Field experiments on the anchoring of economic valuations.

Alevy, Jonathan E. ; Landry, Craig E. ; List, John A. 等

I. INTRODUCTION

Take the last three digits of your social security number (SSN). Turn those numbers into a dollar value (i.e., if your numbers are 462 then they provide a value of $462). Consider whether you would be willing to pay that dollar amount for a first edition of J.R.R. Tolkien's The Hobbit. Now, how much would you actually pay for a first edition original copy? A stylized result from laboratory experiments in economics and psychology is that the answer to the latter valuation question can be strongly influenced by the dollar amount computed at the start. (1)

Critics of neoclassical theory have argued that the influence of uninformative anchors--such as the transformed SSN--refutes the notion that decision makers' preferences are predefined, consistent, and stable; instead they are constructed during the process of choice (Bettman, Luce, and Payne 1998; Hoeffler and Ariely 1999; Slovic 1995). A natural conclusion one might draw from studies of anchoring is that decisions may be influenced by irrelevant circumstances and optimization principles do not apply.

The laboratory evidence consonant with anchoring effects is considerable. Tversky and Kahneman (1974) make a seminal contribution, implementing a protocol similar to the one described above to examine general knowledge questions. (2) Furnham and Boo (2011) provide a recent review of the literature and identify more than 25 studies that report significant anchoring effects. Substantive areas investigated include general knowledge questions (Epley and Gilovich 2006; Tversky and Kahneman 1974), probability estimates (Wright and Anderson 1989), legal judgments (Englich and Mussweiler 2001), forecasting (Switzer and Sniezek 1991), and valuation and purchasing decisions (Ariely, Loewenstein, and Prelec 2003). Taken together, the results suggest strong effects from anchoring protocols, even in areas where subjects have significant experience.

Yet the importance of anchoring for economic outcomes remains an open question. One reason is that research goals and methods differ across the disciplines of psychology and economics (Croson 2005; Hertwig and Ortmann 2001; Plott 1996). (3) Fumham and Boo (2011) note that drawing generalizable conclusions from the existing anchoring studies is difficult as many involve undergraduate students engaged with topics they are unlikely to encounter in field settings. Their observation is consistent with the criticism of the ecological validity of many studies made by Gerd Gigerenzer and colleauges (Gigerenzer et al. 2008) discussed in our footnote 2. While the results of these studies may help distinguish among competing causal claims about the anchoring process, they are less relevant for understanding the potential for anchors to affect market equilibria. Further, many of the studies lack meaningful incentives and we believe that economists are justifiably circumspect about results that may merely reflect mistakes made by unmotivated subjects. Consistent with this view is the idea that, with appropriate incentives and feedback, anchoring effects should diminish and behavior more closely match predictions from neoclassical models. (4)

Recent attempts to examine the relevance of anchoring for economic outcomes closely follow Ariely, Loewenstein, and Prelec (2003, ALP hereafter) who find statistically and economically significant effects of anchors on willingness-to-pay (WTP) for common consumer goods and on willingness-to-accept (WTA) for unpleasant sounds and tastes. Bergman et al. (2010) and Fudenberg, Levine, and Maniadis (2012, FLM hereafter) replicate the consumer goods portion of the ALP study with mixed results. Bergman et al. (2010) find significant anchoring results consistent with the earlier work, although the magnitude of the effect is smaller. Implementing an auxiliary protocol, they find also that anchoring effects diminish with cognitive ability. FLM (2012) attempt to anchor both WTP and WTA and find no evidence of anchoring in the WTP treatment. With respect to WTA they observe that the ratio of valuations for anchors in the highest versus lowest quintiles are greater than one for all goods that "is not likely if there is no anchoring at all." The magnitude of the effects, however, are generally modest. (5)

Maniadis, Tufano, and List (2014) develop arguments on the importance of replication in experimental economics and reexamine ALP's protocol for anchoring the WTA of novel sounds, finding smaller anchoring effects than originally reported. (6) Tufano (2010) attempts to anchor valuations of the same foul tasting drink used by ALP, without success, and conjectures that differences in the response mode--open-ended in ALP and binary in his own study--may be responsible for the difference in results. Tufano (2010) does find evidence of context-dependent pricing in a subsequent market experiment.

Aside from Tufano's assessment of response mode, reasons for the differences in the impact of the anchoring protocol are not easy to discern. The consumer good studies share numerous characteristics including the response mode and the use of the Becker-DeGroot-Marschak (BDM) protocol for eliciting values (Becker, DeGroot, and Marschak 1964). (7) All are conducted with student subjects. Incentives are real, although muted in the consumer good treatments, as only subsets of participants are randomly selected to actually buy (or sell) a good. As a result of this design choice the bulk of the subject payments are in the form of fixed fees not salient payments. Other minor differences include the use of a computer-generated random number for the uninformative anchor by FLM while in the other studies it is derived from a number personal to each subject. FLM also facilitate the purchase of goods in their WTP treatment with a large subsidy ($93) to the subset of randomly selected participants. ALP's treatments, where the largest effects are observed, were conducted in a classroom setting where it is possible that experimenter demand effects play a larger role (Zizzo 2010).

The consumer good studies have some common limitations with respect to learning about the importance of anchoring in field settings. The extent to which consumers have interest, knowledge, or experience with any particular good is unknown. In addition, the large fixed fees and subsidized purchases detract from the salience of incentives and thus the external validity of the conclusions.

We take steps to overcome these limitations by conducting two complementary field experiments within a well-functioning marketplace: the sportscard market. In contrast to anchoring studies conducted in classroom or laboratory settings, the sportscard marketplace is a natural setting for an examination of preference structures as it provides a rich array of subjects making decisions in a familiar environment. Further, we can identify factors that arise endogenously, such as market experience or a person's role in the marketplace, and impose the remaining controls necessary to implement a clean experiment to explore whether these or other factors foster or attenuate anchoring. While we do not consider the sportscard market particularly worthy of study in its own right, when larger or "more important" markets are not available for experiments with parallel control, manipulating smaller scale markets such as the sportscard market has value in that we can learn about behavioral tendencies in a naturally occurring setting. Previous studies that highlight these benefits have explored diverse topics that include individual choice anomalies (Gneezy, List, and Wu 2006; List 2002, 2004a), market performance (List and Lucking-Reiley 2000, 2002; List and Price 2005), and more general questions about the relationship between results in laboratory and field settings (List 2006). (8)

Of relevance for our anchoring hypotheses is previous work in sportscard markets that suggests that heterogeneity in market experience is associated with differences in cognitive costs for valuation tasks (List and Lucking-Reiley 2000). The link between anchoring and heterogeneous cognitive costs is highlighted by the anchoring and adjustment model proposed by Tversky and Kahneman (1974, 1128), and by more recent work that links insufficient adjustment to the need for cognitive effort (Epley and Gilovich 2006; Bergman et al. 2010; see also Oechssler, Roider, and Schmitz 2009).

In our first field experiment, we make use of an anchoring protocol that closely follows Tversky and Kahneman (1974) and the recent valuation studies of consumer goods. To give anchoring effects their best chance we exogenously vary the type of good, between subjects. The first good is a newly introduced variant into the market--an unopened package of sportscards. Given its recent introduction, no established market price for the good existed at the time of our experiment, but subjects entering the market did expect to buy, sell, and trade goods of this type. The second good--a jar of peanuts--is familiar, but unexpected in the sportscard marketplace, and ordinary consumers would not have expected to value such a good in this setting. Novelty is a crucial element in recent behavioral models that surmise that choices will be more anomalous in situations that present themselves as surprises (see, e.g., Koszegi and Rabin 2008). By examining the valuations of both ordinary consumers and professional sports memorabilia dealers over both goods, we are able to explore whether market experience and market roles are associated with susceptibility to the anchoring protocol.

