auction). Variables included in the probit model are dummies for low rise and freehold properties, year and neighborhood (postal code) dummies, floor area, volume of sales in that quarter and change in price relative to purchase date.    23 quarters of negative growth in property prices. We also introduce year dummy variables to control for the timing of the auction (Vanderporten, 1992) and the absolute value of the property price index that we observed at the auction date.  We include a number of property characteristic variables: title type (freehold or leasehold), whether the unit is currently vacant, is the property in a high rise, terrace (townhouse), or detached unit, and property size, either floor or lot area or both.  To capture neighborhood amenities we include postal area fixed effects (twenty eight separate districts).  In addition, we include information on the auction process itself that the literature suggests may be important: turnout at the auctions (Burns, 1985), the number of increments during the bidding process (Ching and Fu, 2003) and whether any bid is received at the auction. We also capture the number of previous auction attempts to account for repeat auctions.7  A central element of our analysis is whether loss aversion varies across individuals.  This may be because of market experience, as suggested by theoretical work or some other factor.  We distinguish between experienced trades, those sales conducted by institutions, and sales by an individual owner.  We expect the individuals responsible for selling the units on behalf of the financial institutions to have more experience with the market than will individuals selling their own units.  However, because sales by financial institutions are typically foreclosure sales, the institutions may only be concerned about the value of their outstanding loan, the appropriate reference point my                                                  7 There is a rich theoretical literature that addresses the association between the number of bidders and the expected price at auction, but with the exception of Burns (1985), there has been little empirical work. Vickrey (1961) shows that under a set of strong assumptions,  as the number of bidders increases the bid that each makes in a multi-unit progressive auction bidding model comes closer to each bidder’s valuation or reserve price. McAfee and McMillan (1987) examine auctions with a stochastic number of bidders, where the probability of observing a certain number of actual bidders depends on the number of potential bidders. Burns (1985), in an experimental setting, tests the reaction of buyers to changes in the number of participants in the market. Contrary to standard expectations, he finds that fewer bidders tend to result in higher prices.   24 be the loan’s current value.  The institutional setting suggest otherwise.  Borrowers in Singapore are liable for negative equity in the event of mortgage default.8 Consequently, lenders owe a fiduciary duty to obtain the best price for defaulted owners.9  This is in addition to the incentive to cover outstanding loan principals. Given that institutional sellers have similar incentives as owner-sellers to obtain the best price possible, any empirical differences in loss aversion behavior between institutions and owners may be attributed to experience or proclivity to loss aversion. Other control variables that are used are the number of days from either the purchase or highest property price index (PPI) value observed during the holding period to date of first, change in PPI from first auction to eventual sale, number of days from date of first auction to censored date and also a dummy variable to indicate properties that are not sold at the auction.  Results  Our first test is whether owners exposed to nominal losses in their properties hold out for higher transactions prices.  As per the treatment in Genesove and Mayer (2001), all else being equal, if loss aversion is present, the eventual sales price should rise with the loss exposure (positive coefficient on the loss aversion measure), but the marginal effect should decline with the size of the loss (negative coefficient on the square of the                                                  8 More precisely, negative equity for Singapore mortgages occurs when the sale proceeds net of repayment of the CPF principal sum plus CPF savings used to pay the legal costs, stamp duty and survey fees is less than the loan principal (CPF Residential Property Scheme). This policy has been amended since September 2002. 9 Owners who perceive that their properties are sold at lower than market prices can and do file legal suits against the bank. For this reason, many banks have to show due diligence in trying to get the best price possible.  25 loss aversion measure). We present the results in Table 3. These are separate for high and low rise units.   