Laboratory incentive structure and control-test design in an
experimental asset market
Olivier Brandouy *
Universitede Droit et des Sciences Economiques, ESRG, 4 Place du Presidial, 87031 Limoges Cedex, France Received 10 October 1999; received in revised form 21 August 2000; accepted 16 October 2000
Abstract
This paper presents the results of a series of experiments in a simulated double-auction stock market driven by orders. It is shown that two small groups of traders should adopt a similar behavior when subjected to identical stimuli in the laboratory. To achieve this hom-ogenous behavior, it is necessary to propose an incentive structure according to the rules of the Induced Value Theory proposed by Smith. The data collected in this experiment clearly show, after a series of co-integration tests and non-parametric tests, that experimental protocols of
`control-test' design should be successfully used in experimental ®nance. Ó 2001 Elsevier
Science B.V. All rights reserved.
PsycINFO classi®cation:2260
JEL classi®cation:C92; B40
Keywords:Induced value theory; Behavior; Double-auction; Design of experiment; Experi-mental asset market; Test-reference protocol
www.elsevier.com/locate/joep
*Tel.: +33-5-55059573.
E-mail address:[email protected] (O. Brandouy).
1. Introduction
Experimental economics has undergone constant development since Chamberlin's founding works Chamberlin (1948). Many economic theories, as well as many models of market-®nance, can be systematically tested using laboratory experiments (see for example Sunder, 1995).
This methodological progress owes much to Smith's (1976) contribution
on `induced value theory'. The theory states, for example, that agents placed
in a simulated environment should adopt a behavior in the laboratory similar to that which they would normally assume in the real world. To achieve this behavioral imitation over the experimental subjects, the researcher must in-stall an incentive (or control) structure which, in general, proposes some type of reward medium to the subjects for their participation in the experimental protocol. This reward medium must have particular speci®cations to ful®l its goal: the suggested payments should be salient (i.e., directly depending on the subjects' actions), should not lead to satiety, and should be designed in such a way they prevent all other factors to disturb the subjects' behavior (i.e., `dominant', they make minor the in¯uence of psychological factors which derive from the laboratory setting). Many related questions have already been examined by various researchers in the aim of determining an optimal level for this incentive structure (Jamal & Sunder, 1991; Smith & Walker, 1993). Its effects are obviously decisive and superior to other stimuli in in-citing a speci®c behavior. For example, Wageman and Baker (1997) com-paring the results of monetary reward and goal setting, have clearly shown that group performance is driven more by the ®rst than by the latter.
These methods have been largely respected by an experimenter in practice and, since Smith, have bene®ted from many practical improvements (see for example the research of Davis & Holt, 1993).
This study proposes an experiment that corroborates the eects of the reward structures according to the induced value theory. The results stress the importance of experimental controls when two groups of small size, one a `test group' (or `treatment group'), and the other a `control group', are used to improve a theoretical model.
sub-jects. They attempted to control for the eects of dierent variables (history, maturation, testing, etc.) to the extent that they would aect both groups. Concerning Marketing, Grossman and Till (1998) have investigated the long-term eects of classically conditioned attitudes toward a brand. Mann, Samson, and Dow (1998) used a CTD in order to analyze the link between benchmarking, goal setting and goal evaluation on company sales perfor-mance.
The present study ®nds evidence which supports the use of control-test
de-signs, with speci®c implications for academic research on experimental asset
markets.
Section 2is devoted to the goals of the applied experiment; it also presents some diculties with the control-test design. The second Section 3 is devoted to the statistical tests. The last section recapitulates and discusses the ob-tained results. Speci®c information regarding the experiment is provided in Appendix A,1in particular the details of the payment structure with regard to `induced value theory'.
2. Purpose of the experiment and problems related to the `control-test' design (CTD)
According to the Popperian tradition, the experiment used in this article should attempt to falsify a theoretical model. This model has been developed in order to describe the eects of speci®c information on the value of some ordinary share quoted on an electronic stock market. The experimenter manipulates the informative signals, which take the form of transmitted of-®cial statements released to a simulated laboratory stock exchange. This experimental stock market uses a double (bid-ask) auction procedure. It is an order-driven market without credits, therefore there is no delay in payments. It also complies with the rules usually found in such real-life market struc-tures (price priority, then time priority, and no quota, etc.). However, the only shares negotiated on this experimental market are those of a single company.