The data provide some unique insights. First, there is suggestive evidence that anchoring matters in the valuation exercise. For ordinary consumers the anchor influences valuations for the good that they did not expect to value when entering the market (the jar of peanuts), but they were not influenced by the anchor when valuing the good they expected to buy, sell, and trade in the market (the unopened package of sportscards). We find that dealers were not influenced by the anchor for either peanuts or the unopened package of sportscards. Pooling subjects across market roles to investigate market experience, we find that individuals with 1 year or less of market experience are influenced by the uninformative anchor.

Our findings suggest that a segment of the population in a naturally occurring market could be susceptible to irrelevant anchors, a novel result that deserves further study. From a policy perspective, the effects of anchoring have been of interest to practitioners of cost-benefit analysis for decades. In the nonmarket valuation setting, evidence of anchoring effects has become an important heuristic for evaluating the reliability of stated preference methods such as contingent valuation that are used to estimate the value of public goods (e.g., Bateman et al. 2008; Green et al. 1998; Holmes and Kramer 1995). Anchoring in this setting is consistent with the idea that the task of valuing nonmarket resources is hampered by consumers' unfamiliarity with such decision environments and the complexity of the exercise. Empirical results thus provide some guidance into the underlying reasons for the observed anchoring.

While these behaviors should have import for survey-based approaches to elicit nonmarket values, whether, and to what extent, these behavioral tendencies influence market equilibria is largely unknown. Extant theory suggests that factors such as the composition of marginal and inframarginal traders, the trading institution, and other market particulars, might matter for the transference of anchored values to markets. To provide insight on this question, we design a second field experiment that makes use of a stronger anchoring treatment: in a decentralized bargaining market, we vary information concerning previous transaction prices, which serve as the focal source of market uncertainty. We find evidence that the anchor has some influence on early market transactions, but that the effect is transient. Even in those cases where the market is populated entirely by inexperienced consumers, quantities and prices approach the intersection of supply and demand after a few rounds of market play.

Taken together, the results in this article suggest that when constant feedback mechanisms are in place and participants are able to receive signals of value and adjust their behavior accordingly, anchoring does not play a significant role in bilateral market outcomes. In other important instances where feedback is limited, such as isolated auctions, or contingent valuation exercises commonly performed by government agencies, anchoring can have important and measurable effects. Hence, the analyst should be aware of such effects and consider the properties of the situation when executing cost-benefit analysis.

The remainder of this study proceeds as follows. Section II summarizes the experimental design and the empirical results for the initial anchoring field experiment. Section III describes the experimental design and results for the bilateral market field experiment. Section IV concludes.

II. EXPERIMENT DESIGN AND RESULTS: VALUATION EXPERIMENT

Our first field experiment was conducted at various sportscard tradeshows in Chantilly and Richmond, Virginia, United States in 2003-2004, where we set up booths similar to those of professional dealers in the sportscard market. Our subjects include both ordinary consumers (nondealers) and professional sports memorabilia dealers. Nondealer subjects attended the show as consumers and their presence in the marketplace indicates an existing interest in sports memorabilia. The nondealers voluntarily approached the experimenter's booth to take part in the protocol. Dealer subjects were approached at their own booths prior to the opening of the show and invited to participate in the study. Informed consent was obtained from all participants before introducing them to the protocol. In the terminology of Harrison and List (2004), we implemented a framed field experiment.

Table 1 presents the 2x2 design we employed in our first experiment; treatments varied by type of subject (dealer or nondealer) and type of good. The choice of commodities with which to endow our subjects was based on approximate market price ($3-$7) and subjects' likely expectations of trading the commodity in the sportscard market. The chosen price range aligns with the domain of our anchoring protocol ($0-$9.99), derived from the last three digits of the subject's SSN. The "expected" good is an unopened pack of Upper Deck National Football League (NFL) collectible cards, very recently released to the market. Importantly, as it was a recent release, consumers and dealers likely have diffuse priors about the equilibrium price as production figures and demand were unknown. While several dealers could be selling these cards at the sportscard show, they are not as common as baseball cards. As with any unopened pack of collectible cards, the value of the contents are uncertain, as different player's cards have different values. The pack we used had an additional element that emphasized the lottery-like aspect of the unopened deck. These card packs had a small probability (approximately 2%) of containing a special trading card with a swatch of fabric from a player's jersey worn during an actual NFL game. The market value for such cards depends upon the player and year, but in general is not well established at the time of pack release. During our experiment, one subject was able to sell a "jersey card" for $15--approximately three times the value of his own estimate of the original pack's value--to a card dealer. Combining the novelty of the good with this greater value uncertainty, we intended to give the anchoring protocol its best chance to succeed with a common, "expected" market good.

Our "unexpected" good is a large jar of unsalted, shelled peanuts, which was chosen as a common ordinary commodity for which consumers may have an established value. Only the dealers in the market might anticipate trading this good at the sportscard show, however. (9) The recent theoretical exercise of Koszegi and Rabin (2008) that examines mistakes in implementing preferences provides the underpinnings for why such expectations might play an important role in observed behavior. One interpretation of their work is that behavior will be more anomalous in situations that present themselves as surprises.

In implementing the protocol, data were collected by a monitor working one-on-one with each subject. Monitors were graduate research assistants in economics who were familiar with the anchoring literature and understood that we were exploring anchoring but did not know the exact research hypotheses being tested. After providing informed consent, each subject was endowed with one, and only one, of the two goods. The endowed good was rotated systematically based on the time the nondealer approached the table, but we intentionally oversampled consumers receiving peanuts, as pilot data showed that the variances were largest in this case, and our theory suggests that we were more likely to find economically important effects with this good. Upon receiving the good, subjects were told, "This good [This pack of cards/ this jar of peanuts] is yours to keep, but we are going to give you the opportunity to sell it back to us." Subjects were then told that they would be asked two questions about selling the good back to the experimenter, after which a coin flip would determine which response was binding. It was emphasized that they would keep either the good or cash, and that their valuation responses and the random process would determine the outcome.

The anchoring protocol was initiated by asking the subjects to write the last three digits of their SSN on the provided questionnaire (see the Appendix for a copy of the questionnaire.) Experimental monitors were careful to pay no regard to this random number so that subjects could make no reasonable inference about potential monitor signaling of commodity value (Plott and Zeiler 2007). (10) Subjects were then asked the first valuation question: "Would you be willing to sell the good back to us for the price derived from the last three digits of your social security number?" For example, if the last three digits of their SSN were 123, their associated question was: would you accept $1.23 to sell the good back to us? Of course, this offer price was clearly uninformative, having been derived from a number that was known only to the subjects.

In the second valuation task, we elicited WTA compensation for the endowed good using the BDM mechanism (Becker, DeGroot, and Marschak 1964). Our BDM protocol made use of a nylon bag containing 41 paper slips, upon each of which was a price. Prices were distributed uniformly between $0.00 and $10.00 in 25 cent increments, similar to the distribution of random anchors derived from the subject's SSN. These ranges reflect the presumed average value ($3--$7) of our chosen commodities. Subjects were clearly informed of the range and density of the BDM price distribution. It was explained to the subjects that we wanted to know the minimum compensation that they required for parting with the good with which they had been endowed. As we were not interested in testing the incentive properties of the BDM, our protocol included an explanation that the optimal strategy was to offer one's true minimum acceptable level of compensation. (11)

After making their BDM offer, a coin was flipped to determine which choice--the dichotomous choice in response to the anchor value or the BDM response--would be binding. If the dichotomous choice question was selected, subjects who answered "no" kept the good, and those who said "yes" sold the good for the $SSN value rounded up to the nearest quarter of a dollar. If the BDM mechanism was chosen, a bid price was drawn randomly from the bag. If the bid was greater than or equal to the subject's offer, they were paid the bid amount and the good was returned to the experimenter; otherwise they received no monetary payment and kept the good. In all cases, subjects were asked to fill out a short survey before the account was settled. Survey responses are used as control variables in the regressions reported below.

