Consumer house price judgements: new evidence of anchoring and arbitrary coherence

Consumer house price judgements: new evidence of anchoring and arbitrary coherence * Peter J. Scotta and Colin Lizieria a Department of Land Economy, University of Cambridge, United Kingdom Individuals are prone to significant errors when making value judgements through the use of heuristics (cognitive short cuts) to simplify decision making. This paper uses an economic experiment to investigate the strength of arbitrary anchors in judgements over house prices among a student group, who are representative of first-time buyers. The study represents a departure from existing property research literature on valuation because it focuses on consumers, not professionals, and uses experiments which are incentivised. Additionally it investigates the evolution of price estimates over multiple sequential property viewings. The results indicate that even in the presence of significant, binary incentives for accurate judgement individuals rely, to a significant degree, on an arbitrarily established anchor value. Such anchors remain powerful enough for transitions to subsequent valuations to remain influenced by this initial value. This is interpreted as a confirmation – and extension – of the arbitrary coherence reported in other studies of consumer judgement (Ariely, Loewenstein and Prelec, 2003). Keywords: house prices; value judgement; anchoring; arbitrary coherence 1. Introduction Today there is a large body of research which accepts that, in a variety of situations, humans can make mistakes when they make judgements. The source of these mistakes is a matter for debate, but a significant strand of thought holds that it lies in the use of heuristics or cognitive short cuts which simplify decision making (Tversky and Kahneman, 1974). Yet while significant research attention has focused on the strength of these errors and how systematically they may affect our judgement in a variety of consumer situations (Kahneman, Knetsch and Thaler, 1990; Ariely, et al., 2003; Simonson and Drolet, 2004), relatively little has focused on perhaps the most important consumer decision of all: housing. Buying a home is one of the most important decisions faced by any household or * Corresponding author. Email: pjs56@cam.ac.uk Pre-print submitted to Journal of Property Research February 2011 Electronic copy available at: http://ssrn.com/abstract=1765974 P.J. Scott and C.M. Lizieri individual during their lifetime. The stakes may be high, but on the face of it the prospect of making good judgements in this area is mixed at best. Since house purchases are infrequent – the time between them is usually measured in years or even decades – it is hard to get experience or expertise. Experience with economic decisions has been found to significantly improve their accuracy and consistency (List, 2003; 2004). Housing markets are decentralised and information difficult to obtain. Information which is available is likely to be provided by an estate agent, introducing a potentially serious principal-agent problem (Levitt and Syverson, 2008; Scott and Lizieri, 2011). Moreover high transactions costs make correcting errors difficult. Errors made in judging value in housing markets are likely to have serious distortive effects on those markets, as well as significant and lasting effects on consumer welfare. This paper investigates the existence and strength of arbitrary anchors in biasing value judgements over houses among a student group who are taken as representative of first-time buyers likely to enter the housing market in the coming years. It is a departure from the majority of existing literature in the area because of its explicit focus on consumer decisions over residential property. Starting with Diaz (1990), there is a large body of research considering the valuation behaviour of real estate professionals (Diaz and Hansz (2007) present a good summary). Some papers have considered consumer valuation biases (Northcraft and Neale, 1987; Levy and Frethey-Bentham, 2010) but these are not incentivised meaning subjects are not paid according to how well they complete the estimation tasks. The methodology in this paper was carefully designed to offer a significant, binary reward to those participants who were able to estimate sale prices accurately. A second important contribution of this paper is that it considers the evolution of price estimates over several sequential viewings. In this way it is able to shed light on the transmission of biases through several estimations. This extends the work of Ariely et al. (2003) who consider a bias they term arbitrary coherence which suggests that once arbitrary valuations become lodged in a decision maker‟s mind they may become coherent, and form the basis of future judgements. Electronic copy available at: http://ssrn.com/abstract=1765974 Journal of Property Research The findings increase our understanding of the influences on consumer decision making in a housing context; influences that lie entirely outside of the rational decision theory framework of von Neumann and Morgenstern (von Neumann and Morgenstern, 1947). They are of interest to real estate academics, particularly those focused on market dynamics; and to practitioners for whom they offer potentially profitable ways to manipulate behaviour. Finally they have implications for us all as decision makers, for the most effective way to make error-free judgements is to understanding the psychological factors which determine how we make them. 2. Literature Review The use of cognitive short cuts in decision making, which can lead to serious judgemental biases, has become one of the most important areas of psychology to reach into economics. It has particularly important implications for choice in all consumer situations. Tversky and Kahneman (1974) report some of the most significant including: representativeness, where assessment of probabilities is biased according to the extent to which an event is representative of another; availability, where probability estimates of the likelihood of an event are affected by the ease with which examples can be recalled; and anchoring. Significant areas of literature which can be included as additions to this list of psychological biases in judgement include: loss aversion which results in a reluctance to part with owned assets known as the endowment effect (Thaler, 1980; Kahneman et al., 1990) and is one of the bases of Prospect Theory (Kahneman and Tversky, 1979); and framing effects which result in phenomena such as preference reversal, where altering the description frame reverses preferences (Slovic and Lichtenstein, 1983; Tversky, Slovic and Kahneman, 1990). Anchoring The current interest is largely confined to the bias of anchoring. It is one of the purest forms of behavioural phenomena which Daniel Kahneman has said is among the most robust observations in the psychological literature (Kahneman, Ritov and Schkade, 1999). Anchoring