Individual Choice Behavior: This is a large, sprawling literature, in economics and psychology, much of which is devoted to testing the predictions of different theories of rational behavior, and to documenting deviations from those predictions. The experiments are mostly simple—often just carefully crafted questions about hypothetical choices. They have given rise to some vigorous debates, on experimental methodology, on the interpretation of the observed choice behaviors, and on their implications for economics. One of the chief methodological debates concerns the use of hypothetical versus real choices. We’ll talk about some series of experiments in which phenomena initially observed in hypothetical choices were reproduced in experimental environments in which subjects made real choices Many of these experiments address questions that arise out of the mathematical structure of expected utility theory and its near relations. So these experiments will also give us a chance to look at the interaction between theory and experiment. Often experiments start as tests of the predictions of a theory of rational behavior, and then move on to become investigations of unpredicted regularities. 1
What do we mean by rationality? There are lots of formulations, involving assumptions of different strength. These assumptions have shaped the experiments designed to test them. Varieties of rationality: Goal oriented, maximizing behavior, Ordinal utility maximization Expected utility maximization, (and its important special case, expected value maximization) Subjective expected utility maximization, as well as some of the component parts of those theories (such as Bayesian belief formation). We’ll also consider whether there are some robust phenomena that, while they may be consistent with rationality broadly defined, violate some of the simplifying assumptions that we sometimes take for granted. 2
Let’s do a simple in class experiment. Half of you have just received a windfall gift of a classy, stylish, desirable Stanford pencil. It is yours to keep, or sell. Please examine it closely, taking note of its sleek lines and prestigious lettering. Think of yourself taking notes with such an instrument. In what follows, you will be referred to as “owners.” Half of you did not receive a pencil. You will be referred to as “non-owners.” Will each owner now please pass his/her pencil to a neighboring non-owner, so that the non-owners can also fully examine the pencil. Because I randomly chose who would become an owner, there may exist some possible gains from trade. In order to assess this, I want to elicit from each owner the minimum price at which he/she would be willing to sell the pencil. From each non-owner, I would like to elicit the maximum price she/he would be willing to pay to buy the pencil. Of course, eliciting this price is a problem that itself presents some challenges to experimental design… 3
Becker, DeGroot, and Marschak (1964) designed a procedure that would give utility maximizers the incentive to reveal their reservation price. Each owner of the object will be asked to name the amount of money for which he would be willing to sell it. Each non-owner will be asked to name the amount of money for which he would be willing to buy it. Next a random price will be determined. (We will draw one of 30 cards, to determine a price between $0.05 and $1.50.) Each buyer seller pair will then transact (the buyer will buy the object from the seller at the random price) if and only if the random price is higher than the seller’s demand and lower than the buyer’s offer. Note that the transaction takes place at the random price, not at the stated “willingness to pay” or “willingness to accept.” It is a dominant strategy for a utility maximizer to state his true reservation price, since if he overstates or understates it he will miss some desirable selling opportunities or be forced to enter into some undesirable transactions. Are there any questions? Would everyone please write down a price. 4
(Note that not only is using the BDM elicitation procedure a part of the design, so is explaining it—some theories of rationality could be taken to imply that the explanation is unnecessary ☺ .) And of course, if subjects aren’t utility maximizers, they may not even have unique reservation prices, so the BDM technique may have unpredictable effects. But because many modern economic theories are based on the assumption that agents are expected utility maximizers, so that it is frequently the case that the predictions of the theory can only be known if the utility functions of the subjects are elicited in an incentive compatible way, this technique has found wide application even in experiments whose primary purpose is not to estimate utility functions. 5
Owner prices (WTA) Non-Owner prices (WTP) 6
A version of this experiment was reported in Kahneman, Daniel, Jack L. Knetsch, and Richard H. Thaler 1990, “Experimental Tests of the Endowment Effect and the Coase Theorem,” JPE, 98, 6, 1325-1348. (Why do the results say something about the ‘Coase Theorem’?) Incidentally, this experiment (with real choices, controlled incentives, etc.) arose from the observation that, in hypothetical questionnaires, that there was often a big gap between reported WTPs and WTAs—e.g. in contingent valuation studies, with questions like these: How much would you pay to eliminate some risk that presently gives you a .001 chance of sudden death over the next five years? How much would you have to be paid to accept an additional .001 chance of sudden death over the next five years? Putting prices on unfamiliar things turns out to be a difficult task, and the results are sensitive to how you’re asked. (Dan Ariely has some nice results on this… ☺ 7
Let’s take a step back and consider some general formulations of what constitutes rational behavior. Two closely related formulations of “simple” rationality: 1. Goal oriented, maximizing behavior in which choices can be represented by preferences . Each individual i’s choices on sets of alternatives can be represented by a preference relation Ri (>) (with strict component Pi and indifference relation Ii) such that an individual i’s choice from a set A can always be represented by [ Ci(A) = {x in A| x Ri y for all y in A}] 2. Ordinal utility maximization: individual i’s choices can be represented by a real valued utility function ui [ Ci(A) = {x in A| ui(x) > ui(y) for all y in A}] 8
Not every binary relation on a set A can be represented by a utility function [u(x) > u(y) iff xRy]. Two necessary conditions for a preference R to be representable by a utility function u are that it be: 1. complete: for each x,y in A either xRy or yRx (since either u(x) > u(y) or u(y) > u(x)). 2. transitive: xRyRz implies xRz (since u(x) >u(y) > u(z) implies u(x) > u(z)). These are sometimes also viewed as prescriptive rationality conditions: Completeness can be viewed either as a formality (if we’re willing to define xIy whenever neither xPy or yPx), or, more interestingly, as a kind of integrated personality condition (you shouldn’t fall apart when presented with choices between x and y) Transitivity can be viewed as an elementary rationality condition insofar as it avoids being the victim of a “money pump” among choices in a cycle xPyPzPx. Theorem: If A is finite or countable, then completeness and transitivity are sufficient as well as necessary conditions for a preference to be representable by a utility function. 9
Some experiments concerned with the rational preference model. An intransitivity demo: you like your tea with two spoons of sugar; you are presented with 101 cups of tea ordered from zero to two spoons of sugar in increments too small to taste the difference. So, you are indifferent between any two adjacent cups. Transitivity implies you should be indifferent between any two cups, but you are not… � If we were testing utility theory to see if it were precisely true, we could stop here (although simple modifications to take account of “just noticeable differences” would quickly suggest themselves). But it’s less clear how we should think about this kind of evidence if we are considering utility theory to be some kind of approximation. (Maybe we could improve the approximation by incorporating just noticeable differences – e.g. by modeling choices via preferences and utilities such that xPy iff u(x) > u(y) + jnd, where jnd is a number to be determined empirically. But maybe this would just make the theory cumbersome, and not matter much for most of the choices we’re interested in… 10
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