A. Experiment I: Results

Summary statistics for the anchoring experiments are presented in Table 2; 45% of our subjects were sportscard dealers, and 65% of subjects were endowed with the jar of peanuts. The WTA {offer) and random anchor (soc) both varied widely, between $0-$10 and $0.09-$9.99, respectively. About 70% of subjects provided an estimate of the market value of the endowed good in the subsequent survey. Average estimated market price for the NFL cards was $3.21 ($3.59) for the dealers (nondealers), whereas average estimated price for the jar of peanuts was $5.65 and $5.79, respectively. For each commodity and subject type, the range of estimated market price was $1 or $2 to $8 or more. Thus, there is considerable heterogeneity regarding perceived market value. Average experience with the sportscard market {mktyrs) was 15 years; our sample consisted primarily of men.

Before we begin with the results summary, we should note that overall, 19% of subjects provided inconsistent responses to the two valuation queries. The inconsistencies were exhibited by subjects who stated a minimum WTA less (greater) than the anchor price that they had initially refused (accepted). Those exhibiting inconsistencies had less market experience than those who were consistent. (12) Approximately 3% provided a minimum WTA exactly equal to their anchors. The remaining 78% provided consistent responses in which WTA was different from the anchoring value. For completeness, we present the results with and without the inconsistent responders in the sample.

Perusal of the data provides a first result:

RESULT 1. In the aggregate data, anchoring does not affect economic valuations.

Preliminary evidence for this result can be found in Table 3. To begin, we use a simple null hypothesis that the BDM valuation responses (offer) are independent of the random anchor (soc). Following Ariely, Loewenstein, and Prelec (2003), we split the aggregate sample by median SSN. Row 1 in Table 3 contains the pooled data summary. In this case, for the entire sample, those with high SSNs place a sell value of $4.41 on average, whereas those with a low SSN place a sell value of $4.17 on the good. A similar data pattern is observed in the data set that excludes inconsistent subjects: a selling price of $4.40 versus $4.22. While the data tendencies are directionally in accord with the anchoring hypothesis, a Mann-Whitney test reveals that the difference is not statistically significant for either the overall sample (p = .38), or the consistent responders (p = .41), at conventional levels.

To provide an additional test of the null hypothesis, we regress offer on the social security value and the control variables age, education, gender, and income that were gathered via the survey. Model 1 in Table 4 provides empirical estimates for all data and the subset of consistent responders. (13) Evidence of the importance of anchoring for market participants in aggregate would arise from a positive coefficient on soc that is both economically and statistically significant. We find that the unconditional results of no effect, summarized in Table 3, are supported by the regression model. Coefficients are small in magnitude and have p values of .69 and .80 for all and consistent responders. Thus, even after controlling for individual-specific observables, we find that the offer is not influenced by the uninformative anchor in the pooled data.

Clearly, however, data aggregation could be masking important heterogeneities. Upon parsing the data at a finer level, we find our next result:

RESULT 2A. There is weak evidence that ordinary consumers are influenced by the random anchor when valuing the unexpected good.

RESULT 2B. There is no evidence that market professionals are anchored for either good.

Table 3 provides the first evidence to support Result 2. First, examining the data by subject type, our nonparametric tests yield evidence that the anchor has a modest effect on values for nondealers who are consistent responders. Offer prices above the median anchor value are 15% higher than those below and the Mann-Whitney test yields a marginally significant result (p = .10). Inspection at the level of treatments makes clear that the result is driven by the valuation of the jar of peanuts: in this case, we find a significant effect of the SSN among the consistent responders at the p = .06 level; those with anchors above the median reveal a WTA for peanuts that is 25% greater than those below. Yet, as Table 3 indicates, there is little evidence of anchoring for nondealers valuing the sportscard pack or for dealers valuing either good. Summarizing, we find no evidence of anchoring for dealers, but some evidence of anchoring for nondealers. (14)

To explore the role of experience in more detail, we pool the dealer and nondealer data and examine the effect of years of experience in the market. Sample sizes are small at low levels of market experience, so we do not present these findings as a formal result, however, we do observe interesting tendencies in the data that are important for the broader questions raised by the anchoring literature.

We find significant evidence of anchoring in the responses of the 14 subjects who have 1 year or less of experience in the market. Again splitting the aggregate sample around the median SSN, we find that the Mann-Whitney test yields a statistically significant difference (p = .08) for new market participants that is consistent with the existence of anchored responses. Among this group, the mean offer for those above (below) the median SSN is 6.00 (4.49), a difference of $ 1.51, or 33%. Furthermore, removing the single inconsistent individual in this sample, who refused to sell at the SSN price of $9.19 and then offered $0.50 in the BDM, yields WTA 51% greater for those with anchors above the median ($6.64 vs. $4.41; p < .02). However, among subjects with more than 1 year of experience we find no significant effects of the anchoring protocol.

Model 2 in Table 4 provides regression results that inform the findings on market experience. The specification includes indicator variables for the dealer subject pool, the peanut treatment (nuts), and for new market participants (new--indicating subjects with 1 year or less experience in the sportscard markets). Interactions of treatment and experience variables with the social security anchor are also included as well as the demographic controls used in Model 1.

As in the pooled results, the coefficient on soc is not statistically significant supporting the nonparametric tests for the nondealers when valuing the sportscards--the baseline in the regression model. The same results hold for the linear combinations of soc when interacted with treatment indicator variables. (15) The fact that the soc variable in combination with soc x nuts is not significant (p = .51, alt, p = .64, consistent) detracts from the robustness of Result 2A regarding the anchoring of peanut valuations by nondealers.

With regard to market experience, however, the nonparametric results are supported by parametric regression. The soc and soc x new coefficients are jointly significant for both all and consistent respondents. (16) The magnitude of the effect is economically significant. As noted in the discussion of the nonparametric results, the difference across median SSN yields a 33% increase in WTA for those with the high anchor. The relevant coefficients suggest that a 1% change in the anchor yields a 0.536% (0.565) change in WTA for all (consistent) respondents. (17)

The coefficients can be interpreted in the context of the anchoring and adjustment model of Tversky and Kahneman (1974). Their model suggests that people first consider the value of the anchor and then move, although often incompletely, toward what would be their unanchored response. As a coefficient of zero implies complete adjustment, the measured coefficient of 0.536, in the model with all respondents, implies that 1 - .536 = 0.464 is the magnitude of the adjustment toward the true value. (18) While the caveat regarding the small sample remains, the result does suggest that this is an area in which additional research is warranted. In conjunction with results from ALP (2003) who showed that arbitrary initial valuations could demonstrate coherence over time, our findings suggest that the question of whether initial innocuous cues have a durable influence is one that deserves further study. Our second experiment examines this question in the field, in a multilateral bargaining setting.

III. EXPERIMENT DESIGN AND RESULTS: BILATERAL MARKET EXPERIMENT

Whether, and to what extent, the anchoring affects observed above influence the operation of markets is an open issue that undoubtedly depends critically on the market institution. For example, making use of the Walrasian tatonnement mechanism, Becker (1962) proved that several fundamental features of economic analysis, such as correctly sloped supply and demand schedules, may result even when agents are irrational, serving to sufficiently relax the utility-maximizing assumption inherent in economic modeling. Similarly, using zero-intelligence traders, Gode and Sunder (1993) illustrate that the efficiency of the double-auctions institution derives largely from its structure rather than from individual rationality.

