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."
Theodore Bergstrom and John H. Miller
“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”
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):
–
–
–
–
–
–
–
•
Other sources
–
–
–
–
–
•
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)
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)
Game theory,
Macro
Applied game theory
(espec.
Field
IO), Micro
In general:
Data
Utility maximization
Auction
Equivalence
Industrial
Organization
Competitive
equilibrium
Asset
Markets
Phenomena
of stock
market in lab
Economic
questions
Psychologica
l questions
Individual
Decision making
Expected utility vs
non-expected utility
Behavioral
economics
Lab as test bed for
new market design:
e.g: FCC-auctions
Field experiments:
Bargaining
Fairness
vs
strategic
Auctions of sports
cards, Newspaper
experiments
External validity
Happiness
Psychology based
Neuro economics:
Descriptive models
e.g experiments with
patients with lesions,
use of brain scans
while being subject in
experiment
(high and low game theory)
Learning
Social utility function
Levels of reasoning
Quantal response eq.
Hyperbolic
discounting
Behavioral finance etc
behavior
Public good
Free riding
??? what is missing
COMPLEX GAMES
Coordination
Multiplicity
Macro experiments
Experimental economics: topic
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
Rules
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 numbers
NY FED data Dec. 2012 micro seminar
0.3
relative frequencies
0.25
0.2
0.15
Mean
10.25
2/3 Mean 6.83
Winner Jason Bram: with 2* PI [= 6.2831853]
(comment: This may complicate calculating an
average ... but I'll take 2 x PI  )
0.1
0.05
0
choices
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 Games
Varying 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
Classification of
choices
Rules
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 numbers

0
14 22 33
0
14 22 33
1. iterated elimination of dominated strategies
 ITERATION
Equilibrium
...
0
... E(4) E(3)
E(2)
13.17 19.75 29.63
2. iterated best response
... ... E(3) E(2) E(1)
0
14.89
22.22 33
33.33
14
22
E(1)
44.44
E(0)
66.66
100
E(0)
50
100
Nagel, AER 1995
Keynes’ Beauty Contest Game
Or, 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 Level 0
of one’s judgment, are really the prettiest, nor even those
Level 1
which average opinion genuinely thinks the prettiest. We
have reached the third degree where we devote our
Level 2
intelligences to anticipating what average opinion expects
the average opinion to be. And there are some, I believe, And
higher
who practise the fourth, fifth and higher degrees.
Keynes (1936, p. 156)
Period 2 behavior
One dot is a subject
Period 1 behavior
Period 3 behavior
Period 2 behavior
Period 4 behavior
Period 3 behavior
Nagel, AER 1995
Mean behavior over time
some variations
100
mean
80
4/3-mean
60
0.7-mean, 3 players
40
20
0
1
2
3
4
5
6
7
8
9
10
time
Nagel 1995, Camerer, Ho AER 1998)
2/3-mean, 15-18
players
1/2-median
Conclusion 1
A. 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 Experiments
Parallelism between lab and field?
Bosch, Montalvo, Nagel, Satorra, AER 2002
Bosch et al
AER 2002
C=level 3 (15)
B=level 2 (22)
A=level 1 (33)
Like NY-FED data
Mixture models
fMRI Experiments
How can the brain inform us about behavior?
Coricelli, Nagel (PNAS 2009)
Example of MRI scanner
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
Nature of fMRI activation
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)
Neural
activity
increasing
Blood
oxygen
increasing
fMRI
signal
increasing
•
Data is usually transformed into
“activation” maps
•
Activation maps show which parts of
the brain are involved in a particular
mental process
Experimental design
Conditions
Guessing game (session 1)
10 participants in each “session” (2 groups)
Human
Computer
Random
Target number = 2/3 *(mean all
numbers)
Target number = 2/3 *(mean all
numbers)
Choose a number between 0-100
Choose a number between 0-100
Choose a number between 0-100
Parameters : 0.20, 0. 33,…. 1 …1.25, 1.66, 1.75 (13 parameters)
Calculation task (session 2)
Calculate
2/3 * 66
Calculate
2/3 * 2/3 * 66
NO info after a period
Random
Choose a number between 0-100
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
dorsal MPfC
0, 48, 24
High level of reasoning
0.4
0.2
beta
0
-0.2
human
-0.4
computer
-0.6
-0.8
High level: Third person perspective
(dorsal MPFC) & thinking about others
as “like me” (ventral MPFC)
-1
high
low
Strategic IQ
mean parameter estimates (0,48,24)
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
0
500
1000
1500
2000
-0.10
-0.15
-0.20
distance to the winning number
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 3
Theory 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 Experiments
Using 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 4
Usefulness 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 GAME
Where 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 4
Macro 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