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Journal of Economic Psychology 22 (2001) 1±26
www.elsevier.com/locate/joep
Laboratory incentive structure and control-test design in an
experimental asset market
Olivier Brandouy
*
Universit
e de Droit et des Sciences Economiques, ESRG, 4 Place du Pr
esidial, 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 homogenous 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; Experimental asset market; Test-reference protocol
*
Tel.: +33-5-55059573.
E-mail address: [email protected] (O. Brandouy).
0167-4870/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 4 8 7 0 ( 0 0 ) 0 0 0 3 4 - 9
2
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
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 install 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 inciting a speci®c behavior. For example, Wageman and Baker (1997) comparing 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.
Few experiments using this control-test design (henceforth CTD) have
been carried out in market-®nance. Nevertheless, some research dealing with
various other aspects of economic life have resorted to such a design, in
general only in the case of long-term ®eld experiments. For example, Hanlon,
Meyer, and Taylor (1994) have conducted a longitudinal study in the aim of
testing the consequences of a pro®t-sharing plan on various groups of sub-
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
3
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 longterm 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 performance.
The present study ®nds evidence which supports the use of control-test designs, with speci®c implications for academic research on experimental asset
markets.
Section 2 is 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 obtained results. Speci®c information regarding the experiment is provided in
Appendix A, 1 in 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 structures (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.
1
The complete set of instructions (in French) is available upon request from the author.
4
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
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 environmentrelated 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 retirement 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 variation 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 purpose of the experiment is to test the isolated eects of critical information on the value of the quoted company shares. To this extent, a
`control group' of experimental subjects exclusively receives throughout the
experiment the simple information set. A parallel `treatment group' is subjected to the critical information set, in addition to the same ¯ow of simple
information.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
5
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 experiment, 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 exogenous 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 validation 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 economics and management science. Three dierent university programs provided 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 experimental 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 size and undoubtedly does not ensure the appropriateness of
2
For a counter-example where a large number of subjects are used, see Isaac, Walker, and Arlington,
1994. For an interesting way to keep the global budget at an acceptable level, see Bolle (1990).
6
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
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 contrasted 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 quotations provided by these two groups in the double-auction market might
present, ceteris paribus, many perturbing differences solely due to psychological characteristics and not due to experimental design factors.
As stated previously, a payment structure according to the rules suggested
by Smith in the Induced Value Theory makes 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 subjects 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
3
A large sample randomly extracted from the total population should have been selected, but in
addition to the problems linked to the size of the samples, the experimental subjects are assumed to be
familiar with many aspects of market-®nance or economic analysis, which renders such a selection
impossible.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
7
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 response to the same
stimulus must converge.
· Secondly, if the two groups have similar behavior, the response to the same
series of stimuli must 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
give the same isolated response to the same problem;
2. Two groups, identical in all respects, should each provide a distinctly different 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 psychological 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.
4
The `tested group' is subjected to both ¯ows; the `reference group' is only subjected to the simple
information set.
8
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
The initial price for each share at the beginning of the experiment is entirely 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 parameters 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 hypothetical 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 b 2), in order to complete the scenario and to oer an evaluation tool for the interested participants. 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-¯uctuations 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 between 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.
The experiment took place during four sessions for each group. The basic
features of each session were standardized (identical laboratory, experimental
procedures and traders) to give a constant and controlled experimental environment. Each session was divided into small intervals called `mini-periods'. Each mini-period was organized with respect to these rules: the auction
market being closed, the experimenter releases information (simple, or a
combination of simple + critical). Then a limited amount of time is allowed
for the agents to analyze this information (from 2 to 6 min depending on its
complexity). After this time, the auction market starts and the subjects are
encouraged to trade their shares ®xing their conditions during a predetermined period (from 90 to 120 s, according to the session). After this interval,
the market closes automatically, ending the mini-period. Each group
participates in 55 mini-periods. The `control group' will have been subjected
to simple information exclusively, and the `treatment group' will have
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
9
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 stimulation can 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 generous 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:
Pn
1
i1 Ask pricet;i Ask quantitiesi;t
Pn
GWQt
2
i1 Ask quantitiesi;t
!