The detention of these securities gives right,at the end of the experiment,to a
dividend that depends on the risks caused or undergone by the company.These
risks are sent to the market using the signals controlled by the experimenter.
At the beginning of the experiment, the quoted company is described to the subjects; its activities are part of a simpli®ed economy (without either taxation or constraining regulation). This economy is precisely parameterized (ten industrial sectors whose exchange links are known, and ten companies which have either single, or multi-sector activities).
Two categories of signals sent to the market can be distinguished:
· One is called the simple information set (SIS). It gathers all
environment-related information for the ®nancial market. Generally speaking, it should include all non-directly interpretable ocial statements or information without major consequences (for example, in¯ation rates close to zero, realized growth identical to the anticipated one, minor ¯uctuations of a market index or even company's internal information such as the retire-ment of a senior ocer, etc). The purpose of this set of simple information is to animate the market and to provoke a minimum level of exchange activity.This information is assumed to have a very limited effect on the vari-ation of the dividend and therefore on the price of the quoted share.
· The other is called the critical information set (CIS). It gathers information
directly connected to the theoretical model. This information provides a better understanding of whether the market power of the quoted ®rm shall increase or decrease, or whether the competitive conditions to which it is subjected shall improve or worsen (for example announcements of mergers with companies in the simpli®ed economy or spin-o, sell-o of activities, etc.).Information of this type is likely to give rise to sharp variation of the dividend paid at the end of the experiment and therefore to the value of the quotations.
The ®nal dividend is known only to the experimenter. It is calculated starting from the initial dividend to which are added increases or decreases, according to the information delivered to the market as anticipated in the predetermined experimental schedule. The amount of this dividend remains secret for the agents throughout the protocol, but they nevertheless express their beliefs for its evolution: they are expected to arbitrate between holding shares, which entitle them to a variable dividend, and holding a riskless asset, which yields a small but ®xed interest.
The difference in quotation observed between the two groups is assumed to represent the impact of critical information on the expectations of the `treated subjects'.
This style of protocol is common for the experimental schedules of the natural sciences (medicine, biology, and agronomy, etc.), for example, when a clinical researcher seeks to verify the eect of a special drug on a sample of patients. Two groups are then constructed. At the beginning of the experi-ment, some parameters describing physiological variables are estimated for each of them, in order to make sense of those that will be collected after the treatment period. Doing this, one seeks to speci®cally neutralize the exoge-nous in¯uences that should aect identically the two groups. Thus, only the endogenous variations in the system are susceptible to have an eect on the results of the test.
Generally speaking, the selected samples are of large size, which makes the
hypothesis of standard parametric framework plausible and allows the valida-tion of this hypothesis.
Obviously, for experimental ®nance, this opportunity is not possible, or if it were, it would require impressive logistics and an equally impressive budget.2 In spite of the precautions taken to avoid selection bias, certain psychological characteristics of the samples might be suciently marked, because of the small number of participants, which renders the interpretation of the results problematic.
The participants, in this experiment, are senior students majoring in eco-nomics and management science. Three dierent university programs pro-vided 24 participants (12 in each group). None of these three programs includes the instructor's course in market ®nance lessons where the same professor should teach. The students' pro®le is suciently varied within both groups, since a range of aptitudes and interests are merged in the experi-mental market (some of them are more experts in `industrial organization ± neo-classical ®nance', others are more specialized in `corporate strategy ± corporate ®nance', etc.). Nevertheless, the two groups are comparable in that they are of balanced diversity (the university origins of the subjects are multiple, but inside each group there is the same range of diversity).
The protocol is built on the comparison of the reactions of two groups of
extremely small sizeand undoubtedly does not ensure the appropriateness of
2For a counter-example where a large number of subjects are used, see Isaac, Walker, and Arlington,
a standard parametric framework. However, it is worth noting that the market value for a common share should be, in real world stock exchanges, the outcome of interaction between a very small number of traders (several pension funds, some abitragists). Thus, in itself, the weakness of the sample is not a problem; Kyle (1989) and Satterthwaite and Williams (1993) clearly show that even a small number of participants is suf®cient for the market ef®ciency assumption, which thus guarantees an acceptable level of credibility for the protocol.
