Linda Dezso1, G

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Linda Dezso1, Gábor Neszveda2 Intertemporal
discounting under stress An experimental study
IAREP/SABE 2009 Conference, Halifax, Canada
1 University Of Szeged, Doctoral School of
Economics, Economic Psychology Program, PhD
student 2 Corvinus University of Budapest, MSc
student
2
Outline of the presentation

• Introduction
• Choice over time and time inconsistency
• Formulas
• Psychological explanations
• Research questions
• Experiment
• Tatiana-design
• Subjects, procedure and treatments
• Results and interpretation
• Two-stage mental process in discounting
• Self-other bias in weighting time
• What is behind hyperbolic function?
• The impact of stress on discounting
• Another interpretation for gain-loss asymmetry

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Choice over time

• Comparing values received in different times
• Investing money, borrowing, lending
• Making decisions with delayed outcome

Abstraction of value and time

• Normative approach Discounted Utility
  (Samuelson, 1937)
• Constant discount rate

Time inconsistency
Anomalies (Loewenstein Prelec, 1992)

• Size effect decreasing rate with size
• Time effect decaying rate in time
• Gain-loss asymmetry smaller rates for losses

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Formulas at the intersection of Psychology and
Economics
Exponentional discounting FV PV(1r)t ,
FV-future value, PV-Present value, r-discount
rate, t -delay
Hyperbolic discounting PVFV(1/1kt),
k-hyperbolic discount parameter,
(ß,d) discounting (Frederick et al, 2002)
SSßdt1-t2LL, ßgt1, t2 gt 0 SS-smaller sooner, LL
larger later
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Psychology at the intersection of Psychology and
Economics
Visceral effects on behavior
Temporal construal
(Loewenstein, 1996)
(Trope Liberman, 2000)

• Strong and disproportionate
• effect on behavior
• Attention narrowing impact
• Crowding out other behaviors
• Increasing impatience

eg. Inviting friends for dinner
Shopping, cooking
Social attractiveness
P
C
C
C
Shopping, cooking,
C
C
P
P
Social attractiveness
time
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Research questions
What is the underlying mental operation,
calculation in discounting?
What is the effect of stress/fear on these mental
operations?
Stress/Fear served as the visceral effect.
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Experiment Tatiana-design
2 (state) X 2 (sign) X 3 (size) X 5 (delay)
within subject, repeated measures
States 1st. Neutral, 2nd stress Sizes 5000,
85000, 1200000 HUF Sign gains and losses,
Delays 3, 6, 9, 12, 18 weeks
Example for real-life scenarios
You received a 5000 HUF bookstore voucher from a
friend as birthday gift. However it turns out
that the bookstore is just being renovated. The
store compensates you by increasing the value of
the voucher. Indicate how much the voucher
should at least be worth 3 weeks from now.
You are fined on the public transportation to pay
5000 HUF on the spot. You do not have cash with
you. You are offered to pay the fine 3 weeks
later, however an increased amount. Indicate the
maximum you are willing to pay 3 weeks from now.
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Subjects, procedure and material
subjects
Pers info personal information DiscMat Discount
ing Tasks FIQ Fake IQ Tests STAI-StateSRPhsy
STAI-State Self- Report Physiological
Group Sample size Average age (ys) and (sd) Gender M-male F- female Handedness Av living stand (sd)
Rediscounting (G2.R) 26 19,807(1,575) M - 30F - 70 right - 88left - 22 3,269(0,533)
Stress (G2.S) 24 20(1,414) M- 13F - 87 right - 96left - 4 3,083(0,583)
Experimental (G2.E) 63 19,841(1,461) M - 49F - 51 right - 95left - 5 3,365(0,702)
Total sample 113 19,867(1,466) male - 37female - 63 right - 94left - 6 3,283(0,647)
Procedure and material
1. Neutral state Pers Info 30 DiscMat
2. Stress state Pers Info 30 DiscMat 27 FIQ
STAI-StateSRPhsy
Randomly ordered tasks and randomly embedded
stressors
Stressors and treatment tasks are perceived in a
same episode by subjects
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Results and interpretation Outline

• Two-stage mental process in discounting
• Self-other bias in weighting time
• What is behind hyperbolic function?
• The impact of stress on discounting
• Another interpretation for gain-loss asymmetry

