Fragile, Error-Prone And Idiosyncratic Behaviour: Informational Cascades

1) Introduction

Macroeconomics deals with the behaviour of the economy altogether and concentrates on fundamental and actual economic problems. Microeconomics deals with the behaviour of individuals and the aggregation of their actions in different institutional frameworks. Thus, both micro- and macroeconomics are doctrines to describe and understand individuals’ behaviour, activities and outcomes. So, why does one try to better understand? ‘Individuals are curious’, is a popular explanation. Another is that understanding may lead to a better outcome for individuals. There exist a lot of patterns of behaviour. One behaviour pattern is the so-called uniform behaviour. Imitation and mimicry belong to the basic instincts of every human being. Indeed, these patterns do not make immediate sense in terms of traditional macro- or microeconomic models. Still, they may be rational for an individual or a group of individuals. Learning by observing other individuals’ past actions and decisions may be of help to explain some otherwise puzzling phenomena about human behaviour. Apprehending individuals’ behaviour is not straightforward. It is not only profit or utility maximising that drives individuals’ minds. Sometimes, individuals just act because others act. An Informational Cascade is a situation in which every subsequent individual, based on the observation of others, makes the same choice or decision independent of his private information. Informational Cascades are present in our everyday life and in fields such as Economics, Politics, Scientific Theory, Finance or Zoology. The fact that this phenomenon does appear in innumerable situations is my motivation to closer examine Informational Cascades.

Economics and above all economic behaviour is more than Statistics or Mathematics. It is Anthropology and Psychology as well.

- To combine and describe economics with the behaviour patterns of human beings, above all Informational Cascades and its ‘environment’, is the base of my licentiate.

To link this phenomenon to economics and to bring it in an economic context, one has to grasp what exactly an Informational Cascade does describe. Why can one define an Informational Cascade as a gap between the practiced and the preached? Definitions and a simple example are given at the beginning of chapter two, followed by a characterisation of an Informational Cascade.

The characterisation deals with the brittleness, idiosyncrasy and the error-sensitivity of Informational Cascades. Cascades are not just good for theory; indeed they do appear in empirical contents. This is illustrated at the end of chapter two, followed by an important tool to understand Informational Cascades: Bayes’ Rule.

- The aim of chapter two is to provide the basics of Informational Cascades and to assure that the reader is prepared to conceive the periphery of this behaviour pattern.

Chapter three will deal with the crucial part of my work. It is dedicated to the dissection and classification of the literature dealing with Informational Cascades.

- What areas, fields or realms influence and form Cascades?

This is the relevant question in the first part. One can subordinate Cascades to clusters such as Economics, Psychology, Sociology and others. In part two, I will dissect Cascades into well-known characteristics, specifications and theories, namely fads, fashions, herd behaviour, bubbles and crashes, and many others. I will also treat unorthodox phenomena such as the hush helix or the snob effect.

- To show that an Informational Cascades’ environment is variegated and complex is this chapter’s assignment.

This is illustrated on the overview map at the end of chapter three.

I will analyse Informational Cascades in the context of financial markets, and show when and how frequently this phenomenon does occur.

- This is the task of chapter four, where I illustrate that Informational Cascades appear within sequential and non-sequential contexts, i.e. when the ordering of individuals is endogenous or exogenous respectively.

For the probability to occur, the selection of the model to describe an Informational Cascade is crucial.

The innumerable ways individuals can understand and interpret the world, is another crucial factor affecting the probability for a Cascade to occur.

Questions in dispute are the relevance and consequences of Informational Cascades. Theoretically, the consequences are manifold. I will go into the effects of Informational Cascades on individuals, banks, rating agencies and financial markets. The last part of this chapter raises the question to what extent such behaviour patterns should be regulated.

Two thirds of my licentiate is descriptive, one third is reserved for mathematical calculations. The descriptive part consists of definitions, elucidations, comments, figures and burlesques. The mathematical modus operandi is dedicated to the modelling of Informational Cascades. Both components are appropriate and neither modelling nor describing in words is better or worse. They are simply two complementary approaches. Both procedures furnish the basis to satisfy the overall aim of this work: To let the reader enter the world of behavioural economics and to let him discover the terra of Informational Cascades with its multifarious environment. I will treat the immediate and intuitive periphery of Informational Cascades. This is mostly consistent with what authors are dealing with. I will for example not handle so called positive feedback or momentum investment strategies.