is a form of heuristic 3 P.J. Scott and C.M. Lizieri which individuals use to aid their decision making process. It is best summed up in the authors‟ own words: “In many situations, people make estimates by starting from an initial value that is adjusted to yield the final answer. The initial value, or starting point, may be suggested by the formulation of the problem, or it may be the result of a partial computation. In either case, adjustments are typically insufficient. That is, different starting points yield different estimates, which are biased toward initial values.” (Tversky and Kahneman, 1974, p. 1174) The use of a mechanism where an initial value is selected and adjustments made to yield a final answer is not a serious flaw in judgement making per se. It is the fact that the selection of the initial value is not independent of the problem‟s framing and that the adjustments made are typically not sufficient, which leads to bias. In their illustrative experiment, participants were asked to estimate quantities, such as the number of African countries in the United Nations, expressed in percentages. Prior to this a number between 0 and 100 was determined by spinning a wheel in the presence of the participants. Having been asked whether they thought the percentage they were being asked to estimate was above or below the number they had just seen, subjects were then asked what they thought the correct number was. Despite the initial number – the anchor – being demonstrably random, judgements were significantly correlated with it. The effect was not reduced by increasing payoffs for accurate judgement. Evidence exists to suggest that anchoring behaviour is widespread among professional real estate valuers when they asses both commercial and residential property. Diaz and Hansz (2007) present a recent summary of this literature. Gallimore (1994; 1996) finds significant evidence of heuristic-driven behaviour among residential valuers including a general tendency to form and early judgement and subsequently seek evidence to justify it1. Diaz and Wolverton (1998) find evidence of anchoring based on Journal of Property Research previous estimates and insufficient updating of estimates in the light of new information, known as appraisal smoothing, a direct confirmation of the anchoring-and-adjustment mechanism proposed by Tversky and Kahneman. Diaz (1997) suggests that where valuers were experts making valuations in areas familiar to them anchoring biases are significantly reduced or even eliminated. However, most consumers make housing choices with relatively little experience, since they make the choice so infrequently. Moreover individuals who are the focus of this study – firsttime buyers – have, by definition, no experience buying property (though they may have rented in a particular location). Some papers do focus on consumer judgements over housing. An early paper by Northcraft and Neale (1987) finds evidence that valuation by non-professionals also use the anchoring heuristic. Following up on this study, Levy and Frethey-Bentham (2010) consider the ways in which context impacts estimations of value among a student group of varying expertise. They find that the level of expertise – measured by training in real estate economics – is an important determinant of the nature of valuation bias. However, neither of these studies uses incentives to reward subjects for accurate judgement. Thus, in first instance this paper builds on this work by using a carefully-designed incentive structure to offer participants a large, binary reward for accurate judgement. Experimental economists argue that the use of incentives is vital to ensure the researcher has control over the motivations of the subject (Freidman and Sunder, 1994). It also uses an anchor delivery methodology drawn from consumer choice literature, which offers a greater spread of anchor values, and thus greater generalisability, than the simple high-anchor/ low-anchor method used in Levy and FretheyBentham. Arbitrary Coherence Ariely et al. (2003) approach the issue of valuation from a different perspective, focusing explicitly on consumers‟ valuation of household goods. They investigate the ability of arbitrary anchors to affect subjective 5 P.J. Scott and C.M. Lizieri valuation, but go further, considering the effect of arbitrary valuations on entire preference patterns. Utilising a procedure first adopted by Wilson, Houston, Etling and Brekke (1996) they asked subjects to write down the last two digits of their social security number (SSN) as a price. Thus, someone whose digits were -23 would have written $23. They then showed subjects a series of consumer products such as computer equipment, wine and chocolates, and asked them whether they would be willing to accept each in turn for the price they had written down using the SSN. Finally subjects were asked the maximum dollar price they would be willing to pay for each product2. The social security number – patently an arbitrary anchor – proves a reliable indicator of willingness to pay in each case. The results are reproduced in Table 1. [TABLE 1 HERE] The results are hugely significant. Subjects with above median SSNs state values between 57% to 107% greater than subjects with below median SSNs. The gap between the bottom and top quintiles is up to a multiple of three. The authors present further evidence in support of the proposition that subjective valuation of goods can be influenced by anchoring. They term the effect arbitrary coherence. It encompasses the idea that values in a subject‟s mind can, relatively easily, be established arbitrarily using anchoring. After that they can shape decision making significantly. They become coherent and form the basis of future judgements. This is important because the carrying forward of biased judgements can result in the illusion of an entire preference relation which is coherent – in other words based upon a stable underlying preference structure – but which is in fact derived arbitrarily. We believe it has particular relevance in housing search because information is received, and judgements made, in a naturally sequential way. If it is possible for an economic agent to use anchors to bias initial judgements, these may come to significantly bias perceptions of value for an entire search process. Journal of Property Research The experimental procedure used in this study is based on Ariely et al. (2003) and follows the evolution of price estimates over four judgements of housing value. It thus allows an examination of how arbitrary influences shape value perception in housing searches. 