Pn
Bid
price
Bid
quantities
t;i
i;t
i1 Pn
Bid
quantities
i;t
i1
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 deterministic trend, and past information has no utility in forecasting the future.
5
We shall denote BSGi : the Bid prices observed for group `i'.
10
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
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 interval in the analysis is reduced, this random walk intuition is 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, examination 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-stationarity for the auction prices provided by the two groups using an Augmented 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 period. Table 1 presents the results of the unit-root tests for each auction miniperiod.
Table 1
Unit root tests results (H0 : series is non-stationary)a
Quotation
Mini-period
101
102
103
104
105
106
107
108
109
110
111
112
GWQG1
GWQG2
BG1
BG2
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1*
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
R*
I 1
I 1
I 1
R*
R*
I 1
I 1
I 1
I 1
I 1
I 1
R*
I 1
I 1
I 1
I 1
I 1
I 1
R*
I 1
I 1
I 1
I 1
I 1
Mini-period
GWQG1
GWQG2
BG1
BG2
a
113
114
115
116
201
202
203
301
302
401
402
403
I 1*
I 1
I 1
I 1*
R
R
I 1
R
R*
R
I 1
R
I 1
I 1
I 1
I 1
I 1
R*
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1*
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
R*
I 1*
I 1
I 1
I 1
R
The 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: 112 means 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*): H0 is rejected with a 1% or 5%
signi®cance level; I 1*: H0 cannot be rejected at a 5% signi®cance level but at a 10% signi®cance level;
decision: ®rst-order integrated series.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
11
Fig. 1. Example of non-stationary quotations GWQG1 and GWQG2 for MP 202.
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
6
I 1 or I n order dierenced series were considered for regression analysis, but this brings up various
concerns with respect to the interpretation (both economic and econometric) of the transformed series. So
this option was not pursued.
12
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Fig. 2. Example of non-stationary quotations BG1 and BG2 for MP 105.
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, constitutes 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 2 proposes the results for the co-integration tests, which were obtained 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: ySG2 b ySG1 ; the
corresponding vector error correction model, for the two endogenous variables ySG1;t and ySG2;t is then:
7
DySG1;t c1 ySG1;t
1
b ySG1;t 1 e1;t ;
DySG1;t c2 ySG1;t
1
b ySG1;t 1 e2;t :
The series form two responses to a same set of stimulation.
13
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Table 2
Co-integration tests results for the quotation series (H10 : the series are not co-integrated. H20 : there exists at
most one co-integrating relationship)
Mini-period
101
102
103
104
105
106
107
108
109
110
111
112
113
116
201
202
203
301
302
401
402
403
BG1=G2
GWQG1=G2
Lags
Signif.
b
Rank 1
Lags
Signif.
b
Rank 1
1±15
1±21
1±27
1±29
1±27
1±23
1±8
N/A
1±3
1±18
1±1
1±17
1±7
1±15
N/A
1±14
1±13
1±12
1±7
1±3
1±4
1±20
5%
5%
1%
1%
1%
5%
5%
)0.9927
)1.0468
)1.1240
)1.0828
)1.0981
)1.0892
)1.1010
>10%
>50%
>50%
>50%
>20%
>20%
>50%
5%
5%
5%
5%
5%
)1.0059
)0.9893
)1.1213
)1.0412
)1.0390
>5%
>20%
>50%
>20%
>20%
5%
)1.1475
>50%
5%
5%
1%
5%
5%
5%
)1.0069
)1.0593
)1.0726
)1.0170
)1.1246
)1.0725
>20%
>50%
>20%
>50%
>10%
>50%
5%
)0.9875
>20%
5%
5%
5%
1%
5%
5%
5%
)1.0319
)1.0526
)1.1427
)1.0519
)0.8521
)0.8331
)0.9239
>5%
>20%
>5%
>50%
>50%
>50%
>50%
1±9
1±13
1±27
1±17
1±25
N/A
N/A
1±10
N/A
1±22
N/A
1±13
1±1
1)9
1±10
1±10
1±7
1±10
1±7
1±3
N/A
N/A
1%
1%
1%
5%
5%
1%
5%
5%
5%
)0.9974
)1.0315
)1.0162
)0.9844
)1.0292
)1.0746
)1.0046
)1.0724
)0.8918
>50%
>50%
>10%
>20%
>20%
>5%
>20%
>20%
>10%
2. The vector error correction model being relative to the short-term dynamics of the processes, the lag interval to make sense, must be chosen according to the length of the tested series. 8
For the results presented in Table 2, H20 denotes the hypothesis of one cointegrating 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 Osterwald-Lenum (1992) tables. The signi®cance level associated with this decision, 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
8
The number of lags included for the estimation of the co-integration relationship does not exceed one
third of the mini-period length.