2) Basics

It is my intention to show what an Informational Cascade accurately represents. I will start with some facile and straightforward definitions, followed by more sophisticated ones, an easy to understand example and the characterisation. It is possible to grasp these definitions without tools such as Bayes’ Rule or Game Theory. However, these are useful when it comes to modelling Cascades. Presenting the tools is the task in part three. Part two will address itself to examples of Informational Cascades in Financial Markets, Politics and Academics. Moreover, it will point out an Informational Cascade Experiment. The chapter concludes with illustrating burlesques and cartoons in the fourth part.

Definitions, together with examples and illustrations, are an appropriate way and method of understanding the phenomenon of Cascades and of going into behavioural economics. After having studied this chapter, the reader should be ready to understand the environment of terms around Cascades in the third chapter.

2.1) Definitions, an Example and Characterisation of Informational Cascades

What does the word Cascade mean - apart from its semantical relevance in the context of Uniform Behaviour?

To cascade: To arrive copiously (Der Grosse Eichborn 1981, p.133).

To cascade: To fall; 1. A small, steep waterfall, esp. one of a series; 2. To connect in a series; 3. A connected series, as of amplifiers for an increase of output (Webster’s new world dictionary 1974, p.219).

Cascade: System, in which various units are linked in sequence, each unit regulating the operation of the next unit in line (Wirtschaftswörterbuch 1986, p.102).

There is a strong link between the semantics of the word cascade and Informational Cascades in an economic behaviour sense. This is shown in selected definitions below. The order is such that easy definitions pose at the beginning, followed by more sophisticated ones:

2.1.1) Definitions

„An informational cascade occurs if an individual’s action does not depend on his private information signal.” (BHW 1992, p.992).

“An informational cascade occurs when it is optimal for an individual, having observed the actions of those ahead of him, to follow the behaviour of the preceding person without regard to his own information.” (Hirshleifer 1995, Abstract).

“An informational cascade occurs when an infinite cluster of decision makers ignore their private information when making a decision.” (Çelen and Kariv 2001, p.2).

“The theoretical literature on ‘herding’ pertains to situations where people with private, incomplete information make public decisions in sequence. Hence, the first few decision makers reveal their information, and subsequent decision makers may follow an established pattern even when their private information suggests that they should deviate. This type of ‘informational cascade’ can occur with perfectly rational individuals, when the information implied by early decisions outweighs any one person’s private information.” (Anderson and Holt 1997, p.1).

“…call information cascades, during which individuals in a population exhibit herd-like behaviour because they are making decisions based on the actions of other individuals rather than relying on their own information about the problem.” (Watts 2002, p.5766)

This definition is problematic, not making the crucial difference between Herd Behaviour and Cascades! I will come back to this problem in the last part of this chapter.

“The basic cascade model applies when actions rather than private information are publicly visible, and when there are finite limits to agent’s private information and possible actions. The idea is that individuals gain useful information from observing previous agents’ decisions, to the point where they optimally and rationally completely ignore their own private information.” (Devenow and Welch 1996, p.609).

Cao and Hirshleifer (2000, p.1) explain that models of Informational Cascades have examined how rational individuals learn by observing predecessors’ actions, and show that when individuals stop using their own private signals, improvements in decision quality cease.

According to Cao and Hirshleifer, the basic idea of Cascades is that an individual who acts rationally, based on information gleaned from the observation of predecessors, makes his own action less informative to later observers than it might otherwise be. An individual may find it optimal to choose an action consistent with the choices or experience of others regardless of his own (possibly opposing) private signal. In such a situation he is said to be in an Informational Cascade, and his action is uninformative to later agents. If agents are ex ante identical, and the only sources of information available to an individual is his private signal and past actions, then all subsequent agents are also in an Informational Cascade – information aggregation ceases!

