Cash inflows and bubbles in asset markets with constant fundamental values.

Noussair, Charles N. ; Tucker, Steven

Previous experimental research on asset markets has reported that the level of cash available to traders does not affect asset prices when fundamentals follow a time trajectory that is constant over time. This contrasts with other research indicating that greater cash levels increase prices when fundamental values are decreasing over time. We report a new experiment in which we show that greater initial cash levels are indeed associated with higher prices when fundamental values are constant over time. Thus, high cash levels will lead to bubbles, if the cash is introduced before the market opens. Our results reconcile the two previous sets of findings. (JEL C90, D03, G02, G12)

I. INTRODUCTION

Smith, Suchanek, and Williams (1988) initiated the experimental study of markets for multiperiod, finitely lived assets. A considerable subsequent literature has consistently observed price bubbles in such markets. This consistency makes the Smith et al. paradigm a popular one for identifying and studying the factors that promote or dampen bubbles (see Palan 2013, for a survey of this literature). It is known that some key market parameters influence prices and the tendency for bubbles to form. Two of these parameters are (1) the time trajectory of fundamental values, and (2) the quantity of cash available for purchases compared to the quantity of assets available for sale.

A number of studies in this literature have contrasted the behavior of different fundamental value time paths. The speed and effectiveness of price discovery, the tendency of market prices to track fundamentals, depend on the time path of the fundamental value trajectory (Breaban and Noussair 2015; Giusti, Jiang, and Xu 2012; Noussair and Powell 2010; Stockl, Huber, and Kirchler 2014). A trajectory that is constant over time generates closer adherence to fundamental values than a time path that is monotonically decreasing (Kirchler, Huber, and Stockl 2012; Noussair, Robin, and Ruffieux 2001; Smith, Van Boening, and Wellford 2000). (1)

Another variable influencing market prices is the amount of liquidity traders have available for purchases. It is well established that in the case of decreasing fundamentals, the price level is affected by liquidity, as measured by cash endowment levels. Greater cash endowments lead to higher prices (Caginalp and Ilieva 2008; Caginalp, Porter, and Smith 1998, 2000, 2001; Haruvy and Noussair 2006). Cash and asset endowment levels are typically normalized into a measure of liquidity called the cash-to-asset (C/A) ratio (Caginalp, Porter, and Smith 2001). This is the ratio of cash in the economy, the total amount available for purchases of assets, to the value of all of the units of asset in the economy, evaluated at the fundamental value. In period t, the C/A ratio is given by

[(C/A).sub.t] = [summation over (i)][c.sub.it]/[summation over (i)][q.sub.it][f.sub.t]

where [(C/A).sub.t] is the C/A ratio in period t, [c.sub.it] is the cash available to trader i in period t, [q.sub.it] is the quantity of units that trader i holds in period t, and [f.sub.t] is the period t fundamental value. The ratio can be interpreted as the ratio of the largest long position to the largest short position an average trader can take, assuming that the market price is equal to the fundamental.

To date, it has been shown that the cash asset ratio affects prices only for the case when fundamental values are decreasing. To our knowledge, only two studies have explored the effect of cash on prices when fundamentals are constant over time (Kirchler, Huber, and Stockl 2012, hereafter KHS, and Kirchler et al. 2015). In both of these studies, the additional cash is introduced after one or more periods of trading have elapsed, rather than before the market opens. KHS report that increases in cash endowments do not affect prices in the case of constant fundamental values. Because the authors interpret bubbles as a consequence of subject confusion about the experimental environment, they conclude that the constant fundamental value setting leads to less confusion on the part of subjects. Kirchler et al. (2015), in a paper mainly focused on the consequences of the entry and exit of traders, include two treatments without entry and exit and a constant fundamental value trajectory. The two treatments differ only in the time profile of cash endowments. In one treatment, the level is constant, and in the other it increases over time from the same initial level as in the first treatment. They observe pricing close to fundamentals in both treatments. The result that cash levels do not affect prices is surprising at first glance because it is not evident why traders' stock of cash would increase prices when fundamentals are decreasing, but not when they are constant.

