S UBJECTIVE S URVIVAL B ELIEFS AND
A MBIGUITY: T HE R OLE OF P SYCHOLOGICAL
AND C OGNITIVE FACTORS
Nils Grevenbrocka
a,c SAFE,
Max Groneckb Alexander Ludwigc
Alexander Zimperd
Goethe University Frankfurt b Stockholm School of Economics
d University of Pretoria
QSPS 2017 Workshop
Jon M. Huntsman School of Business, May 18-20, 2017
Motivation & Objectives
I
Motivation:
I
Expectations about survival prospects relevant for
inter-temporal decisions
I
Most models use objective survival probabilities (OSPs)
I
On average subjective survival beliefs (SSBs) deviate from
OSPs
I
Objectives:
I
Characterize deviations at individual level
I
What drives these deviations?
1/34
Approach
I
Construct individual-level OSPs
I
Descriptive analysis of biases: SSBs versus OSPs
I
Structural interpretation: probability weighting functions
(PWFs), cumulative prospect theory (Kahneman and Tversky)
I
Regression analysis of structural models: role of newly
available psychological and cognitive measures
I
Decomposition analysis: quantitative relevance of each factor
2/34
Main Findings
I
Substantial biases: Age 70: −10%p, age 85: +20%p
I
Descriptive: age-specific probability weighting functions
I
Theory: increasing pessimism and likelihood insensitivity
I
Direct psychological measures: analogous age trends
I
Quantitative relevance (non-linear and linear PWFs):
I
Optimism: overestimation by 10 − 12%p
I
Pessimism: underestimation by 3 − 5%p
I
Cognitive weakness: age pattern
1. from −5%p to +5%p
2. from +5%p to +15%p
3/34
Related Literature
I
Biases: Hamermesh (1985), Elder (2013), Ludwig & Zimper
(2013), Peracchi & Perotti (2012)
I
Econometric models: Hurd & McGarry (1995), Smith et al.
(2001)
I
Savings behavior: Groneck, et al. (2015), Heimer et al.
(2015)
I
Construction of objective survival rates: Khwaja et al. (2007,
2009), Winter & Wuppermann (2014)
I
Role of psychological measures: Griffin et al. (2013), Kim et
al. (2012)
4/34
Outline
Introduction
Data
Stylized Facts
Theory on Subjective Beliefs
Psychological and Cognitive Variables
Structural Estimation
Conclusions
5/34
Data and Sample
I
I
Health and Retirement Study (HRS)
I
U.S. representative biennial panel survey since 1992
I
Individuals older than 50 and spouses
I
Including cognitive and psychosocial measures since 2006
Sample restriction
I
Focus on individuals with: 65 ≤ age ≤ 89
I
Focus on different waves
6/34
Data: Subjective Survival Beliefs (SSB)
’What is the percentage chance that you will live to be [target age]
or more?’
Interview age h
65-69
70-74
75-79
80-84
85-89
Target Age m
80
85
90
95
100
7/34
Data: Objective Survival Probabilities (OSP)
I
Previous studies use averages of life-table data
I
Interested in individual-level survival misconception
I
(Cohort) life-table estimates ill-suited for our analysis
I
Adapt estimation approach of Khwaja et al. (2007, 2009)
I
Weibull hazard modell
I
Time trends: Lee-Carter procedure (Lee & Carter 1992)
I
Condition on several explanatory variables (sociodemographic,
health etc.)