The need to exclude units that do not transact in the observation period restricts the total sample size to 631 observations.  As noted above, loss aversion is measured as the change in the overall market index between three separate reference point date and the sales date. In general, we see little evidence of loss aversion behavior around sales price for high rise units, but more for low rise units.  For the latter, it is clear that the choice of reference point matters.10  In our data, loss aversion does not affect sales prices when the reference point is the initial purchase price.  Regressions (1) and (4) use the change in the market price index between the unit’s purchase and sales dates to measure loss aversion for high and low rise units respectively.  In both cases, the standard errors of coefficient estimates greatly exceed the point estimates, which are even negative for low rise units.  Sellers appear to be more sensitive to forgone wealth opportunities than an actual loss.  Sales prices for the low-rise units, though not for the high-rise sample, rise with loss aversion when the reference point to measure this loss is the highest possible value achievable over the whole period and over the last 2 years prior to sale.  In regressions (5) and (6), for low-rise units only, when the reference point is the highest achievable price over the whole period and the last 2 years prior to sale, the coefficient estimates on loss aversion are of the expected signs and either statistically different than zero at the 10 percent level                                                   10 These regressions include year and neighborhood (postal area) dummies; unit characteristics such as whether the unit is vacant, title is freehold, unit size (high-rise only), and lot size (low rise only); and auction variables are auction attendance, # of previous auction attempts, dummy for no bidders, and # of steps in auction bidding.  Results on property type and size are sensible and robust across specifications within a type class   26Table 3: Regressions on Log Sales Price   (1) (2) (3) (4) (5) (6)   High Rise High Rise High Rise Low Rise Low Rise Low Rise Constant 5.85*** (0.06) 5.80*** (0.06) 5.81*** (0.06) 6.04*** (0.07) 6.06*** (0.07) 6.06*** (0.07) Dummy: =1 if market prices have fallen for 2 successive quarters -0.02 (0.03) -0.01 (0.03) -0.001 (0.03) -0.08** (0.03) -0.10*** (0.03) -0.13*** (0.04) Days from Reference Point  to 1st Auction Date -0.000002 (0.00002) 0.0001 (0.0001) 0.0001 (0.0001) 0.00002 (0.00002) -0.0001 (0.0001) -0.00010.12 (0.0001) Days from 1st Auction Date to Eventual Sale -0.00002 (0.00004) -0.00003 (0.00004) -0.00003 (0.00004) -0.00002 (0.00002) -0.00003 (0.00002) -0.00003 (0.00002) Dummy: =1 if unit is being sold by institution (foreclosure sale) -0.04 (0.03) 0.002 (0.06) -0.004 (0.05) -0.07** (0.03) -0.01 (0.06) -0.04 (0.04) Dummy: =1 if unit is sold at auction -0.02 (0.05) -0.01 (0.05) -0.001 (0.05) -0.02 (0.05) -0.02 (0.05) -0.02 (0.05) Dummy: =1 if unit is sold at 1st auction 0.02 (0.05) 0.02 (0.05) 0.01 (0.05) -0.05 (0.05) -0.04 (0.05) -0.04 (0.05) Change in housing price index from1st auction to eventual sale dates 1.25* (0.68) 1.30* (0.68) 1.20* (0.69) 0.39 (0.39) 0.35 (0.27) 0.35 (0.27) Reference Point for Loss Aversion Measure Purchase Price Highest Over Holding Period Highest Over Last 2 Years Purchase Price Highest Over Holding Period Highest Over Last 2 Years Loss aversion measure 1.37 (1.74) 1.92 (2.30) 0.53 (3.16) 0.02 (0.94) 1.96* (1.12) 1.88* (1.01) Interaction:  Loss aversion  x sold by institution  -0.49 (1.99) -1.11 (1.96) -0.86 (2.48) 0.64 (1.15) -0.88 (0.98) -0.27 (0.91) Loss aversion^2 -18.9 (22.2) -25.20.12 (16.0) -20.4 (27.1) 0.58 (6.74) -5.60 (4.24) -4.89 (4.29) Interaction:  Loss aversion^2 x sold by institution 15.0 (25.1) 10.6 (17.2) 10.1 (26.2) -5.38 (8.48) 3.05 (4.38) 0.06 (4.82)        Number of Observations 338 338 338 293 293 293 R-Squared 0.71 0.71 0.71 0.80 0.80 0.80  Standard errors are in parentheses.  All the models include year and neighborhood (postal area) dummies; hedonic variables include whether unit is vacant, title is freehold, unit size (high-rise only), and lot size (low rise only); and auction variables are auction attendance, # of previous auction attempts, dummy for no bidders, and # of steps in auction bidding but are in the table.   ***, ** and * denote significance level at 1%, 5% and 10% respectively  27 or close to this criteria.  The marginally significant negative coefficient on the square of the loss aversion measure is consistent with prospect theory (Kahneman and Tversky, 1979) that the marginal value declines with the magnitude of loss.   In general, institutions are selling units at a lower price. However, this result is only statistically different from zero for low-rise units in regression (4). It is possible that this reflects unobserved quality, where owners are more likely to default of lower quality units, which must be resold at lower prices.  