14
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Fig. 3. Quotation and real prices for mini-period 114.
(no co-integration relationship between the series). b are the normalized cointegrating coef®cients.
Finally, the `lack of co-integration' hypothesis between the series is rejected (at a 5% level). Furthermore, the hypothesis of `at most one co-integrating relationship' cannot be rejected at standard levels, it is therefore likely
that the long run behavior of the two groups, expressed in the quotations
GWQSGi and 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 intertemporal behavioral similarity in the behavior of the groups. Instead of
working with the auction quotations that reveal a `price discovery mechanism', we need to consider the series of prices actually observed after information 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
15
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Table 3
Mean real prices, standard deviations and activity per group
Mean
Group of traders No. 1
4.5393
Total number of stocks in the experiment: 160
Group of traders No. 2
4.1120
Total number of stocks in the experiment: 170
a
r
Activitya
0.3065
310
0.0971
123
Quantity of traded stocks during the session.
book for example, which shifts the middle of the Bid-Ask-Spread). Thus,
during the mini-period No. 114, the traders from group 2 maintained very
steady real prices whereas the GWQSG2 quotation experienced erratic ¯uctuations.
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 contracts, 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.
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
Pend
t0
Transaction pricet Transaction quantitiest
of the mini-period
Transaction quantitiest
:
10
There is no distinction here between `tested group' or `reference group', because in this session, both
received strictly the same set of information.
16
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Fig. 4. Group 1, quotation and real prices (time reported in abscissa). (From mini-period No. 101 to miniperiod No. 110).
Fig. 5. Group 1, quotation and real prices (time reported in abscissa). (From mini-period No. 110 to miniperiod No. 116).
Beyond a certain time accorded to familiarization, the problems associated
with the use of the software manipulation should have, for the most part,
disappeared.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
17
Fig. 6. Group 2, quotation and real prices (time reported in abscissa). (From mini-period No. 101 to miniperiod No. 110).
Fig. 7. Group 2, quotation and real prices (time reported in abscissa). (From mini-period No. 110 to miniperiod No. 116).
Then, ¯uctuations in the real prices, due exclusively to the interpretation of information, start to resemble each other. This homogenization
of the behaviors is very clear in the two following ®gures. The ®rst one
18
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Fig. 8. Mean real prices (MRPi ) by mini-period, session No. 1.
(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 learning-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. 11 This 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
11
Given that those problems have not been totally eliminated during the training session devoted to the
use of the quotation software.
12
This analysis will be referred as `cluster analysis' for the remainder of the article.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
19
Fig. 9. Sliding correlation calculated on the MRPi .
Fig. 10. MRPi , calculated by period (cluster analysis).
mini-periods subjected to the same but slightly evolving signal. The comparative evolution of the MRPi , by period, reveals a marked similarity in the
response processes between the two groups (Fig. 10).
20
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Table 4
Non-parametric correlation on MRPG1 and MRPG2 (Observation: mean price over mini-periods) (H0 :
``G1 and G2 are independent''.)
a
Period
Range
qS
Critical values of the q-statistics
101±116
101±109
110±116
16
9
7
)0.1798
)0.3667
0. 6071a
)0.341 at a 10% s.l.
)0.483 at a 10% s.l.