„An information cascade is a pattern of matching decisions. A cascade can occur when people observe and follow the crowd, which can be rational if the information revealed in earlier decisions outweighs one’s own private information.” (Anderson and Holt 2000, p.1).

“…a gap between public behaviour and private attitudes or beliefs” (Bicchieri and Fukui 1999, p.96).

“…the gap between the practiced and the preached” (Bicchieri and Fukui 1999, p.96).

The elementariness of these definitions should not hide the fact that Informational Cascades models, discussed in chapter four, can get fairly demanding. It is therefore vital to deal with Bayes’ Rule and Game Theory. Before presenting Bayes’ Rule, I want to closer examine an Information Cascade, describe it more exactly and reveal its traits.

2.1.2) An Example

Welch (2002, online) provides one of the most intuitive and understandable examples of an Informational Cascade. For simplicity, I have modified it:

Presume that Anna and a lot of other people have to find their way to a new destination. They come to a crossway where they can (only) either go left or right. Everyone has a private imperfect signal (call it ‘judgment’ or ‘opinion’). For simplicity, let everyone have a private signal ‘left’ (‘right’) with probability 2/3 if the true best choice is to go left (right). So, the signal helps - but it is not perfect. Everyone's signal is equally good.

Now, assume that Anna is the third person to choose, and she first saw a man and then a woman go left. It is optimal for Anna to go ‘left’ even if her private signal/intuition says ‘right’. Why? She knows that the man must have had an ‘l’ signal, because he went left. The woman saw the man go ‘left.’ She would have figured out that the first individual's signal was ‘left’. If her private signal were ‘left’, she would have surely walked left, too. If her signal were ‘right’, she would have been aware of one right and one left signal. She might have walked either way (maybe tossing a coin before).

Now it is Anna’s turn. Having seen both the man and the woman walk ‘left,’ she knows that the man had a ‘left’ signal and the woman had a better than even chance of having had a ‘left’ signal. Loosely speaking, the actions of Anna’s predecessors give her more than one ‘left’ signal. Even if her private information is one ‘right’ signal, net-in-net she should choose ‘left’ if she is acting rationally - and so will everyone, choosing after her. Now, everyone after Anna will know that what she did, had nothing to do with her private information - but they will be in the same boat. The optimal decision will be to do the same thing and go left.

One major consequence of I nformational Cascades is that Anna may get a million rational individuals walking ‘left’ just because the first two individuals walked ‘left’, even if the true best choice was ‘right.’

So, what does this mean for society? Cascades predict that one can get massive social imitation, occasionally leading everyone (the ‘crowd’) to the incorrect choice.

Because everyone knows that there is very little information in a Cascade, Cascades are ‘fragile’; a little bit of new public information (or an unusual signal) can make a big difference. That is, even though a million people may have chosen one action, little information can induce the next million people to choose the opposite action. Fragility, as I will show in 2.1.3, is an integral component of the Informational Cascades theory.

2.1.3) Characterisation

Informational Cascades can be characterised by words such as fragile, brittle, idiosyncratic, long-run inefficient or error-prone. But what does this mean in detail? I will, in turn, illuminate their meanings. As I illustrated above, the actions of early individuals can influence the behaviour of others, so that later individuals ignore their own information and follow. Cascades cause a so-called uniformity. That people are seen as uniform in their opinion is one condition to produce conformity to the perceived value or norm, the other is that the people observed must serve as a reference group.

Bikhchandani and Sharma (2000, p.3) state that a reason for imitation (and hence an Informational Cascade) may be an intrinsic preference for conformity. “Because the conformity of individuals in a cascade has no informational value, cascades are fragile and can be upset by the arrival of new (truthful) public information.” (Bicchieri and Fukui 1999, p.104). Not only the arrival of a little bit of information can break up a Cascade. The mere possibility of a value change (even if it does not actually occur) is enough. It is the fallibility of Cascades causing them to be brittle . If some people have more precise signals than others, or if the relative desirability of adopting versus rejecting (going left versus right, investing or not, …) changes, then Cascades can easily be broken. Hirshleifer (1995, p.26) describes this as: “But while this cascade of identical or conformist behaviour can become quite long , it is not strong (not strong is to equate with brittle)” In other words: A Cascade is not robust to small shocks, but prone to shatter easily. Cao and Hirshleifer (1995, p.8) declare that an information regime is fragile at a given point in time if an additional public disclosure with precision less than or equal to the information signal possessed by an individual will with positive probability shift the behaviour of the next individual. BHW (1992, p.1004) state that the ‘depth’ of an Informational Cascade need not rise with the number of adopters: Once a Cascade has started, further adoptions are uninformative. Thus, conformity is brittle. BHW use conformity interchangeable with the term uniformity. This is not in the sense of Bicchieri and Yoshitaka.