In this section, we explore how anchoring in markets affects outcomes in multilateral bargaining contexts. Our market treatments are similar to Chamberlin (1948), as extended to naturally occurring markets by List (2004b) and List and Millimet (2008), of which the design description follows. In our bilateral market sessions, each participant's experience typically followed four steps: (1) consideration of the invitation to participate in an experiment, (2) learning the market rules, (3) actual market participation, and (4) conclusion of the experiment and exit interview.

In Step 1, before the market opened, a monitor approached dealers at the sportscard show and inquired about their interest in participating in an experiment that would take about 45 minutes. As most dealers are accompanied by at least one other employee, it was not difficult to obtain their agreement after it was explained to them that they could earn money during the experiment. Nondealers were recruited from people milling around the marketplace.

Once the prerequisite number of dealers (sellers) and nondealers agreed to participate, monitors thoroughly explained the experiment's rules in Step 2. The experimental instructions were standard, and borrowed from Davis and Holt (1993, 47-55) with the necessary adjustments. Before continuing, a few key aspects of the experimental design should be highlighted. First, all individuals were informed that they would receive a $10 participation payment upon completion of the experiment. In addition, following Smith (1964), to ensure that marketers would engage in a transaction at their reservation prices, we provided a $0.05 commission for each executed trade for both buyers and sellers.

Second, the nondealers were informed that they would be buyers and that the experiment consisted of five periods. In each of the five periods, we used Smith's (1976) induced value mechanism by providing each buyer with a "buyer's card" containing a number--known only to that buyer--representing the maximum price that he or she would be willing to pay for one unit of the commodity. Dealers were informed that they would be sellers in the market and, in each of the five periods, that each would be given a "seller's card" containing three sequential numbers--known only to that seller--representing the minimum price that he or she would be willing to sell up to three units. Importantly, both buyers and sellers were informed that this information was strictly private and that reservation values would change each period. They were also informed about the number of buyers and sellers in the market (explained more fully below) and informed that agents may have different values.

Third, the monitor explained how earnings (beyond the participation and commission payments) would be determined. The difference between the contract price and the maximum reservation price determined the market earnings of buyers; the difference between the contract price and the minimum reservation price determined sellers' earnings. Several examples illustrated the irrationality associated with buying (selling) the commodity above (below) the induced value.

Fourth, the homogeneous commodities used in the experiment were 1982 Topps Ben Oglivie baseball cards, upon which decorative moustaches had been drawn, thereby rendering the cards valueless outside of the experiment. Consequently, the assignment given to buyers was clear: enter the marketplace and purchase the Oglivie "moustache" card for as little as possible. Likewise, the task confronting sellers was equally as clear, and an everyday occurrence: sell the Oglivie "moustache" card for as much as possible. The cards and participating dealers were clearly marked to ensure buyers had no trouble finding the commodity of interest. Finally, buyers and sellers engaged in two 5-minute practice periods to gain experience with the market.

[FIGURE 1 OMITTED]

In Step 3, subjects participated in the bilateral market. Each market session consisted of five market periods, each lasting 5 minutes. After each 5-minute period, a monitor privately gathered the buyers and gave each a new buyer's card; a different monitor privately gave each seller a new seller's card. Note that throughout the market process careful attention was paid to prohibit discussions between sellers (or buyers) that could induce collusive outcomes. Much like the early writers in this area, we wanted to give neoclassical theory its best chance to succeed. Step 4 concluded the experiment, where subjects were paid their earnings in private.

We follow this procedure in each of three treatments. Treatment 1 is the baseline, which includes 12 (4) buyers (sellers). The buyers have unitary demand whereas the sellers have up to three items they can sell. Figure 1 presents buyer- and seller-induced values, which are taken from Davis and Holt (1993, 14-15). In Figure 1, each step represents a distinct induced value that was given to buyers (demand curve) and sellers (supply curve). The extreme point of the intersection of the buyer and supplier rent areas in Figure 1 yields $37 in rents per period, which occurs at the static price/quantity of Price = $13 - $14 and Quantity = 7.

Treatments 2 and 3, which are the novelty of this experiment, augment Treatment 1 by announcing a price that was realized in past experiments. This price is announced to all experimental participants in the following form: "in a previous experiment identical to this one, the first transaction occurred at a price of $X." Previous literature (e.g., Simonson and Drolet 2004) suggests that once the decision to buy (or sell) has been taken, value judgments "are most susceptible to influence by anchors relating to market prices." Indeed, summarizing the results from four experiments, Simonson and Drolet (2004) support this reasoning and highlight the importance of the source of uncertainty as a moderator of susceptibility to anchoring effects. Thus, given that our buyers and sellers have certainly taken the step to be buyers or sellers of their good, anchoring the source of uncertainty is important.

In Treatment 2 only one price realization is announced (either a high or a low price), and this announcement takes place directly before market period 1 commences. When announcing a high (low) price, we use the second step on the aggregate demand (supply) function: $18 ($9), which were each observed as the first transaction price in previous experiments. Owing to symmetry, this price is $4 from the equilibrium price boundary of $14 ($13).

In Treatment 3, we announce a specific high or low price directly before each of the five market periods commences. The high price signal is drawn randomly from integers on the uniform distribution [15, 18]; the low-price signal is drawn randomly from integers on a uniform distribution [9,12]. Together, these treatments allow us to explore both short- and long-run effects of price anchors. Our usage of randomly selected anchors from previous market outcomes is at the heart of the source of uncertainty in these markets. By appropriately choosing plausible realized prices (taken from our previous experiment to avoid deception), we give anchoring its best shot because this announced price might contain important information pertaining to the underlying equilibrium price (indeed, by rewarding the entire source of price variation to anchoring we overestimate the power of anchoring). Alternatively, by following the literature and using the same induced value schedules across all five market periods, our tests represent a demanding one for anchoring.

A. Experiment 2: Results

Table 5 contains summary statistics for the experimental data. We gathered data from three baseline sessions, six "Treatment 2" sessions (three high signal and three low signal), and six "Treatment 3" sessions (three high signal and three low signal). Given that there are 16 unique subjects in each session, our entire design includes data drawn from 240 subjects. Entries in Table 5 provide summary price (quantity) data in the top (bottom) panel. A first insight is that the baseline treatment yields results that suggest the predictive power of supply and demand functionals. This result is in line with previous research, and points to the power of the simple situation of supply and demand curves. (19) Perusal of the data summary for the various treatments yields a first formal comparative static finding:

RESULT 3. Price and quantity realizations in bilateral trading markets are influenced by anchors, but the effect is transient.

A first piece of evidence to support Result 3 is that prices realized for the first market trade are linked to the anchor. While the average price in the high anchor Treatment 2 is $17.70, the average price is only $9.50 in the low anchor Treatment 2. These differences are statistically significant at conventional levels using a Wilcoxon signed rank test. While the average price differences for the low and high anchor Treatment 2 remain in the first few periods, by period 3 the prices have reasonably converged. Any remaining price differences are small in periods 4 and 5 of Treatment 2. These data patterns suggest that the initial anchor does not have important long-run effects on prices.

Treatment 3 data provide a different test in that agents receive a fresh signal at the beginning of each market period. Similar to the Treatment 2 data, in this case we again find that in the early periods the signal (high or low) influences prices. For example, the initial trade is $16.30 ($13.30) in the high (low) treatment, and the first few periods show that prices in the high anchor treatment are above those observed in the low anchor treatment. Yet, the signals lose their power in the latter periods, where we find that little difference in prices exists across the high and low anchor treatments. Interestingly, in a regression model that uses the observed price as the regressand, and the signal, the market period, and the interaction of signal and market period as regressors, we find that in the early periods the signal has a significant influence, but by period 3 the signal no longer has an influence on the market transaction prices. This result suggests that even in the short run, anchors do not have considerable influence for those agents who are experienced with market fundamentals.

