Modern Views on Risk Attitudes Explained through a History of

Interactions between Psychologists and Economists

San Diego, May 5 '04by Peter P. Wakker, Econ. Dept.,

Univ. of Amsterdam

$ 100

$ 0

½

½

or $50 for sure

What would you rather have?Such gambles occur in games with friends.More seriously:

Don’t forget to make this invisible.

Don’t forget to make this invisible.

Torino: 45 minutes.

Is about history of DUU/R. From perspective of prospect theory ...

You will see it has really been interaction of seconists.

At certain stage, only econists could make next step. Then, only s. Etc.

Present state is a building, and you can see the blocks from s and econists.

Torino: 45 minutes.

Is about history of DUU/R. From perspective of prospect theory ...

You will see it has really been interaction of seconists.

At certain stage, only econists could make next step. Then, only s. Etc.

Present state is a building, and you can see the blocks from s and econists.

This is the kind of questions that I and all my colleagues spend all our lives studying.

This is the kind of questions that I and all my colleagues spend all our lives studying.

2

More seriously: - Whether you can study medicine in the Netherlands;- In the US in the 1960s, whether you had to serve in Vietnam.

Even more seriously: Investments, insurance, medical treatments, etc. etc.

This lecture is on the history of risk-theory.

In public lotteries, casinos, and horse races.

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1) General modeling of risk attitude. Is it determined by:

- sensitivity towards outcomes (utility);

- sensitivity towards chance (probability weighting)?

2) Particular form of risk attitude. Is risk-aversion

- universally valid (modulo noise);

- systematically violated?

Two questions/lines-of-talk:

Well, on aspect thereof.

Well, on aspect thereof.

4

Expected value

Simplest way to evaluate risky prospects:

$ 100

$ 0

½

½

½100 + ½0 = 50

General:

x1

xn

p1

pn

.

.

.... p1x1 + ... + pnxn

5

Risk aversion!

Falsification of expected value.

To explain it, “expected utility” (Bernoulli, 1738).

However, empirical observations:

$ 100

$ 0

½

½

$ 50

6

Bernoulli (1738) entails a departure from objectivity.

U is subjective index of risk attitude.

Expected utility is the classical economic risk theory.

x1

xn

p1

pn

.

.

.... p1 x1 + ... + pn xnU( ) U( )

For economists this is just fine. Risk attitude = sensitivity towards outcomes?We arrived at Bernoulli (1738).I’ll give an example of how this works.

For economists this is just fine. Risk attitude = sensitivity towards outcomes?We arrived at Bernoulli (1738).I’ll give an example of how this works.

7

Theorem (Marshall 1890). Risk aversion holds if and only if utility U is concave.

Risk aversion in general:

U

$ U is used as the subjective index of risk attitude!

x1

xn

p1

pn

.

.

.... p1x1 + ... + pnxn

say, before formula, that EV comes.

say, before formula, that EV comes.

End: Typical of economists, risk attitude = U($); completely happy, no questions. Psychologists: different. Then "implant memory", see comment to the right.

End: Typical of economists, risk attitude = U($); completely happy, no questions. Psychologists: different. Then "implant memory", see comment to the right.

My next argument works best for those of you who never saw this result before, and see it for the first time. If you saw this theorem before, I want to carry you back to a memory of your youth, revive this memory. Try to remember what you felt when you first saw it. @@Praten alsof therapie.

It is odd, that your risk attitude is determined by how you feel about money??? Shouldn’t these be different things? How can your feeling about money determine risk attitude? Shouldn’t your feelings about probability play a role in some sense?

I’d like to implant in your memory the memory that you also felt this when you first saw this result.

Economists are used to express everything in terms of money, and utility of money. So a claim that risk attitude is determined by utility of money will not make alarm bells ring in the economist’s mind. It will do so, however, with psychologists.

My next argument works best for those of you who never saw this result before, and see it for the first time. If you saw this theorem before, I want to carry you back to a memory of your youth, revive this memory. Try to remember what you felt when you first saw it. @@Praten alsof therapie.