In the two treatments of KHS relevant for the issues considered here, the fundamental value is constant for the entire life of the asset so that [f.sub.t] = [f.sub.0] for all t. In the treatment they call T4, the C/A ratio also remains constant throughout the life of the asset at a value equal to one, identically to the series labeled LowConstant in Figure 1. In this figure, the horizontal axis indicates the period number t. The vertical axis is the C/A ratio prevailing in the current period. In the treatment KHS call T2, the C/A ratio is equal to 1 in period 1, but is increased throughout the life of the asset with cash infusions disbursed to each trader in each period. The resulting time profile of the C/A ratio is illustrated in Figure 1, in the series labeled Increasing. The cash infusions are relatively small in the early periods, and increase monotonically over the life of the asset. By the end of the life of the asset, the C/A ratio equals 19. (2) KHS find that prices track fundamental values closely in both the T4 and T2 treatments.

This result seems to suggest that market prices for long-lived assets with constant fundamental values readily track their fundamentals, regardless of the cash that traders have at their disposal to make purchases. In this article, in contrast, we show that prices do not necessarily adhere to fundamental values under a constant fundamental value trajectory, and that bubbles and crashes are common even in such a setting if the initial quantity of cash available for purchases is sufficiently high. We also show that, just as in the case of declining fundamentals, increasing the initial cash available to traders by a sufficient amount does increase prices and generate bubbles even when fundamental values are constant, provided that the cash is introduced prior to the market open.

We demonstrate these points with a new experiment consisting of three treatments. Two of the treatments, LowConstant and Increasing, replicate the T4 and T2 conditions of KHS. We obtain results that are nearly identical to theirs. Prices adhere very closely to fundamental values throughout the life of the asset. However, in our third treatment, HighConstant, where we impose a constant C/A ratio of 20 for the entire life of the asset, we consistently observe price bubbles.

This suggests that the reason that bubbles are not observed in cases where the C/A ratio increases gradually via increasing infusions of cash, such as in the Increasing treatment, is that the injections of cash occur too late in the life of the asset to allow bubbles to form. To illustrate this, we can think of the C/A ratio as the ratio of the largest long position to the largest short position an individual can take at a price equal to the fundamental value. Because short selling is not permitted, the maximum short position one can take is to sell all of one's units. This results in revenue for the seller exactly equal to one multiple of the C/A ratio. The maximum long position one can take is to spend all of one's cash on units of asset. Suppose, for example, we have a market with homogeneous endowments and a C/A ratio of 1. This allows an individual to double the number of shares he holds at the fundamental value. At a C/A ratio of k, a bullish individual can purchase assets to acquire a maximum inventory of k + 1 times her initial endowment. Thus, it takes only one bullish trader making purchases, offsetting the selling of k bearish traders, to maintain a price equal to fundamentals. Similar arguments apply on an average basis for markets with heterogeneous endowments of units and cash. The implication is that in a market with a high C/A ratio, bullish traders constituting a small fraction of participants can launch a bubble as the available supply from other traders is bought up. On average, in a market with lower C/A ratios, a greater percentage of bullish traders are required to cause a bubble to form.

[FIGURE 1 OMITTED]

This bullishness may stem from a number of sources, but two appear most plausible, and have the most support in prior experimental work. One of these is a speculative motive, the belief in the possibility of selling at a higher price in the future. Because the life of the asset is finite, and the asset has a fixed buyout value at the end of its life, a speculator presumably expects prices to equal fundamentals at the end of the final period of trading. Thus, in order to entice him to buy for speculative purposes, there must be enough time remaining to allow a high likelihood of selling to another trader at a sufficiently high price to realize a profit. At the end of the life of the asset, it is redeemed for its intrinsic value. Thus, as the end of the life of the asset approaches, such speculation becomes more risky and speculative demand declines. Another possible source of bullishness is confusion (Kirchler, Huber, and Stockl 2012; Lei, Noussair, and Plott 2001; Lei and Vesely 2009) about the experimental environment. The greater the available cash, the looser the constraints are on the highest purchase prices that confused traders can offer or accept. In Section IV, we argue, using independent measures of cognitive ability, that the incidence of confusion is likely to be very similar in all treatments. This indicates that it is the relaxation of constraints on bullish traders (confused or otherwise) making purchases that drives up prices in high cash settings. The only difference between the LowConstant treatment, where bubbles do not occur, and the HighConstant treatment, where bubbles consistently occur, is the timing of the infusion of cash. We conjecture that an increase in price did not occur in the LowConstant treatment, and similarly in T2 of KHS, because the large increases in cash occurred too late to enable the bullish traders to exhaust the available supply at the fundamental value for the cash to drive prices up beyond that level. Therefore, both the timing and the size of the cash infusion appear to be critical influences on whether, and the extent to which, the infusion increases price level. When the initial cash available for purchases is sufficiently high, prices exceed fundamental values.