Cascades often spontaneously develop on the basis of very little information. People converge upon one action quite rapidly and their decisions are idiosyncratic . A plausible explanation for the idiosyncrasy of mass behaviour (such as an Informational Cascade) is that individuals aggregate information poorly. BHW (1998, p.163) describe it in the following way: If Cascades lead to a positive probability that wrong decisions are made in the long run, then decisions are (long-run ) inefficient, or idiosyncratic.

Bikhchandani and Sharma (2000, p.6) are more comprehensive: “Herd Behaviour (Informational Cascades [Andreas Heller]) is idiosyncratic, in that random events combined with the choices of the first few players determine the type of behaviour on which individuals herd (crowd [Andreas Heller]).” At this point, it has become inevitable to explain what a herd and accordingly, Herd Behaviour, is and where one can find the difference between Cascades and Herd Behaviour. It is, according to Çelen and Kariv (2001, p.2), fatal to confound Informational Cascades and Herd Behaviour. I will use the term herd in the context of Herd Behaviour and crowd when debating on Cascades. This is indeed a subtle but important difference.

Most authors use Herd Behaviour and Informational Cascades interchangeable. An Informational Cascade occurs when an infinite cluster of decision-makers ignore their private information when making a decision. Herd Behaviour occurs when an infinite cluster of decision-makers make an identical decision, not necessarily ignoring their private information. An IC implies a herd (crowd [Andreas Heller]), a herd is however not necessarily the result of an IC. In a herd, every decision-maker chooses the same action, but they might have chosen a different sequence of actions if the realization of their private signals had been different. In an IC, there is no private signal that could lead decision-makers to do anything else but follow the herd since their beliefs are so strongly held that no signal can outweigh them (this assumption is too thoroughgoing!) In other words, one can regard an IC as convergence of beliefs and Herd Behaviour as convergence of actions.

Once again: An individual exhibits Cascade behaviour, acting irrespective of his own signal, when it chooses the same action as his predecessors for any realization of her private signal. Opposed to this, an individual who joins the herd (exhibiting Herd Behaviour), given the realization of his private signal, acts as his predecessors did, but might have acted differently if the realization of his signal had been different. An individual who cascades (and is in a crowd) is therefore more eradicative and more unquestioning than one, who is herding.

Figure 1: Difference between Herd Behaviour and Informational Cascades

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Figure 1: Herd Behaviour versus Informational Cascades

Source: Çelen and Kariv (2001, p.2)

BHW (1998, p.154) elucidate that behaviour (in terms of Cascades) is idiosyncratic, in the sense that the error-prone choices of a few early individuals determine the choices of all successors.

It is possible to describe or characterise a Cascade as an information externality. Individuals act in their self-interest (without altruistic behaviour), rationally taking uninformative imitative actions. Thereby, the information externality (Informational Cascade) leads to an inefficient outcome. However, when an individual chooses an action that is informative to others, it provides a positive externality. This desirable information externality is weaker when only past actions are observed (instead of past signals).

Typically, Cascades begin surprisingly soon . Calculations show that even when information signals are very noisy (so that the signal ‘left’ is only slightly more likely to arrive when going left is the right choice as when it is the false one, see 2.1.2), the probability of a Cascade forming after ten individuals is greater than 99 per cent (Hirshleifer 1995, p.10).

I claim that Cascades carry inherently the potential to tip , another lineament of IC. This is consistent with a society that often lands precariously close to the borderline (Hirshleifer 1995, p.5).