3. Methodology and Data Collection The aim of this study is to understand the extent to which individual perceptions of value in housing can be biased through the use of arbitrary anchors delivered at the start of the valuation process. A secondary aim is to examine the whether these biases are transferred to subsequent valuations, even in the presence of significant incentives for accurate judgement. The subjects of the experiment were student volunteers who were paid for their time and for the accuracy of their judgements using a carefully designed procedure. Subjects were exposed to a presentation giving them contextual information about the local property market including recent average sale prices. An arbitrary anchor was then delivered to them individually using a procedure based on Ariely et al. (2003) involving their mobile telephone numbers. Then they were given information about four houses recently sold in their local area. After each property viewing an estimated valuation was sought. This procedure is explained in more detail after we consider the research hypotheses. Research Hypotheses We have already argued that the student group used are a good proxy for one particularly important part of the housing market: first time buyers. These decision makers enter the market for buying a home with extremely limited experience and so are heavily reliant on information provided by an external economic actor, possibly an estate agent3. Thus there is a significant risk that their value perception will be influenced by an arbitrary anchor, if it attaches itself in the mind of the decision maker. This occurs because of the psychological mechanism of anchoring-and-adjustment, a heuristic proposed by Tversky and Kahneman (1974) where decision makers form initial judgements before making adjustments to yield a final 7 P.J. Scott and C.M. Lizieri answer. Both the picking of the initial value and the subsequent adjustments are sources of bias. This leads to the first research hypothesis. Hypothesis 1: Subjects‟ valuation of a property they have just viewed will be reliably influenced by the arbitrary anchor they are given prior to making the judgement, even in the presence of incentives for accuracy. Having become lodged in the mind of the decision maker, the arbitrary valuation can influence subsequent judgements by the repeated use of the same mechanism. In other words, the most recent judgement forms the most salient estimate on which to base the next estimate and so on. Of course given limited information, or limited time in which to obtain information, basing a particular judgement on a previous one may represent the decision maker‟s best way of estimating value4. However, Tversky and Kahneman (1974) make it clear that they expect these adjustments to be systematically insufficient, which introduces further bias. Moreover if the initial valuation is based on arbitrary influences, this will be transmitted to the subsequent estimation, at least in part. Entire patterns of value are thus expected to be coherent, and so appear as if they are generated by a rational underlying preference structure, yet ultimately arbitrary in the manner suggested by Ariely et al. (2003). This leads to our second research hypothesis. Hypothesis 2: Transitions to subsequent valuations of houses will be influenced by the valuation immediately prior to it. The influence of an initial arbitrary anchor will remain detectable across several such estimations. Data Collection The data was collected from an experiment carried out at the University of Cambridge in a classroom setting. In total 139 subjects took part. The majority were undergraduate students recruited at random by advertising on Journal of Property Research campus for volunteers to take part in a decision making experiment5. There is a lengthy debate surrounding the applicability of results gained from student volunteers (such as Calder, Phillips and Tybout, 1981; Shuptrine; 1975). One thing that cannot be doubted is that the use of student volunteers is widespread in experimental economics (Kagel and Roth, 1995). We believe that the student group used here is relevant because they represent first-time buyers, an important sub-section of the housing market, well. We do not make any claims about the generalisability of the results beyond that sub-section, instead leaving it to future research to extend our findings. The majority of participants were aged 18-22 at the time of the experiments and had little experience in matters connected with home buying. These very same people are likely to be entering housing markets in the coming years. Also, using University students builds in a further test of the hypotheses proposed because they are likely to be at the sophisticated end of the market and so perhaps less vulnerable to perceptual bias6. All experiments were completed using a standardised procedure which adhered to best practice in the experimental field (Kagel and Roth, 1995). It is described below. Careful attention was paid to the room used so that every participant had a good view of the information – which was presented on an overhead screen – and could hear clearly. Experiments lasted a maximum of 45 minutes to minimise the risk of subject fatigue. Subjects were given a fee of £5 for participating in the experiment and, as described below, were able to earn either £10 or £20 extra depending on their performance. On average 10% of subjects earned some extra payment, which was made in cash at the end of the experiment. Experimental Procedure Great care was taken with the experimental procedure, including a pilot study. All the experimental sessions were carried out by the authors using standardised written procedures. The task in the experiment was simple: based on some information about a house that you are given, estimate what it is worth. Once preliminaries had been completed, subjects were given instructions. These are reproduced in Figure 1. Students received these 9 P.J. Scott and C.M. Lizieri instructions in written form and they were read aloud. An important part of the judgement experiments was that students would not be asked simply to pick a value for a house value at random with no context to guide them. Background information about current conditions in the housing market both on a national and local level was provided. There were several reasons for this. Foremost was the need to provide a minimum level playing field for all subjects given their relative lack of experience in housing choices. This procedure also made the experiment more realistic because in real housing choice situations decision makers would be expected to spend at least some time familiarising themselves with their local market though research on the internet local press. [FIGURE 1 HERE] Thus subjects were given a 10 minute presentation on the UK and Cambridge housing markets which included facts and figures on the following:  Commentary on current national house price trends  Current average house prices as estimated by leading market researchers  Regional market moves and average house prices  Background on the Cambridge housing market: number of dwellings, tenure pattern  Average house prices in Cambridge‟s five central post-code areas This method also presented a significant challenge to the anchoring manipulation that was to follow because it presented subjects