Information cascades in the laboratory


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Information cascades in the laboratory

  1. 1. INFORMATION CASCADES IN THE LABORATORYINFORMATION CASCADESIN THE LABORATORYPresented by Babacar SECKDirected by Philippe MadièsMASTER 2 Finance field Empirical Finance and Accounting
  2. 2. [Tapez un texte] Page 2Babacar SECK M2 Empirical Finance and AccountingINFORMATION CASCADES IN THE LABORATORYLisa R. Anderson and Charles A. Holt*This paper titled “information cascades in the laboratory” aims at reporting a cascadeexperiment that is based on a specific parametric model taken from Bikhchandani, Hirshleifer,and Welch (1992).In fact, when people are connected by a network, it becomes possible for them to influenceeach other’s behavior and decisions. Therefore, this kind of behavior gives rise to a range ofsocial processes in which networks serve to aggregate individual behavior and thus producepopulation-wide, collective outcomes. Such basic principle can be defined as an “informationcascade” which occurs when initial decisions coincide in a way that it is optimal for each ofthe subsequent individuals to ignore their private signals and follow the established pattern.In other words, an information cascade can result from rational inferences that others’decisions are based on information that dominates one’s own signal.I. A SYMMETRIC MODEL :They propose a model with two equally events denoted A and B and each event has is ownprivate signal. For event named A the signal is called a and they of B is b.In addition, the posterior probability of event A given signal a is 2/3 because of the fact that 2of the 3 balls labeled a are in urn A. In respect with the event A given signal b, the posteriorprobability is estimated at 1/3.Moreover concerning their supposition in this model, individuals are approached in a randomorder to receive a signal and make a decision. Then, when they are made decisions, the lastsare publicly announced.The urn with the greater posterior probability will always be prefered by an expected-utilitymaximizer, if each subject is paid a fixed cash amount only for a correct decision.The prediction made by the first decision maker in the sequence with the private draw as onlyinformation will reveal that person’s private draw.Then the second person should also follow the first two person’s prediction, in the case wherehe’s draw matches the label of the first person’s prediction. However, cascade can occur in sofar as the decision made by the first decision maker in the sequence differs from the one of thesecond person and the next two match.
  3. 3. [Tapez un texte] Page 3Babacar SECK M2 Empirical Finance and AccountingIf we assume that each subsequent individual consideres that others use Bayes’ rule1tomake predictions, the third person should predict event A in spite of the private b signal.Therefore, the first two decisions can start a cascade in which the third and subsequentdecision makers don’t take into account their own private information. Regardless of theirown private information, all subsequent decision makers should always follow the predictionsmade by the two first decision makers.Moreover, according to the authors, relevant signals are those inferred from decisions madebefore a cascade starts, from the two decisions that start a cascade, and from non-Bayesiandeviations from a cascade.Indeed, in order to compute for any combination of draws the ex ante likelihood of theoccurence of event A, one can use Bayes’ rule2. Hence, Bayes’rule corresponds to a simplecounting heuristic.II. PROCEDURES :Their experiment is made in the sample of 72 students from undergraduate economicsprogram. They were paid $5 upon arrival and privately in cash an average of $20 at the end ofthe experiment.In each session, six subjects were decision makers and one was randomly chosen to serve as a“monitor”. Moreover, each session is composed by 15 periods and lasted for about one and ahalf hours.1For example, if the first two decisions are A and the third person observes a b signal, then this person isresponding to an inferred sample of a on the first two draws, and b on the third draw.2In probability theory and applications, Bayes rule relates the odds of event to event , before andafter conditioning on event . The relationship is expressed in terms of the Bayes factor, . Bayes rule isderived from and closely related to Bayes theorem. Bayes rule may be preferred to Bayes theorem when therelative probability (that is, the odds) of two events matters, but the individual probabilities do not. This isbecause in Bayes rule, is eliminated and need not be calculated. Source: wikipedia.