8/34
Outline
Introduction
Data
Stylized Facts
Theory on Subjective Beliefs
Psychological and Cognitive Variables
Structural Estimation
Conclusions
9/34
0
.2
.4
.6
.8
Average Misconception
65
70
75
80
85
90
Age
SSBs
OSPs (Indiv. Estimate)
I Biases over age as in numerous previous studies
I
10/34
0
0
.2
.2
.4
.4
.6
.6
.8
1
.8
Average Misconception
65
70
75
80
85
90
0
.2
.4
Age
SSBs
.6
OSP
OSPs (Indiv. Estimate)
SSBs
45°-line
I Biases over age as in numerous previous studies
I 50-50 bias may explain pattern
10/34
.8
1
Average Misconception: Age-Groups
Age group 65 - 69
Age group 70 - 74
1
.8
.8
.6
.4
.4
0
.2
.2
0
0
.2
.4
.6
.6
.8
1
1
Full Sample
0
.2
.4
.6
OSP
.8
1
0
.4
.6
OSP
.8
1
.4
.6
OSP
.8
1
.4
.6
OSP
.8
1
1
.8
.6
.6
.4
.4
0
.2
.2
0
.2
.2
Age group 85 - 89
.8
1
.8
.6
.4
.2
0
0
0
Age group 80 - 84
1
Age group 75 - 79
.2
0
.2
.4
.6
OSP
.8
1
0
.2
.4
.6
OSP
.8
1
I Intercept decreases across age groups
I Slope decreases
11/34
Outline
Introduction
Data
Stylized Facts
Theory on Subjective Beliefs
Psychological and Cognitive Variables
Structural Estimation
Conclusions
12/34
Probability Weighting Function (PWF)
I
PWF: Important concept of (cumulative) prospect theory
(Tversky & Kahneman 1992; Wakker & Tversky 1993)
I
People focus (too) much on extreme probabilities
I
Two components explaining probability weighting (Wakker
2010)
1. Psychological: optimism/pessimism
2. Cognitive: likelihood insensitvity (=lack of probabilistic
sophistication)
13/34
Shape of PWFs: Expected utility
1
0.9
0.8
0.7
SSP
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
OSP
14/34
Shape of PWFs: Likelihood Insensitvity
1
0.9
0.8
0.7
SSP
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
OSP
14/34
Shape of PWFs: Increase in Likelihood Insens.
1
0.9
0.8
0.7
SSP
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
OSP
14/34
Shape of PWFs: Increase Pessimism
1
0.9
0.8
0.7
SSP
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
OSP
14/34
Shape of PWFs: Increase Optimism
1
0.9
0.8
0.7
SSP
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
OSP
14/34
Fitting PWFs: Prelec-Function
I
Take two parameter PWF of Prelec (1998)
θ
ξ
1. SSB = exp −[− ln(OSP)]
2. θ: pessimism
3. ξ: sensitivity to likelihood / probabilistic sophistication
I
Fit PWFs by minimizing euclidean distance
min
ξ,θ
I
( Nm
Xh
i SSB h,m
−i SSBh,m
i2
)
.
i=1
Back out ξ and θ to get age-dependent PWFs
15/34
Fitting PWFs: Predicted Values
0
.2
.4
.6
OSP
.8
1
.8
0
.2
.4
.6
.8
.6
.4
.2
0
0
.2
.4
.6
.8
1
Age group 70 - 74
1
Age group 65 - 69
1
Full Sample
0
.4
.6
OSP
.8
1
.4
.6
OSP
.8
1
.4
.6
OSP
.8
1
1
1
.2
.4
.6
.8
.8
.4
.2
0
0
.2
.2
Age group 85 - 89
.6
.8
.6
.4
.2
0
0
0
Age group 80 - 84
1
Age group 75 - 79
.2
0
.2
SSBs
45°-line
.4
.6
OSP
.8
1
0
.2
.4
.6
OSP
.8
95%-CI
16/34
1
Probabilistic Sophistication and Pessimism
.4
.6
1
1.2
.2
.8
0
Fitting PWFs: Coefficients
65
70
75
80
85
90
Age
Probabilistic Sophistication
95%-CI Prob. Soph.
Pessimism
Bootstrapped (1,000 replications) confidence-intervals based on the percentile method.