with many other potential and highly salient anchors from which they could base their estimate. All the information contained within the presentation was based on internet research readily available to any real home-buyer on websites including rightmove.co.uk and primelocation.com. Having listened to the market trends presentation the next phase of the experiment was to give subjects the arbitrary anchor. Subjects were told that Journal of Property Research before we viewed the first property they needed to write down a number. The anchoring procedure asked subjects to write down on their answer sheets the last three digits of the mobile telephone number as a price in thousands of pounds. Thus a subject with the digits -204 would have written £204,000. This procedure ensured each participant had a transparently random number in front of them to form the anchor. Its inspiration is the procedure developed by Ariely et al. (2003), who used digits of US Social Security numbers to produce an anchor. The procedure used was in fact somewhat more stringent their method, because it leaves less room for the arbitrary anchor to take hold. Specifically, they asked subjects to appraise the item at hand in terms of the anchor (in other words whether it was more or less expensive than the anchor) in first instance. In the experiments reported here no mention was made of the anchor value once it was written down. Having received the arbitrary anchor participants were presented with information about the properties. These were in the form of „virtual tours‟ including photographs and textual information. All tours were based on real properties, which had recently been on the market in Cambridge, supplied by a local estate agent. An example of the information provided is reproduced in Figure 2. [FIGURE 2 HERE] The first property (Property A) was a three-bedroom maisonette towards the east of the city of Cambridge. It offered a riverside location and extremely pleasant communal gardens. The decor was slightly dated, however. It sold for £240,000 in January 2010. Property B was a one-bedroom split-level flat in a prime location near the city centre and train station. It was visibly fitted out with modern appliances, though was a little small. It sold in January 2010 for £207,000. The third property (Property C) was a three-bedroom 1960s terraced property located in suburban Cambridge. It was clearly on a quiet street and offered good amenities including garage and good sized garden. The interior decor was somewhat outdated though and it was in a noticeably poorer state of repair than the others. It sold for £215,000 in 11 P.J. Scott and C.M. Lizieri January 2009. The final property (Property D) was a two-bedroom ground floor flat in a good location near the large Addenbrooke‟s Hospital site to the south of the city. It was decorated in a modern style and was spacious with a light feel given its large patio doors onto communal gardens. It was sold in November 2009 for £195,000. After each viewing, which lasted approximately 2-3 minutes, subjects were asked what they thought the house was worth. They were reminded that, as per the instructions, the house was sold within the last four months and were to think carefully about their answer before writing it down. The procedure was repeated. No price feedback of any kind was given in between each valuation. Having completed the experiment subjects were asked to complete a questionnaire before incentive payments were made. Incentive Structure Incentive payments are an important part of economic experimentation. The induced-value theory of Smith (1976) suggests that providing incentives correctly is a sufficient way to control the behaviour of respondents in the desired way, despite their heterogeneous preferences and attitudes. In this experiment our aim was to induce participants to estimate the value of one or several properties as accurately as they could, given the information available to them. Incentives were thus designed for this purpose. Housing choices are among the most important that can be made in a lifetime by any individual or household. As discussed in earlier sections, this is part of the reason that it is a vital area to examine behavioural biases. Many economic experiments employ incentive schemes which are graduated: participants earn increasing amounts as they perform better and better with some extra money almost guaranteed. We do not believe that housing choice is like this, especially where judgement of value is concerned. Judging incorrectly means paying thousands of pounds too much, thus consigning the decision maker to years of paying over the odds for their purchase. Or perhaps it means paying too little, therefore missing out on properties altogether and a stressful and extended search process. Both result in significant, binary, effects on welfare and utility. Journal of Property Research As such a binary incentive scheme was designed for the judgement experiments. Subjects could earn one of two amounts: £10 or £20. They would earn £20 if they estimated to within £2,000 of the true sale price, and £10 if they estimated to within £10,000 and £2,000 of the correct price. Any judgements outside of this boundary would not be rewarded7. All subjects earned a fee of £5 for participating in experiments, matching standard practice in experimental economics (Kagel and Roth, 1995). Thus, for judging accurately, the student volunteers could earn up to four times their show up fee as a reward. Smith‟s (1982) parallelism precept says that inductive reasoning allows one to say that behavioural regularities from laboratory experiments will persist in real world situations as long as the relevant underlying conditions remain substantially unchanged. The incentive scheme was high-stakes to the students involved and it was binary, conditions we believe match those in real world housing choices. Subjects made four valuations during the experiment. However the paying of rewards was based on only one of these properties. A randomisation procedure was conducted at the end of the experiment to determine which property that would be, a method carefully explained to subjects at the beginning. This ensures the subject‟s best strategy is to value as accurately as possible for each of the properties. 