  4. 4. [Tapez un texte] Page 4Babacar SECK M2 Empirical Finance and AccountingIndeed, urn A contained two a balls and one b ball, and urn B contained two b balls and one aball (see fig.1).Urn A was used if the throw of the die was one, two, or three; urn B was used otherwise.In each period, subjects were randomly chosen. In addition, each one of them knew his or herown private draw and the prior decisions of others, if any, before making a prediction.Then the participants recorded their earnings: $2 for a correct prediction and nothingotherwise.III. RESULTS :Their findings show evidence of cascade behavior in 41 of the 56 periods in which animbalance of previous inferred signals occurred.Another important finding found in the boxes via shading is that decisions were consistentwith Bayes’ rule and inconsistent with private information. But, they’ve also found a reverse3cascade in the period 9 of the session 2 by the fact that, despite the prediction of urn A by thefirst two decision makers, B was used by four subsequent decision makers inspite of theirprivate b draws.Moreover, the results in period 8 show that the third decision Maker decides consistent withprivate information. However, the over all six sessions suggest that about 4 percent of thedecisions were inconsistent with both Bayes’ rule and private information.They also found rounds in which the decision was optimal but inconsistent with privateinformation.Besides, in order to assess both the extent to which subjects do worse than choosing optimallyand the extent to which they do better than just choosing randomly, they use expected payoffcomputations on the basis of the Bayes distribution at the time where the decision was made.3The reverse cascade is a juggling pattern in which the props follow the same path as the cascade, but with timegoing backwards, hence the reverse. Source: wikipedia
  5. 5. [Tapez un texte] Page 5Babacar SECK M2 Empirical Finance and AccountingTherefore the procedure is dichotomous and is as follow, they firstable start by normalizingthe efficiency measure by calculating the actual efficiency which is the difference between theactual expected payoff and the random-choice payoff expressed as a percentage of thedifference between the optimal expected payoff and the random-choice payoff. Then, theyassess the private information efficiency which is between 0 and 100. This measure used as abenchmark is useful as a basis of comparison with actual efficiency, to determine the extent towhich a person used information inferred from public decisions.Their results suggest that, actual efficiency, averaged over all subjects was 91.4%, andprivate-information efficiency was 72.1%. Moreover, 22 of the 36 subjects (ie. 2/3) obtainedactual efficiencies of 100 percent consistent with perfect conformity with Bayes’ rule. Inaddition, 2/3 of the remaining others did better than they would have with decisions basedsolely on private information. Another important finding is that there is an important numberof the subjects who seemed not taking into account the the information in others’ priorpredictions, which is a plausible reaction to the possibility that others are making errors.So in order to shed the light on the effects of decision errors, caused by independent additiveshocks, on posterior probabilities, they perform a logit model.IV. AN ECONOMETRIC ANALYSIS OF ERRORSIn order to assess the error rates, they use an econometric model by firstable computing theexpected payoffs. Indeed, the logit model specifies that the probability that the decisionmaker in round i chooses urn A is an increasing exponential function of the expected payofffor urn A. Therefore, the likelihood of choosing urn A is an increasing function of thedifernce between payoff of urn A and urn B. Moreover, the tendency to make errorsdiminishes as ß 4and the probability of making the decision with the highest payoffgoes to 1. The decision probabilities approach 1/2, regardless of expected payoffs if behaviorbecomes essentially random. However, regarding their analysis, the logit function specifies aprobability of 1/2 for each decision in the case where the expected payoffs are the same.Besides, they assume that the second person’s expected payoffs for each prediction determinedecision probabilities via the logit choice function because of the fact that he may also makean error. In fact, the error structure is recursive; the second person’s expected payoffs areaffected by the parameter for the first person in the sequence.4parameterizes the sensitivity to payoff differences
  6. 6. [Tapez un texte] Page 6Babacar SECK M2 Empirical Finance and AccountingThen, regarding the econometric results by Report we observe about a 5 % a change of theerror classification of the individual decisions, while they were no error on the previousanalysis.In addition, the second person in the sequence should not be indifferent when the drawobserved in the second round is inconsistent with the first-round prediction, because, the first-round prediction is a noisy signal of the first-round draw.In the same vein, the analysis of the parameter results shown in the table wich reports theeconometric results shows that the third person should still start the cascade, if the first personand the second one predict A and the third person sees a b draw, since the posterior for urn Ais 0.5745 consistent to the calculations of Anderson (1994). Likewise, the logit probability fordecision A is greater than 1/2.Another important finding is that the information inherent in whether or not someone deviatesfrom a cascade is incorporated into the posteriors that are based on the application of Bayes’rule in a probabilistic choice context. This argument is corroborated by the fact that 15 of the16 deviations from cascade patterns were made after seeing a private draw that favored theurn that was not predicted by previous decision makers.In short, the most important series of actions of behavior can be explained in the case of theanalysis is changed in order to incorporate the possibility that others make errors.Substantially, the estimations of the errors are small enough so that it is still optimal to followa cascade as much as it starts even if one’s private information point out the contrary.Frequently, other’s decisions are poor in terms of information because of the possibility oferror. Futhermore, some subjects make systematic deviations from Bayesian decision making.IV. BIASES :The calculations of the biases are done without random decision error and the focus is onother (non-random) biases that might be present.A. Status Quo and Representativeness Bias:The status quo bias should show up most clearly when the Bayes distribution for A is close to½ as much as there is an additional preference to follow the consensus. With respect to thesecond round, the most common are posteriors of ½.The results show 68 instances in which the Bayes distribution was 1/2; at the same time, theprivate information did not match the label of the previous decision for the over all 6 sessionswith the symmetric design. In addition, most of the cases the subject did not go along with theprevious decision. This pattern is found in 57 of that 68 cases.