I Increasing Pessimism
I Decreasing probabilistic sophistication
17/34
Outline
Introduction
Data
Stylized Facts
Theory on Subjective Beliefs
Psychological and Cognitive Variables
Structural Estimation
Conclusions
18/34
Data: Psychological & Cognitive Variables (1/3)
I
I
Dispositional Optimism and Pessimism
I
Questions as in Life-Orientation Test-Revised (LOT-R)
I
Rate question: 1. (strongly agree) to 6. (strongly disagree)
I
Recode: Higher scores ⇒ higher optimism (pessimism)
Cognitive Weakness
I
Summary score: 35 subquestions
I
Higher score ⇒ more cognitive weakness
Psycho Example Questions.
Cognitive Example Questions.
Summary Statistics.
19/34
Average Disp. Optimism
4.5
4.3
4.7
Average Optimism across Age
65
70
75
80
85
90
Age
Avg. Disp. Optimism
95% Confidence interval
Fitted Line
I Dispositional optimism decreases with age
20/34
2.4
Avg. Disp. Pessimism
2.6
2.8
Average Pessimism across Age
65
70
75
80
85
90
Age
Avg. Disp. Pessimism
95% Confidence Interval
Fitted Line
I Dispositional pessimism increases with age
21/34
12
Average Cognitive Weakness
16
14
18
Average Cognitive Weakness across Age
65
70
75
80
85
90
Age
Avg. Cognitive Weakness
95% Confidence Interval
Fitted line
I Cognitive weakness increases with age
22/34
Outline
Introduction
Data
Stylized Facts
Theory on Subjective Beliefs
Psychological and Cognitive Variables
Structural Estimation
Conclusions
23/34
The Relationship between Psychological
Measures and SSBs
I
I
Main Hypothesis:
I
OSPs predict SSBs
I
Pessimism leads to downward bias
I
Optimism leads to upward bias
I
Cognitive weakness affects formation of SSBs
Approach:
I
Non-linear estimation of PWF
I
Linear approximation and estimation
24/34
Non-Linear PWF: Specification
I
Specification:
ξ θh
SSBi,h,m(h) = exp − − ln OSPi,h,m(h) h
+i,h,m(h) ,
where
ξh = ξ0 + ξ1 ci,h−2
θh = θ0 + θ1 pi,h−2 + θ2 oi,h−2 .
25/34
Non-Linear PWF: Estimates
point estimate
CI-
CI+
Cog.Weak. Intercept (ξ0 )
Cog.Weak. Slope (ξ1 )
Psycho. Intercept (θ0 )
Pessimism Slope (θ1 )
Optimism Slope (θ2 )
0.5457
-0.0134
1.0285
0.0295
-0.0583
0.4945
-0.0167
0.9482
0.0171
-0.0732
0.5922
-0.0095
1.1239
0.0413
-0.0442
AIC
BIC
2990.0
3025.5
2784.7
2820.0
3195.5
3230.9
26/34
0
.2
.4
SSB
.6
.8
1
Non-linear PWF: Decomposition I
0
.2
.4
.6
.8
1
OSP
45°-line
Pred.: base
Pred.: base+optm.
I Optimism: Upward shift
I Pessimism: Downward shift
I Cognitive weakness: Clockwise tilting
Pred.: full
Pred.: base+pess.
Pred.: base+cog.W.
27/34
0
-.05
.2
0
.4
.05
.6
.1
.8
.15
Non-linear PWF: Decomposition II
65
70
75
80
85
90
65
70
75
Age
OSP (indiv. est.)
pred.: all
I
I
I
I
80
85
Age
SSB (data)
pred.: base
D pred.: all
D pred.: base+optm.
Base bias: initial underestimation, later overestimation
Optimism: overestimation by 10%p
Pessimism: underestimation by 3%p
Cognitive weakness: from −5%p to +5%p
D pred.: base+pess.
D pred.: base+cog.W.