4. Results The results from the experiments are reported in two sections. First we consider evidence for anchoring in the first property value estimate. We then present analysis of the transitions to subsequent valuations looking for evidence of Ariely et al. (2003) arbitrary coherence. Anchoring and Adjustment Figure 3 reports the results of the estimation of Property A. The responses are split according to the arbitrary anchor each participant wrote down. Estimates are placed into „anchor buckets‟ according to the first digit of the anchor. Thus if the arbitrary anchor that a subject wrote down was £125,000 they would be placed in bucket 1. If it was £576,000 they would be placed in bucket 5. Buckets 0 and 9 are excluded for the entire analysis because 13 P.J. Scott and C.M. Lizieri they do not provide reasonable anchors. Finally buckets are grouped so that the data is effectively split into quartiles by anchor. Different methods were used to truncate the data and exclude extremely inaccurate answers. In Figure 3 the top and bottom 5% of observations listed by error margin are truncated. This reduces the sample size to 99. [FIGURE 3 HERE] There is evidence that arbitrary anchors had an influence on value judgements of houses. For example, those with an anchor of £100,000 to £299,900 on average estimated the property to be worth £246,100. While those with an anchor of £700,000 to £899,900 estimated on average that the property was worth £268,200. However, as visually compelling as these results are, an F-test of the joint equality of means does not allow a rejection of the hypothesis that they are equal (F=1.142, p-value: 0.336). Another way to consider the relationship between the anchor and the valuation of Property A is to use an ordinary least squares regression. A least squares regression of the relationship is reported in Table 2. It has the following form: Due to non-linearity in the value estimates they are taken as natural logarithms. Two different specifications for the independent variable, Anchor Bucket are reported. Each employs a different method for truncating wildly inaccurate estimates. In Column (1) the top and bottom 5% of observations listed by error margin are removed. In Column (2) the truncation is relative. Observations are removed if they are more than 60% above or below the true value. Both regressions yield significant coefficients. For example when the top and bottom 5% of inaccurate estimates are truncated the model predicts that being in anchor bucket 1 will produce an estimate of £240,700, whereas being in anchor bucket 8 will result in an estimate of £264,800. The model is significant at the 10% level Journal of Property Research (p-value: 0.063). We believe the considerable noise inherent in data of this type makes it appropriate to consider significance at this lower level. [TABLE 2 HERE] Another way to analyse the data and remove a significant amount of the noise which is present is to use the simple average of the estimates in each anchor bucket as the dependent variable. This is reported in Table 3. Here there is stronger evidence of a relationship between the anchor seen and the estimate made. The truncation method is the same as in Table 2. In Column (1) with the top and bottom 5% of observations being removed, the average estimate increases by £3,730 for each digit increase in the anchor with the coefficient significant at the 5% level. If all errors of greater than +/- 60% are removed from the data the independent variable exerts a highly significant effect on the ultimate value judgement made (Column (2)). [TABLE 3 HERE] This is a significant result. For the student group who took part in the study, it was possible reliably to influence their judgement of the value of Property A by having them write down a patently arbitrary number before they completed the estimation. This was true even given the significant incentive for accurate judgement and the provision of information to help make a good decision. In this way it confirms and extends the findings of Levy and Frethey-Bentham (2010). Arbitrary Coherence Having established that there is a detectable arbitrary element to the valuation of Property A based on the use of the anchoring heuristic, we examine whether this process is used repeatedly in establishing other valuation estimates. Can the valuation structure be said to be coherent despite being based on arbitrary foundations? Table 4 reports the correlations between estimates of Properties A, B, C and D. 15 P.J. Scott and C.M. Lizieri There is evidence of a correlation between sequential estimates. Having estimated Property A, the correlation with the resulting estimate of Property B is 0.195 which is significant at the 5% level. There is some correlation between the estimates of House B and C, but it is not significant. The greatest significance occurs between the estimates of Houses C and D. The correlation coefficient of 0.397 is highly significant. [TABLE 4 HERE] This result can be understood further when we take a look at House C. House C was significantly different to others in the set in one critical factor – it was in noticeably shabby repair and would clearly need some work in order to bring it up to a modern standard. This introduced a significant source of uncertainty for the student participants: they knew that it would get a reasonably large discount as a result, but had no clear way of assessing how big that discount might be. In this scenario it seems reasonable that there would be a „break‟ in the transition structure from House B to C. It is significant though that the use of the previous judgement as the most salient anchor for the following one is quickly re-established: estimates of House D are highly correlated with House C. An analysis of the transitions between property viewings illustrates this further. Table 5 reports transition matrices for the transitions from Property A to B; from Property B to C; and from Property C to D. Taking the first of these transitions, for example, the rows split the estimates of Property A into two halves. The columns split the estimates of Property B into halves. Thus the position in the matrix illustrates the transition from Property A to Property B. Therefore the diagonals in the matrix represent individuals who stayed in the same half of the distribution of estimates during the transition. Thus the top left-hand square in the matrix represents individuals who were in the top half of the distribution of estimates for Property A and stayed in the top half of the distribution in their estimate of Property B. The figures reported are percentages of the total. Journal of Property Research [TABLE 5 HERE] There is clear evidence that the valuation of a subsequent property is strongly influenced by the estimate of the most recent property. If the estimate for Property B were unrelated to Property A, numbers would be evenly distributed across each row. However a chi-squared test of this matrix reveals a significant relationship in the estimations of Properties A and B (χ2 = 3.804, p-value: 0.051): participants were significantly more likely to estimate below the median for Property B having done so for Property A; and visa versa. Confirming the correlation analysis, there is no evidence of the estimate of Property C being influenced by Property B (χ2 = 0.064, p-value: 0.780). Finally an examination of the transition from Property C to Property D reveals the most significant evidence of a connection. Of those subjects who were in the top half of the estimations for Property C, 64% of them remained in the top half in their estimate of Property D (χ2 = 10.940, p-value: <0.001). This evidence strongly supports