Nevertheless, with such groups, there is an increased likelihood of con-trasted or aberrant behaviors. Merely considering their restricted size, the teams of traders may reveal an excessive level of risk aversion, or on the other hand, may show a strong tendency to be risk takers, etc. As such, the quo-tations provided by these two groups in the double-auction market might present, ceteris paribus, many perturbing differences solely due to
psycho-logical characteristicsand not due to experimental design factors.
As stated previously, a payment structure according to the rules suggested by Smith in theInduced Value Theorymakes it possible to obtain laboratory behavior close to reality. In addition to this primary advantage, we ®nd that the payment structure in experimentation is bene®cial for other reasons. It allows a reduction in the bias associated with small samples that may be too typi®ed (with non-uniformly distributed psychological characteristics 3). Furthermore, it allows the use of particularly interesting protocols, from a methodological point of view.
In the aim of establishing a comparative procedure for the tests, we are led to consider whether the revealed behaviors of the two experimental groups of small size, when subjected to the same treatments, are similar.
If this hypothesis of homogeneity is justi®ed (i.e., the two groups have the same responses when subjected to similar treatments), then the variation in quotations provided by the `control group' should be considered as identical to the variation in quotations observed from the `treatment group', when the latter has not received the critical information set.
Failing that, (i.e., the two groups have dierent responses when one sub-jects them to the same treatments), this construction is ineective because one can only judge the `normal reactions' for a speci®c group by subjecting it
3A large sample randomly extracted from the total population should have been selected, but in
strictly to `normal stimuli'. Thus bias (behavioral structural dierences), if it exists from the start, is precisely identi®ed and is held constant. However, in this case, the corroborative (or falsi®cation) protocol is less powerful: it will be dicult to distinguish how much of the quotation ¯uctuations are attributable to the eects of the simple information set, and how much is attributable to the eects of the critical information set. 4
How should this equivalence conjecture between the two groups be tested?We
shall say that the hypothesis of homogeneity is satis®ed if the two following conditions are simultaneously veri®ed:
· First, if the two groups are similar, the processes of responseto the same
stimulus must converge.
· Secondly, if the two groups have similar behavior,the response to the same
series of stimulimust be positively and strongly correlated.
It can be easily imagined, within an experimental framework using small samples of subjects, and for an isolated stimulus that:
1. Two groups, which are in fact of distinctly dierent `behaviors', should
givethe same isolated response to the same problem;
2. Two groups, identical in all respects, should each providea distinctly
dif-ferent response to the same problem.
In the ®rst case, the experimental protocol is skewed, and the experimenter is `lucky'; in the second case, the `control-test' protocol is valid, but the small amount of data will lead to erroneous conclusions.
However, if the number of observations increases such that they form a quasi-continuous response process to the signals, the process must:
· Converge, if the structure of incentives works correctly.
· Diverge, if the structure has not been able to correct the natural
psycho-logical dierences that are quasi-unavoidable for small samples.
As stated previously, in the framework of this experiment, the subjects were rewarded by a monetary payment that was directly related to their pro®ts on the laboratory-simulated stock market. The traders (experimental subjects) were given identical initial portfolio endowments of cash and shares. During the trading activity, these assets evolved dierently. Each subject was paid a variable participation fee prorated according to their ®nal portfolio; this payment structure was to incite a competition and to comply with the rules of monotony, salience and dominance, as it is exposed in Appendix A.
4The `tested group' is subjected to both ¯ows; the `reference group' is only subjected to the simple
The initial price for each share at the beginning of the experiment is en-tirely subjective. The market has no fundamentals to estimate this value (PER, re-evaluated net assets, capital structure or sectorial estimations). Its only way to infer a starting price for the ®rst trades is to refer to a series of quotations, obtained from a simulated random walk, and additional pa-rameters of the simpli®ed economy. This series suggests an average value `over the last hundred days of trading' close to 4 experimental dollars.