28/34
90
Linear PWF: Specification
I
Linear approximation:
SSBi,h,m(h) = θ0 + θ1 pi,h−2 + θ2 oi,h−2 + θ3 ci,h−2
+ θ4 (ci,h−2 × oi,h−2 ) + θ5 (ci,h−2 × pi,h−2 )
θ6 OSPi,h,m(h) + θ7 (ci,h−2 × OSPi,h,m(h) ) + i,h
I
Decision theoretic foundation: neo-additive beliefs in Choquet
expected utility theory (Gilboa 1987; Schmeidler 1989;
Chateauneuf et al. 2007; Wakker 2010)
29/34
Linear PWF: Estimates
point estimate
CI-
CI+
0.0441
0.6415
0.0112
-0.0001
-0.0163
0.0259
-0.0003
-0.0001
-0.0487
0.5721
0.0040
-0.0002
-0.0316
0.0114
-0.0014
-0.0011
0.1441
0.6985
0.0185
-0.0001
-0.0015
0.0407
0.0008
0.0010
2943.5078
3000.2205
2741.4094
2798.1226
3146.1782
3202.9202
Constant
OSP
Cog. Weak.
OSP × Cog. Weak.
Pessimsim
Optimism
Opt. × Cog. Weak.
Pess.× Cog. Weak.
AIC
BIC
I Information criteria: Linear model fits equally well
I Interpretational advantage
30/34
0
.2
.4
SSB
.6
.8
1
Linear PWF: Decomposition I
0
.2
.4
.6
.8
1
OSP
45°-line
Pred.: base
Pred.: base+optm.
I Optimism: Upward shift
I Pessimism: Downward shift
I Cognitive weakness: Clockwise tilting
Pred.: full
Pred.: base+pess.
Pred.: base+cog.W.
31/34
0
-.05
0
.2
.05
.4
.1
.6
.15
.2
.8
Linear PWF: Decomposition II
65
70
75
80
85
90
65
70
75
Age
OSP (indiv. est.)
pred.: all
I
I
I
I
80
85
Age
SSB (data)
pred.: base
D pred.: all
D pred.: base+optm.
Base bias: initial underestimation, later overestimation
Optimism: overestimation by 12%p
Pessimism: underestimation by 5%p
Cognitive weakness: from +5%p to +15%p
D pred.: base+pess.
D pred.: base+cog.W.
32/34
90
Outline
Introduction
Data
Stylized Facts
Theory on Subjective Beliefs
Psychological and Cognitive Variables
Structural Estimation
Conclusions
33/34
Conclusion
I
Substantial biases in SSBs relative to OSPs
I
Biases can be modelled through age-dependent PWFs
I
Pessimism & likelihood insensitivity increase in age
I
Quantitative relevance (non-linear and linear PWFs):
I
Optimism: overestimation by 10 − 12%p
I
Pessimism: underestimation by 3 − 5%p
I
Cognitive weakness: age pattern
1. from −5%p to +5%p
2. from +5%p to +15%p
34/34
Summary Statistics
Psychological Variables
Dispositional Optimism
Dispositional Pessimism
Cognitive Variable
Cognitive Weakness
Explanation
Range 1-6
Range 1-6
Mean
4.56
2.57
SD
1.14
1.28
Range 0-35
21.47
5.16
Table: Psychological & Cognitive Variables
Return.
35/34
Questions: Psychological Variables
’Please say how much you agree or disagree with the following
statements’
Dispositional Optimism
1. I am always optimistic about my future
2. In uncertain times I usually expect the best
3. Overall, I expect more good things to me than bad
Dispositional Pessimism
1. If something can go wrong it will
2. I hardly ever expect things to go my way
3. I rarely count on things happening to me
Return.
36/34
Questions: Cognitive Variables
Cognitive Weakness
A composite score combining questions such as:
1. Name current (Vice) President of the United States
2. Today’s Date
3. Count backwards for 10 continuous numbers beginning with
the number 20
.
4. ..
Return.
37/34