0.571 at a 10% s.l.
Rejection at a 10% signi®cance level.
Table 5
Non-parametric correlation on MRPG1 and MRPG2 (cluster analysis) (H0 : ``G1 and G2 are independent''.)
a
Cluster
Range
qS
Critical values of the q-statistics
1±6
2±6
3±6
6
5
4
0.200
0.400
1a
)0.341at a 10% s.l.
)0.483 at a 10% s.l.
0.571 at a 10% s.l.
Rejection at a 1% signi®cance level.
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 anything above a 7.4% signi®cance level. Similarly, the following results are
presented for the `cluster analysis' (Table 5).
The observed MRP on the two experimental groups tend to be concordant in
a second half of the experimental session No. 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 supports 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
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
21
could have very dierent to identical series of stimuli, may, when subjected to
a well-designed incentive structure, operate identically ceteris 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 consistent (as though by magic) with predictive models based on individual rationality . . .''
Two experimental groups in the laboratory, subjected to identical stimulation, both tend to serve up a certain `type' of results, that is, results concordant 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 behavioral 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 dierences that remain, in other respects, evident within this experimental
protocol. That is, all the dierences do not disappear. For example, the
quantities of exchanged shares (Table 3) like the real transaction prices
22
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Table 6
Statistics on the Bid-Ask-Spread, by experimental session
Session No. 1
BAS G1
BASG2
WBAS G1
WBASG2
Session No. 2
Session No. 3
Session No. 4
Mean
r
Mean
r
Mean
r
Mean
r
0.528
0.294
1.697
0.684
0.502
0.334
0.469
0.254
0.425
0.236
0.621
0.617
0.376
0.183
0.497
0.363
0.430
0.157
1.392
0.705
0.582
0.090
0.524
0.116
1.149
0.725
2.109
3.074
1.566
0.890
1.579
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.
**
(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' individual 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 statistical procedure 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 session, thus motivating the use of preliminary training periods, which are
subsequently withdrawn from the collected results. In many cases, this prudential 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-integration tests could not be systematically used, the ®rst series being alternatively 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,
13
This does not preclude to the fact that the equilibrium prices can be alike, as in the case of the auction
series provided by the two groups: two BAS of dierent width may well lead to the same indicators.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
23
thanks to the structures of incentives suggested by induced value theory.
Nevertheless, it is appropriate to remain attentive with respect to the practical 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 element.
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 protocols.
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 describes 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 experiment.
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 instruction sets are available from the author.
The sessions took place in a computer lab of the university containing a
local network of PCs.
No abandonment was observed during the experiment; all the participants
respected their engagements.
24
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
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. For t 1, 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 remuneration 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
French Ma^õtrise de Sciences Economiques
French Ma^õtrise d' Administration
Economique et Sociale
French Ma^õtrise des Sciences et Techniques
Comptables et Financieres
Total
Total sta
Real sta
72
52
10
4
39
10
179
24 (13.4%)
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
25
The following table sums up the speci®c academic competencies of the subjects according to their university origin.
Academic origin of the students
`Ma^õtrise de Sciences Economiques'
`Ma^õtrise AES'
`MSTCF'
Relevant course for the experiment
Market ®nance, Industrial
economics, Corporate strategy
Finance, Corporate strategy
Financial markets, Corporate
®nance, Corporate strategy
References
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Economic Psychology, 11(2), 157±168.
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Davis, D. D., & Holt, C. A. (1993). Experimental Economics. Princeton, NJ: Princeton University Press.
Demsetz, H. (1968). The cost of transacting. Quarterly Journal of Economics, 33±53.
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Grossman, R. P., & Till, B. D. (1998). The persistence of classically conditioned brand attitudes. Journal of
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Hanlon, S. C., Meyer, D. G., & Taylor, R. R. (1994). Consequences of gainsharing: A ®eld experiment
revisited. Group and Organization Management, 19(1), 87±112.
Isaac, R. M., Walker, J. M., & Arlington, W. W. (1994). Group size and the voluntary provision:
Experimental evidence utilizing large groups. Journal of Public Economics, 54(1), 1±37.