The rest of the article is structured as follows. Section II describes the experimental design and procedures. Section III presents the results and Section IV the conclusions.

II. THE EXPERIMENT

The experiment consisted of 20 sessions that were conducted in November 2011 at the University of Canterbury in Christchurch, New Zealand and October 2014 at the University of Waikato in Hamilton, New Zealand. A total of 142 subjects participated in the experiment. They were recruited from undergraduate courses across the university using ORSEE (Greiner 2004). Some of the subjects had participated in previous experiments, but all were inexperienced with asset markets and only participated in a single session of this study. The experiments were computerized and programmed with the z-Tree software package (Fischbacher 2007). The experimental currency used in the markets was Taler, which was converted to New Zealand dollars at the end of the experiment at a predetermined, publicly known, conversion rate. (3) Each session lasted approximately 1 hour, including an instructional period and the payment of subjects. Subjects earned on average $20NZ. (4)

In each session, either 8 or 10 subjects traded assets in a market over a sequence of 10 trading periods. (5) In all treatments, each unit of the asset paid an uncertain dividend at the end of each trading period as well as a final terminal payment at the end of the 10th period. Fundamental values followed a constant time trajectory. The dividends in each period were drawn independently from a two-point dividend distribution of either -5 or 5, with each value occurring with equal probability. (6) Therefore, the expected value of the dividend payment in any period was equal to zero. The asset had a terminal value of 50 Taler. Thus, the fundamental value in any period was 50 Taler. Subjects were endowed with Taler and assets at the beginning of each session.

Table 1 presents an overview of the treatments. In all treatments, we employed the procedures of KHS, including the use of their z-Tree program, instructions, and questionnaires. (7) The treatments differed from each other only in the time profile of the C/A ratio. Treatments LowConstant and Increasing were identical to the T4 and T2 treatments of KHS, respectively. In the LowConstant treatment, half of the subjects were endowed with 20 units of asset and 3,000 Taler, and the other half were endowed with 60 units of asset and 1,000 Taler. Since the initial fundamental value of the asset was 50 Taler, the expected value of each subject's endowment was 4,000 Taler. The total endowment of cash of all traders equaled the total expected value of the assets of 20,000 Taler, and thus the resulting C/A ratio was equal to one.

Our only treatment variable was the time profile of cash endowment, and thus that of the C/A ratio. The HighConstant treatment was exactly the same as LowConstant, except that the total cash endowment was 20 times greater. Half of the subjects were endowed with 20 assets and 41.000 Taler, and the other half were endowed with 60 assets and 39,000 Taler. Therefore, the total cash endowment in the market with 10 traders was 400,000 Taler in the HighConstant treatment, compared to 20,000 Taler in LowConstant. The total number of units of asset in circulation was 400.8 The expected value of each subject's endowment in HighConstant, taking into account both units of asset and cash, was 42,000 Taler. With the entire market cash endowment equal to 400,000 Taler and total expected value of the assets in the market equal to 20,000 Taler, the C/A ratio was constant over time at 20.

The Increasing treatment had a rising C/A ratio over time, ranging from 1 in the first period to 19 in period 10. In order to create the increasing C/A ratio, exogenous cash injections were made to each trader's cash account at the end of each period. The amounts of these payments are presented in Table 2, which indicates the relationship between the per capita cash injection and the period number in Increasing. The resulting C/A ratios are depicted in Figure 1. In all treatments, the dividend payments, whether positive or negative, were added to or subtracted from a separate account so that they did not affect the amount of cash available for purchases of assets. This enables us to control the C/A ratio precisely over the course of a session.