Such transient effects are also found when examining quantities traded in the market. In this case, however, there are no observed differences across the high- and low-price signal treatments: in each instance the market is stifled by the anchor in the early periods. This is because of one side of the market holding out for unrealistic prices, because of the random price signal. Yet, this too wanes, as by the fourth period the expected market quantity is realized in all treatments.

IV. CONCLUSIONS

Many of the standard results of welfare economics--such as the interpretation of market surplus measures, the Pareto Efficiency of perfectly competitive market outcomes, and the rationing and allocative functions of market prices--are predicated on the notion of durable and meaningful consumer preferences. An individual demand schedule should reflect maximum WTP for units of a commodity, ceteris paribus. Likewise, producer decisions should be grounded in an understanding of technology and cost that reflects the profit motive. The assumption that primais of preference and technology are well-defined and stable has immense normative significance as the correspondence between observed market behavior and underlying theoretical foundations is at the heart of the application of microeconomic theory to welfare analysis and public policy.

This assumption has been challenged over the past three decades by those who argue that agents construct their preferences during the valuation process. Our study begins by extending the investigation of anchoring--one of the modalities through which preferences may be constructed--to a field environment. The extent to which decisions might be influenced by random signals is a topic that has received less attention in the economics and business literatures (Rothschild 1973; Schoemaker 1990; Sterman 1989), but of course represents one of the most robust findings in experimental psychology. (20) We conduct both a valuation exercise and complementary market experiment to examine the effect of anchoring in a field setting. We view this effort as an initial step in exploring anchoring in a natural trading institution with salient incentives.

We find evidence that anchoring has weak effects in the valuation exercise. For ordinary consumers valuing an unexpected commodity in our field setting, our results suggest that the random anchor does have an influence on expressed values. Conventional levels of statistical significance are only found among consistent responders (those that made a WTA offer consistent with their dichotomous-anchor response), but the magnitude of anchoring (25% greater WTA for those with SSN greater than the median) is economically meaningful (p =.06). The anchor did not have a statistically significant impact on ordinary consumers valuing the good that they could reasonably expect to trade in our market setting. There is no evidence to support anchoring of sportscard dealers' values for either of the examined commodities.

We find suggestive evidence that inexperienced market participants (less than 1-year market experience; n = 14) in the aggregate were affected by the anchoring protocol. Focusing on consistent respondents, WTA offers were 51% greater for those with anchors above the median (p <.02). The small sample size, however, limits the power of this result. Among subjects with more than 1 year of experience, however, we find no significant effects of the anchoring protocol.

The overarching results on individual anchoring are consistent with the theme in List (2003, 2004a), who implements experiments with a similar structure--varying market experience levels and familiarity with goods--to examine exchange anomalies in individual choices that have been attributed to endowment effects. He finds that nonprofessionals exhibit substantial exchange asymmetries, which are significantly reduced among the most experienced market participants. (21) Jointly, these findings along with the work of Plott and Zeiler (2005, 2007) suggest that subjects in novel situations make use of available cues to help inform valuations.

Despite the similarities in protocols and findings, anchoring and endowment effects are distinct theoretically and in their implications for market equilibria. List (2003) examines the inefficiencies that can arise from the reluctance to trade associated with a reference-dependent endowment effect. ALP's (2003) notion of coherent arbitrariness suggests that anchoring effects in markets can be more subtle, as valuations may be affected by an initial anchor but nonetheless appear consistent with demand theory (see also Becker 1962). The findings of Plott and Zeiler (2005, 2007) which suggest that exchange anomalies reflect processes similar to those occurring during an anchoring protocol increases the importance of understanding whether and how anchors may endure in the marketplace.

The results of our bilateral trading field experiment complement the valuation exercise and inform concerns about the enduring effects of anchors. We find that price and quantity realizations are influenced by anchors, but the effect is transient. Price realizations for the first market trade are significantly influenced by the anchor, but price and quantity realizations converge to neoclassical predictions by the third round of trading. Thus, potentially informative anchors appear to have little influence on aggregate market behavior in a bilateral trading experiment in either the short run, when a new signal is offered up before each trading period, or the long run when multiple rounds of trading occur after exposure to an anchor. Overall, our results provide evidence that anchoring effects are not persistent in markets with repeated opportunities to engage in exchange within a common, static trading regime.

In light of concerns about replication and validity (Maniadis, Tufano, and List 2014), it is important to continue to explore anchoring effects in field environments. Complications in the field are many, including identifying appropriate commodities for which subjects could have well-defined preferences that may not be censored by the existence of field substitutes. Collecting information on estimated market value of commodities used in the experiment allows for an examination of potential buyers and non-buyers of the commodities (in comparison with their offers). Breaking the data down along these lines, we find no evidence of anchoring effects for either group. Nonetheless, the role of field substitutes could be explored in greater detail through greater care in estimating individuals' perceived market values (both ex-ante and ex-post valuation and perhaps with different elicitation mechanisms) or seeking out novel goods for which field substitutes are limited or nonexistent; auctions could be used as valuation mechanisms if commodities are limited in quantity and researchers want to measure WTP. In any event, even if ambiguity about market value of endowed commodities is called into question, a primary motivation for moving to the field is to study anchoring in a more realistic environment. Our results offer some initial evidence of anchoring in the field.

Methodologically, our study highlights that using field experiments and/or "special" markets (like those for sportscards) to focus on deep questions that are hard to take on with observational field data, or in markets that are more important per se, represents a useful first attempt in the field to learn about fundamental tenets of human behavior. In this spirit, continued exploration of the extent to which individuals with different levels of market experience are influenced in the valuation of both private and public goods should provide fundamental insight into basic assumptions of microeconomic theory and the functioning of various market structures.

APPENDIX: EXPERIMENT INSTRUCTIONS

EXPERIMENT 1 : ANCHORED VALUATION INSTRUCTIONS

In this experiment we will ask you three questions.

First what are the last three digits of your social security number?

Please write them here--

You have been given good "X" and we will now ask you two questions about selling it. After answering the two questions, we will flip a coin and your answer to one of the questions will be carried out. If the coin turns up heads your answer to the first question is used and you will either keep the good or sell it based on your answer. If the coin turns up tails we will use the second question, and you will either keep the good or sell it depending on your answer to that question.

Question 1.

You have the opportunity to sell "X" back to us for $S.SN, the value of the last three digits of your social security number converted into dollars and cents.

Would you accept SS.SN to sell the good back to us? Yes No

For question 2 you will tell us the price at which you are willing to sell the good. Details of the procedure are on the next page.

Detailed instructions: BDM Individual Choice Elicitation Method

Welcome to Lister's Auctions. You have been given good "X" and have the opportunity to either keep it or sell it back for a price that will be determined in the following way.

I am holding a bag that contains 20 slips numbered 1 through 20. You are welcome to verify this. I am going to ask you to write on the offer sheet a price at which you are willing to sell X. If the number I draw from the bag, lets call it $A, is greater than or equal to the price you have written down you will receive $A and return the good to me. If $A is less than the price you have written on the offer sheet then you keep the good.

With this method of determining the selling price the best thing for you to do is use your true value for the good as the selling price. Let's see why this is true. First consider the case where you offer to sell for less than your true value. Suppose you offer $B, which is less than you really value the good. If the draw of $A is greater than $B but still less than your true value you must sell the good for a price that is less than your value. Your loss is the difference between $A, the price you receive, and your value, which is greater than $A.

Suppose instead that you write on your offer sheet a price greater than your true value. Let's call your offer price $C. If my draw of $A is greater than your true value but less than $C, you keep the good when you would have preferred to sell it and receive $A. The amount of your loss is the difference between your value and $A.