the suggestion, expressed in Hypothesis 2, that the valuation judgement of subsequent properties is strongly influenced by the most recently-valued property, because that valuation serves as an anchor for the next. It is important to emphasise again at this point that the use of this rule-of-thumb does not itself guarantee biased decision making. The bias comes from the fact that the adjustments made from the anchor point are typically not sufficient – clearly confirmed by the transition analysis – and the fact that the source of the initial anchor may not be independent of the context. In this case the initial anchor point was a demonstrably random number placed before subjects, which the previous section found to significantly influence the judgement of value over Property A. It is in this sense that the entire valuation structure, while coherent, could be ultimately arbitrary in the manner suggested by Ariely et al. (2003). A final way to examine this data, and provide further evidence of arbitrary coherence is to consider the evolution of estimates across all four judgements. In other words, do participants whose anchor is above the 17 P.J. Scott and C.M. Lizieri median tend to estimate above the median in each of their judgements in the estimation phase? Starting with the anchor it is possible to produce a decision tree showing this evolution. At each node (ie. each new estimation) participants‟ estimates can either be above or below the median. A participant whose estimates were always below the median would have a route through the decision tree of H1-H1-H1-H1-H1. One who was in the first half for the first three, then switched to being above the median, before returning to being below the median for the final estimation would have the following route: H1-H1-H1-H2-H1. The paths of all 139 participants through the decision tree are reported in Figure 4. For clarity this shows that 7 participants (out of 139) were in H1 for all four estimations and the anchor, in other words these 7 individuals consistently estimated below the median. At the opposite end of the distribution 11 individuals estimated above the median for all estimates. Fourteen individuals were in H1 for all four estimates having been in H2 for the anchor. [FIGURE 4 HERE] Because the expectation is that the estimation of houses is independent, that is individuals do not use a previous estimate as an anchor for their next estimate, we can say a lot about how the decision tree should look. In particular if we take as a random variable the number of times a participant is in H1, given independence, we would expect this random variable to follow the binomial distribution with p=0.5 and n=5. Using the binomial distribution we can extrapolate how many of the participants should be in each category of the random variable. Comparing this to what is actually seen will demonstrate whether there is a tendency for individuals to stay in the same half of the distribution. The results are reported in Table 6. [TABLE 6] The distribution of frequencies of H1s deviates significantly from our expectation. Table 6 shows that 13% of participants remained in the same half of the distribution for all four estimates, far in excess of the 6% Journal of Property Research expected. Forty six percent of participants were in the same half of the distribution for four out of five estimations (anchor included), well above the 31% expected. A chi-squared test of goodness of fit is strongly rejected (χ2 = 32.764, p-value: <0.001). This is compelling evidence of arbitrary coherence. The repeated use of the anchoring heuristic transmits the bias, which was created by the use of the arbitrary number as an anchor point, across multiple valuations. Subjects were able to come up with a coherent valuation structure for all four properties, but in a large sense this structure was arbitrary. 5. Concluding Remarks This paper presents an experiment which examines whether the use of the anchoring heuristic originally proposed by behavioural psychologists in the 1970s (Tversky and Kahneman, 1974) has important effects in consumer value judgements over housing. Furthermore it considers whether this process imparts an arbitrary element to the valuation; an arbitrary element which survives transitions to future estimates resulting in a valuation structure which is coherent, but ultimately arbitrary. This latter process was suggested in a prominent study in the consumer choice literature (Ariely et al., 2003). This is an important area of study primarily because of the importance of housing choices to individual welfare, and the significant costs likely if misperceptions of value are significant and persistent. The majority of existing research which considers valuation biases in property is focused on the behaviour of professionals (Diaz and Hansz, 2007). That which does focus on consumer judgements is typically not incentivised (Northcraft and Neale, 1987; Levy and Frethey-Bentham, 2010). We employ an experimental methodology which is drawn from the consumer choice literature and incorporates a carefully designed incentive structure to offer participants a significant and binary incentive to make accurate choices. As suggested above our methodology also allows us to track the evolution of value estimates across multiple properties to see if initial biases are transmitted to subsequent estimates. This goes beyond any existing behavioural research in property. 19 P.J. Scott and C.M. Lizieri There is significant evidence that subjects‟ valuations of a property are influenced by an arbitrary anchor which is based on their mobile telephone number. An ordinary least squares regression found a significant relationship between the anchor bucket (of which there were eight) and the logarithm of the value estimate, though it must be noted there was a significant amount of noise associated with this data. Subsequent analysis which used as the dependent variable the average estimate of each anchor bucket was even more conclusive. There is significant evidence that the transition to subsequent judgements was also biased resulting in a preference structure that displayed arbitrary coherence. That is, though it appeared to be sensible and coherent, it was ultimately arbitrary because each valuation was based to a significant degree on the one which went immediately before. Forty six percent of the 139 participants remained in the same half of the distribution of estimates for four of the five judgements (including the anchor). This confirms – and extends – the results of Ariely et al. (2003). We believe that the results here apply most particularly to first-time buyers entering the housing market without significant experience, since the student group used represent this group well. Many of the participants in the experiments will, themselves, be entering the housing market for the first time in the coming years. It is important to note that in interpreting these results we are not suggesting that it is