Jamal, k., & Sunder, S. (1991). Money vs. Gaming: eects of salient monetary payments in double oral
auctions. Organizational behavior and human decision processes, 49, 151±166.
Jobert, T. (1992). Tests de racine unitaire: une strat. Cahiers de recherche E.M.A-M.A.D-Paris I, 44(92).
Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian autoregressive
models. Econometrica, 59, 1551±1580.
Kyle, A. S. (1989). Informed speculation with imperfect competition. Review of Economic Studies, 56(3),
317±355.
Mann, L., Samson, D., & Dow, D. (1998). A ®eld experiment on the e
www.elsevier.com/locate/joep
Laboratory incentive structure and control-test design in an
experimental asset market
Olivier Brandouy
*
Universit
e de Droit et des Sciences Economiques, ESRG, 4 Place du Pr
esidial, 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 homogenous 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; Experimental asset market; Test-reference protocol
*
Tel.: +33-5-55059573.
E-mail address: [email protected] (O. Brandouy).
0167-4870/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 4 8 7 0 ( 0 0 ) 0 0 0 3 4 - 9
2
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
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 install 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 inciting a speci®c behavior. For example, Wageman and Baker (1997) comparing 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.
Few experiments using this control-test design (henceforth CTD) have
been carried out in market-®nance. Nevertheless, some research dealing with
various other aspects of economic life have resorted to such a design, in
general only in the case of long-term ®eld experiments. For example, Hanlon,
Meyer, and Taylor (1994) have conducted a longitudinal study in the aim of
testing the consequences of a pro®t-sharing plan on various groups of sub-
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
3
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 longterm 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 performance.
The present study ®nds evidence which supports the use of control-test designs, with speci®c implications for academic research on experimental asset
markets.
Section 2 is 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 obtained results. Speci®c information regarding the experiment is provided in
Appendix A, 1 in 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 structures (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.
1
The complete set of instructions (in French) is available upon request from the author.
4
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
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 environmentrelated 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 retirement 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 variation 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 purpose of the experiment is to test the isolated eects of critical information on the value of the quoted company shares. To this extent, a
`control group' of experimental subjects exclusively receives throughout the
experiment the simple information set. A parallel `treatment group' is subjected to the critical information set, in addition to the same ¯ow of simple
information.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
5
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 experiment, 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 exogenous 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 validation 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 economics and management science. Three dierent university programs provided 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 experimental 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 size and undoubtedly does not ensure the appropriateness of
2
For a counter-example where a large number of subjects are used, see Isaac, Walker, and Arlington,
1994. For an interesting way to keep the global budget at an acceptable level, see Bolle (1990).
6
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
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 contrasted 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 quotations provided by these two groups in the double-auction market might
present, ceteris paribus, many perturbing differences solely due to psychological characteristics and not due to experimental design factors.
As stated previously, a payment structure according to the rules suggested
by Smith in the Induced Value Theory makes 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 subjects 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
3
A large sample randomly extracted from the total population should have been selected, but in
addition to the problems linked to the size of the samples, the experimental subjects are assumed to be
familiar with many aspects of market-®nance or economic analysis, which renders such a selection
impossible.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
7
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 response to the same
stimulus must converge.
· Secondly, if the two groups have similar behavior, the response to the same
series of stimuli must 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
give the same isolated response to the same problem;
2. Two groups, identical in all respects, should each provide a distinctly different 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 psychological 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.
4
The `tested group' is subjected to both ¯ows; the `reference group' is only subjected to the simple
information set.
8
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
The initial price for each share at the beginning of the experiment is entirely 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 parameters 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 hypothetical 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 b 2), in order to complete the scenario and to oer an evaluation tool for the interested participants. 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-¯uctuations 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 between 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.