It is odd, that your risk attitude is determined by how you feel about money??? Shouldn’t these be different things? How can your feeling about money determine risk attitude? Shouldn’t your feelings about probability play a role in some sense?

I’d like to implant in your memory the memory that you also felt this when you first saw this result.

Economists are used to express everything in terms of money, and utility of money. So a claim that risk attitude is determined by utility of money will not make alarm bells ring in the economist’s mind. It will do so, however, with psychologists.

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Psychologists objected:

U=

sensitivity towards money

≠risk attitude.

Economists do not like such “unfounded” (non-revealed-preference based) reasoning.

Line (1) of this talk:

the general modeling of risk attitude.Tell I don’t want to discuss now whether or not risk aversion does hold true. I want to discuss how at all to model risk attitude, no matter what it is.

Tell I don’t want to discuss now whether or not risk aversion does hold true. I want to discuss how at all to model risk attitude, no matter what it is.

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Intuition: risk attitude (also) through

processing of probabilities.

x1

xn

p1

pn

.

.

.... p1 U(x1) + ... + pn U(xn)w( ) w( )

w(0) = 0,

w(1) = 1,

w is increasing.

w

p

00 1

1

p

w(p)

Transition to next page. Already here say that psychologist Lopes often wrote about this.

Transition to next page. Already here say that psychologist Lopes often wrote about this.

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Prob. weighting already considered in 1950s (Ward Edwards).Called subjective expected utility (unfortunate term).'s argument intuitive, not theoretical.economists: Such argumentation is an error!Subj. exp. utility theory never became “big."

Lola Lopes (1987): “Risk attitude is more thanthe psychophysics of money.”

utility

Money is physical thing, utility is how you feel about it so it is psychological. So utility is the psychophysics of money.

Money is physical thing, utility is how you feel about it so it is psychological. So utility is the psychophysics of money.

Arrived in 1950. In this manner, my lecture has moved from economists of 1890 to s of 1950s. Announcement: We now leave line 1, general way of modeling risk attitude, and go to line 2 (risk aversion universal?).

Arrived in 1950. In this manner, my lecture has moved from economists of 1890 to s of 1950s. Announcement: We now leave line 1, general way of modeling risk attitude, and go to line 2 (risk aversion universal?).

Economists did not like this reasoning. Considered it lose-hand. s adhered to it throughout.

Economists did not like this reasoning. Considered it lose-hand. s adhered to it throughout.

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Economic arguments for universal risk aversion:

1) diminishing marginal utility is intuitively plausible;

2) concave utility is needed for existence of equilibria;

3) no concave U market for lotteries;

Line (2) of this talk: risk aversion.

Peter & Paul meet on the street, can gamble, etc.

Peter & Paul meet on the street, can gamble, etc.

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about risk-seeking individuals:

... since experience shows that they are likely to engender a restless, feverish character, unsuited for steady work as well as for the higher and more solid pleasures of life.

Marshall, A. (1920)Principles of Economics

You may have noticed that, typical of economists’ thinking, these arguments are based on all kinds of reasonings, but not, or only indirectly (arguments 2 and 3), on empirical reality.

You may have noticed that, typical of economists’ thinking, these arguments are based on all kinds of reasonings, but not, or only indirectly (arguments 2 and 3), on empirical reality.

Of course he wrote this tongue-in-cheeck.

Of course he wrote this tongue-in-cheeck.

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Public lotteries!?!?

Friedman & Savage (1948):

Problem:

U

$

Great intellectual move (first serious attempt to use expected utility to explain things), but empirically flawed: there is no 50-50 gambling in middle region.

Empirical problems in middle, no systematic 50-50 gambles there.

Empirical problems in middle, no systematic 50-50 gambles there.

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I will not dwell on this point extensively, emulating rather the preacher, who, expounding a subtle theological point to his congregation, frankly stated: 

Brethren, here there is a great difficulty; let us face it firmly and pass on.

Psychologists: ?????

Arrow (1971, p.90) (about lotteries)

Aan eind: We arrived at 1970. Now return to line 1, general modeling of risk attitude.

Aan eind: We arrived at 1970. Now return to line 1, general modeling of risk attitude.

