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Sequential decision behavior with reference-point preferences:

Theory and experimental evidence

- Daniel Schunk -

Center for Doctoral Studies in Economicsand Sonderforschungsbereich 504

University of Mannheim, Germany

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Introduction

• Why study sequential decision behavior? • Applications in labour economics, consumer economics,

business management, etc.

• Why a laboratory experiment?

• What does existing literature say? • Heterogeneity• Early stopping

• Research question: What is the relationship between individualpreferences and behaviour in sequential decision tasks?

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Outline of talk

1 – THEORETICAL PART• The sequential decision problem• Development of 2 models Hypotheses on the relationship between individual preferences

and sequential decision behavior

2 – EMPIRICAL PART• Experimental design• Inference about behavior (preferences, sequential decisions)• Testing the hypotheses

- Correlation analysis- Panel duration analysis- Alternative experimental design

3 – CONCLUSIONS

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THEORETICALPART

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The sequential decision problemInstructions:

• Goal: Purchase a good that you value at 100 €. • Good sold at infinitely many locations, visiting a new location costs 1 €.

• Price at each location is drawn from a discrete uniform distribution- lower bound: 75 €- upper bound: 150 €

• You are allowed to recall previously rejected offers.

Important: No losses !

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Search Behavior

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Stop searching as soon as a price lower than or equal to € Xt is found.

Optimal search rule:

Stopping rule:

Constant, then fallingreservation price

1 3 5 7 9 11 13 15 17 19 21 23

Number of Searches

Opt

imal

Res

erva

tion

Pric

e Xt

85

95

75

90

80

Risk-averse

Risk-seeking

1

m – minimal price observed so farc – search cost per periodSt ={t,m} – state vector after t steps

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)())(1(

)()(

cmF

xdFcxmm

cm

Search Behavior

0)0( u

Stop

search

Continue search

cm

xdFcxm75

)()( Higher payoff achieved Gain

No higher payoff achieved Loss

Reference point

1-F(m-c)

F(m-c

)

?

m – minimal price observed so farc – search cost per periodF() – distribution function of prices

Reference point model:2

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Search Behavior

Reference point model:

1 3 5 7 9 11 13 15 17 19 21 23

Number of Searches

Opt

imal

Res

erva

tion

Pri

ce X

t

Loss-averse

Loss-seeking

Stop searching as soon as a price lower than or equal to € Xt is found.

Stopping rule:

Constant, then fallingreservation price

85

95

75

90

80

2

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We have 2 models…

1 21 3 5 7 9 11 13 15 17 19 21 23

Number of Searches

Opt

imal

Res

erva

tion

Pric

e Xt

1 3 5 7 9 11 13 15 17 19 21 23

Number of Searches

Opt

imal

Res

erva

tion

Pric

e Xt

1 2

EU-preferences

Risk aversion explains level of reservation price path

RP-preferences

Loss aversion explains level of reservation price path

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EMPIRICAL

PART

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Experimental Design: Overview

2 parts of the experiment Obtained data

• 1 : Lottery questions

• 2 : Price search task Sequential decision behavior

Preferences: Risk attitude, loss attitude

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Experiment: Part 1 (Risk Attitude)

• Use certainty equivalent method

37% risk-neutral, 37% risk-averse, 26% risk-seeking

0

0.25

0.5

0.75

1

0 6 12 18 24

x

u(x

)50%

50%A €

Lottery I Lottery II

x100%~

[€]x0

x1

x2

x3

x4

Estimate risk attitude αi (CRRA) and γi (CARA)

B €

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Experiment: Part 1 (Loss Attitude)

• Use trade-off method

Estimate loss aversion index λi

69% loss-averse, others loss-neutral

50%

50%

x

-A €

Lottery I Lottery II

100%~ 0 €

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Experiment: Part 2 (Price search task)

Instructions: • Goal: Purchase a good that you value at 100 €.

• Good sold at infinitely many locations, visiting a new location costs 1 €.

• Price at each location is drawn from a discrete uniform distribution- lower bound: 75 €- upper bound: 150 €

• You are allowed to recall previously rejected offers.

• Statistical classification algorithm assigns decision rule di

• Considerable heterogeneity in sequential decision behavior

• Play 15 payoff-relevant search games, no losses !

• Length of practice period „ad libitum“ Assume each subject i follows a single decision rule

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Testable Hypotheses

Preference elicitation part(Part 1)

Sequential decision part(Part 2)

EU preferences

(H1) risk aversion # search steps

(H2) risk aversion risk aversion

RP preferences

(H3) loss aversion # search steps

(H4) loss aversion loss aversion

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Results (1)All results hold under

CARA and CRRA specification of the

utility function(a) Correlation analysis:Investigate correlation between preference parameters and search parameters Loss attitude correlates, risk attitude does not correlate = Support for (H3) and (H4)

(b)Unobserved effects panel duration analysis:Exploit …discrete time-to-event nature, and …panel nature of data in multivariate model, and explain stopping behavior with preference parameters Loss attitude has predictive power, risk attitude not = Support for (H3)

Note: Relationships are particularly strong on a subgroup that is classified based on additional questions about decision behavior

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Results (2)

(c) Alternative experimental design- uses Abdellaoui-(2000) procedure for elicitation of risk attitude

- confirms that risk attitude is not related to search behavior

(d) Weber et al.- (2002) psychometric instrument for measuring risk attitude- measures risk attitude on different domains

- risk attitude measured on the domain of gambling is related to search behavior

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Conclusions

• Considerable heterogeneity in sequential decision behavior

• Loss aversion helps explain heterogeneity, risk aversion not;confirmed in different experimental designs

• Many subjects set reference points in sequential decision tasks

• Relevance of findings:• In general:

Labor and consumer economics, marketing and finance (e.g.: Eckstein/V.d. Bergh, 2005; Gneezy, 2003; Zwick et al., 2003)

• In the context of my research:Related to work on life-cycle decision-making and statistical classification of individual differences in dynamic choice contexts