original axiomatic formulation of the theory.

In contrast to the theory under certainty, economists typically do not

treat their theories of expected utility as tautologies. To the extent that

empirical tests reject the axioms, there are grounds for rejecting the

theory. Those who work with narrower versions of the von Neumann“

Morgenstern approach typically admit that some degree of falsi¬cation

has occurred. They do not defend the theory on tautological grounds

but rather question whether some equally tractable alternative has been

developed and whether the extant alternatives in fact yield better predic-

tions across the board.

Several axioms of the von Neumann“Morgenstern approach are sub-

ject to falsi¬cation. Most notorious in this regard is the so-called “in-

dependence axiom.” The independence axiom typically speci¬es that an

additional percentage chance of some outcome has the same utility value

to an individual, whether it is added to a 30, 40, or 50 percent probability

of the outcome in question. In other words, mutually exclusive world-

states (“what I could have had”) should not in¬‚uence the value of what I

have, according to this postulate.

This axiom is contradicted by the evidence, whether we look at ques-

tionnaires or experiments with real dollar prizes. Notice, for instance,

that the phenomenon of “nerves” often falsi¬es the independence ax-

iom. If I move from a .99 chance of a good outcome to a 1.0 chance

of that same outcome (certainty), I can stop worrying about what will

happen. This extra 1 percent, in this context, may be worth more than

moving from an .01 chance to an .02 chance. For some individuals, the

move from .00 to .01, or to some smaller positive increment, is especially

important. This can be taken to represent the value of hope and may

explain why so many people play the lottery. Similarly, regret may falsify

the independence axiom. If we feel bad about what we could have had

Tyler Cowen

218

but did not get, then the values of mutually exclusive world-states will

in¬‚uence one another.7

Note that even here we could try to de¬ne the expected utility axioms

as tautologies. Assume, for instance, that an individual values the “move

from .00 to .01 chance of becoming a millionaire” more than the “move

from .90 to .91 chance of becoming a millionaire.” This would appear to

falsify the independence axiom. Yet such behavior is consistent with the

independence axiom if we specify the relevant outcomes differently. Per-

haps “the chance of becoming a millionaire” is not the relevant outcome.

Instead, imagine that the relevant outcome is “the chance of becoming

a millionaire, plus the hope that is enjoyed in the process of waiting to

discover one™s fate.” The moves from .00 to .01 and from .90 to .91 thus

represent different outcomes, and valuing them differently can be fully

rational. Under this approach, no observed behavior could refute the

independence axiom.

Taking this logic further, any apparent violation of the independence

axiom could be taken to mean that we had not speci¬ed the appropri-

ate outcomes or world-states correctly. Under this maneuver, however,

the de¬nition of an outcome varies with the probability of that outcome.

For technical reasons, this interdependence of outcomes and probabili-

ties would make expected utility theory intractable, because an outcome

could never be de¬ned as separate from its probability. Common judg-

ment holds that expected utility theory would cease to be a useful tautol-

ogy if it were treated in this fashion.

Note that the “tautologizing moves” in choice theory under certainty

are seen as less destructive of tractability. They may decrease the useful-

ness of the theory, but they pose no immediate technical problem com-

parable to the intermingling of outcomes and probabilities, as we ¬nd

in the theory of choice under uncertainty. For this reason, economists

treat the theory of consumer behavior under uncertainty as having falsi-

¬able axioms to a greater extent than they do the theory of choice under

certainty.

Some choice theorists have attempted to reconstruct expected utility

theory without the independence axiom.8 In this theory, expected utility

is linear in the probabilities only locally, not globally. Yet even this the-

ory admits of possible empirical refutation. It implies particular attitudes

toward how gambles are resolved over time and how individual prefer-

ences will change with the temporal resolution of uncertainty. Although

these propositions are considered dif¬cult to test, they are not tautologies

either.