Do you have any questions about the selling process?

Please indicate the price at which you are willing to sell the good:--

EXPERIMENT 2: MARKET INSTRUCTIONS

Thanks for participating! Today, we are going to set up a market in which some of you will be buyers and some of you will be sellers. The good to be traded is the 1982 Topps Ben Oglivie baseball card, which has a moustache drawn on it.

Trading will occur in a sequence of trading rounds. Besides the $10 that you will receive for taking part in the experiment, the prices that you negotiate in each round will determine your earnings. You will be paid all earnings for the session at the end in cash.

The experiment will consist of 7 rounds that each last 5 minutes. The first 2 rounds will be for practice only and will not affect your earnings for the experiment.

Before every round you will receive a card. If you are a seller of the Oglivie card, the 3 numbers on the card represent your 3 "costs" for each of the 3 Oglivies that I give you. Each cost represents the minimum amount for which you can sell each card. This information is strictly private. Your costs may change each round.

Sellers earn money by selling cards at prices that are above their cost. Earnings from the sale of each card are the difference between the sales price and the cost. For example, if a seller has a cost for the first card of $100 and sells their first card for $150, they earn $150- $100 = $50.

If a seller does not sell any of their cards, they earn exactly zero for that round. You will only be allowed to sell at a price equal to or greater than your cost. If you attempt to sell a card at a price that is less than your cost, your trade will be canceled. Let's go through a few examples now.

[go through examples]

Prior to the start of each round, buyers will be provided a buyer's card. The number on the buyer's card is known as their "value." Your value represents the maximum amount for which you can purchase the card. The information contained on the buyer's card is strictly private and a buyer's value may change each round.

Buyers earn money by buying a card at a price below their value. Earnings from the purchase of each card are the difference between the value and the purchase price. For example, if a buyer has a value of $200 and buys a card for $ 120, they earn $200 - $ 120 = $80.

Buyers can buy one card per round. If a buyer does not buy a card in a period, they earn exactly zero that round. You will only be allowed to buy at a price equal to or below your value. If you attempt to purchase a card at a price that is greater than your value, your trade will be canceled. Let's go through a few examples now.

[go through examples]

In addition to earnings from buying (selling) at a price that is less than your value (greater than your cost), we will provide a commission of 5 cents] to both the buyer and seller for each card traded.

Let's summarize. Each trading round will be up to 5 minutes long. During the round, buyers can approach dealers (sellers) to negotiate a potential purchase of one Oglivie card (each buyer can buy up to one card per period and each seller can sell up to 3 cards). There will be 12 buyers and 4 sellers in the experiment.

There are three rules that you must follow during the experiment.

1. You are not allowed to threaten or intimidate other traders.

2. You are not allowed to discuss or disclose your cost or value with any other trader.

3. You are not allowed to discuss post-session side payments with any other trader.

If you violate any of these rules, you will be asked to leave the experiment and will earn nothing for participating.

If you make a trade, you and your trading partner should approach me immediately and inform me of the trade price to confirm that it is a legitimate trade. After I have recorded the trade price I will announce it to the market. Remember that you cannot trade in a way that gives you negative earnings. That means sellers can only trade at a price above their cost and buyers can only trade at a price below their value.

The first two trading rounds will be for practice so you understand the rules. After that, the next five rounds will be for real earnings. Your total earnings for the experiment will be the sum of your earnings from all 5 rounds plus your $10 for participating.

I will now hand out practice trading cards. Remember: you are not allowed to discuss the information on the cards with any other trader. Please take care not to reveal it accidentally to curious traders looking over your shoulder.

[Treatment 2: Read this passage directly after the 2nd practice round and before the real experiment begins--I will let you know what $X should be.]

Before we begin the trading for real earnings, I want to let you know that in a previous experiment identical to this one, the first transaction occurred at a price of $X.

[Treatment 3: Read this passage directly after the 2nd practice round and before the real experiment begins and after each round of the experiment--I will let you know what $X should be.]

Before we begin the trading in this period, I want to let you know that in a previous experiment identical to this one, the first transaction for this period occurred at a price of $X.

ABBREVIATIONS

ALP: Ariely, Loewenstein, and Prelec

BDM: Becker-DeGroot-Marschak

FLM: Fudenberg, Levine, and Maniadis

NFL: National Football League

SSN: Social Security Number

WTA: Willingness-to-Accept

WTP: Willingness-to-Pay

doi: 10.1111/ecin. 12201

Online Early publication February 6, 2015

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JONATHAN E. ALEVY, CRAIG E. LANDRY and JOHN A. LIST

Alevy: Associate Professor, Department of Economics and Public Policy, University of Alaska Anchorage, Anchorage, AK 99508. Phone (907) 786-1763, Fax (907) 786-4115, E-mailjalevy@uaa.alaska.edu

Landry: Associate Professor, Department of Agricultural and Applied Economics, University of Georgia, Athens, GA 30602. Phone (706) 542-0747, Fax (706) 542-0739, E-mail clandry@uga.edu

List: Chairman, and Homer J. Livingston Professor of Economics, Department of Economics, University of Chicago, Chicago, IL 60637. Phone (773) 702-8176, Fax (773) 702-8490, E-mailjlist@uchicago.edu

(1.) For those interested Tolkien fans, only 1,500 copies of the first edition were printed. An Arizona buyer recently purchased a first edition copy for $65,000 from a New York bookseller. See http://www.abebooks.com/docs/10anniversary/powers-lO.shtml.

(2.) Along with their anchoring results, Tversky and Kahneman (1974) report findings on the representativeness and availability heuristics and on overconfidence that are seminal for the large literature on heuristics and biases (see, e.g., Gilovich, Griffin, and Kahneman 2002; Kahneman 2003). Gigerenzer (1991, 1996) and coauthors (Gigerenzer et al. 2008) articulate both general and specific criticisms of the heuristics and biases literature. A general criticism derives from the notion that "cognitive functions are adaptations to a given environment" (Gigerenzer 1991) and research in the heuristics and biases literature often lacks connection to the relevant environment. The framed field experiments that we conduct contribute to addressing this concern in the anchoring literature. Specific criticisms of the heuristics and biases program focus concretely on base rate neglect, the conjunction fallacy, overconfidence, and availability, i.e., on the presentation and interpretation of probabilities, and are less relevant for anchoring (Gigerenzer et al. 2008). Responses to the "Gigerenzer critique" include Jones, Jones, and Frisch (1995), Kahneman and Tversky (1996), and Polonioli (2012). Samuels, Stich, and Bishop (2002) assess the disagreement and argue that the core claims in each literature are compatible.

(3.) Plott (1996) characterizes the core differences as follows: "For the most part economists have not been interested in what goes on inside the head of individuals. Thought or thought processes are seldom considered as part of the phenomena to be studied as a part of the science. Economics is primarily a study of choice behaviors and their properties as they become manifest in the context of specific organizational units. By contrast, psychological focus on the individual is derived from a long history of research on the nature of thought and thought processes" (225). Nonetheless, he notes that "Economists have a need to look ... deeper into the decision process" (Plott 1996, 227). See also Caplin and Schotter (2008) for a more recent exploration of these issues.

(4.) The potential for convergence to neoclassical stability is more consistent with the notion of discovered preferences elaborated by Plott (1996) than the literature cited previously on constructed preferences.