  7. 7. [Tapez un texte] Page 7Babacar SECK M2 Empirical Finance and AccountingConsistent to Kahneman and Tversky, 1973, subjects tend to underweight prior probabilitiesand focus on the similarity of their sample to a particular population.In ten of the thirty-six cases resulting from the combination of the two public draws and theprivate draw, the Bayesian posterior for the urn that the sample “represented” was less than1/2, and the subject made a decision consistent with Bayes’ rule in all ten cases. However, inthis context, the representativeness is not proved consistent to Grether (1980 and 1992).B. Counting Heuristic :Here, they conducted six supplemenatry sessions with an asymmetric design in whichcounting can be distinguished from Bayesian behavior.The asymmetry is brought out by the fact that the b signal is much more informative than thea signal, so that just the fact of counting the number of relevant decisions made previouslydoes not necessarily point out a correct Bayesian decision.Futhermore, refering to the table which represents the Posterior Probability of Event A for theAsymmetric Design, we find that the four cases where Bayes’ rule and the counting rule makedifferent predictions are consistent to situations in which there are more a signals, but asmaller number of informative b signals causes the Bayesian posterior for urn A to be lessthan 0.5.In the same vein, the analysis of the table which represents Data for Selected Periods ofSession shed the light the fact that with respect to period 2, the first three subjects saw asignals and correctly predicted urn A. At the same time and still in the same period, the fourthdecision maker saw the more informative b signal. The latter would also predict urn A, withthree a signals and only one (observed) b signal by using a conting rule.Conversly, the findings suggest that only 0.46 represents the posterior for urn A due to theasymmetry in the contents of the urns. Futhermore, this subject predicted urn B. Regardingthe fifth round the decision maker have made a correct Bayesian decision if counting wouldhave given a different forecast. In addition, we also found in the fifth and sixth roundBayesian decisions that are inconsistent with counting. Moreover, decision that wasinconsistent with Baye’s rule and counting are made by the last subject in the sequenceconcerning the period 2. Another type of error made by subject is the one made by the fourthsubject in the sequence in respect with the third period. However, that decision contrary to thelast one is inconsistent with Bayes’ rule but consistent with counting. There are also,concerning periods 4 and 5 a reverse cascade that was caused by an error in the second round.For the entire sessions with asymmetric design cascades formed in 46 out of the 66 periods
  8. 8. [Tapez un texte] Page 8Babacar SECK M2 Empirical Finance and Accountingwhere they were an optimal Bayesian decision was inconsistent with a subject’s privateinformation. The results also show that in 18 out of 46 incidence of reverse cascades washigher in this asymmetric design, against 13 out of 41 regarding the symmetric design.We find that in half of the cases, subjects make a correct (Bayesian) decision when thepredictions emanating from Bayes’ rule and counting differ.Also, in the absence of prediction of counting we find without a big surprise an increase of 66percent of correct decisions.The overall results show that, a significant part of the decisions (115 out of 540) differs fromthe principle of Bayes’ rule. Then, the counting can explain over the 1/3 of those decisions.Furthermore, the computations emanating with data from asymmetric design show that actualprivate information efficiencie represent 67.6 percent for over all subjects while privateinformation efficiencie is about 45.2 percent. However, the comparison of these figures andthe ones of the symmetric design where counting and Bayes’ rule always coincide shows thatthe lasts are relatively greater.Conversly, the counting efficiency calculation point out that 21 out of 36 subjects in terms ofasymmetric design did better than counting. But in such situation counting efficiency isapproximately the same as actual efficiency for averaged over all subjects.