Thursday, July 29, 2010

Is it Irrational Behavior or Risk Aversion? (Round Two)

On July 15, 2010, I posted a blog with the same title except that it was round one. Today, I write a follow up hence the label round two. Why the designation? In the first round, I have contrasted the outcome of choice involving two medical options (pp.2, 3). The options involve a risky choice. One of the options had a certain outcome—the individual knows with certainty the outcome of the choice whereas the other was labeled “risky” choice as it involves uncertainty. I discussed how the individual calculates the outcomes of the two options by assigning what economists call utiles, a scale of measurement for the utility of the choice. My example was intended to show that the risk averter is likely to choose the certain outcome over the risky choice. I have also shown, that to make the uncertain option equally valued would require (given my numerical assignment) a reduction of the risk valuation ascribed to the risky option. In this round I would like to put forth another scenario. I would like to suggest another way of making option Y the winning option. For this to take place option X is rendered an “uncertain” option. Given that my examples are medical intervention options, the agent who can alter this and hence the choice is the “physician”.
Now assume that the physician who monitors the patient were to inform the patient that the certainty attached to the outcome of option X is no longer valid. That is, the probability of success now is equals to zero. Moreover, assume that the physician were to point out that there exists the probability that a side effect that did not exist earlier will materialize if option X is chosen. This means that not only the intervention with 100 percent probability has become ineffective, but also it carries with it a “negative” outcome. The comparison between the two options will hinge on the value a risk averter will assign to this negative effect. Note that in comparison to option Y there is no benefit attached to continuing the treatment. This scenario then pushes the individual to choose option Y without a change in its probabilities or the negative valuation attached to the side effect, a component of the option.
In short, the purpose of the exercise was to show how difficult it is for the individual to exercise choice when faced with uncertainty, not only because information may be incomplete but also because of his/her dependence on the market (third party) to evaluate the risky options. When an option is chosen in situations involving risk or uncertainty it is not an easy task to label the choice as rational or irrational. The saving grace is that in some situations a choice can be amended, in others the loss arising from the “wrong” choice cannot be recouped. That brings me to the literature that brought the risky choice models to the theory of consumer choice.
I have mentioned in the previous blog the seminal article by Milton Friedman and L.J. Savage (1948). A year earlier a most influential contribution by Von Neumann, J and O. Morgenstern’s Theory of Games and Economic Behavior (1947) offered utility functions that permit the complete ranking of options in situations involving uncertainty; the comparison of utility differences and the calculation of expected utilities thus making it possible to analyze choice in situation involving uncertainty (see chapter 1 of their book). Since then we have gained insight into this issue through contributions by several economists about consumer choice in situations characterized by risk and uncertainty. It is worth noting that risk has an objective probability while uncertainty involves assigning “subjective” probability. Hence the importance of ascertaining the individual type: whether he/ she is a risk averter, a risk neutral or a risk lover as this is critical to understanding choice. It is of note that an individual may be a risk averter in one situation and a risk lover in another. Now, I turn to the contribution of Behavioral Economists to the study of consumer choice.

Behavioral economists reject the economist models’ assumptions of rationality and maximization of utility. Rationality is defined as the “cognitive abilities” for solving economic problems .Behavioral economists dispute full rationality on the basis of research findings by psychologists and some economists “people exhibit preference reversals; have problems with self control and make different choices depending on how the issue is framed.” For a number of reasons, people make errors and behave in a manner contrary to their self interest. Given this premise, placing constraints on the exercise of free choice may be called for. That is, “paternalistic” intervention by the state or the community may be called for.
There are many variants of state paternalism: Paternalism (Mead, editor 1997), Patronizing Paternalism (Burrows, 1993), Libertarian Paternalism (Sustains and Thaler 2003), Permissible Paternalism (Goodin 1991), Benign Paternalism (Choi et al.2003), and Asymmetric Paternalism (Cramer et al. 2003). The different labels notwithstanding, the underlying premise of paternalism is simple: intervention by the state or the community will generate significant welfare gains. Sources that give rise to “bad” individual choice are: bounded rationality, slow learning, framing and lack of self control.