The experiment took place during four sessions for each group. The basic
features of each session were standardized (identical laboratory, experimental
procedures and traders) to give a constant and controlled experimental environment. Each session was divided into small intervals called `mini-periods'. Each mini-period was organized with respect to these rules: the auction
market being closed, the experimenter releases information (simple, or a
combination of simple + critical). Then a limited amount of time is allowed
for the agents to analyze this information (from 2 to 6 min depending on its
complexity). After this time, the auction market starts and the subjects are
encouraged to trade their shares ®xing their conditions during a predetermined period (from 90 to 120 s, according to the session). After this interval,
the market closes automatically, ending the mini-period. Each group
participates in 55 mini-periods. The `control group' will have been subjected
to simple information exclusively, and the `treatment group' will have
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
9
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 stimulation can 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 generous 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:
Pn
1
i1 Ask pricet;i Ask quantitiesi;t
Pn
GWQt
2
i1 Ask quantitiesi;t
!
Pn
Bid
price
Bid
quantities
t;i
i;t
i1 Pn
Bid
quantities
i;t
i1
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 deterministic trend, and past information has no utility in forecasting the future.
5
We shall denote BSGi : the Bid prices observed for group `i'.
10
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
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 interval in the analysis is reduced, this random walk intuition is 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, examination 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-stationarity for the auction prices provided by the two groups using an Augmented 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 period. Table 1 presents the results of the unit-root tests for each auction miniperiod.
Table 1
Unit root tests results (H0 : series is non-stationary)a
Quotation
Mini-period
101
102
103
104
105
106
107
108
109
110
111
112
GWQG1
GWQG2
BG1
BG2
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1*
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
R*
I 1
I 1
I 1
R*
R*
I 1
I 1
I 1
I 1
I 1
I 1
R*
I 1
I 1
I 1
I 1
I 1
I 1
R*
I 1
I 1
I 1
I 1
I 1
Mini-period
GWQG1
GWQG2
BG1
BG2
a
113
114
115
116
201
202
203
301
302
401
402
403
I 1*
I 1
I 1
I 1*
R
R
I 1
R
R*
R
I 1
R
I 1
I 1
I 1
I 1
I 1
R*
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1*
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
I 1
R*
I 1*
I 1
I 1
I 1
R
The 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: 112 means 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*): H0 is rejected with a 1% or 5%
signi®cance level; I 1*: H0 cannot be rejected at a 5% signi®cance level but at a 10% signi®cance level;
decision: ®rst-order integrated series.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
11
Fig. 1. Example of non-stationary quotations GWQG1 and GWQG2 for MP 202.
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
6
I 1 or I n order dierenced series were considered for regression analysis, but this brings up various
concerns with respect to the interpretation (both economic and econometric) of the transformed series. So
this option was not pursued.
12
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Fig. 2. Example of non-stationary quotations BG1 and BG2 for MP 105.
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, constitutes 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 2 proposes the results for the co-integration tests, which were obtained 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: ySG2 b ySG1 ; the
corresponding vector error correction model, for the two endogenous variables ySG1;t and ySG2;t is then:
7
DySG1;t c1 ySG1;t
1
b ySG1;t 1 e1;t ;
DySG1;t c2 ySG1;t
1
b ySG1;t 1 e2;t :
The series form two responses to a same set of stimulation.
13
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Table 2
Co-integration tests results for the quotation series (H10 : the series are not co-integrated. H20 : there exists at
most one co-integrating relationship)
Mini-period
101
102
103
104
105
106
107
108
109
110
111
112
113
116
201
202
203
301
302
401
402
403
BG1=G2
GWQG1=G2
Lags
Signif.
b
Rank 1
Lags
Signif.