(5.) The elicited values are reported by anchor quintile in each of the consumer good studies. For ALP, the ratio of values in high and low quintiles varied between 2.16 and 3.45 for the five consumer goods (calculated mean = 2.90 based on ALP, Table 1). For Bergman et al. (2010) the values range from 1.19 to 2.68 with a mean value of 1.75 for the six goods reported by the authors. FLM report WTP values from 0.65 to 1.48 (calculated mean = 0.94 based on FLM, Table 1), and WTA values from 1.09 to 3.12 (calculated mean = 1.55 based on FLM, Table 3). The anchoring effects for ALP (2003) and Bergman et al. (2010) are statistically significant, whereas for FLM (2012) one of five goods in the WTA treatment exhibits significant anchoring effects; none in their WTP treatment are statistically significant.

(6.) The interested reader should also see Simonsohn, Simmons, and Nelson (2014).

(7.) FLM (2012) implement treatments with and with out explanations of the BDM protocol and find very similar results.

(8.) The contributions made by previous studies in the sportscard market make clear that experimental work in laboratory and field settings can be useful complements. List (2002), for example, examines preference reversals due to evaluation mode effects that had previously been observed in hypothetical choice settings and finds them robust for sportscard consumers but not professional dealers. Laboratory studies can also usefully explore the robustness of field results. Several laboratory studies have reexamined Gneezy, List, and Wu's (2006) findings on the uncertainty effect finding both support for the effect (Newman and Mochon 2012; Simonsohn 2009) and sensitivity of the results to changes in instructions (Keren and Willemsen 2009), and the presentation of goods (Rydval, Ortmann, and Prokosheva 2009). Andreoni and Sprenger (2012) also find indirect support for the uncertainty effect.

(9.) We note that dealers entering the market likely expect to be offered a trade with just about anything in this market. For instance, one of the coauthors was once offered a pair of "personally worn" Marilyn Monroe panty hose in trade for a Ken Griffey Jr. rookie card. He politely declined.

(10.) Further mitigating potential experimenter demand effects is the fact that the monitors learned about the subject's SSN only after the subject was endowed with the good. Variations in the protocol at the moment of endowment were shown by Plott and Zeiler (2007) to provide important valuation cues that led to exchange asymmetries. In our setting these cues would need to be tailored to specific anchors that was not possible given the sequencing of the protocol.

(11.) A deviation from this strategy is possible if market prices are well known and transaction costs are low. In this case it is possible that a seller of the good could be better off stating a value that is the sum of market price and transaction costs and either reselling the good in the market or purchasing it elsewhere with the cash received. However, we believe neither of these conditions are met in our study. For the sportscards, several dealers did sell this pack of cards, however the sum of transaction costs associated with search, negotiation, and the dealer bid-ask spread are considerable. In addition there is value uncertainty associated with the new product. The strategy would be even more difficult for the peanuts for which there is little resale value at the sportscard show.

(12.) A Mann-Whitney test of differences in market experience, measured in market years, across groups of consistent and inconsistent responders yielded p = .08. Further, roughly three-fourths of the inconsistent responders made offers to sell at a price greater than their SSN when they had previously agreed to sell at that price. The attempt to sell at a price higher than the anchor value suggests that the inconsistent subjects misunderstood the properties of the BDM mechanism, and may have believed they were in a bargaining situation.

(13.) In our regressions, we exclude two influential observations from both nondealer models. These individuals refuse to sell at anchor values greater than $9.00 but then make offers of 50 cents or less in the BDM, indicating confusion or inattention. Standard errors are calculated using the White sandwich estimator (White 1980) as the Breusch-Pagan test detects heteroscedasticity (Breusch and Pagan 1979).

(14.) Following a reviewer's suggestion, we explore an auxiliary hypothesis that there may be differential anchoring effects for those in and out of the market. Splitting the data into "potential buyers"--those that state a BDM value greater than or equal to their estimate of market value--and "nonbuyers"--those that state a BDM value less than their estimate of market value--we find no evidence of anchoring for either of these groups (though our sample sizes are somewhat small given item nonresponse to the market value question on the survey instrument). We do find a high and statistically significant correlation between subject's offer and market price estimate (ranging from 0.60 to 0.72), but this is not surprising given that the market price estimates were queried after the valuation exercise and the existing evidence suggesting that people's predictions about other's preferences are egocentric, inducing positively correlation with one's own preferences (Lusk and Norwood 2009; Van Boven, Loewenstein, and Dunning 2005).

(15.) Consistent with the fact that dealer valuations are somewhat higher for those with SSN below the median, there is what appears to be a negative anchoring effect associated with the soc + soc x dealer coefficient. Given the one-sided nature of our hypothesis we believe that this is an artifact and do not believe we have discovered a new phenomenon of economic significance. The positive coefficient on soc x dealer x nuts restricts this artifact to the dealers in the sportscard treatment.

(16.) For all (consistent) respondents the joint significance of soc and new yields p = .035 (p = .035).

(17.) The decision to specify the experience variable as dichotomous was influenced by the unconditional results, however, robustness tests were also conducted. We estimated regression models that employed the continuous variable "mktyrs" and alternative categorical specifications of experience interacted with the SSN anchor to provide for a deeper exploration of the role of market experience. We find significant anchoring with models that consider those with 4 years or less the "new" group, however, this result is an artifact of the strong anchoring effect among those reporting 1 year or less of market experience. Taken as a whole, our results suggest that there is not a continuous response to experience, and that only those with 1 year or less have a distinct inexperience effect that is important for anchoring.

(18.) The insignificant coefficients for the other treatments imply complete adjustment from the anchored value.

(19.) We also gathered data in a treatment that used an anchor of $13.50, the midpoint of the equilibrium prediction of the supply and demand curve intersection. These data did not significantly differ from the baseline treatment data, suggesting that this market can yield efficient outcomes with or without anchors present.

(20.) One should take care not to jump too quickly to inference concerning underlying preferences from these experiments. In many cases, important properties of the situation change across exercises, and changes in these properties themselves might induce agents to behave differently (see Levitt and List 2007).

(21.) Plott and Zeiler (2005, 2007) examine the underlying reasons for exchange asymmetries in a laboratory setting and argue that experimental procedures and subject misconceptions underlie behaviors typically attributed to reference-dependent preferences. Their results suggest that "signals built into the experimenter's actions and language choice ... in combination with the possibility of asymmetric information about the relative value of the goods might influence choices" (Plott and Zeiler 2007). In this context, the anchoring literature can be understood as stressing the findings on exchange asymmetry by introducing a clearly uninformative element into the experimenter's "actions and language choice." Isoni, Loomes, and Sugden (2011) extend Plott and Zeiler's work and highlight the importance of experience effects associated with the paid practice component of the exchange asymmetry protocol.

TABLE 1
Anchoring--Experimental Design and Sample Size

                Nondealers      Dealers     Row Totals

Sportscards     Treatment 1   Treatment 2
                  n = 34        n = 32        n =66
Peanuts         Treatment 3   Treatment 4
                  n = 75        n = 46       n = 121
Column totals     n = 109       n = 78       N = 187

TABLE 2
Anchoring--Descriptive Subject Pool Characteristics

Variable                       Sportscards

                  Nondealers                  Dealers

           Mean    SD    Min    Max    Mean    SD    Min    Max

Offer      3.47   1.56    0     6.00   3.80   2.04   0.50    10
Soc        4.73   2.92   0.09   9.50   5.05   2.94   0.26   9.99
Sell       0.62   0.49    0      1     0.72   0.46    0      1
Education  3.85   1.46    2      6     4.09   1.61    2      6
Age        35.97  12.17   18     70    49.19  13.30   19     74
Gender     0.15   0.36    0      1     0.09   00.30   0      1
Income     59.39  32.37  5.00  125.00  66.98  41.85  5.00  125.00
Mktyrs     13.06  7.89    0      35    19.23  15.83   1      68

                               Peanuts

                  Nondealers                  Dealers

Variable   Mean    SD    Min    Max    Mean    SD    Min    Max

Offer      4.18   2.11    0      10    5.43   2.32   1.5     10
Soc        4.62   2.63   0.23   9.47   5.03   3.20   .35    9.99
Sell       0.63   0.49    0      1     0.59   0.50    0      1
Education  4.03   1.61    2      6     4.00   1.72    0      6
Age        41.20  14.13   19     70    46.33  13.92   19     68
Gender     0.13   0.34    0            10.09  0.29    0      1
Income     56.41  35.07  5.00  125.00  62.56  36.44  5.00  125.00
Mktyrs     14.24  10.07   0      50    16.9   11.3    1      50

Notes: The variables offer and soc are in dollars. Sell indicates
the response (1 = yes, 0 = no) to the dichotomous choice question
on willingness to sell at the soc value. Education is categorical
with attainment ranging from incomplete grammar school to completed
graduate education. Gender is defined as 1 = female, 0 = male.
Mktyrs represents years of activity in the sportscard market.
Income is in thousands of dollars.