A question that needs to be posed: when people choices are ‘bad’, should the state and /or the community (a) Override their choices? (b) Steer them towards ‘welfare’ improving choices? (c) Encourage “good” choices without being coercive? or (d) Do nothing?
I have explored this issue in a conference presentation: “State Paternalism and the Rules of Reason” at the International Atlantic Economic Society meeting, which took place in Savanna, GA, on October 2007. In the paper presented, I have summarized the arguments put forth in a number of papers pointing out differences in the policies advocated to deal with “irrational” behavior. In a nut shell, paternalistic policies are advocated to help those individuals whose rationality is bounded (i.e. less than perfect) from costly errors. In the medical intervention example, if the individual was to reject option Y then he/she will bear a costly outcome.
It needs to be emphasized that not all policies advocated by behavioral economists call for coercion. Libertarian paternalism for example allows for differences between individuals and ‘covert’ coercions are not contemplated. At this juncture, it is befitting to call upon one of the architect of liberalism in economic thinking, John Stuart Mill. In his essay on liberty (1859), Mill wrote: “the only purpose, for which power can rightfully be exercised over any member of a civilized community against his will, is to prevent harm to others” (1984 edition, p.92). Following the writing of Nobel Laureate James Buchanan in his Logic of Limits (Buchanan and Musgrave 2000, p.111), one may ask: Why should constraints be placed on the individual when his actions do not infringe on others?
An understanding of the logic of limits may be gained by examining individuals choice in situations where they voluntarily impose restrictions on own actions. Behavioral economists advocating paternalistic intervention do so because they doubt the validity of the logic of limit concept altogether or at least as it applies to those individuals exhibiting bounded rationality. Buchanan’s observation that persons do adopt rules that they intend to abide by is valid for many but not for all. Not all smokers purchase stops smoking aid; alcoholics join Alcoholics Anonymous (the examples given by Buchanan, p.112).
Ruling out the logic of limits as it applies in the example of medical intervention given above in favor of paternalistic intervention; it is imperative to recall that “state or community” intervention most often entails coercion for they command the tools to implement said intervention (power to tax, impose fines, outlaws certain actions and so forth). Paternalism exercised by a parent and/ or a care giver does not command the same coercive power. In the medical intervention example cited above, the physician may attempt to move the patient towards his preferred option but he cannot coerce the patient to do so. Unlike the state, or the community, his power over the individual is not absolute; the patient can opt out of his care.
To conclude:
Behavioral economists have made a significant contribution towards our understanding of human behavior. It is undoubtedly true that some “bad choices” at least from the point of view of society are likely to be made, others are not .But placing constraints on free or voluntary choice of the individual should not be taken up lightly. To err on one side or the other demand more empirical proof that we currently do not have.
Each and every one of us can relate to situations where choices made were far from utility maximizing and/ or ‘fully’ rational. Most of us believe that the choices we voluntarily make are optimal in the sense that their expected costs are below those associated with alternative-dictated choices.

Thursday, July 15, 2010

Is it Rational Behavior or is it Risk Aversion?