It was speci®ed that this series had been established over a period without any critical information. In addition, the subjects were provided with a hy-pothetical index of the market where the share was traded (simulated by the same means, indicative value set close to 1000 points). A diagonal model, that of Sharpe (1970), was estimated (with market b2), in order to com-plete the scenario and to oer an evaluation tool for the interested partici-pants. Throughout the experiment, an estimation of the market index was issued to the agents (after simulation): this signal was part of the set of simple information.
These two factors in the experiment (the share's fundamental value and the evolution of the market index) are of particular interest: depending on the psychological characteristics of each group,it is possible that the
micro-¯uc-tuations of the market index are not identically perceived by the two groups.
One group, when compared to the other, may exhibit an excessive response, or alternatively, an excessive apathy. If a signi®cant difference appears be-tween their respective expectations, then the control-test design is ineffective, since the `control group' cannot be used as baseline to the `treatment group'. The experimental design is then jeopardized.
responded to the same simple information set and occasionally received critical information related to the model.
Thus, at times both experimental groups will have received exactly the same stimuli (which is true for all the 15 mini-periods of the ®rst session and for approximately 5 mini-periods for each of the sessions 2, 3 and 4, in general located at the beginning of each session).
Two time series, resulting from these mini-periods where the two groups
were exposed to the same stimulationcan thus be compared in order to judge
the behavioral homogeneity of the agents.
3. Design of the tests of behavioral homogeneity for the experimental groups
The data used to examine the behaviors of both groups while subjected to identical stimuli come from two distinct quotations:
· One is the `Bid quotation'5: it captures, in continuous time, the most
gen-erous demand oer emitted by traders. It constitutes the price at which a shareholder will always ®nd a corresponding buyer, if he wishes to sell at least one of his shares.
· The other is a global weighted quotation, noted GWQt, which synthesizes
the set of the agents' positions in the market book (supply and demand), weighted by the quantities oered or demanded at the displayed prices:
GWQt
We ®rst considered the structure of the auction process resulting from each
signal emitted to the market (i.e., inside each mini-period). This analysis was
restricted exclusively for the periods where both groups had received exactly the same information.
Assuming an ecient ®nancial market, the price logarithms, in theory, should follow purely non-stationary stochastic processes: there is no
deter-ministic trend, and past information has no utility in forecasting the future.
5We shall denote B
However, even if intuitively such a process for a market animated by a constant and unpredictable ¯ow of information is conceivable, such a process appears to only ®t long-enough intervals (daily, hourly). When the time in-terval in the analysis is reduced, this random walkintuitionis not so evident. Even less so for this experimental market, where random information is transmitted to the participants and where other unexpected stimuli are not supposed to modify the quotation, except those endogenously created by the traders during their activity, throughout the mini-period. Nevertheless, ex-amination of the simple and partial auto-correlation diagrams suggests the existence of a random-walk process for the realized quotations.
We subsequently verify the acceptance of the null hypothesis of non-sta-tionarity for the auction prices provided by the two groups using an Aug-mented Dickey-Fuller test. We further con®rm acceptance of the null hypothesis with a Phillips-Perron test. The test strategy carried for unit-root detection was the sequential-test strategy of Jobert (1992).
For each mini-period, the tests were conducted on the full sample of quotations, minus the observations during the ®rst few seconds. The reason for this is to exclude the tatonnement process towards the equilibrium market price commonly observed on ®nancial markets during the pre-opening pe-riod. Table 1 presents the results of the unit-root tests for each auction mini-period.
Table 1
Unit root tests results (H0: series is non-stationary)a
Quotation Mini-period
101 102103 104 105 106 107 108 109 110 111 112
GWQG1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 R* I 1 I 1 I 1 I 1
GWQG2 I 1 I 1 I 1* I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1
BG1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 R* I 1
BG2 I 1 I 1 I 1 I 1 I 1 R* R* I 1 R* I 1 I 1 I 1
Mini-period
113 114 115 116 201 202 203 301 302 401 402 403
GWQG1 I 1* R R* I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1
GWQG2 I 1 R R I 1 R* I 1 I 1 I 1 I 1 I 1 I 1 I 1
BG1 I 1 I 1 I 1 I 1 I 1 I 1 I 1* I 1 I 1 I 1 R* I 1
BG2 I 1* R R I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1* R aThe number in the ®rst row in the table gives the identi®cation of the mini-period for which the unit root
test has been carried-out: 112means that the test concerns the 12th mini-period of the ®rst session;I 1: The hypothesis is not rejected: ®rst-order integrated series;R (or*): H
0 is rejected with a 1% or 5%
signi®cance level;I 1*: H0cannot be rejected at a 5% signi®cance level but at a 10% signi®cance level;
One can legitimately doubt the hypothesis of existence of random walk on our market: as noted by Demsetz (1968), the GWQ does not yield real
prices, that is equilibrium prices which would exist in a world without the
immediacy requirement and where all the traders are equally and perfectly informed. In a perfect market, these real prices would indeed follow a random walk (see Beja & Goldman (1980)), but since here, the GWQ is a weighted price in¯uenced by the Bid-Ask Spread, it is not necessarily the case. Nevertheless it appears that in the large majority of the cases, the series are non-stationary, as illustrated for some representative mini-periods in Figs. 1 and 2.