My illustration should clarify this point:

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Figure 2: Precarious resting point

Source: Andreas Heller

The critical point is that the system bounces around randomly until it reaches a point of precarious stability. At this state, the potential to tip, i.e., of an Informational Cascade to occur, is high. As decisions are made, evidence (reflected in people’s decisions) gradually accumulates in favour of one action or another.

An action is fixed upon when the weight of the evidence grows to be just enough to overcome one person ’s opposing information. At this point, if the next individual is similar, he is also just barely willing to ignore his own information (signal), i.e., he is in a Cascade. Thus, a very small preponderance of evidence causes a saltation (a turnaround) and the majority to take one action over the other. It is characteristic that Cascades can explain the process by which people (society) switch from one steady state to another (Hirshleifer 1995, p.27).

Cascades are most important for phenomena that have an important element of discreteness (yes-or-nor-, true-or-false-, 0-or-1-decisions). Still, Informational Cascades can occur if there are more than just two possible action alternatives. Furthermore, individuals tend to divide up actions into discrete choices, even when those actions have continuous character (BHW 1998, p.159). The main contribution of the Informational Cascades theory is to show that when individuals see past signals only through a crude and discrete filter (whether an action was adopted or rejected), then learning is imperfect and can quickly become completely blocked, i.e. information aggregation ceases. (BHW 1998, p.159)

2.2) Examples in empirically relevant Economic Contexts

Informational Cascades can appear everywhere. I argue that no human being is exempt; everybody carries the potential to crowd. Any individual can imagine and detect Cascades in his immediate environment. I depict three (common) fields:

2.2.1) Financial Markets

Especially Bikhchandani and Sharma (2000, p.9 et seqq.) discuss the impact of Herd Behaviour on financial markets. They do not use the terms Herd Behaviour and Informational Cascades properly. I would even say that when reading their working paper, one should substitute the notion Herd Behaviour with Informational Cascade, or at least having in mind that their Herd Behaviour could be an Informational Cascade.

Cascades can be applied to stock market (investments). This is not astonishing, since market price movements and fluctuations are often described with such notions as fads, spirits, frenzies, manias or investor sentiment. The basic Cascade models in Banerjee (1992), BHW (1992), and Welch (1992) are not convenient to grasp these phenomena. They assume that the investment opportunity is available to all individuals at the same price, i.e., that the supply is perfectly elastic.

This may be a reasonable assumption for foreign direct investment in countries with fixed exchange rates. It is normally not the case that the price for taking an action is fixed and remains so. It is rather true that after every buy or sell decision by an investor, the price of a stock (bond, option, …) adjusts, to take into account the information revealed by this decision. The price will always be the expected value of the investment, conditional on all publicly available information. Therefore, an investor who has only publicly available information (and the actions of his predecessors) will be indifferent towards buying or selling. What is more, the action of any privately informed investor will reveal his information and an Informational Cascade will never start. A crowd will thus not arise when the price adjusts to reflect available information.

Now, let us suppose that there are two types of investors. One type has accurate information (H), the other noisy information (L). The proportion of the types in the population is no common knowledge among the market participants. The (stock-market) price reflects all public information, but not the private information of all previous investors. Identical decisions can arise naturally in a well-informed market (most of the investors are of type H) due to the fact that most of them have the same (very informative) private signal realization. Identical decisions are also natural in a poorly informed market (most of the investors are of type L), because of the crowding of type L-investors who mistakenly believe that most of the other investors are of type H. According to this, a Cascade may occur and can lead to bubbles (frenzies) or crashes if the accuracy of the information with market participants is not common knowledge. Investors and traders may mimic the behaviour of an initial investor group in the erroneous belief that this group knows something (more accurately). Such an Informational Cascade can lead to bubbles/frenzies and crashes, to mass errors caused by the fickle nature of crowds. The Tulip Mania or the South Sea Bubble may be appropriate examples for such a uniform behaviour.

In general, an individual will be in an Invest Cascade if the number of predecessors who invest exceeds the number of predecessors who do not invest by two or more. The probability that a Cascade starts after the first few individuals is very high. Even if the signal is arbitrarily noisy, a Cascade starts after the first four individuals with a probability greater than 0.93. (Bikhchandani and Sharma 2000, p.7) Especially for noisy signals, the probability that the Cascade is incorrect (that is: a reject Cascade when the signal was good/invest or an invest Cascade when the signal was bad/do not invest) is significant.