As I was struggling with a “medical” decision as to whether to continue a “mode” of treatment that has run its course and is no longer viable or alternatively embark on a new treatment with a new technology, I read a most interesting and to the point write up in THE WEEK. It goes without saying that the “old” is familiar; the new is approached with apprehension if not suspicious. Hence, anything that makes the “new” a bit “old” helps. In the June 18th issue of THE WEEK, under the heading of “Author of the Week” , a story unfolds about a medical choice made quite a few years back by Dan Ariely who has written a couple of books using this choice to facilitate the understanding of a relatively new theory of economics.
Dan Ariely is a fellow economist, a “behavioral economist”, who according to THE WEEK has written a 2008 bestselling book: “The Upside of Irrationality”. Behavioral economists are a new breed of economists who are challenging the standard “textbook” notion of human “rationality”, a notion so fundamental to main stream economics. Rationality is a basic assumption economists use to analyze the individual decision, whether the choice is that of a consumption basket, a choice of occupation, and work versus leisure and so on. It is assumed that the individual knows the alternatives and chooses the one that “maximizes” his or her utility. This assumption is essential to our understanding of choice exercised in the market place in a setting which does not involve risk or uncertainty. When the individual is confronted with a choice that involves “RISK”, the choice is not as simple. In this situation we need to sort out individuals in terms of their “sensitivity” to risk taking.
Economists analyze three categories of risk taking exhibited by the individual: Risk averter, Risk lover and Risk neutral. The individual is said to be “risk averse” when he/she places a much higher weight to a choice that “minimizes” taking of risk; a risk lover goes for a risky choice while a risk neutral gives equal weight to risky and non-risky options.
That was more or less all we needed to know to decipher choices of the individual. But then, a group of economists mainly from the “Chicago School” revived a critique levied against the assumption of rationality and self control (See for example Schelling, T., (1978) Economics or the Art of Self Management, Am. Eco. Rev. pp. 290-94). The new group including Sunstein, Thaler, Laibson, O’Donoghue and Rabin to name but a few, earned the label: Behavioral economists for their contributions to the understanding of human decisions. In a nut shell, behavioral economists challenged the notion of rationality and maximization of utility. In effect, they argue that observed behavior is more likely to exhibit “irrational” rather than a rational decision making process. An example that is often cited has to do with the consumption of “sin” goods—cigarettes, alcohol, drugs and the like. Lack of self control is essential to the analysis, as well as the dimension of choice.
Back to the choice made by Dan Ariely, which THE WEEK Magazine uses in alluding to his book on the thesis of behavioral economics. As the magazine tells it (I have yet to read the book), Dan uses his own choice to explain one of the tenants of the behavioral economists’ theory—that people are less than perfectly rational in their choices. The author uses his own choice which he has made several years back to make the point. The choice involved two types of “medical intervention”. According to the write up, at the age of 18, the author suffered burns on 70% of his body. Two medical options were put before him: Amputate his right arm and replace it with a “hook”, or retain the arm after an excruciating surgery and endure severe pain and partial use of the arm for the rest of his life. At the time, at the age of 18, the choice he made was to retain the arm. Was this a rational or irrational decision?
At the time the decision was made, the author, in my view, exhibited what traditional economists label as “risk aversion”. As he put it: I was “incredibly attached to my hand—in multiple ways”. On backward reflection on such decision, Dan Ariely posits that the decision made at the time was “irrational”. When revisiting the decision about his own arm, as it is retold by THE WEEK, he admits that IRRATIONALITY may have led him astray. On revisiting the decision, at least for the book’s benefit Dan Ariely speculated about whether “prosthesis might have been more functional—that keeping my arm was, in a cost-benefit sense, a mistake”.
This reflection on a past decision causes me to revisit in this blog the assumption of rational choice not in terms of one period horizon but intertemporally. In simple terms, a choice with consequences lasting more than one period, for example, a choice involving one period can be depicted by the consumption of an ice cream cone, a cup of tea or a glass of mineral water. An intertemporal choice is a choice with consequences beyond the period when the item is consumed. As an example, cigarette smoking in one period gives satisfaction in that period but carries with it undesirable consequences in subsequent periods.
A great deal has been written about this type of choice. Traditional economists have advanced theories explaining intertemporal choice. The add-on by behavioral economists is that the individual may exhibit what is called “bounded rationality”—that the individual lacks self control when it comes to consumption of sin goods. Accepting this proposition has led some behavioral economists to advocate “paternalism”. Government or some higher authority would override individuals’ preferences for society’s preferences (the ban on smoking in public places, restaurants and bars is an example). For more on this point and references see Bae and Ott “The Public Economics of Self Control”, Journal of Economics and Finance (October 2008. Pp. 356-367).
Let us contemplate a decision at time t, involving two courses of action: An action A and action B. If one knows with “certainty” the outcomes of both, then the standard economist model applies. That is if a choice of A gives pleasure or satisfaction equal to X utiles, and B gives satisfaction equal to Y utiles (discounted if it were to materialize in a future period), then if A is chosen rather than B, then X utiles are greater than Y’s and vice versa. The individual choice maximizes his/her utility. Two problems arise in this scenario: first, a choice with outcome extending beyond the one period (future period(s)), involves uncertainty or unmeasured risk. Secondly, what discount rate to apply to future outcomes?