We then analyzed the link between the auction processes to answer this question: do the two groups' quotations maintain some relation?
Is it possible to uncover a behavioral convergence of the two groups over time, when the relative series have an underlying stochastic trend? 6
Fig. 1. Example of non-stationary quotations GWQG1and GWQG2for MP 202.
6
Since we had, in most cases, non-stationary pairs of series, testing for co-integration relationship was carried out, according to the proposals in Johansen (1991). The interpretation of co-integration being the existence of a long-run equilibrium relationship between the series, which, if veri®ed, con-stitutes a clue to the behavioral homogeneity between the groups, within the
same mini-period. 7 More speci®cally, a long-run stationary relationship
would exist between the two sets of observed quotations.
Table 2proposes the results for the co-integration tests, which were ob-tained according to the following hypothesis and methods:
1. The series of quotations do not present a deterministic trend, and their long-run equilibrium is assumed to be a proportion: ySG2b ySG1; the
corresponding vector error correction model, for the two endogenous vari-ablesySG1;t and ySG2;t is then:
DySG1;tc1 ySG1;t 1 b ySG1;t 1 e1;t;
DySG1;tc2 ySG1;t 1 b ySG1;t 1 e2;t:
Fig. 2. Example of non-stationary quotations BG1and BG2for MP 105.
2. The vector error correction model being relative to the short-term dynam-ics of the processes, the lag interval to make sense, must be chosen accord-ing to the length of the tested series.8
For the results presented in Table 2, H20 denotes the hypothesis of one co-integrating vector against the alternative hypothesis that both series are stationary. This hypothesis cannot be rejected with a 5% signi®cance level. The critical values to judge this hypothesis were extracted from the Oster-wald-Lenum (1992) tables. The signi®cance level associated with this deci-sion, is reported in Table 2, column `Rank 1'.
`Lags' indicates the number of lags included in the co-integration equation;
`Signif.' corresponds to the test signi®cance level (Prob. Type I error) for H10
Table 2
Co-integration tests results for the quotation series (H1
0: the series are not co-integrated. H20: there exists at
most one co-integrating relationship)
Mini-period GWQG1=G2 BG1=G2
Lags Signif. b Rank 1 Lags Signif. b Rank 1
101 1±15 5% )0.9927 >10% 1±9 5% )1.0059 >5%
8The number of lags included for the estimation of the co-integration relationship does not exceed one
(no co-integration relationship between the series).bare the normalized co-integrating coef®cients.
Finally, the `lack of co-integration' hypothesis between the series is re-jected (at a 5% level). Furthermore, the hypothesis of `at most one co-inte-grating relationship' cannot be rejected at standard levels, it is therefore likely that the long run behavior of the two groups, expressed in the quotations GWQSGiand BSGi, is said to be `homogeneous' within each mini-period.That
is,both groups,considered within a single period(a mini-period)when subjected
to the same experimental conditions, reveal an identical standard behavior.
Would it be the same over multiple periods?
As a ®nal analysis, it was veri®ed whether an identical¯ow of information did indeed lead to the same sequence of reactions for the traders.
The series considered up to this point are not suited for checking the
inter-temporal behavioral similarity in the behavior of the groups. Instead of
working with the auction quotations that reveal a `price discovery mecha-nism', we need to consider the series of prices actually observed after infor-mation has reached the market and trade has occurred (which we shall now refer to as `real prices').