The trading institution in all markets was a computerized open book continuous double auction. Short selling of assets and negative cash balances were not allowed. Each of the 10 trading periods was 120 seconds long. Individual inventories of assets and Taler carried over from one period to the next. There were no interest payments on cash holdings and no transaction costs on trades.

Ten sessions were conducted under HighConstant treatment and five sessions under LowConstant and Increasing treatments. At the beginning of each session, subjects completed the three question cognitive reflection test (CRT) developed by Frederick (2005). (9) Then, the subjects were given 15 minutes to read the instructions for the asset market on their own. (10) Afterwards, the experimenter provided a detailed description of the trading screen, which was presented on an overhead projector. Two practice trading periods were conducted to allow subjects to become comfortable with the interface.

Upon completion of the market at the end of the session, the subjects were asked to complete a questionnaire, which tested their understanding of the dividend and fundamental value processes, and requested some demographic data. To check for understanding of the fundamental the questionnaire asked the following "Do you remember the process of fundamental value? Based on a fundamental value of 50, with dividends of -5 or 5 being equally likely, what is the value of the asset in the following period?" The subject could choose an answer by selecting one of the following values: 40, 45, 50, 55, or 60. In 13 of the sessions, the question was not incentivized and was accompanied by a number of other questions. In the remaining seven sessions, subjects received one New Zealand dollar if they indicated the correct answer of 50.

[FIGURE 2 OMITTED]

III. RESULTS

Figures 2A-2C show the time series of average transaction prices by period in each session of the three treatments. In the figures, the vertical axis measures price and fundamental value in terms of the experimental currency and the horizontal axis indicates the market period. Each time series corresponds to one session. Figure 2A presents the data for LowConstant, and shows that prices adhere closely to the fundamental value for the entire life of the asset. Figure 2B, which displays prices in Increasing, reveals a nearly identical price pattern. Both of these treatments closely replicate the T4 and T2 treatments of KHS, respectively. Figure 2C illustrates the data from HighConstant, and shows a strong tendency for price bubbles to form. In 7 of the 10 sessions, prices are at least as great, or greater, than the fundamental value in every period. Prices exceed the fundamental value by approximately 50% on average in each period beginning in period 6.

The upper portion of Table 3 shows the average value of three measures of bubble magnitudes that previous authors have introduced, Relative Absolute Deviation (RAD), and Relative Deviation (RD), as well as Turnover, in each treatment. (11) The averages are taken over all the sessions that comprise each treatment. RAD is a measure of absolute difference between prices and fundamental values, while RD is a measure of price level relative to fundamental values. Both of these measures were first proposed by Stockl, Huber, and Kirchler (2010). If prices track fundamentals, both measures take on low values. If they exceed fundamentals by a considerable amount in a sustained manner, both measures will be positive. If prices are below fundamentals, RAD will be positive and RD negative. Turnover (Van Boening, Williams, and LaMaster 1993) equals the total quantity of units of asset traded over the entire lifespan of the asset divided by the total stock of units in the market. Although units are traded among agents, the total stock of units of asset remains constant over time, because no units are added or subtracted from the total inventory held by all agents at any time. A high turnover indicates a high volume of trade, which in experimental markets is typically associated with prices becoming decoupled from fundamental values. The intuition for this relationship is that markets that track fundamentals are more likely to be characterized by common expectations among traders about future prices, and less disagreement about future prices leads to lower trade. The table shows that the value of each of the measures is much greater in the HighConstant treatment than in the other treatments.

To determine whether these differences are statistically significant, we conduct Mann-Whitney-Wilcoxon rank-sum tests. The unit of observation is an individual session. The bottom part of Table 3 reports the z-scores and corresponding significance levels for each pairing of treatments and for each bubble measure. The table shows that both LowConstant and Increasing generate bubble measures close to each other in magnitude and insignificantly different from each other. These results reflect the close adherence of prices to fundamental values in each of these conditions. In contrast, HighConstant generates values of RD that are significantly greater at p < .01 than in LowConstant and Increasing as well as significantly greater RAD values than LowConstant (p < .01). Furthermore, HighConstant has more than twice the transaction volume as the other two treatments.