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Applied formulas
Exponentional equation was applied to infer
discount rates (unit and total rates) ru(FV/PV)1
/t -1, ru - unit rate rt FV/PV-1, rt total
rate
Hyperbolic formula was not used in this study
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Two-stage mental process in discounting
Frequency () of unsubstansive rates in gains
0 r 0,006 - unsubstantansive rates
State Sum/time (weeks) 3 6 9 12 18
neutral 5000 3,17 0,00 1,59 0,00 0,00
stress 5000 0,00 0,00 1,59 1,59 1,59
neutral 85000 1,59 0,00 1,59 0,00 3,17
stress 85000 1,59 4,76 3,17 0,00 3,17
neutral 120000 3,17 3,17 4,76 4,76 1,59
stress 120000 12,70 7,94 14,29 12,70 12,70
NO leads to unsubstansive rates YES leads to
calculation
Frequency () of unsubstansive rates in losses
State Sum/time (weeks) 3 6 9 12 18
neutral -5000 1,59 3,17 3,17 1,59 3,17
stress -5000 1,59 1,59 0,00 3,17 3,17
neutral -85000 0,00 1,59 3,17 1,59 4,76
stress -85000 0,00 1,59 3,17 1,59 4,76
neutral -120000 11,11 9,52 15,87 11,11 9,52
stress -120000 15,87 12,70 17,46 17,46 19,05
p lt 0,05, p lt 0,1
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Self-other bias in weighting time
Neutral state total rates
Sum (HUF) GAIN - function R2 LOSS - function R2
5000 y 0,1134x 1,1215 y 0,3102Ln(x) 1,176 0,9894 0,9409 y 0,0599x 1,1495 y 0,1693Ln(x) 1,1731 0,9647 0,9773
85000 y 0,0526x 1,0562 y 0,1436Ln(x) 1,0818 0,9706 0,9193 y 0,0196x 1,0899 y 0,0581Ln(x) 1,0949 0,8434 0,9393
1200000 y 0,0303x 1,0909 y 0,0865Ln(x) 1,1019 0,9013 0,9317 y 0,0141x 1,077 y 0,0423Ln(x) 1,0801 0,7495 0,8589
Gain weighting selfs time
Loss weighting others time
Stress state total rates
Sum (HUF) GAIN - function R2 LOSS - function R2
5000 y 0,104x 1,0584 y 0,2817Ln(x) 1,111 0,9955 0,9287 y 0,2458Ln(x) 1,1079 y 0,0886x 1,0686 0,9665 0,9891
85000 y 0,0423x 1,0465 y 0,1118Ln(x) 1,0706 0,9755 0,8673 y 0,0676Ln(x) 1,0722 y 0,024x 1,0625 0,9804 0,9768
1200000 y 0,0312x 1,0459 y 0,0871Ln(x) 1,0591 0,9777 0,9699 y 0,0554Ln(x) 1,0634 y 0,0192x 1,057 0,9873 0,9355
The decay in weighting others time stable
through states
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What is behind hyperbolic function ?
Focusing only linear functions
Hyperbolic function fits to unit rates
Linear function fits to total rates
rt Ft c
C-transaction cost (fixed cost) F variable cost
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Connection between hyperbolic and linear
Effect of variable is quasi stationary
Deconstructing unit rate

Effect of fixed cost follows hyperbolic function
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The impact of stress on discounting
Reduces substantive unit rate in a special pattern
p values for each one sample T-test for
corresponding differences of substantive logrates
Sum (HUF)/ time (weeks) 3 6 9 12 18
5000 0,000 0,000 0,009 0,262 0,191
-5000 0,000 0,047 0,105 0,524 0,809
85000 0,746 0,027 0,034 0,125 0,316
-85000 0,016 0,097 0,081 0,154 0,463
120000 0,000 0,000 0,004 0,006 0,041
-120000 0,462 0,124 0,245 0,718 0,782
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Another interpretation for gain-loss asymmetry
Based on linear functions
Transaction cost (c) in percentage of the total
rate for gains and losses in neutral and
stressed state
CGlt CL decreasing in time
State//Sum (HUF) 5000 5000 85000 85000 1200000 1200000
State//Sum (HUF) Gain Loss Gain Loss Gain Loss
Neutral 12,15 14,95 5,6 8,99 9,09 7,7
Stress 5,84 6,86 4,65 6,25 4,59 5,7
Stress reduces C
Variable costs (F ) in percentage of the total
rate for gains and losses in neutral and
stressed state
State//Sum (HUF) 5000 5000 85000 85000 120000 120000
State//Sum (HUF) Gain Loss Gain Loss Gain Loss
Neutral 11,34 5, 99 5,26 1,96 3,03 1,41
Stress 10,4 8,86 4,23 2,4 3,12 1,92
FG gt FL
Stress reduces FG
Stress increases FL
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THANK YOU FOR YOUR ATTENTION!
linda.dezso_at_uni-corvinus.hu gabor.neszveda_at_gmail.
com