How Do Economists Think About Rationality? 219

For these reasons, few economists interpret expected utility theory

as a tautology. Instead, expected utility theory is considered as either a

testable hypothesis, a normative standard, or a useful analytical category,

depending on the ¬eld of investigation. When economists do choice

theory, especially in a laboratory setting, the expected utility approach

serves as a testable hypothesis, to be either supported or falsi¬ed by the

data.

For more general theoretical purposes, the expected utility hypothesis

is a useful building block for presenting some larger idea. In labor eco-

nomics, for instance, it is commonly postulated that workers choose some

degree of shirking, depending on their chance of being caught and ¬red.

Expected utility theory, especially in its simplest forms, is used to repre-

sent this problem. Most of the economists who use expected utility theory

in this way do not believe that it is descriptively true. Nonetheless, they

hold it to be the most tractable and convenient approach at hand. They

regard the theory as both falsi¬able and false, yet useful nonetheless. The

empirical failings of expected utility theory are considered inessential to

the basics of work/shirk decisions.

Expected utility theory also can be used normatively. The experimental

literature now shows that people do not satisfy the independence axiom

across probabilities. Nonetheless, a normative theorist still might believe

that people ought to satisfy such axioms. The entire ¬eld of risk analysis

tries to help people make better decisions under uncertainty. Risk analysis

has been used to advise the U.S. Department of Defense, to help adjudi-

cate lawsuits, to make securities markets more ef¬cient, and to help com-

panies make decisions about how to invest and when to buy insurance.

Normative risk analysis forms a substantial part of applied economics “

often in the context of consulting “ even when it does not show up in

academic research more narrowly de¬ned.

Macroeconomics

A large body of macroeconomics uses the assumption of rational expecta-

tions, henceforth RE. Although a majority of working macroeconomists

do not accept the empirical validity of RE, most of the important work

in macroeconomics over the past thirty years has used the RE assump-

tion. Rationality, for macroeconomists, refers primarily to rationality of

expectations, rather than to some property of preferences.

RE has been de¬ned in several ways that may be coextensive. Under

one account, RE means that individuals understand the “true model” of

the economy; in other words, trading individuals have the understanding

Tyler Cowen

220

of a fully accomplished macroeconomist. Under another account, indi-

vidual forecasts of economic variables are correct on average. This can

mean either that the errors of an individual average out to zero over time,

or that at any point in time, individual forecasts are scattered around the

true variable but with a correct mean. Finally, RE may mean that errors

are serially uncorrelated over time. That is, if I guess too high one period,

that has no predictive power for whether I guess too high or too low the

next period. Again, this proposition can hold for either individuals or

groups.9

Economists put these assumptions into macroeconomic models for

several reasons. First, some economists believe that those assumptions

are roughly true. A more common view is that they provide a kind of

modeling discipline. The view is commonly voiced that “errors can be

used to explain anything.” By forcing the theorist not to rely too heavily

on errors, the RE assumption makes it harder to come up with ad hoc

models. Finally, the RE assumption may be useful as a foil, to see what

a world without systematic errors would look like. By comparing this

idealized picture with the real world, we may get a better sense of whether

systematic errors are central to the phenomenon of business cycles and

other economic problems.

The RE assumption has received a wide variety of tests. When we look

at questionnaires about expectations, RE commonly fails to predict mea-

sured expectations. Similarly, RE fails tests in the laboratory setting. Some

RE predictions, however, are commonly (though not always) validated at

the macroeconomic level. It appears that the money supply does not af-

fect real output, once we take interest rates into account, and that budget

de¬cits do not cause real interest rates to rise.10 Both of these predictions

follow from some standard RE models, though of course the studies test

several hypotheses jointly, rather than just RE taken alone.

Rationality, in the form of RE, is considered testable, both in principle

and in reality. Failing the tests lowers the status of the RE assumption with-

out making it worthless altogether. RE thus has descriptive, pragmatic,