If, for example, a creditor refuses to renegotiate debt with a distressed firm, others may do so as well (not because of their own information signal, but because others do it).

Alike, the start of a bank run can be viewed as a Cascade in which (small) depositors fear for the solvency of a bank and act by observing the withdrawal behaviour of other depositors (see Diamond and Dybvig 1983). (BHW 1992, p.1013)

Keynes’ (1936) famous saying was that the stock market was mostly a beauty contest in which judges picked who they thought other judges would pick, rather than who they considered to be the most beautiful. (Hirota and Sunder 2001, p.3 et seqq.; Devenow and Welch 1996, p.605)

2.2.2) Politics

Neither voters nor politicians and public protests are immune against one of our basic instincts: imitation. As it is, voters are influenced by opinion polls to vote in the direction that the poll predicts will win.

If one looks at presidential nomination campaigns, there can be observed a so-called ‘cue-taking’: One person’s assessment of a candidate is influenced by the choices of others. Bartels (1988) points out that there need not be any actual process of persuasion; the fact of the endorsement (affirmation) itself motivates the voter to change his substantive opinion of the candidate. (Hirshleifer 1995, p.16)

Susanne Lehman (1992) has examined a model of political revolution in which public protests, demonstrations and riots occur repeatedly in time, and the turnout fluctuates until a Cascade forms. (Hirshleifer 1995, p.17)

2.2.3) Academics

Informational Cascades are at work when, for example, academic researchers choose to work on a topic that is currently ‘in’ or ‘hot’.

Hirshleifer (1995, p.4) considers the submission of a paper to a journal. The referee will read the paper, assess its quality, and accept or reject it. A referee at a second journal learns that the paper was previously rejected. On the assumption that the referee cannot assess the paper’s quality perfectly, knowledge of the prior rejection should tilt him towards rejection. Let us suppose that the second journal rejects as well. When the paper is submitted to a third journal, the third referee learns that the paper was rejected at two previous journals. Obviously, this further raises the chance of rejection.

In general: At some stage, a decision maker will ignore his private information and act only on the information obtained by previous decisions. Once this stage is reached, his decision is uninformative to others (followers) and a Cascade is the consequence.

2.3) Tools: Bayes’ Rule and an Experiment

Methods, techniques and tools to deal with Cascades are found in areas such as Economics (Game Theory), Mathematics (Combinatorics, Probability Calculus, Chaos Theory), and Econometrics or Statistics (Bayes’ Rule). Apart from these, there exist intuitive and non-numerical respectively non-quantitative ‘measures’ and propositions. ‘The human being carries inside the potential to crowd (i.e. to find itself in a Cascade)’ could be such an intuitive resp. non-quantitative prediction.

Bayesianism (Bayes’ Rule) is a controversial but increasingly popular approach to statistics that offers many benefits - although not everyone is persuaded of its validity. Bayes’ Rule is a useful tool in the analysis of economic data. Its importance in economic theory has increased because of the study of markets with asymmetric information.

Here is a simple introduction to Bayes' rule:

The essence of the Bayesian approach is to provide a mathematical rule explaining how you should change your existing beliefs in the light of new evidence. In other words, it allows scientists to combine new data with their existing knowledge or expertise. The canonical example is to imagine that a precocious newborn observes his first sunset, and wonders whether the sun will rise again or not. He assigns equal prior probabilities to both possible outcomes, and represents this by placing one white and one black marble into a bag. The following day, when the sun rises, the child places another white marble in the bag. The probability that a marble plucked randomly from the bag will be white (i.e., the child's degree of belief in future sunrises) has thus gone from a half to two-thirds. After sunrise the next day, the child adds another white marble, and the probability (and thus the degree of belief) goes from two-thirds to three-quarters. And so on. Gradually, the initial belief that the sun is just as likely as not to rise each morning is modified to become a near-certainty that the sun will always rise.

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Figure 3: Bayes’ Rule and Bayesianism

Source: The Economist (2000)

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