The greater availability of cash early on in the life of the asset in HighConstant allows bullish traders to make large purchases and accumulate large inventories to an extent that is not possible in the other two treatments. The result is greater variance of asset holdings between individuals within a market. Table 4 presents the results of Mann-Whitney-Wilcoxon rank-sum tests comparing the cross-sectional variance of individual stock holdings across treatments for the entire market and the first three periods. The data in the table are the test-statistics, with the associated significance levels in parentheses. The table shows that the level of dispersion is significantly greater in HighConstant than in both Increasing and LowConstant for both time intervals. The variance of stock holdings in Increasing is significantly greater than in LowConstant over the entire 10-period market, but insignificant when comparing only the first three periods, suggesting that the greater cash balance in HighConstant allowed some traders to purchase large quantities, and they would be constrained from doing so in the other two treatments. When cash balances become large in the Increasing treatment, in the late periods, the variance in holdings exceeds that in LowConstant.

IV. COGNITIVE ABILITY

Who are the traders that purchase large quantities and force up prices in the HighConstant treatment? A number of authors have suggested that mispricing in experimental markets is related to confusion about the environment. We measure the level of comprehension about the fundamental value process with a questionnaire administered at the end of the session. As described in Section II, one question asked individuals to make a simple calculation of the fundamental value. The graph in Figure 3 shows the incidence of deviations from the correct answer of 50. A correct answer is indicated as a 0 on the horizontal axis, an answer of 45 is labeled as -5, etc ... The vertical axis is the percentage of respondents submitting each response. (12)

The figure reveals that nearly all subjects give the correct answer. This indicates that by the end of the session, very few subjects fail to understand the fundamental value process. This is the case for all three treatments, which shows that it is not the case that misunderstanding of the fundamental value process was greater in HighConstant than in the other two treatments, at least by the end of the sessions. Therefore, subject confusion about the fundamental value process cannot account for the differences between treatments, although a misunderstanding about the relationship between the fundamental value and appropriate transaction prices might be at work. High cash endowments in and of themselves do not cause confusion about the fundamental value process.

[FIGURE 3 OMITTED]

An understanding of the fundamental value process does not guarantee that individuals will use rational trading strategies or that markets will price at fundamentals. The CRT data allow us to consider the different behavior exhibited by traders with differing levels of sophistication. There are four possible scores on the test, ranging from 0 to 3, depending on the number of correct responses. 21%, 24%, 21%, and 35% obtained scores of 0,1,2, and 3, respectively. Thus, higher CRT scores can be interpreted as indicating a higher degree of sophistication.

The average asset holdings of traders of each sophistication level over time in each treatment are shown in Figures 4A-4C, and tabulated in Table 5. In the LowConstant treatment, illustrated in Figure 4A, there is no consistent relationship between trader sophistication and asset holdings. The most sophisticated traders, with CRT scores of three, hold the most units of asset. However, the group with the next highest holdings are the least sophisticated traders with CRT score equal to 0. We conduct rank-sum tests to consider whether the differences in holdings between individuals with different CRT scores are significant. Each individual is taken as a unit of observation and the holdings of those with a given CRT level are compared with those of each other level. We conduct the tests for holdings over two different time horizons. One time horizon is the entire 10 period life of the asset, where we use the average quantity an individual holds over the horizon as the unit of observation. The other is the holding of individuals at the end of the final period 10. None of the pairwise comparisons is significant at the 5% level, except for the final holdings of those with CRT = 2 and CRT = 3, which are significant from each other at p = .0347. This reflects the absence of opportunities for more sophisticated traders to earn profits at the expense of the less sophisticated in a market that is tracking fundamentals. As can be seen in Table 5, the differences in earnings between the four levels of sophistication are quite small in LowConstant, though higher CRT scores are associated with greater earnings.