Fig. 3 illustrates this necessity: the real prices at which transactions were carried out yield very dierent information from that obtained by considering the continuous quotations. The latter exhibits wide ¯uctuations, which can be solely due to mechanical corrections (destruction of a position in the market
book for example, which shifts the middle of the Bid-Ask-Spread). Thus, during the mini-period No. 114, the traders from group 2maintained very steady real prices whereas the GWQSG2 quotation experienced erratic
¯uc-tuations.
The ®rst experimental session (mini-periods 1xx) was used as a basis to test the similarity in the groups' responses to a same series of stimuli. The aim of this session was to train the traders in the mechanics of market in the context of simple information that required no complicated analysis. The events that animated this session were thought to be of low importance, and theoretically should not have had any speci®c impact on the quotation.
The two groups have produced the following series of mean real prices 9 (henceforth MRPi), on the whole session (Table 3).
Group No. 1 10 was especially active: they traded 310 shares in 108 con-tracts, that is on average 2.87 shares each time. Group No. 2 traded 123 shares in 73 contracts (1.68 shares on average per contract).
It has already been established that the groups' behavior is homogeneous throughout each mini-period. Figs. 4±7 present the evolution of the real prices and quotations by group.
For the ®rst mini-periods, the real prices determined by group No. 1 are de®nitely more volatile than those of group No. 2. Thus, the information given to the traders does not appear to have been interpreted in the same way. Table 3
Mean real prices, standard deviations and activity per group
Mean r Activitya
Group of traders No. 1
4.5393 0.3065 310
Total number of stocks in the experiment: 160 Group of traders No. 2
4.1120 0.0971 123
Total number of stocks in the experiment: 170
a
Quantity of traded stocks during the session.
9
The Mean Real Price, for one mini-period, is equal to the average of the prices at which transactions have occurred, weighted by the quantity of exchanged stocks, that is:
MRPmini-period i
Pend of the mini-period
t0 Transaction pricetTransaction quantitiest
Pend of the mini-period
t0 Transaction quantitiest
:
10There is no distinction here between `tested group' or `reference group', because in this session, both
Beyond a certain time accorded to familiarization, the problems associated with the use of the software manipulation should have, for the most part, disappeared.
Fig. 4. Group 1, quotation and real prices (time reported in abscissa). (From period No. 101 to mini-period No. 110).
Then, ¯uctuations in the real prices, due exclusively to the interpreta-tion of informainterpreta-tion, start to resemble each other. This homogenizainterpreta-tion of the behaviors is very clear in the two following ®gures. The ®rst one Fig. 6. Group 2, quotation and real prices (time reported in abscissa). (From period No. 101 to mini-period No. 110).
(Fig. 8) sums up, by mini-period, the evolution of the mean real prices (MRPi):
The second (Fig. 9) is a ®gure of sliding correlation between the series MRPSG1 and MRPSG2, of 5 mini-periods clusters of observations.
These correlations grow systematically from mini-period No. 110: a learn-ing-element seems fully achieved at this date, and the diculties encountered by the traders, due essentially to questions of data-processing techniques and management of the information ¯ow, have almost disappeared. 11This eect clearly strengthens from the beginning of the twelfth mini-period. Even if the continuous quotations generated by the two groups remain entirely dierent throughout the session, the same is not true of the MRPi series, which are
steadier and which follow a`homogeneous'joint evolution.
This analysis was repeated considering the experimental session not as a succession of mini-periods, but rather as sequence of 6 clusters,12 each cluster corresponding to a speci®c `event', that is, several consecutive
Fig. 8. Mean real prices (MRPi) by mini-period, session No. 1.
11Given that those problems have not been totally eliminated during the training session devoted to the
use of the quotation software.
mini-periods subjected to the same but slightly evolving signal. The com-parative evolution of the MRPi, by period, reveals a marked similarity in the response processes between the two groups (Fig. 10).
Fig. 10. MRPi, calculated by period (cluster analysis).
These conclusions based on graphical analysis are obviously not sucient. Non-parametric tests using a q-statistic, Spearman's correlation coecient based on the ranks, were performed to judge this similarity (Table 4). This statistic is well suited for small samples of observations, as is the case in this paper.