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End of seventies: renewed interest in probability weighting, a.o. because of violations of EU (Machina '82).

A.o. by Handa (1978, J. of Pol. Econy), Kahneman & Tversky (1979, Econometrica, "prospect theory").

Prominent economic journals ... !

Back to line (1), the general modeling of risk attitude.

Handa: reconnect with prob. weighting.

Handa: reconnect with prob. weighting.

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Of those, Fishburn (1978, JPE) was published.

(Among non-published reactions, one by the unknown Australian John Quiggin.)

Prospect theory is an exceptionally big succes; 2nd most cited economic paper 1975-2000!Is theoretically problematic though.

To Handa (1978), the JPE received some 10 comments.

Theoretical problem violation of stoch. dom., nog niet noemen. Komt pas op volgende pg.

Theoretical problem violation of stoch. dom., nog niet noemen. Komt pas op volgende pg.

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Amazing, that model could survive in the psychological literature for 30 years ...

Probability-weighting violates

stochastic dominance!

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Only, one should weight the "right“ probabilities.

Not probability of: a specific outcome,butprobability of: at least an outcome.

Yet, "risk-attitude through probability weighting"is good intuition.

19

Evaluation of lottery

with x1 … xn 0: w(p1)U(x1) +

(w(p2+p1) - w(p1))*U(x2) + ...

(w(pj+...+p1) - w(pj-1+...+p1))*U(xj) + ...

(w(pn+...+p1) - w(pn-1+...+p1))*U(xn)

Idea of Quiggin (1981), Rank-Dependent Utility.

x1

xn

p1

pn

.

.

....1. Arrived in 1980s.

2. Prospect theory

3. s - econs interactions

We are now in the 1980s. When line 1 was understood by economists (not yet s), they were still thinking that universal risk aversion. In this period, 1980s, economists more advanced on line 1, s on line 2.

I should qualify “economists.” I mean here, a few economics specialists in DUR. The great majority today still uses EU, and utility curvature, to model risk attitude. A recent paper by Rabin (2000, Econometrica) has brought new arguments for why solely utility curvature is not a good tool for modeling risk attitude.

1. Arrived in 1980s.

2. Prospect theory

3. s - econs interactions

We are now in the 1980s. When line 1 was understood by economists (not yet s), they were still thinking that universal risk aversion. In this period, 1980s, economists more advanced on line 1, s on line 2.

I should qualify “economists.” I mean here, a few economics specialists in DUR. The great majority today still uses EU, and utility curvature, to model risk attitude. A recent paper by Rabin (2000, Econometrica) has brought new arguments for why solely utility curvature is not a good tool for modeling risk attitude.

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In the beginning, economists' views:

Risk-aversion is universal.

U concave and prob. weighting wsimilar.

Impulses from empirical investigations by psychologists (Tversky and others).

Back to line 2, risk aversion.

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Small chances at large gains

Large chances at small losses

Amazing, that “universal” risk aversion could survive in the economics literature for 30 years …

Systematic risk-seeking for:

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Tversky, A. & D. Kahneman (1992),“Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty 5, 297 – 323.

Synthesis:

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Risk-attitudes in terms of - utilities ánd - probability weighting (- and loss aversion).

Risk-aversion prevailing,but, systematic deviations.

Reference point ("framing").

Theory combines - descriptive force of '79 prospect theory - theoretical force of economic theories.

New prospect theory:

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1. Classical econs: Expected utility; Risk at- titude = U($) (Bernoulli 1738, Marshall 1890).2. s: risk attitude also w(p) (Edwards, 1954). Took wrong probabilities.3. Economists: Take right ("cumulative“) p’s (Quiggin, 1981). Thought universal risk aversion; convex/cave. 4. s: diminishing sensitive iso risk aversion (Tversky & Kahneman, 1992); inverse-S.

Synthesis: New prospect theory

Summary:

Inverse-S: need new maths, iso convex analysis. Need new concepts Isensitivity towards information, it’s cognitive).

New data …

Inverse-S: need new maths, iso convex analysis. Need new concepts Isensitivity towards information, it’s cognitive).

New data …