[FIGURE 4 OMITTED]

In the Increasing treatment, a different pattern appears. This can be seen in Figure 4B. Early in the sessions, in which the C/A ratio is increasing slowly, all four groups have similar holdings. However, late in the sessions, when the C/A ratio accelerates to high levels, the relatively unsophisticated agents who have CRT equal to zero accumulate units. The most sophisticated, with CRT equal to three, hold the fewest units. The large injections of cash near the end of the life of the asset appear to result in less sophisticated traders buying up units from the more sophisticated. Final asset holdings are significantly different between individuals with CRT = 3 and those with CRT = 0 (p = .0319), while all other pairwise differences are insignificant. Over the session, there is no difference between average holdings of traders with different CRT levels. This reveals that the trend over time is for those with CRT = 0, the least sophisticated, to accumulate units relative to those with CRT = 3, the most sophisticated. In the Increasing treatment, this does not have strong consequences for earnings, since the price tracks fundamental value closely over the course of the session. This means that purchases and sales tend to be equally profitable and earnings differences, while greater than under LowConstant, are still quite modest. The purchases by the unsophisticated traders do not begin sufficiently early and occur rapidly enough to exhaust the supply of units held by sophisticated traders. The purchases thus fail to drive up prices by the end of the session. Nevertheless, similarly to the LowConstant treatment, there is a monotonic, positive relationship between earnings and CRT score.

The pattern in Figure 4B suggests that many unsophisticated traders tend to purchase large quantities when they have the cash to do so. This effect is clearly visible in Figure 4C, which contains the data from the HighConstant treatment. It shows that those traders with the highest CRT scores hold the fewest units throughout the time horizon. Those with relatively low CRT scores of one hold the most, and those with zero and two hold quantities that are typically between those of the other two groups. The differences are significantly higher over the entire session for those with CRT = 1 compared to those with CRT = 3 (p = .032). Final holdings are significantly greater for those with CRT = 0 than those with a score of 3 (p = .0686). They are also significantly higher for traders with a score of 1 than those with 3 (p = .0385). This also indicates that the trend over time is for those with CRT scores of 0 to accumulate units relative to those with scores of 3. This pattern indicates that the most sophisticated traders tend to sell off units at the inflated prices that characterize this treatment. Table 5 reveals the consequences for earnings. There is a strong positive correlation between CRT and earnings, with the relationship steeper than in the other two treatments.

We use rank-sum tests to compare the earnings of players with different CRT scores in each treatment. In the Low Constant treatment, those with CRT = 3 earn borderline significantly more than those with CRT = 0 (p = .0943). A similar pattern appears in the Increasing treatment, in which those with CRT = 3 earn more than those with CRT = 0 and CRT = 1, with the differences being borderline significant (p = .0926 and p = .0613, respectively). However, in the HighConstant treatment, stronger differences appear. Individuals with a CRT score of 3 earn significantly more than those with scores of 0 and 1 (p < .0001 and p = .0006, respectively). Those with a score of 2 earn more than individuals with 0 and 1 (p = .0069 and p = .043, respectively). Finally, those with 0 have earnings that are borderline significantly below those with a score of 1 (p = .0965).

V. DISCUSSION

Previous experimental work has reported that greater liquidity available for purchases leads to higher price levels, and consequently, bubble magnitudes, when fundamental values are decreasing over time (Caginalp, Porter, and Smith 1998, 2001; Haruvy and Noussair 2006). However, KHS find that this does not occur in a setting in which fundamentals follow a constant time trajectory. Our focus here is on why the positive association between liquidity and prices, so robust in the case of decreasing fundamentals, would not carry over to the constant fundamental value case. In this article, we show that greater initial cash endowments increase prices and exacerbate bubbles, even when fundamentals are constant. It seems to be critical that the cash is introduced early enough in the life of the asset to have an impact. The positive relationship between cash holdings and price level appears to be quite general and not specific to the decreasing fundamental value trajectory.

Experimental markets for assets with decreasing and constant fundamental values do differ in a number of ways that make bubbles more likely in the decreasing case, regardless of the amount of liquidity available. Negative dividend realizations are common in the typical implementation of constant fundamentals while they are not possible under decreasing fundamentals. This may deter demand from loss-averse agents in the constant case, leading to lower prices. In the declining fundamental value case, frequent changes of fundamental values to a new level each period may make the price discovery process more difficult. The fact that the dividend payments in the declining case go to individuals who have been purchasing the asset, and thus with the greatest propensity to buy, disproportionally directs more cash to them that they can use to bid up prices. It is possible that each of these forces make it more likely that price discovery is more effective for assets that have constant, rather than declining, fundamental value trajectories.