The prices at which institutions sell units appear to be somewhat less affected by losses than is the case for individual owners: the coefficients on the interaction between loss aversion and sold by institution are negative in five of the six regressions, but the point estimates are never statistically different from zero.   In Table 4 we present results for the test of the relationship between loss aversion and time to sale.  The empirical specification uses a proportional hazard model, so that the coefficients reflect the hazard of sale, rather than days to sale. Thus a positive coefficient means the probability of sale, contigent upon not having sold to date, increases in the variable.  This is analogous to a decrease in the expected time to sale.  There is right censoring in the data for the 120 of our 751 units that do not sell in the sample period, which closes in Dec. 2004.  Genesove and Mayer (2001) were the first to identify the expect effects of loss aversion on sales time in search markets such as housing. We find support for Genesove and Mayer (2001) only in regression (3) where the loss aversion is measured relative to highest price over the recent past. For the other two reference points, the coefficients are also both negative, but with smaller point estimates.  What is intriguing are the results for institutions.  While the time to sale for   28 Table 4: Time to Sale (Proportional Hazard Model)  (1)   (2) (3) (4)  (5)  All Sales Institution SalesDummy: =1 if market prices have fallen for 2 successive quarters 0.32** (0.14) 0.29** (0.14) 0.15 (0.17) 0.33* (0.19) 0.13(0.22Price index at auction date 0.48*** (0.17) 0.42*** (0.17) 0.44*** (0.17) 0.39 (0.41) 0.27(0.41Price index at eventual sale -0.35** (0.17) -0.30* (0.17) -0.29* (0.17) -0.30 (0.42) -0.14(0.43Dummy: =1 if unit is low rise structure -1.26*** (0.18) -1.07*** (0.23) -1.38*** (0.27) -0.62** (0.32) -1.15*(0.38Dummy: =1 if unit is being sold by institution (foreclosure sale) 0.04 (0.13) -0.16 (0.20) -0.22 (0.15)   Dummy: =1 if unit is sold at auction 0.87*** (0.23) 0.84*** (0.24) 0.77*** (0.24) 0.82*** (0.25) 0.76**(0.25Dummy: =1 if unit is sold at 1st auction 6.33*** (0.77) 6.40*** (0.77) 6.46*** (0.77) 5.89*** (0.77) 5.93**(0.78Change in housing price index from 1st auction to eventual sale dates 59.3*** (18.1) 53.7*** (17.9) 54.0*** (17.9) 52.9 (47.8) 37.1(43.8Reference Point for Loss Aversion Measure Purchase Price Highest Over Holding Period Highest Over Last 2 Years Highest Over Holding Period HigheOver LaYearLoss aversion (relative to price index at purchase date) -0.64 (2.60)     Interaction:  Loss aversion (relative to purchase price) x sold by institution 3.48* (1.96)     Loss aversion (relative to highest price index over holding period)  -1.76 (3.89)  3.60 (3.16)  Interaction:  Loss aversion (relative to highest price index over holding period) x sold by institution  3.47** (1.72)    Loss aversion (relative to highest price index over 2 years prior to sale)   -3.47* (2.16)  3.45(4.91Interaction:  Loss aversion (relative to highest price index over 2 years prior to sale) x sold by institution   5.73*** (1.67)   Number of observations 751 751 751 430 430Likelihood ratio 983 980 990 629 632Dependent Variable: Number of Days from 1st Auction to Eventual Sale Either by Auction or Private Negotiated Sale.  Standard errors are in parentheses.  All the models include year and neighborhood (postal area) dummies.  Other variables included in the regression, but not shown here are auction attendance, # of previous auction attempts, dummy for no bidders, interaction between loss aversion and low rise, dummy for unit is not occupied, and # of steps in auction biddings.   ***, ** and * denote significance level at 1%, 5% and 10% respectively.  29units being sold by financial institutions does not differ from that of individuals, as loss aversion increases institutions do sell their units more quickly than do individuals.  This result is statistically different than zero at the 5 percent level for both highest price and the highest price in the last two years as the reference points, in regressions (2) and (3).  Like the results in Table 3, we find the highest point over the recent past to be the most influential reference point. We control for whether the unit is sold at first auction, or even sold at auction, as both of these shorten time to sale, increasing the probability of sale hazard at any point in time.  Other robust results are that it takes longer to sell low rise units, a market for which there are fewer properties and buyers.  The higher the market price index at the time of first auction, the more likely a sale.  