Introduction BLEESS-13

Rosemarie Nagel

UPF-ICREA-BGSE

Visiting NYU

Our Aims

• Macro research questions visited via – Theory – Experimental methods.

• Why experiments and not empirical data?• Closeness to theory • Empirical data for research question not available

• Spread the word that macro experiments are possible

Konfuzius ( 孔夫子 )551 b. C.- 479 b. C.

• "By three methods we may learn wisdom: First, by reflection, which is noblest; Second, by imitation, which is easiest; and third by experience, which is the bitterest.”

• "Tell me, and I will forget. Show me, and I may remember. Involve me, and I will understand."

“Taking a course in experimental economics is a little like going to dinner at a cannibal's house. Sometimes you will be the diner, sometimes you will be part of the dinner, sometimes both” Quote from “Experiments with Economic Principles”

Theodore Bergstrom and John H. Miller

Four step model to write/work on a research question(adapted from “On Teaching syntactic Argumentation

by D.M. Perlmutter, MIT)

• Step 1 : Find some interesting facts (which facts are interesting will depend of course on the current theory, state of the art etc.)

• Step 2: Construct hypothesis and alternative hypothesis to account for the facts

• Step 3: find grounds on which to choose between the two hypotheses:– Theoretic model construction– Experimental design– Empirical data

• Step 4: get results:– Theoretic solution– (experimental/empirical) data– Tests etc. , new theories

In red: what you typically learn in an economic class

Sources for experimental economics

• Books and surveys (experimental economics-behavioral surveys):

– Collection of experimental facts: Davis&Holt (1992), Kagel & Roth (1995)– Experimental methods: Friedman & Sunder (1994),– Facts and models: Camerer (2003),– Behavioral economics: Camerer & Loewenstein (2005);– Field experiments: Harrison and List (JEL, 2005)– Neuro economics: Camerer, Loewenstein, and Prelec (JEL, 2005)– Soon to come: Kagel & Roth second volume! (see already Al Roth homepage)

• Other sources

– Classroom experiments and webgames: Charles Holt (2006)– Web experiments: Rubinstein, Plott etc. – Field experiments: List’s webpage with papers– Critics about experimental economics: Al Roth– Working papers: Charles Holt

• Micro text books with experimental economics– Schotter (1996)– Bergstrom and Miller (1997)

Public goodFree riding

CoordinationMultiplicity

BargainingFairness vs strategic behavior

IndustrialOrganization Competitive equilibrium

Asset MarketsPhenomena of stock market in lab

AuctionEquivalence

Individual Decision makingExpected utility vs

non-expected utility

Game theory, Applied game theory (espec.IO), MicroIn general: Utility maximization

Macro Economic questions Psychologica

l questionsField Data

Behavioral economics

Psychology based

Descriptive models (high and low game theory)

LearningSocial utility functionLevels of reasoning

Quantal response eq.Hyperbolic discounting

Behavioral finance etc

Lab as test bed for new market design:e.g: FCC-auctions

Neuro economics:e.g experiments with patients with lesions,use of brain scans while being subject in experiment

Field experiments:Auctions of sports cards, Newspaper experimentsExternal validity

??? what is missingCOMPLEX GAMES

Experimental economics: topics

Macro experiments

Happiness

The Beauty Contest: Rational Expectations and Keynesian Level of Reasoning

(and a tour through experimental economics)

Rosemarie Nagel

ICREA-UPF-BGSE Barcelona, Spain

Visiting NYU

Winner Jason Bram: with 2* PI [= 6.2831853] (comment: This may complicate calculating an average ... but I'll take 2 x PI )

Mean 10.252/3 Mean 6.83

RulesChoose a number between 0 and 100. The winner is the person

whose number is closest to 2/3 times the average of all chosen numbers

Outline (this talk is also a tour through experimental economics using the BCG)

• Lab experiment to show regularities, construct models of behavior

• Field experiment to show parallelism between field and lab data

• fMRI experiment (brain) to inform about behavior

• Survey to induce policy implication through guesses and guesses of guesses

• Macro theory: generalization of BCG

through shocks and signal extraction

General rule

• Choose a number between 0 and 100. The winner is the person whose number is closest to 2/3 times the average of all chosen number. He gets 10 Euros. If there is tie, the pie is split amongst those who tie. (Tournament rule)

• Alternative payment rule: Profit (i) =100-(choice (i) – 2/3 average)^2

Where does this game come from?