Nevertheless, in markets with either constant or decreasing fundamental values, greater initial liquidity available for asset purchases increases market prices. The size and timing of the cash infusion seem to play a critical role in bubble formation in the case of constant fundamental values. In the Increasing treatment, the initial C/A ratio is equal to one and increases over time. The relatively large cash injections appear to have been introduced too late in the life of the asset for them to have an impact. As we have argued in Section I, confusion is likely to be less prevalent and speculation is typically more risky, later in the life of the asset. If confusion and speculation are the sources of the demand that generate bubbles, it is less likely that bubbles occur the later the cash that enables the purchases at high prices is injected. High levels of cash at the outset of the life of the asset readily lead to prices that exceed fundamentals.

As observed in other studies (Breaban and Noussair 2015; Chamess and Neugebauer 2014; Corgnet et al. 2015), CRT score correlates with the use of profitable strategies in the asset market. Endowing traders with more cash allows relatively unsophisticated traders to more readily take large long positions, and permits a relatively small number of traders to drive up prices. In this study, we observe no evidence that more cash is associated with more confusion. Rather, the greater cash unleashes unsophisticated traders to take large long positions. Our results also indicate that there is no confusion, at least by the end of the sessions, about the fundamental value process. Any potential confusion concerns the relationship between the fundamentals and the trading strategies one ought to employ.

ABBREVIATIONS

C/A: Cash-to-Asset

CRT: Cognitive Reflection Test

RAD: Relative Absolute Deviation

RD: Relative Deviation

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SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Appendix S1. Experiment Instructions Table Al. Bubble Measures for Each Session

Noussair: Professor, Department of Economics, Eller College of Management, University of Arizona, Tucson, AZ. Phone +1 520 621 6229, Fax +1 520 621 8450, E-mail [email protected]

Tucker: Associate Professor, Department of Economics, University of Waikato, Hamilton, New Zealand. Phone +64 7 838 4477, Fax +64 7 838 4063, E-mail [email protected]

doi: 10.1111/ecin.12320

(1.) In the experiment of Smith, Van Boening, and Wellford (2000), a constant fundamental value was generated with the payment of a one-time dividend at the end of the life of the asset. In the studies of Noussair, Robin, and Ruffieux (2001) and Kirchler, Huber, and Stockl (2012), there were multiple dividend payments, but the dividend distributions allowed for negative realizations and had an expected value of 0.

(2.) The reason that KHS chose this specific sequence of cash infusion magnitudes was to allow for the clean comparison of the case of a constant fundamental value trajectory to the case of a decreasing trajectory. The typical implementation of a decreasing fundamental value time profile features the payment of dividends into traders' cash accounts. This has the effect of increasing the cash available for transactions and thus increasing the C/A ratio. Fundamental values are decreasing over time linearly, which causes further increases in the C/A ratio at an increasing rate over time. The overall effect is an acceleration in the C/A ratio over the life of the asset, as in the Increasing treatment shown in Figure 1.

(3.) The specific conversion rate differed between treatments to maintain comparable expected hourly earnings for participants in different treatments. Specifically, the conversion rates were 225 Taler, 2300 Taler, and 2400 Taler to 1NZD for treatments LowConstant, Increasing, and HighConstant, respectively.

(4.) At the time of the experiment, the minimum wage was 13NZD per hour (1USD = 1.26NZD).

(5.) We recruited with an expectation of 10 traders participating in each session. Unfortunately, in five of the sessions, only eight subjects appeared. Thus, two sessions of HighConstant, one session of LowConstant, and two sessions of Increasing had 8 traders, while the remaining markets had 10 traders.

(6.) KHS randomly drew a stream of dividend payments prior to running of any of the sessions and used the predetermined sequence of dividend payments in all of their sessions. Likewise, we used the same dividend payment sequence in all of our sessions.

(7.) In sessions 6-10 of the HighConstant, only the question testing understanding of the fundamental process was given as the end of session questionnaire, and it was incentivised by paying subjects $1 for correct answers. All other sessions' questionnaires were nonsalient. The results are reported in Section IV.