As well, if prices rise following the auction date, a subsequent sale of a unit not sold at auction is more likely. Institutions do not necessarily act to sell units more quickly as in neither of regressions (1), (2) and (3) is the coefficient on sale by institutions statistically significant.  The results do indicate that they are less affected by loss aversion than are individual sellers. Relative to individuals, increases in the perceived loss increase the sale hazard (accelerate the time to sale) for institutions relative to the hazard for units sold by individuals: the coefficient on the loss aversion by institution interaction variable is negative and statistically different than zero in regressions (1), (2) and (3).  However, institutions themselves do not display explicit loss aversion behavior.  When the sample is limited to sales by institutions in regression (4) and (5); the coefficient on potential loss is far from statistically different than zero.    One interesting point from Tables 3 and 4 is that institutions tend to sell at a faster pace as compared to owners when faced with losses, but they do not necessarily sell at a lower price than the owners. In other words, institutions wanted to recoup their losses at the soonest possible but still  30appear to sell at the highest price achievable. This result is supportive of the claim that financial institutions follow their fiduciary duty to exercise care in trying to obtain the best price possible for defaulted properties.  In Table 5 we look at a variant of the time to sale questions, by examining the role loss aversion may play in influencing whether a property sells at the first attempted auction or not.11  Sale at auction is a likely explanation for the shorter mean selling times for units sold by institutions, as those units sold at first auction comprise a mass at zero in the time to sale data.  Whether a unit is sold at auction depends both on interest in the property and on the opening minimum bid set by auctioneer.  We presume the latter reflects the reservation price set by the seller as the auctioneer learns of the seller’s reservation price on the day of the auction.  Consistent with the treatment in the sale hazard model in Table 4, we expect that the probability of a unit being sold at auction falls with loss aversion, reflecting the higher reservation prices associated with loss aversion.  This expectation is confirmed in regressions (2) and (3) where the coefficient on loss aversion is negative and statistically significant, reflecting a lower probability of sale at auction.  Here again we find that the relevant reference point is not the purchase price, but the highest price achieved since purchase, or in the past two years.                                                   11 This follows work by Ong, Lusht, and Mak (2005) on this question.    31Table 5: Probability Property Will Be Sold at Auction  (Logit for All Auction Attempts)  (1) (2) (3) (4) (5) (6)  All Sample Institutional Sale Only Constant 17.7 (14.8) 20.3 (19.0) 7.77 (24.7) 16.6 (13.1) 18.5 (14.8) 0.75 (20.5) Dummy: =1 if title is freehold 1.17*** (0.45) 1.04** (0.43) 0.98** (0.43) 0.72* (0.40) 0.57 (0.39) 0.590.13 (0.39) Dummy: =1 if no bids made at auction -4.86*** (1.05) -4.87*** (1.06) -4.83 (1.06)    # of steps in auction bidding 0.53*** (0.08) 0.53*** (0.08) 0.54*** (0.08) 0.80*** (0.08) 0.79*** (0.08) 0.80*** (0.08) Dummy: =1 if market prices have fallen for 2 successive quarters -0.68 (0.60) -0.10 (0.60) 0.12 (0.63) -0.16 (0.53) -0.02 (0.57) 0.14 (0.59) Price index at auction date -0.20 (0.14) -0.22 (0.18) -0.10 (0.23) -0.21* (0.12) -0.220.13 (0.14) -0.05 (0.19) Days from purchase to 1st auction date 0.00004 (0.0004)   -0.00002 (0.0004)   Days from highest price over holding period to 1st auction date  0.002 (0.001)   0.0002 (0.001)  Days from highest price over past 2 years prior to sale to 1st auction date   0.002 (0.001)   0.001 (0.001) Dummy: =1 if unit is low rise structure -0.31 (0.72) -2.26 (2.14) -1.75 (1.63) 0.64 (0.73) 0.27 (0.99) -1.30 (1.44) Dummy: =1 if unit is being sold by institution (foreclosure sale) 1.29* (0.69) 0.06 (1.13) 0.40 (0.88)     Reference Point for Loss Aversion Measure Purchase Price Highest Over Holding Period Highest Over Last 2 Years Purchase Price Highest Over Holding Period Highest Over Last 2 Years Loss aversion (relative to price index at purchase date) 6.12 (14.9)   11.8* (6.68)   Interaction:  Loss aversion (relative to purchase price) x sold by institution 11.2 (14.6)      Loss aversion (relative to highest price index over holding period)  -35.6** (15.0)   -3.78 (15.7)  Interaction:  Loss aversion (relative to highest price index over holding period) x sold by institution  15.70.13 (10.3)     Loss aversion (relative to highest price index over past 2 years prior to sale)   -53.7*** (21.1)   -21.8 (17.2) Interaction:  Loss aversion (relative to highest price index over past 2 years prior to sale) x sold by institution   20.10.13 (12.8)           Number of observations 938 938 938 570 570 570 Log likelihood -132 -132 -132 -149 -151 -150        Dependent Variable: Dummy variable of value = 1 if property is sold at auction and 0 else Standard errors are in parentheses.  