The null hypothesis that the traders' responses are independent between the two groups (H0) cannot be rejected for the 101±109 interval at a 10%
signi®cance level.
Nevertheless, after the mini-period No. 110, H0 should be rejected for
any-thing above a 7.4% signi®cance level. Similarly, the following results are
presented for the `cluster analysis' (Table 5).
The observedMRPon the two experimental groups tend to be concordant in
a second half of the experimental sessionNo. 1, although they do not present
any sort of de®nite relation in its ®rst half.
4. Discussion
The intra- and inter-mini-period homogeneity that has been shown sup-ports the utility of calibrated rewards in providing experimental control on induced characteristics. Small groups of traders, which a priori do not have any reason to share similar psychological characteristics, and which therefore Table 4
Non-parametric correlation on MRPG1 and MRPG2 (Observation: mean price over mini-periods) (H0:
``G1 and G2are independent''.)
Period Range qS Critical values of theq-statistics
101±116 16 )0.1798 )0.341 at a 10% s.l.
101±109 9 )0.3667 )0.483 at a 10% s.l.
110±116 7 0. 6071a 0.571 at a 10% s.l.
a
Rejection at a 10% signi®cance level.
Table 5
Non-parametric correlation on MRPG1and MRPG2(cluster analysis) (H0: ``G1 and G2are independent''.)
Cluster Range qS Critical values of theq-statistics
1±6 6 0.200 )0.341at a 10% s.l.
2±6 5 0.400 )0.483 at a 10% s.l.
3±6 4 1a 0.571 at a 10% s.l.
could have very dierent to identical series of stimuli, may, when subjected to a well-designed incentive structure, operate identicallyceteris paribus, within a laboratory framework.
From an economic point of view, these results are consistent with Smith's
Smith (1991) observation: ``. . .human subjects in the laboratory frequently violate the canon of rational choice when tested as isolated individuals, but in the social context of exchange institutions serve up decisions that are con-sistent (as though by magic) with predictive models based on individual ra-tionality. . .''
Two experimental groups in the laboratory, subjected to identical stimu-lation, both tend to serve up a certain `type' of results, that is, results con-cordant with individual rationality. Moreover, the similarity of results between groups will be only as close as the incentive structure is capable of subjugating their psychological dierences.
The incentive structure seems to be a necessary but not sucient condition to support the use of CTD in laboratory experiments. It is our opinion that it is of signi®cant importance even although this is not entirely consistent with Thaler (1987): ``First, monetary incentives do induce subjects to pay a little more attention, so the data generated with incentives tend to have less noise. Second, the violation of rationality observed tends to be somewhat stronger in the incentive condition (see e.g., Grether & Plott, 1979)''. But considering Smith and Walker (1993), whatever the institutional framework in which the experiment takes place (double auction markets, casino betting, etc.), the eect of an increasing reward seems to signi®cantly improve the subjects' response quality with respect to a criterion of `rational choice'. For Smith (1991) ``. . .these results are consistent with decision costs models that postulate a trade-off between the bene®ts of better decisions and the subjective cost of
taking them''.
In summary:
· The market institution should have a determinant role in the observed
be-havioral convergence in the experiment although the fundamental reasons that lead subjects with dierent attitudes to serve up similar quotations are as yet imperfectly understood.
· The second force that should be evoked is the power of the ®nancial
incentives that may alone be sucient in subjugating psychological dier-ences that remain, in other respects, evident within this experimental protocol. That is, all the dierences do not disappear. For example, the
(Table 3 and Figs. 4±7) are indications of this persistent heterogeneity. Likewise, if it is admitted that the Bid-Ask-Spread reveals a market risk (because it derives from the competitive substitution of the traders' indi-vidual positions), it is notable that this risk perception remains markedly different between the two experimental groups,13 as is recapitulated in Table 6.
A few remarks on the statisticalprocedure are also in order. Even though a
reward structure is often proposed to the participants of an experiment, a CTD is more rare, in particular for asset market experiments.
The robustness of such a protocol is however prone to conditions: the statistical results obtained reveal that such a framework has a remaining weakness with respect to its dependence upon the achievement of a learning element. This eect seems to have been recurrent in each experimental ses-sion, thus motivating the use of preliminary training periods, which are subsequently withdrawn from the collected results. In many cases, this pru-dential step may not be super¯uous.