(8.) In the sessions with eight traders, the total asset endowment in the market was 320, and total cash endowment was 16.000 and 320,000 in the LowConstant and HighConstant treatments, respectively.

(9.) The three cognitive reflection test questions are: (1) If it takes 5 machines 5 minutes to make 5 widgets, how long does it take 100 machines to make 100 widgets? (2) A bat and a ball cost 1.10 in total. The bat costs 1.00 more than the ball. How much does the ball cost in cents? (3) If a pond takes 48 days to be covered in lily pads, and the lily pad cover doubles in size every day, how long does it take the lily pads to cover half of the lake? The correct answers to the three questions are 5, 5, and 47 while the intuitive/spontaneous incorrect answers are 100, 10, and 24. Subjects received $2 for each correct answer. No earnings information was provided until the end of the session. The correlation between CRT score and subject behavior in asset markets has been previously established by Corgnet et al. 2015, who find that traders with high CRT scores earn significantly more than those with low CRT scores in experimental asset markets. Agents with low CRT scores tend to make unprofitable purchases at prices above, and sales at prices below, fundamentals. In contrast, those with high CRT scores exhibit the opposite pattern.

(10.) The instructions are given in Supporting Information.

(11.) RAD, relative absolute deviation, is defined as (1/T)*([[summation].sub.t][absolute value of [p.sub.t] - [f.sub.t]])/([[summation].sub.t], [f.sub.t]/T]), where T is the total number of periods in the life of the asset, [p.sub.t] is the price in period t, and [f.sub.t] is the fundamental value in period t. RD, relative deviation, is equal to (1\T)*([[summation].sub.t]([p.sub.t] - [f.sub.t]))/([[summation].sub.t][f.sub.t]/T). Turnover is equal to [[summation].sub.t][q.sub.t]/TSU, where [q.sub.t] is the quantity transacted in period t and TSU is the total stock of units. The values of the bubbles measures for each individual session are given in Supporting Information.

(12.) The questionnaire data from session 1 of treatment HighConstant was not recorded, and thus not included in the analysis. TABLE 1 Summary of Treatments in the Experiment Low High Increasing Constant Constant Expected dividend 0 0 0 Fundamental value 50 50 50 Total asset endowment 400 400 400 Total cash endowment 20,000 20,000 400,000 C/A ratio 1-19 1 20 TABLE 2 Increasing Treatment Cash Injections Period 1 2 3 4 5 6 Payment 444 556 714 953 1,333 2,000 Period 7 8 9 10 Payment 3,333 6,667 20,000 0 TABLE 3 Bubble Measures across Treatments Treatment Sessions RAD HighConstant 10 0.631 LowConstant 5 0.023 Increasing 5 0.069 Treatment comparisons Z-scores (p values) HighConstant versus LowConstant -2.694 *** (0.007) HighConstant versus Increasing -1.592 (0.111) LowConstant versus Increasing 1.358 (0.175) Treatment RD Turnover HighConstant 0.624 4.068 LowConstant -0.009 1.613 Increasing -0.033 1.862 Treatment comparisons HighConstant versus LowConstant -2.939 *** -1.470 (0.003) (0.142) HighConstant versus Increasing -2.694 *** -1.715 * (0.007) (0.086) LowConstant versus Increasing -0.104 -0.313 (0.917) (0.754) * and *** denote the 10% and the 1% significance levels, respectively. TABLE 4 Tests of Equality of the Variance of Individual Stock Holdings across Treatments High High Low Constant Constant Constant versus Low versus versus Constant Increasing Increasing All periods -3.062 *** -2.082 ** 2.402 ** (0.002) (0.037) (0.016) Periods 1-3 -2.082 ** -1.960 ** -0.313 (0.037) (0.050) (0.754) Note: The unit of observation is the session. ** and *** denote the 5% and the 1 % significance levels, respectively. TABLE 5 The Relationship between Cognitive Reflection Test Scores and Average Earnings High Constant Low Constant Increasing CRT = 3 $22.49 $17.50 $19.35 CRT = 2 $19.07 $17.38 $18.94 CRT = 1 $17.81 $17.28 $18.56 CRT = 0 $16.90 $17.24 $17.62