DECISION MAKING UNDER RISK

DECISION MAKING UNDER RISKAinhoa Jaramillo Gutiérrez

Aurora García-GallegoLEE-Ec. Dpt., U. Jaume I castellon

Nikolaos GeorgantzísGLOBE-Economics Dpt., Universidad de Granada & lee castellon

Ainhoa Jaramillo-GutiérrezERICES, Universidad DE VALENCIA

Melanie ParravanoLEE-Economics Dpt., Universitat Jaume I

The Lottery-panel test for bi-dimensional, parameter-free elicitation of risk attitudes

Ejemplo: •Elegir entre

•Mucha gente prefiere la opción A porque

•En vez de:

•Maximizan:

A B

1000€ 50% 2000€ 50% 0€

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iii XpV

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·

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)(·

EUT, “Risk aversion” es una función de utilidad cóncava

Ejemplo 2:Allais paradox (1954) [Econometrica, Example from Kahneman & Tversky, Econometrica (1979)]• Problema 1: Elegir entre

• Problema 2: Elegir entre

• Más de la mitad de la gente cambia de C en el problema 1 a D en el problema 2 Violación de EUT

C D

20% 4000€80% 0€

25% 3000€ 75% 0€

C D

80% 4000€20% 0€

100% 3000€

LEINCOMPATIBEU

UUPROBL

UUPROBL

Entonces

UUPROBL

UUPROBL

5/4€)4000(/€)3000(2

5/4€)4000(/€)3000(1

:

€)4000(%·80€)3000(%·100:2

€)4000(%·20€)3000(%·25:1

Kahnemann & Tversky (1979): Prospect Theory

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Los sujetos infravaloran (sobrevaloran) las probabilidades altas (bajas)

Prospect Theory (con loss aversion) necesita un mínimo de 2 (4) grados de libertad

Con respecto a un punto de referencia determinado, las personas tienen aversión al riesgo en el dominio de las ganancias y son amantes del riesgo en el dominio de las pérdidas y pueden mostrar una mayor sensibilidad a las pérdidas que a las ganancias (loss aversion).

Conclusión•Hay mucho que aprender en la toma de

decisiones económicas bajo riesgo•Existen muchas teorías: EUT, PT, RDU, TAX, …•Pero de momento esta es la mejor parte de

nuestra disciplina que evoluciona en el sentido “Teoría-Disciplina-Teoría”… y en colaboración de más de una disciplina.

•Medición del riesgo Si queremos caracterizar las actitudes individuales de riesgo para su uso como una variable explicativa en cualquier tipo de experimento, se debe tomar esta exigencia de una caracterización multi-dimensional.

Holt & Laury (2002)

Sabater-Grande & Georgantzis (2002)

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0.0%-2.0% 2.0%-4.0% 4.0%-6.0% 6.0%-8.0% 8.0%-10.0%

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25

30

.1 .2 .3 .4 .5 .6 .7 .8 .9 1 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

Hypothetical Real

Percent

normal p3

Pe

rcen

t

Panel 3

Graphs by Pay

05

10

15

20

25

30

.1 .2 .3 .4 .5 .6 .7 .8 .9 1 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

Hypothetical Real

Percentnormal p1

Pe

rcen

t

Panel 1

Graphs by Pay

Females Males

.1.2.3.4.5.6.7.8.91

Pa

ne

l 2

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 3

1 obs. Each petal = 1 obs. Each petal = 3 obs. Histograms for Panel Lottery Choices By Gender and Payoff Type

¡Cooperation correlates negative to risk aversion!

Mathematical ability does not matter (Brañas et al. EcLett)

Two principal components identified

Component Cumulative %

Comp. 1 2.742 *** 68.54 68.54Comp. 2 0.670 *** 16.75 85.29Comp. 3 0.307 *** 7.67 92.96Comp. 4 0.282 *** 7.04 100

Std. ErrorComp. 1

0.489 *** 0.0160.517 *** 0.0130.521 *** 0.0130.472 *** 0.017

Comp. 2-0.577 *** 0.029-0.372 *** 0.0350.317 *** 0.0360.654 *** 0.027

*** significant at 1% level of confidence.

Panel 1Panel 2Panel 3Panel 4

Panel 3Panel 4

Eigenvalue

Panel

Panel 1Panel 2

Percentage (%)