possible to influence perceptions of value in housing simply by writing down a random number and showing it to the home buyer. Rather we believe the design of the experiment shows three things: i) that there is a strong tendency to use an anchoring and adjustment mechanism as a rule of thumb to make value judgements in housing scenarios even in the presence of significant incentives for accurate judgement; ii) that it is relatively easy to establish anchors to engage this mechanism; and iii) once they become established in our perceptions, biased anchors exert a lasting influence on our perceptions. We believe the results are of interest to both policy makers and real estate economists interested in the microeconomic dynamics of housing markets. Academics are increasingly adopting a micro-scale perspective to Journal of Property Research uncover more about the true dynamics of housing markets (Hwang and Quigley, 2004; Munro and Smith, 2008). This paper continues in that vein and opens up a new avenue of research by demonstrating that housing choice at an individual level may incorporate significant non-rational aspects. This insight has the potential to re-shape how we think about the way property markets clear to establish value. The findings are likely to be of particular interest to estate agents who have, given the information asymmetry involved in housing choices, significant power to control the information given to home buyers. There would seem to be significant scope to establish anchors in home buyers‟ minds leading them to incorrect perceptions of housing value. These mistakes are likely to be far more costly than any covered in the existing consumer choice literature. It is important to note that we have not attempted to provide evidence to confirm that estate agents actually do use these manipulations in their professional practice. However we believe that where they are able they would clearly be expected use them. Making sales for higher values results in higher commissions notwithstanding arguments surrounding the optimal effort function used to extract the marginal sales commission (on which see, for example, Sappington, 1991; Rutherford, Springer and Yavas, 2005). Nevertheless, confirmation that such practices do occur – likely a contentious finding – is left to future research. Finally the findings are of interest to researchers with a broader interest in consumer behaviour and marketing. Purchasing a house is perhaps the single biggest choice a consumer will make in his lifetime. Yet house purchasing decisions are necessarily made with little market experience. Much of the consumer decision literature considers small-scale purchases, over items such as food and household appliances, which are made regularly. Thus the results reported here extend our knowledge of consumer behaviour in an important direction. As with all research, this study has limitations. Experimental methods are clearly abstracted from reality. This means an obvious criticism is that the results would not be replicated in the field. A large-scale empirical study of many live property searches would clearly take our findings further. 21 P.J. Scott and C.M. Lizieri However we do not believe this invalidates the results reported here. Experimental work is gaining greater acceptance across many parts of economics where it is recognised that is can contribute to our understanding. A particular advantage is that it allows for significantly greater control than empirical work. By controlling the entire information set, the researcher can say with precision that the only variable which was altered was the one desired – in this case the arbitrary anchor. Experimental work here allows us to examine the nature of the valuation process occurring and so lead the way for future, perhaps empirical, research in this important area. Acknowledgements The authors would like to acknowledge the kind assistance of Vincent Rogowtzow and his staff at Hockeys Estate Agents, Cambridge. The research was achieved with the financial assistance of St. John‟s College, Cambridge for which the authors are grateful. Notes on Contributors Peter Scott is a doctoral student in the Department of Land Economy, University of Cambridge. His research interests include choice theory, behavioural economics and their influences on housing economics and property investment. He has presented his work at European and American Real Estate Society Meetings and was jointly awarded the “Best PhD Presentation” prize the ERES meeting in Milan, Italy in 2010. Colin Lizieri is the Grosvenor Professor of Real Estate Finance in the Department of Land Economy at the University of Cambridge where he directs the MPhil in Real Estate Finance. He is also a fellow of Pembroke College. Colin‟s research interests including modelling office markets, financial innovation and global capital flows. Notes 1. In psychology literature, this is widely known as confirmation bias (Nickerson, 1998). 2. Note that the procedure uses the Becker-DeGroot-Marschak procedure (1963) for eliciting willingness-to-pay and ensures that some of the transactions – Journal of Property Research determined randomly – will be carried out, thus ensuring the reality of the situation to participants. 3. We acknowledge that the growing use of the internet and property search websites, including those that report recent sale prices in a particular area, is diminishing the ability of an estate agent to control the information set to potential buyers and thus their ability to manipulate value perception. However, we believe that evidence of perceptual bias in these decisions is still important, especially because there may be significant opportunities for manipulation in the new medium by engaging the same psychological flaws. For example the designers of online search algorithms to return results which bias value perceptions may be even more powerful. This is a potentially fruitful avenue for further research. 4. This explanation lies in the notion of bounded rationality first suggested by Simon (1957). 5. A minority were postgraduate students. 6. Simon (1957) makes the link between individuals with greater cognitive ability and the ability to make more „rational‟ less error-prone decisions. 7. In one experimental treatment there was the possibility of earning a top prize of £100 for the best overall estimate. This did not make a significant difference to the results. References Ariely, D., Loewenstein, G. and Prelec, D. (2003). Coherent Arbitrariness: Stable Demand Curves without Stable Preferences. Quarterly Journal of Economics, 118(1), 73-105. Becker, G., DeGroot, M. and Marschak, J. (1963). An Experimental Study of Some Stochastic Models for Wagers. Behavioral Science, 8(3), 199-202. Calder, B., Phillips, L. and Tybout, A. (1981). The Concept of External Validity. Journal of Consumer Research, 9(3), 240-244. Diaz, J. (1990). How Appraisers Do Their Work: A Test of the Appraisal Process and the Development of a Descriptive Model. Journal of Real Estate Research, 5(1), 1-15. Diaz, J. (1997). An Investigation into the Impact of Previous Expert Value Estimates on Appraisal Judgement. Journal of Real Estate Research, 13(1), 57-66. Diaz, J. and Hansz, J. (2007). Understanding the behavioural paradigm in property research. Pacific Rim Property Research Journal, 13(1), 16-32. 