b
Rank 1
1±15
1±21
1±27
1±29
1±27
1±23
1±8
N/A
1±3
1±18
1±1
1±17
1±7
1±15
N/A
1±14
1±13
1±12
1±7
1±3
1±4
1±20
5%
5%
1%
1%
1%
5%
5%
)0.9927
)1.0468
)1.1240
)1.0828
)1.0981
)1.0892
)1.1010
>10%
>50%
>50%
>50%
>20%
>20%
>50%
5%
5%
5%
5%
5%
)1.0059
)0.9893
)1.1213
)1.0412
)1.0390
>5%
>20%
>50%
>20%
>20%
5%
)1.1475
>50%
5%
5%
1%
5%
5%
5%
)1.0069
)1.0593
)1.0726
)1.0170
)1.1246
)1.0725
>20%
>50%
>20%
>50%
>10%
>50%
5%
)0.9875
>20%
5%
5%
5%
1%
5%
5%
5%
)1.0319
)1.0526
)1.1427
)1.0519
)0.8521
)0.8331
)0.9239
>5%
>20%
>5%
>50%
>50%
>50%
>50%
1±9
1±13
1±27
1±17
1±25
N/A
N/A
1±10
N/A
1±22
N/A
1±13
1±1
1)9
1±10
1±10
1±7
1±10
1±7
1±3
N/A
N/A
1%
1%
1%
5%
5%
1%
5%
5%
5%
)0.9974
)1.0315
)1.0162
)0.9844
)1.0292
)1.0746
)1.0046
)1.0724
)0.8918
>50%
>50%
>10%
>20%
>20%
>5%
>20%
>20%
>10%
2. The vector error correction model being relative to the short-term dynamics of the processes, the lag interval to make sense, must be chosen according to the length of the tested series. 8
For the results presented in Table 2, H20 denotes the hypothesis of one cointegrating 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 Osterwald-Lenum (1992) tables. The signi®cance level associated with this decision, 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
8
The number of lags included for the estimation of the co-integration relationship does not exceed one
third of the mini-period length.
14
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Fig. 3. Quotation and real prices for mini-period 114.
(no co-integration relationship between the series). b are the normalized cointegrating coef®cients.
Finally, the `lack of co-integration' hypothesis between the series is rejected (at a 5% level). Furthermore, the hypothesis of `at most one co-integrating relationship' cannot be rejected at standard levels, it is therefore likely
that the long run behavior of the two groups, expressed in the quotations
GWQSGi and 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 intertemporal behavioral similarity in the behavior of the groups. Instead of
working with the auction quotations that reveal a `price discovery mechanism', we need to consider the series of prices actually observed after information 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
15
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Table 3
Mean real prices, standard deviations and activity per group
Mean
Group of traders No. 1
4.5393
Total number of stocks in the experiment: 160
Group of traders No. 2
4.1120
Total number of stocks in the experiment: 170
a
r
Activitya
0.3065
310
0.0971
123
Quantity of traded stocks during the session.
book for example, which shifts the middle of the Bid-Ask-Spread). Thus,
during the mini-period No. 114, the traders from group 2 maintained very
steady real prices whereas the GWQSG2 quotation experienced erratic ¯uctuations.
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 contracts, 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.
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
Pend
t0
Transaction pricet Transaction quantitiest
of the mini-period
Transaction quantitiest
:
10
There is no distinction here between `tested group' or `reference group', because in this session, both
received strictly the same set of information.
16
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Fig. 4. Group 1, quotation and real prices (time reported in abscissa). (From mini-period No. 101 to miniperiod No. 110).
Fig. 5. Group 1, quotation and real prices (time reported in abscissa). (From mini-period No. 110 to miniperiod No. 116).
Beyond a certain time accorded to familiarization, the problems associated
with the use of the software manipulation should have, for the most part,
disappeared.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
17
Fig. 6. Group 2, quotation and real prices (time reported in abscissa). (From mini-period No. 101 to miniperiod No. 110).
Fig. 7. Group 2, quotation and real prices (time reported in abscissa). (From mini-period No. 110 to miniperiod No. 116).
Then, ¯uctuations in the real prices, due exclusively to the interpretation of information, start to resemble each other. This homogenization
of the behaviors is very clear in the two following ®gures. The ®rst one
18
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Fig. 8. Mean real prices (MRPi ) by mini-period, session No. 1.
(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 learning-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. 11 This 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
11
Given that those problems have not been totally eliminated during the training session devoted to the
use of the quotation software.
12
This analysis will be referred as `cluster analysis' for the remainder of the article.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
19
Fig. 9. Sliding correlation calculated on the MRPi .