Objective: Minimize distance between own number x(i) and 2/3 average

<=> x(i)=2/3 average )

Lab Experiments

Systematic variation of parameters to find pattern of behavior in relation with theory

Surveys: Camerer 2002, Crawford, Costa Gomes, Iriberrim, JEL 2012

Basic Beauty Contest GamesVarying Parameters

The rules of the basic beauty-contest game: • N participants (individuals vs teams/experienced vs

inexperienced) are asked to guess a number from the interval 0 to 100. N=2 is very different from N>2

• The winner is the person whose guess is closest to (2/3 times the mean of the all choices) plus constant

• The winner gets a fixed/variable prize of $20. In case of a tie the prize is split amongst those who tie.

• The same game may be repeated several periods• Subjects are (not) informed of the mean, 2/3 mean and

all choices in each period/get a signal about current choices

• Time to think: from seconds up to two weeks• Participants: students, theorists, “newspaper readers” etc

text in bold italics indicates the variations in the different experiments

Rules, theory, and data for basic game

RulesChoose a number between 0 and 100. The winner is the person whose number is closest to 2/3 times the average of all chosen numbers

1. iterated elimination of dominated strategies Equilibrium ITERATION

... ... E(4) E(3) E(2) E(1) E(0)

0 13.17 19.75 29.63 44.44 66.66 100

Nagel, AER 1995

0 14 22 33

0 14 22 33

2. iterated best response ... ... E(3) E(2) E(0)

E(1)

0 14.89 22.22 33.33 50 100 0 14 22 33

Classification of choices

Keynes’ Beauty Contest GameOr, to change the metaphor slightly, professional investment may be likened to those newspaper

competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize

being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best

of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We

have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe,

who practise the fourth, fifth and higher degrees.Keynes (1936, p. 156)

Level 0

Level 1

Level 2

And higher

Nagel, AER 1995

Period 1 behavior

Period 2 behavior

Period 2 behavior

Period 3 behavior

Period 3 behavior

Period 4 behavior

One dot is a subject

Mean behavior over time

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

time

mea

n

4/3-mean

0.7-mean, 3 players

2/3-mean, 15-18players

1/2-median

some variations

Nagel 1995, Camerer, Ho AER 1998)

Conclusion 1A. Descriptive model interpretation a la Keynes

• Level 0: no understanding of the game (=no game form recognition=random play=zero intelligence)

• Level 1: game form recognition, but do not have a model of other players’

behavior (no theory of mind), thus assume random play = as if playing against nature, non changing past

• Level 2: model others as level 1 players => have model of other players’

behavior (theory of mind)

• Level 3: model others as level 2 players etc. (theory of mind)

• Equilibrium: assume common knowledge of rationality or assume that others go through an infinite level of reasoning and thus assume all are equally smart

(rational expectation) (theory of mind??? or just calculation mode)

Conclusion 1 (cont.)

• Typically level of reasoning remains between random and level 3 even over time.

• Unraveling towards the rational expectation equilibrium but never reaching it (this is probably only true when zero is the equilibrium)

• The level k model has been used in many other games like auctions, matching pennies

*see survey by Crawford, Costa Gomes, Iriberri JEL 2012

Conclusion 1 (cont.)Modeling behavior

• Level k (Stahl-Wilson, 1994, Nagel 1995)

• Cognitive hierarchy (Camerer-Ho 1998)

• QRE with heterogeneous errors (Breitmoser, 2012)

• (in future, modeling behavior (after learning has occurred through shocks and signal extraction?)

Field ExperimentsParallelism between lab and field?

Bosch, Montalvo, Nagel, Satorra, AER 2002

C=level 3 (15)B=level 2 (22)A=level 1 (33)

Bosch et alAER 2002

Like NY-FED data

Mixture models

fMRI Experiments

How can the brain inform us about behavior?

Coricelli, Nagel (PNAS 2009)

Scanner

a very powerful electro-magnet

field strength of 3 teslas (T), ~60,000 times greater than the Earth’s field

During the experiment: subject lies in the scanner and is

exposed to the stimuli scanner tracks the signal throughout

the brain

Example of MRI scanner

When a brain area is more active it consumes more oxygen Changes in blood flow and blood oxygenation in the brain

are indirect measures of neural activity (Blood Oxygenation Level Dependent (BOLD) signal)

• Data is usually transformed into “activation” maps

• Activation maps show which parts of the brain are involved in a particular mental process

Nature of fMRI activation

Experimental designConditions

H um an

2/3Target num ber = *(m ean a ll num bers)

Choose a num ber between 0-100

R andom

Choose a num ber between 0-100

C om pu ter

2/3Target num ber = *(m ean a ll num bers)

Choose a num ber between 0-100

C a lcu la te

2/3 * 66

C a lcu la te

2/3 * 2 /3 * 66

R andom

Choose a num ber between 0-100

G uess ing gam e (sess ion 1)

C a lcu la tion task (sess ion 2 )

Parameters : 0.20, 0. 33,…. 1 …1.25, 1.66, 1.75 (13 parameters)

NO info after a period

10 participants in each “session” (2 groups)

Behavior of one subject: High level reasoner

Parameter 2/3

Aim: categorization of behavior of each subject into either High or low level player === difference in brain between high and low?