Coefficient

010

2030

010

2030

.1 .2 .3 .4 .5 .6 .7 .8 .9 1

.1 .2 .3 .4 .5 .6 .7 .8 .9 1

Hypothetical Real

Class Scores


Percent

Panel 4

Graphs by Pay

.1.2.3.4.5.6.7.8.91

Pa

ne

l 2

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 3


0.2

.4.6

Den

sity

-4 -2 0 2Scores for 2nd PC, Hypothetical and Real Payoffs

Real Hypothetical

kernel = epanechnikov, bandwidth = .16

By Payoff TypeKernel Density Estimate for 2nd Principal Component

0.1

.2.3

Den

sity

-4 -2 0 2 4 6Scores for 1st PC, Hypothetical and Real Payoffs

Real Hypothetical


By Payoff TypeKernel Density Estimate for 1st Principal Component

0.0

5.1

.15

.2.2

5D

ensi

ty

-4 -2 0 2 4 6Scores for 1st PC, Real Payoffs

Males Females


Kernel density estimate0

.1.2

.3D

ensi

ty

-4 -2 0 2 4 6


Scores for 1st Principal Component

0.2

.4.6

Den

sity

-4 -2 0 2kernel = epanechnikov, bandwidth = .16

Scores for 2nd Principal Component

.1.2

.3.4

.5.6

.7.8

.91

Pa

ne

l 2

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 3


0.0

5.1

.15

.2.2

5D

ensi

ty

-4 -2 0 2 4Scores for 1st PC, Hypothetical Payoffs

Males Females


Kernel density estimate

0.2

.4.6

.8D

ensi

ty

-3 -2 -1 0 1 2Scores for 2nd PC, Hypothetical Payoffs

Males Females



0.1

.2.3

.4.5

Den

sity

-3 -2 -1 0 1 2Scores for 2nd PC, Real Payoffs

Males Females



.1.2

.3.4

.5.6

.7.8

.91

Pan

el 2

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 1

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 3

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 1

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 4

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 1

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 3

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 2

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 4

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 2

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 4

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 3

Real PayoffsSunflower Density Distribution

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 2

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 1

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 3

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 1

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 4

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 1

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 3

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 2

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 4

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 2

.1.2

.3.4

.5.6

.7.8

.91

Pan

el 4

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 3


0.0

5.1

.15

.2.2

5D

ensi

ty


Males Females



0.2

.4.6

.8D

ensi

ty

-3 -2 -1 0 1 2Scores for 2nd PC, Hypothetical Payoffs

Males Females



0.0

5.1

.15

.2.2

5D

ensi

ty


Males Females



0.1

.2.3

.4.5

Den

sity

-3 -2 -1 0 1 2Scores for 2nd PC, Real Payoffs

Males Females



0.0

5.1

.15

.2.2

5D

ensi

ty


Males Females


By GenderKernel Density Estimate for 1st Principal Component0

.05

.1.1

5.2

.25

Den

sity


Males Females



0.1.2.3

Den

sity

-4 -2 0 2 4 6


Scores for 1st Principal Component

0.2.4.6

De

nsity

-4 -2 0 2kernel = epanechnikov, bandwidth = .16

Scores for 2nd Principal Component

.1.2.3.4.5.6.7.8.91

Pa

ne

l 2

.1 .2 .3 .4 .5 .6 .7 .8 .9 1Panel 3


0.0

5.1

.15

.2.2

5D

ensi

ty


Males Females


Kernel density estimateBy Payoff Type and Gender

Using the two componentsDependent variable: price

Variable Std. Errors

dummy_loose (t-1) 95.09 *** 5.63period -1.55 *** 0.18dummy_t1 73.63 *** 18.54dummy_t2 68.10 *** 18.59dummy_t3 -4.57 18.64pc1_scores -7.54 * 4.02pc2_scores -20.24 *** 6.95constant 461.70 *** 14.53

Number of obs = 8820

Breusch and Pagan LM test for random effectschi2(1) = 13584.52Prob > chi2 = 0.0000

Coeffi cient

Number of groups = 180

We can better explain pricing behavior in a search market experiment with mixed strategy equilibria

Dependent variable: price

Variable Std. Errors

dummy_loose (t-1) 95.09 *** 5.63period -1.55 *** 0.18dummy_t1 73.63 *** 18.54dummy_t2 68.10 *** 18.59dummy_t3 -4.57 18.64pc1_scores -7.54 * 4.02pc2_scores -20.24 *** 6.95constant 461.70 *** 14.53

Number of obs = 8820

Breusch and Pagan LM test for random effectschi2(1) = 13584.52Prob > chi2 = 0.0000

Coeffi cient

Number of groups = 180

Parametrizing the data

WST Expected utility Rank-Dependent utility

Coefficient Std. Errors Coefficient Std. Errors

α Real .6004834 .0100422*** .6002101 .0095474***

Hypothetical .6390580 .0108721*** .6341118 .0104128***

γ Real .6477575 .0096938***

Hypothetical .6784579 .0144159***

𝐻0: 𝛼𝑅𝑒𝑎𝑙 = 𝛼𝐻𝑦𝑝𝑜𝑡ℎ𝑒𝑡𝑖𝑐𝑎𝑙 p-value= 0.003 p-value= 0.006 𝐻0: γ𝑅𝑒𝑎𝑙 = γ𝐻𝑦𝑝𝑜𝑡ℎ𝑒𝑡𝑖𝑐𝑎𝑙 p-value= 0.028

BST Expected utility Rank-Dependent utility

Coefficient Std. Errors Coefficient Std. Errors

α Real .6213423 .0049761*** .6194322 .0047398***

Hypothetical .6654572 .0048251*** .6585140 .0045997***

γ Real .6389014 .0053369***

Hypothetical .6813902 .0095887 ***

𝐻0: 𝛼𝑅𝑒𝑎𝑙 = 𝛼𝐻𝑦𝑝𝑜𝑡ℎ𝑒𝑡𝑖𝑐𝑎𝑙 p-value= 0.000 p-value= 0.000

𝐻0: γ𝑅𝑒𝑎𝑙 = γ𝐻𝑦𝑝𝑜𝑡ℎ𝑒𝑡𝑖𝑐𝑎𝑙 p-value=0.000

(***)significant at 1% confidence level

Literatura

•Economía Experimental y del Comportamiento, ed. P. Brañas-Garza, xx-xx, Barcelona: Antoni Bosch Editores.

•Risk Aversion in Experiments (Research in Experimental Economics, Volume 12), ed. James C. Cox, Glenn W. Harrison ,Emerald Group Publishing Limited, pp.41-196

Documents

DECISION MAKING UNDER RISK