A contrario, a possible effect of weariness or boredom could lead the
groups' behaviors to diverge after a certain time. In addition, the co-inte-gration tests could not be systematically used, the ®rst series being alterna-tively stationary, the other being non-stationary, which complicates the analysis.
Finally, these results are encouraging and should allow for the conception of experimental protocols of `control-test' design for asset market research, Table 6
Statistics on the Bid-Ask-Spread, by experimental session
Session No. 1 Session No. 2Session No. 3 Session No. 4
Mean r Mean r Mean r Mean r
BAS
G1 0.528 0.502 0.425 0.376 0.430 0.582 1.149 1.566
BASG2 0.294 0.334 0.236 0.183 0.157 0.090 0.725 0.890
WBAS
G1 1.697 0.469 0.621 0.497 1.392 0.524 2.109 1.579
WBASG2 0.684 0.254 0.617 0.363 0.705 0.116 3.074 1.096
*Bid-Ask-Spread, that is the best Ask minus the best Bid observed in the market book.
**Weighted BAS, that is the mean of Ask prices weighted by quantities minus the mean of Bid prices
weighted by quantities.
13This does not preclude to the fact that the equilibrium prices can be alike, as in the case of the auction
thanks to the structures of incentives suggested by induced value theory. Nevertheless, it is appropriate to remain attentive with respect to the prac-tical implementation of such protocols.
First, it seems reasonable to systematically carry out tests in the same way as those proposed in this paper to check the behavioral homogeneity of both groups' subjects. Second, it is necessary to remember that this behavioral homogeneity is subjected to the achievement of a learning
ele-ment.
This learning-eect is already underlined by Smith and Williams (1983), who recommend the use of experimental subjects already familiarized with the laboratory techniques. Our research provides support for this recommendation within the framework of control-test designed proto-cols.
Appendix A
A.1. Instructions given to the subjects
Two instruction sets were communicated to the subjects. One presents
the operation instructionscontained in the software that were used as
support for collecting the information (ESLDA, from the experimental economics laboratory, University of Tucson, Arizona). The other explains to the participants how the experimental economy is structured. It de-scribes the industrial sectors, the companies that are established there, and the dependence links they maintain. These instructions specify the role of the agents and what is awaited from them during the experi-ment.
These instructions were the subject of an oral presentation in the form of 1 h interactive talk for each one of them (on 1998, the 17th of March). A written document was given to the participants showing their integrality in these instructions.
Oral examination tests of comprehension and a control manipulation of the software were applied at the end of these presentations. The two in-struction sets are available from the author.
The sessions took place in a computer lab of the university containing a local network of PCs.
A.2. Nature of the reward
Remuneration is monetary. No prestige is associated to the duties in the
market or to the detention of a particular asset. Fort1, only the hope of a higher remuneration than the one obtained in t can justify the agents' choices. No satiety is possible, the ®nal amount which one can obtain in the experiment is a function of the losses in¯icted by others (it is a competitive
market). Moreover, the experimental subjects do not know their
remunera-tion at any particular moment.
The rules of pro®t are known in advance and the remuneration of the subjects depends on the management of their individual original endowment. The reward exceeds the opportunity cost of the subjects considering the latter is roughly ®xed to the guaranteed minimum wage used in the country where the experiment took place. Thus, a 250 French francs (henceforth FRF) average pro®t for 6 h of experiment (that is to say a 41.5FRF hourly wage) was paid (maximum pro®t paid to an agent at the end of the experiment: 342FRF; minimum pro®t: 210 FRF).
A.3. Existence of a preliminary training session
A two hour training session was held on the 03/18/1998. It did not include any remuneration. The main diculties for the subjects were related to the use of the software.
A.4. Experimental subjects
24 students responded to a recruiting announcement released in January 1998. The table below speci®es their academic origin.
Academic origin of the students Total sta Real sta
French Ma^õtrise de Sciences Economiques 7210
French Ma^õtrise d' Administration Economique et Sociale
524
French Ma^õtrise des Sciences et Techniques Comptables et Financieres
39 10
The following table sums up the speci®c academic competencies of the sub-jects according to their university origin.
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