BEHAVIOR OF TWO PLAYERS:Low vs high level

Dorsal and ventral MPFC: self-other distinction

High level of reasoning

High level: Third person perspective (dorsal MPFC) & thinking about others as “like me” (ventral MPFC)

dorsal MPfC0, 48, 24

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

high low

beta human

computer

Strategic IQ

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0 500 1000 1500 2000

distance to the winning number

mea

n pa

ram

eter

est

imat

es (0

,48,

24)

Increasing strategic IQ

The activy in the MPfC is correlated (r = 0.67, P = 0.005) with our measure of Strategic IQ (the inverse of the distance to the winning number).

Conclusion 3Theory of Mind

• Guessing, estimating, predicting is a key feature of human activity

• Desintangling low vs high reasoning: – Through fMRI we find level (0), 1 vs level 2 and higher – (as Keynes also has argued.. Not favorite face and not average face

VS

– Through behavior we found level 0 vs level 1 and higher

• Application in psychology, neuro science,

• Difference to animals?

Survey ExperimentsUsing guess and guess of guesses

to make policy changes

Gender composition in ESA 2011-2012(ESA is the Association of Experimental Economics)

DATA:

There were 95 positions (keynote speakers, committee members etc) in 2011/2012 related to ESA positions of which 4 are occupied by women (4.2%)

In particular there was one woman in ESA committee out of 19 members

In 2012 there are about 27% (149/555) women members in ESA

Survey by H Llavador, M Nagel, R Nagel A Perdomo

How to induce change

1. Survey method– Create awareness through guesses (90% participants of survey

were not aware of gender gap!)– Create cognitive dissonance between own guess guess of other

people guesses and actual facts– Ask participants for different reasons for the actual gender

composition– Ask participants for proposals how to change gender composition. – Ask participants for women eligible for EC

2. Document of results send to EC with actual proposals and other results of survey

Four different guessing games plus incentives

1. Guess how many women are in ESA – EC– No incentives– Number can be found on web

2. Guess the guess of others about women in ESA – EC – Right guess: 100 Euros

3. How long will it take to make a change without this survey– No incentives

4. Make a proposal how to change the composition – If your proposal is implemented within next 2 years, 400 Euros (note:

NO democracy, or guess of most chosen proposal, instead best guess/prediction/adapted proposal.. The real beauty contest, as e.g. in procurement auction

• The prizes are given separately to men and women• Additional prize: one randomly chosen man and woman receives 100 Euros

for participation

Result of new election within Committee 2012

• While there was one women in 2011 in the committee, there are 4 women in 2012 in committee.

• However, in 2011 the women with most votes lost by one or two votes against the elected men.

• Now in 2012 the women elected won by one or two votes against the loosing men with most votes

=> More campaigning is necessary

Conclusion 4Usefulness for surveys

• Guessing, estimating, predicting is a key feature of human activity

• We can create cognitive dissonance about the state of nature/status quo and the guess/ guesses of guesses of subjects

• The guesses might indicate how the ideal state should be or not be

• Proposals for changes by participants

=> Policy change

Generalized Macro Beauty Contest Model

Long term aim:

Macro foundation of Micro

Some new modeling on BCG

• BASIC GAMEWhere c is

• A known constant (experiment Gueth, Kocher, Sutter 2002)• A common fundamental value (theory Morris Shin 2002),

private and public signals about fundamental value

• An ideosyncratic error with signal extraction (theory Benhabib, Wang, Wen 2012): experimental results in preparation

Conclusion 4Macro experiments

• The guessing game/beauty contest game is embeded in many macro models (think of inflation expectation)

• Adding shocks and signal extraction, macro context (sentiments, animal spirits) offers maybe a macro fundation of micro

• Some might just be semantics like in micro we talk of errors (typically endogenous) while macro talks of shocks (typically exogenous)

Conclusion

We showed the relationship between rational expectation and Keynesian level of reasoning with experiments in the lab, field, brain, survey and new theorizing through macro, bridging the gap between zero intelligence and equilibrium behavior.

“Experiments without Theory is useless,

Theory without Experiments is dangerous”

adapted from Confucius (551–479 BCE) : “learning without thinking is useless, thinking without learning is dangerous”

Coauthors on the Beauty contest game (in order of appearance): R Selten J Duffy A Bosch J Montalvo A Satorra B Grosskopf G Coricelli C Plott E Chou M McConnell V Crawfort M CostaGomes C Bühren B Frank H Llavador M Nagel A Perdomo J Benhabib