Back in the late 1940’s, Milton Friedman and T. J. Savage put this issue before us in their seminal article “The Utility Analysis of Choice Involving Risk” in the Journal of Political Economy (August 1948, pp. 279-304). In order to get as close as possible to explaining the individual temporal choice—a choice involving one period when faced with risky choice, they use the categorization of individuals as risk averter, risk lover and risk neutral. In their example the choice involved two options: a “certain sum of money”, and a chance (game) with two outcomes: losing with a high probability a small sum of money and winning with a very small probability a very large sum of money. Depending on the threshold of risk a choice is made among the two options. If the individual is risk averse he is likely to choose the “certain outcome”, if risk lover he will choose the “bet”. Nothing in the second choice is said to exhibit irrational behavior even if the individual were to bet the house and looses it.
Fundamental to the analysis of choice involving risk, is not only the computation of the expected value of the bet so that it can be compared with the “certain” option, but also the expected utility of the uncertain outcome. The expected utility depends on the shape of the utility function of the individual exercising the choice. Such utility is a function of the individual tolerance of risk. Unfortunately, this is a subjective value that can only be assigned by the individual. Which brings me back to Dan Ariety’s choice, and to a choice I am contemplating.
To illustrate:
Using the example of medical intervention, let option X be current treatment mode which has lost most of its effectiveness in the face of the disease progression. Staying with option X is given a probability Pr. =0.2 that it will have some effect. Let individual A be designated as “risk averter”. He/she assigns a utility value to this option as equal to 100 utiles (some scale of value). Hence:
Pr* Ux= 0.2(100) +0.8(0) =20 is the expected utility.
Option Y has the probability of success of 0.7 that it will be effective, (1-0.7) it will not be. If effective, the utility is 1,000. Accordingly:
Pr*Uy=0.7(1,000) + (1-0.7) (0) =700.
Comparing the expected utility of the two options clearly indicates that option Y will be chosen.
This however is not the complete story. If the new technology carries with it, in addition to the failure probability, a probability of adverse side effects then such probability has to be incorporated to arrive at the expected utility of this option. This complicates the analysis as one needs to know, in addition, something about the risk tolerance of the individual.
Let the side effects (usually ascertained from clinical trials) to have a low probability equals (0.007) such that if it materialized will have severe consequences, even death. To calculate the expected utility of option Y one needs to account for this second component.
But there the problem with the optimal choices lies: one needs to know the risk profile of the individual.
As I have mentioned earlier, the individual can be a risk averter, risk lover or risk neutral (this last category is not likely to be prevalent in the population). Hence, I focus on the risk averter.
Suppose that the risk of side effect was evaluated as equal to -100,000 utiles and a probability of occurrence equals to 0.007. The calculation of the expected utility of option Y is: 0.7(1,000) + (1-0.7) (0) +0.007(-100,000) =0. Option Y will be rejected. For it to win over option X the evaluation of the risk has to be lowered. The equivalent value of the option Y to X requires a risk evaluation equals -97,142 utiles. With this value the individual would be indifferent between the two options. For Y to be chosen over X the risk tolerance has to be reduced so that the expected value of the loss is below the threshold of -97,142 utiles.
This is a problem a concerned physician is likely to face: First, he/she has to ascertain the risk tolerance of the patient (that can be done with a full review of the patient medical history a time consuming process to be sure), and secondly, how to induce the patient to lower the evaluation of risk as the probability of occurrence of the side effects is not subject to change without new information. The solution of this problem is not easy, not for the physician or for the patient.
It needs to be emphasized that at the time one is contemplating a choice involving risk, risk assessment has to be made so that the appropriate discount rate can be applied (the discount rate is used to convert future values to the present. This is ignored in this presentation). The choice Dan Ariely faced was a choice involving risk. His first option, keeping the arm may be viewed as the “sure bet” or the “certain” option. The second option is the uncertain option or the risky choice. The uncertainty about the outcome of the second option with all its ramifications would suggest that at the time the decision was made a very high discount rate was applied to the utility derived from choosing the second option to tip the scale in favor of the first option. In my view, that decision has nothing to do with being “IRRATIONAL”.
In a dynamic world, the discount rate does not remain constant. The discount rate that one would use at the age of 20, 30 versus 50, 60 or 70 is not likely to be the same. Accordingly, many years after the fact the author may have denigrated the discount rate he has used when he was at the age of 18. The traditional theory still holds in that intertemporal choices are made at the beginning of the period. However, nothing is irrational about revising the choice in subsequent periods when more information becomes available.
Having cleared up in my own mind as to how my own choice of the two medical options is likely to come down to, I maintain that “given the information at hand whatever option I choose”, my choice will be a “RATIONAL” choice. A fundamental lesson I have learned during my studies, teaching and research is the value of information and the quality of said information. Without good information the discount rate will be faulty and the choice “suboptimal” although “not irrational.”
A final note to reflect upon:
In a decision involving medical intervention, with an option that has an uncertain outcome, a physician uses his/her expertise to calculate the probability of a successful outcome of the option so that it can be compared with the status quo or some other less uncertain options. This probability when communicated to the patient would help the patient to calculate the discount rate that must be applied to obtain the expected value (and utility) of the uncertain mode of intervention, which can then be compared with the outcome of other options including the status quo. It is worth emphasizing at this juncture that the discount rate computed by the patient reflects his/her type, whether, he/she is risk averter, risk lover or risk neutral. As only the individual can put himself/herself in one of these three categories, a choice that may appear “irrational” is in effect completely “rational.”
In my next blog I shall review some of the literature on risky choice and some of the contributions of the behavioral economics especially as some aspects of the theory pits individual choice against societal choice.