TABLE 3
Evidence of Anchoring

                                           All Respondents

Population                      Median   Mean    Mean            p
                                Split     SSN    Offer    N    Value

Pooled                           High    7.25    4.41    94     .38
                                 Low     2.35    4.17    93
Cards                            High    7.30    3.43    33     .19
                                 Low     2.47    3.83    33
Nuts                             High    7.22    4.91    61     .12
                                 Low     2.28    4.39    60
Nondealers                       High    6.93    4.11    55     .44
                                 Low     2.33    3.80    54
Dealers                          High    7.70    4.74    39    1.00
                                 Low     2.38    4.78    39
Treatment 1: nondealers/cards    High    7.19    3.38    17     .88
                                 Low     2.26    3.54    17
Treatment 2: dealers/cards       High    7.42    3.62    16     .33
                                 Low     2.69    3.97    16
Treatment 3: nondealers/nuts     High    6.81    4.43    38     .31
                                 Low     2.36    3.91    37
Treatment 4: dealers/nuts        High    7.85    5.36    23     .87
                                 Low     2.20    5.50    23

                                   Consistent Respondents

Population                      Mean    Mean            p
                                 SSN    Offer    N    Value

Pooled                          7.47    4.40    75     .41
                                2.52    4.22    75
Cards                           7.51    3.56    29     .40
                                2.50    3.80    28
Nuts                            7.36    5.00    48     .07
                                2.53    4.33    47
Nondealers                      7.03    4.34    46     .10
                                2.40    3.70    45
Dealers                         7.97    4.23    31     .11
                                2.71    5.20    30
Treatment 1: nondealers/cards   7.22    3.53    15     .84
                                2.14    3.54    14
Treatment 2: dealers/cards      7.81    3.59    14     .23
                                2.85    4.06    14
Treatment 3: nondealers/nuts    6.94    4.73    31     .06
                                2.51    3.77    31
Treatment 4: dealers/nuts       8.07    4.99    17     .19
                                2.62    5.94    16

Notes: The Mann-Whitney test was used to test the null hypothesis
that the distribution of offers did not differ above and below the
median SSN anchor. The test was conducted on the entire sample and
subpopulations by treatments and factors, as well as a subset that
was consistent in their responses to the valuation questions. Among
the consistent responders we find support for the anchoring
hypothesis among those who valued peanuts, particularly among
nondealers.

TABLE 4
Evidence of Anchoring--GLS Estimates

Dependent
Variable                Model 1                    Model 2

Offer               All        Consistent       All        Consistent

Soc               0.022         0.016         0.109         0.118
                 (0.055)       (0.062)       (0.110)       (0.118)
New                                          -0.442        -0.513
                                             (1.274)       (1.420)
Soc x New                                     0.427 *       0.448 *
                               (0.239)       (0.252)
Dealer                                        1.135 *       1.470 **
                                             (0.596)       (0.711)
Soc X Dealer                                 -0.350 ***    -0.394 ***
                                             (0.131)       (0.144)
Nuts                                          0.544         0.637
                                             (0.605)       (0.689)
Soc x Nuts                                   -0.051        -0.072
                                             (0.126)       (0.137)
Soc x Dealer x                                0.276 **      0.294 **
Nuts
                                             (0.120)       (0.129)
Education         0.156         0.188         0.208 **      0.269 **
                 (0.108)       (0.130)       (0.104)       (0.125)
Age               0.031 ***     0.030 **      0.035 ***     0.034 **
                 (0.011)       (0.013)       (0.011)       (0.013)
Gender            0.161         0.197         0.376         0.464
                 (0.471)       (0.531)       (0.463)       (0.524)
Income           -0.137        -0.194 *      -0.151 *      -0.216 **
                 (0.088)       (0.101)       (0.085)       (0.098)
Constant          2.878 ***     3.081 ***     1.584 *       1.613 *
                 (0.802)       (0.890)       (0.925)       (1.030)
N                   172           143           172           143
[R.sup.2]         0.060         0.063         0.184         0.199
F                 2.11          1.95          2.98          2.69
Prob > F          0.067         0.047         0.001         0.003

Notes: Standard errors are in parentheses beneath the coefficients
and are calculated using the Hulbert-White estimator. The dependent
variable offer is the willingness-to-accept elicited from the BDM
protocol. Soc is the anchor value derived from the subject's SSN.
New is 1 if market experience is less than or equal to 1 year and
zero otherwise. Model 1 includes control variables for individual
characteristics and Model 2 adds treatment indicators and interactions.
The interaction soc X new provides evidence of the effectiveness of the
anchoring protocol on those with the least market experience.

* p < .10; ** p < .05; *** p<.01.

TABLE 5
Bilateral Trade Experiment

                                      Treatment 2     Treatment 3

                           Baseline   High     Low    High     Low

Prices
First trade price            13.7     17.7     9.5    16.3    13.3
                            (4.0)     (0.6)   (0.7)   (1.5)   (4.2)
First period avg. price      13.5     17.1    10.0    15.9    11.7
                            (2.0)     (0.7)   (1.2)   (1.2)   (2.7)
Second period avg.           14.0     15.9    11.1    14.5    12.0
  price                     (1.7)     (1.4)   (1.7)   (1.5)   (2.5)
Third period avg.            13.7     14.4    13.4    14.0    13.2
  price                     (1.9)     (1.8)   (2.1)   (1.4)   (2.4)
Fourth period avg.           13.8     14.1    14.1    13.9    13.3
  price                     (1.5)     (1.4)   (1.7)   (0.9)   (1.9)
Fifth period avg. price      13.1     13.8    13.5    13.5    13.6
                             (13)     (1.3)   (1.1)   (1.1)   (1.2)
Quantities First period      7.3       2.3     1.7     3.3     3.0
  avg. quantity             (0.6)     (1.2)   (1.5)   (2.5)   (2.0)
Second period avg.           8.0       4.3     3.7     5.0     4.3
  quantity                   (10)     (1.2)   (1.5)   (2.6)   (1.5)
Third period avg.            7.0       6.7     5.3     6.0     6.0
  quantity                  (0.0)     (0.6)   (1.5)   (1.7)   (1.0)
Fourth period avg.           8.0       7.3     7.0     7.7     6.7
  quantity                  (1.0)     (0.6)   (1.0)   (1.5)   (1.5)
Fifth period avg.            7.3       6.7     7.3     7.3     7.0
  quantity                  (0.6)     (0.6)   (0.6)   (0.6)   (1.0)

Notes: First trade price is the first executed transaction
in the session. For the baseline this price is the average
over the three sessions; for Treatments 2 and 3 this price
is the average over the five sessions. The other figures
represent the average of the session averages in each of the
given periods. High and Low represent the high and low
signal treatments. Standard deviations are in parentheses
underneath the means.