Fig. 10. MRPi , calculated by period (cluster analysis).
mini-periods subjected to the same but slightly evolving signal. The comparative evolution of the MRPi , by period, reveals a marked similarity in the
response processes between the two groups (Fig. 10).
20
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Table 4
Non-parametric correlation on MRPG1 and MRPG2 (Observation: mean price over mini-periods) (H0 :
``G1 and G2 are independent''.)
a
Period
Range
qS
Critical values of the q-statistics
101±116
101±109
110±116
16
9
7
)0.1798
)0.3667
0. 6071a
)0.341 at a 10% s.l.
)0.483 at a 10% s.l.
0.571 at a 10% s.l.
Rejection at a 10% signi®cance level.
Table 5
Non-parametric correlation on MRPG1 and MRPG2 (cluster analysis) (H0 : ``G1 and G2 are independent''.)
a
Cluster
Range
qS
Critical values of the q-statistics
1±6
2±6
3±6
6
5
4
0.200
0.400
1a
)0.341at a 10% s.l.
)0.483 at a 10% s.l.
0.571 at a 10% s.l.
Rejection at a 1% signi®cance level.
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 anything above a 7.4% signi®cance level. Similarly, the following results are
presented for the `cluster analysis' (Table 5).
The observed MRP on the two experimental groups tend to be concordant in
a second half of the experimental session No. 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 supports 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
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
21
could have very dierent to identical series of stimuli, may, when subjected to
a well-designed incentive structure, operate identically ceteris 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 consistent (as though by magic) with predictive models based on individual rationality . . .''
Two experimental groups in the laboratory, subjected to identical stimulation, both tend to serve up a certain `type' of results, that is, results concordant 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 behavioral 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 dierences that remain, in other respects, evident within this experimental
protocol. That is, all the dierences do not disappear. For example, the
quantities of exchanged shares (Table 3) like the real transaction prices
22
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
Table 6
Statistics on the Bid-Ask-Spread, by experimental session
Session No. 1
BAS G1
BASG2
WBAS G1
WBASG2
Session No. 2
Session No. 3
Session No. 4
Mean
r
Mean
r
Mean
r
Mean
r
0.528
0.294
1.697
0.684
0.502
0.334
0.469
0.254
0.425
0.236
0.621
0.617
0.376
0.183
0.497
0.363
0.430
0.157
1.392
0.705
0.582
0.090
0.524
0.116
1.149
0.725
2.109
3.074
1.566
0.890
1.579
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.
**
(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' individual 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 statistical procedure 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 session, thus motivating the use of preliminary training periods, which are
subsequently withdrawn from the collected results. In many cases, this prudential 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-integration tests could not be systematically used, the ®rst series being alternatively 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,
13
This does not preclude to the fact that the equilibrium prices can be alike, as in the case of the auction
series provided by the two groups: two BAS of dierent width may well lead to the same indicators.
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
23
thanks to the structures of incentives suggested by induced value theory.
Nevertheless, it is appropriate to remain attentive with respect to the practical 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 element.
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 protocols.
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 describes 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 experiment.
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 instruction sets are available from the author.
The sessions took place in a computer lab of the university containing a
local network of PCs.
No abandonment was observed during the experiment; all the participants
respected their engagements.
24
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
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. For t 1, 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 remuneration 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
French Ma^õtrise de Sciences Economiques
French Ma^õtrise d' Administration
Economique et Sociale
French Ma^õtrise des Sciences et Techniques
Comptables et Financieres
Total
Total sta
Real sta
72
52
10
4
39
10
179
24 (13.4%)
O. Brandouy / Journal of Economic Psychology 22 (2001) 1±26
25
The following table sums up the speci®c academic competencies of the subjects according to their university origin.
Academic origin of the students
`Ma^õtrise de Sciences Economiques'
`Ma^õtrise AES'
`MSTCF'
Relevant course for the experiment
Market ®nance, Industrial
economics, Corporate strategy
Finance, Corporate strategy
Financial markets, Corporate
®nance, Corporate strategy
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