23 P.J. Scott and C.M. Lizieri Diaz, J. and Wolverton, M. (1998). A longitudinal examination of the appraisal smoothing hypothesis. Real Estate Economics, 26(2), 141148. Friedman, D. and Sunder, S. (1994). Experimental Methods: A Primer for Economists. Cambridge: Cambridge University Press. Gallimore, P. (1994). Aspects of Information Processing in Valuation Judgement and Choice. Journal of Property Research, 11(1), 97110. Gallimore, P. (1996). Confirmation Bias in the Valuation Process: A Test for Corroborating Evidence. Journal of Property Research, 13(4), 261-273. Hwang, M. and Quigley, J. (2004). Economic Fundamentals in Local Housing Markets: Evidence from US Metropolitan Regions. Working Paper W03-005, IBER. Kagel, J. and Roth, A. (1995). The Handbook of Experimental Economics. Princeton, NJ: Princeton University Press. Kahneman, D., Knetsch, J. and Thaler, R. (1990). Experimental Tests of the Endowment Effect and the Coase Theorem. Journal of Political Economy, 98(6), 1325-1348. Kahneman, D., Ritov, I. and Schkade, D. (1999). Economic Preferences of Attitude Expressions? An Analysis of Dollar Responses to Public Issues. Journal of Risk and Uncertainty, 19(1), 203-235. Kahneman, D. and Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), 263-297. Levitt, S. and Syverson, C. (2008). Market Distortions When Agents Are Better Informed: The Value of Information in Real Estate Transactions. Review of Economics and Statistics, 90(4), 599-611. Levy, D. and Frethey-Bentham, C. (2010). The effect of context and the level of decision maker training on the perception of a property‟s probable price. Journal of Property Research, 27(3), 247-267. List, J. (2003). Does Market Experience Eliminate Market Anomalies? Quarterly Journal of Economics, 118(1), 41-71. List, J. (2004). Neoclassical Theory versus Prospect Theory: Evidence from the Marketplace. Econometrica, 72(2), 615-625. Munro, M. and Smith, S. (2008). Calculated Affection? Charting the Complex Economy of Home Purchase. Housing Studies, 23(2), 349367. Nickerson, R. (1998). Confirmation Bias: A Ubiquitous Phenomenon in Many Guises. Review of General Psychology, 2(2), 175-220. Northcraft, G. and Neale, M. (1987). Experts, Amateurs, and Real Estate: An Anchoring-and-Adjustment Perspective on Property Pricing Decisions. Organizational Behaviour and Human Decision Processes, 39(1), 84-97. Rutherford, R., Springer, T. and Yavas, A. (2005). Conflicts Between Principals and Agents: Evidence from Residential Brokerage. Journal of Financial Economics, 76(3), 627-665. Sappington, D. (1991). Incentives in Principal-Agent Relationships. Journal of Economic Perspectives, 5(2), 45-66. Scott, P. and Lizieri, C. (2011). Preference Construction and Housing Choice: The Role of the Estate Agent. Unpublished manuscript. Journal of Property Research Shuptrine, F. (1975). On the Validity of using Students as Subjects in Consumer Behavior Investigations. Journal of Business, 48(3), 383390. Simon, H. (1957). Models of Man: Social and Rational. New York, NY: Wiley. Simonson, I. and Drolet, A. (2004). Anchoring Effect on Consumers' Willingness-to-Pay and Willingness-to-Accept. Journal of Consumer Research, 31(3), 681-690. Slovic, P. and Lichtenstein, S. (1983). Preference Reversals: A Broader Perspective." American Economic Review, 73(4), 596-605 Smith, V. (1976). Experimental Economics: Induced Value Theory. American Economic Review, 66(2), 274-279. Smith, V. (1982). Microeconomic systems as an Experimental Science. American Economic Review, 72(4), 923-955. Thaler, R. (1980). Toward a Positive Theory of Consumer Choice. Journal of Economic Behavior and Organization, 1(1), 39-60. Tversky, A. and Kahneman, D. (1974). Judgement under uncertainty: Heuristics and biases. Science, 185(4157), 1124-1131. Tversky, A., Slovic, P. and Kahneman, D. (1990). The Causes of Preference Reversal. American Economic Review, 80(1), 204-217. von Neumann, J. and Morgenstern, O. (1947). Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press. Wilson, T., Houston, C., Etling, K. and Brekke, N. (1996). A new look at anchoring effects: Basic anchoring and its antecedents. Journal of Experimental Psychology: General, 125(4), 387-402. 25 P.J. Scott and C.M. Lizieri Table 1. Ariely et al. (2003) willingness-to-pay under the influence of an arbitrary anchor. Quintile of SSN distribution 1 2 3 4 5 Correlation Cordless trackball $ 8.64 $ 11.82 $ 13.45 $ 21.18 $ 26.18 .415 p = .0015 Cordless keyboard $ 16.09 $ 26.82 $ 29.27 $ 34.55 $ 55.64 .516 p < .0001 Average wine $ 8.64 $ 14.45 $ 12.55 $ 15.45 $ 27.91 .328 p = .014 Rare wine $ 11.73 $ 22.45 $ 18.09 $ 24.55 $ 37.55 .328 p = .0153 Design book $ 12.82 $ 16.18 $ 15.82 $ 19.27 $ 30.00 .319 p = .0172 Belgian chocolates $ 9.55 $ 10.64 $ 12.45 $ 13.27 $ 20.64 .419 p = .0013 Source: Ariely et al. (2003). Table 2: Relationship between the natural logarithm of the value estimate and arbitrary anchor bucket. Intercept, α Anchor 1 – top/ bottom 5% truncated Anchor 2 – errors +/- 60% truncated n Adjusted r2 Significance F Note: * Significant at the 10% level. Estimated Value of House (1) (2) 5.470 5.452 (0.037) (0.039) * 0.014 (0.007) 0.013* (0.008) 99 105 0.025 0.018 0.063 0.088 Journal of Property Research Table 3: Relationship between the average value estimate and arbitrary anchor bucket Intercept, α Anchor 1 – top/ bottom 5% truncated Anchor 2 – errors +/- 60% truncated Average Estimated Value of House (1) (3) 239,218 236,276 (3,398) (2,769) ** 3,730 (672.8) 3,445*** (548.3) n r2 Significance F 8 0.84 0.014 8 0.85 <0.001 Notes: *** Significant at the 1% level. ** Significant at the 5% level. Table 4: Correlation between sequential house price estimates House B A 0.195** (0.021) B C 0.109 (0.202) C 0.397*** (<0.001) D Notes: *** Significant at the 1% level. ** Significant at the 5% level. Table 5: Transitions between estimates of property value. H2 H1 58 42 H2 42 58 (a) H1 H2 H1 51 49 H2 49 51 (b) 27 Property D Property C H1 Property C Property B Property A Property B H1 H2 H1 64 36 H2 36 64 (c) P.J. Scott and C.M. Lizieri Table 6: Distribution of frequency of H1s. Freq. of H1s Expected Observed 0 3 8 1 16 21 2 31 22 3 31 19 4 16 25 5 3 5 100% 100% Notes: The expected percentages are found by the use of the binomial formula: Journal of Property Research Figure 1: Instructions for anchoring experiment. Figure 2: Example of information given to subjects about a property. Figure 3: Mean value judgements listed by anchor bucket. 270 Value Estimate (£000s) 265 260 255 250 245 240 235 1-2 3-4 5-6 Anchor Bucket 29 7-8 P.J. Scott and C.M. Lizieri Figure 4: Decision tree showing the evolution of price estimates from Anchor to House D.