All the models include year and neighborhood (postal area) dummies.  Other variables included in the regression, but not shown here are auction attendance, # of previous auction attempts, interaction between loss aversion and low rise, a dummy for unit is not occupied, and dummy if unit is vacant.   ***, ** and * denote significance level at 1%, 5% and 10% respectively.  32 We find weak evidence that the probability a financial institution sells a unit at auction increases with the perceived loss, relative to the probability for an individual seller.  The coefficient estimates for institutions (the interaction effect) are positive and statistically different from zero at the 13 percent level in regressions (2) and (3). This finding is consistent with the time to sale results. With the exception of regression (1), institutional sellers are not more likely to sell at auction in general, a surprising outcome given the difference in means. When we limit the sample to sales by institutions in regressions (4) and (5), we find that institutions are in general, not subject to loss aversion behavior.   Conclusion  This papers uses real estate auction data from Singapore to better understand loss aversion.   There are two principal questions explored in this paper.  First, when loss aversion is observed, what is the relevant reference point?  Second, is loss aversion behavior common across all market participants?  Our data identify differences in auction participants, individual sellers and financial institutions, which allows us to test for differences in loss exposure behavior.  Because we are able to construct repeat sales indexes for the market as a whole and we know the date the property was last sold, we can construct loss aversion measures where the reference point is either the initial purchase price or the highest price the property would have been able to achieve over the holding period/over last 2 years prior to sale.   33  Our results suggest that loss aversion is not a single clear characteristic.  Probably our most robust result is that the relevant reference point for measuring the change in the value function is not the initial nominal purchase price, but rather the highest value. Though there are strong evidences for the reference points to be both the highest price, we do observe that the highest price over the most recent past to be more robust.  Our other findings include that institutions are less susceptible to loss aversion than individuals.  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Vanderporten, B., “Timing of Bids at Pooled Real Estate Auctions,” Journal of Real Estate Finance and Economics, 5(3) (1992), 255 – 267.  Vickrey. W., “Counterspeculation, Auctions and Competitive Seal Tenders,” Journal of Finance, 16(1) (1961), 8 – 37  38Appendix A  Define a unit’s i log market value at time t as Pit, and the current log market index as Pt . The observed transaction price of an individual unit depends on both the current market, the unit’s quality/quantity deviation from the market index, and the outcome of bargaining process between the buyer and seller vit.  We assume that the price of the housing services delivered from the unit’s structure is a function of observable characteristics ?(Xi) and unobserved quality ei.  For convenience we assume that both are time-invariant relative to the market index.  We assume further that both e and v are distributed with mean zero and each with its own variance.  The observed transaction price of unit i at time t becomes: .)( itiitit veXPP ???? ?       (1) Loss at time t  Lit is defined as maximum of zero and the expected price at the reference point minus the current expected value.  So for a reference point of the unit’s value at time 0:  ? ?.)()(,0max 0 itiit PEPEL ??       (2) Substituting from (1) into (2):  ? ?).()())()(()(,0max 00 itiiiiitit vvEeeXXPPEL ???????? ??   (3)  Eliminating the time invariant components reduces to an expression of the market index and the seller’s bargaining strength at times 0 and t. ? ?.)()(,0max 00 ititit vvEPPEL ????     (4) If we impose the assumption that a seller expects her relative bargaining skill to be constant over time, so that in the population vit is mean zero, but individual i has E(vit) = E(vi,t+j), then  39the expected change in the price index will measure an owner’s expected loss aversion between any two dates.    Lit will thus be a function of actual price index values for any analysis of loss aversion that involves current and past dates.    


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