Post on 13-Apr-2018
How to measure risk and time
preferences of savers:
France: 1998, 2002 and 2007
Luc Arrondel & André Masson CNRS-PSE Chaire Transition Démographique 6è rencontre Vendredi 12 juin
1. Measuring individual preferences: scores
2. Checking that effects of scores on wealth behaviors agree with theoretical predictions
3. Crossing preferences : a typology of (French) savers
2
De gustibus and wealth inequalities
3
Outline of the talk
(Life-cycle) standard theory and beyond Standard : only 2 or 3 preference parameters… but 4 specific saving regimes => typology of savers
Measuring preferences a method of scoring derived from many different questions Scores are « averages » on individual responses
Results: 1998 to 2007 Properties of preference scores Score « robustness » on 3 surveys :
Internal consistency and most contributing questions Determinants Wealth effects Correlations between preferences
2007 extensions : panel data ; couples ; future agenda
4
Standard (life-cycle) model (1)
No uncertainty: DU & T (DU: Discounted Utility)
Exponential discounting : ! may depend on t but not on s (time consistency)
Homothetic preferences (Theorem)
γ : elasticity of – u’, inverse of σ , intertemporal elasticity of substitution γ : desire for intertemporal consumption smooting
dttCtutTCsCUT
st
s )](,[)(]()...([ α∫ ==
No uncertainty : DU & T & Homothetic preferences
),(exp)(:)( si;0)(/)()( ttttdttdt δαδδ
αα
δ −==≥−=
γ
γ
−==
−
1)()]([)](,[1tCtCutCtu
5
Standard (life-cycle) model (2)
Uncertainty: subjective probabilities EU (Expected Utility)
ρ : aversion relative pour le risque Prudence, temperance…: depend only on γ
Lifetime uncertainty : survival law s(t) interacts with α(t)…
Intergenerational Altruism: degree of altruism θ
α(t): present self has a project & altruism for future self in t Determines the decisional horizon jointly with s(t)
Uncertainty : EU ⊕ intergenerational altruism
ρσγ == /1
enf
T
tpar UndttCutU )()]([)(0
θα += ∫ =
dttCutstEUTm
t)]([)()(
0α∫ =
=
6
Standard (unrealistic) predictions
γ (risk) separated from δ (time over the life-cycle), θ (children)
Total wealth (adequacy of saving) Rises with γ : precautionary saving Decreases with δ : life-cycle & retirement saving Rises with θ : motive for (planned) bequests
Portfolio (completely diversified if perfect markets) Risky share decreases with γ, long-term saving decreases with δ
Real world: inadequate & heterogeneous retirement saving A quarter of HH save too little for retirement (consumption drop) Other save a lot: high concentration of wealth
Real world: undiversified & diverse portfolios In France, a quarter of HH own stocks : directly or indirectly Little diffusion of annuities
3 independent preference parameters
7
Standard more interesting predictions
According to the value of the couple of preference : (γi * !i) Two frontiers
γ < 1 (not known) vs. γ ≥ 1 (known) Caroll’s “impatience condition” (gY > gC) : would be optimal (under certainty)
to borrow against future expected resources => ! high (> r)
Conservative investors” : γ ≥ 1, ! low (Modigliani) prudent & far-sighted “life-cycler”: hump + precautionary saving
“Short-sighted Prudent” : γ ≥ 1, ! high (Caroll-Deaton) “Buffer-stock” investors, target saving (trade off prudence /”impatience”)
“Hotheads” or “Achilles” : γ < 1, ! high (?) adventurous & short-sighted, prone to (here rational) addiction (Becker)
“Enterprising” or “Ulysses” : γ < 1, ! low (?) adventurous and far-sighted
4 different accumulation regimes
8
Non standard (behavioral), approach (1) : Non DU
Kreps & Porteus Time recursivity (≠ time additivity) ; still forward-looking & homothetic
& EU on static bets
γ = ρ ≠ 1 / "
Laibson : (quasi-) hyperbolic discounting
β = short-term (time inconsistent) impatience: cognitive or self-control
Time non separable preferences Habits ; dread or savoring (+ utility of leisure, etc.)
Limited rationality Limited propensity to plan; “emotions”; computation & strategic errors
One additional preference for us: short-term impatience
∑−
=++
−+ +−+=
tT
kktkt
kttTtt
t CuCuCCCU1
1 ),()1()1()()...,,( δβ
9
Non standard (behavioral), approach (2) : Non EU
Kahneman & Tversky : (cumulated) prospect theory v (x) = xa if x gain (≥ 0); v (x) = - λ(- xb) if x loss (< 0); λ loss aversion Weighing of (cumulated) probabilities : optimism or pessimism
gains : power c; losses power c’ 5 parameters required…: a, b, λ, c, c’ Loss aversion explains a lot of wealth behaviors (limited ownership of
life annuities, or even stocks)
Aversion to ambiguity, information bias, wrong beliefs, overconfidence, etc....
Our scores of preference, especially towards risk, will include a non (standard) rational component
Pitfall: from “pure” risk aversion to induced risk aversion Why retired self-employed owing more stocks than self-employed ?
A profusion of non-standard preference parameters…
10
Main Issues with preference measures
Robustness To different data sets To alternate approach (choices of questions, experimental method) Determinants of parameters & wealth effects of parameters
Stability over time Preferences or beliefs or short-term perceptions Panel data (Sahm, 2007); individual or macro factors of change?
Typology of savers Crossing risk & time (and other) parameters – see theory Saver types over time
Couples: preferences of both spouses to explain HH behavior Risk theory (Chiappori & Reny, 2004): negative assortative mating Data: homogamy or heterogamy in preferences, in saver types?
Not too many parameters
1 Liege, June 2, 2009
Measuring preferences : what economists usually do
Ask one or two abstract questions (too theoretical) placing the subject in a somewhat artificial situation in only one domain of life (job for instance)
directly linked, under suitable assumptions, to a specific preference parameter of the theory… Risk : choice between lotteries => standard theory : relative risk aversion
Time : choice between consumption life profiles of the same discounted value
…in order to get a cardinal, precise measure of this parameter
Indicator poorly explained by HH characteristics
Indicator has little explanatory power of savers’ behaviors
2 Liege, June 2, 2009
How to measure preference towards risk
Barsky, Juster, Kimball and Shapiro (1997)
Suppose that you have a job which guarantees for life your
household’s current income R. Other companies offer you
various contracts which have one chance out of two (50%)
to provide you with a higher income and one chance out of
two (50%) to provide you with a lower income. Do you
accept?
3 Liege, June 2, 2009
Measuring relative risk aversion : the lottery (first contract)
R : current (lifetime) income
Contract A
R
R
2/3R
R
1/2
1/2
4 Liege, June 2, 2009
The lottery (continuation)
Contract A
R
R
0.5R
R 1/2
1/2
yes no
4/5 R
1/2
1/2
R R
R
5 Liege, June 2, 2009
Interpretation of the lottery
The rational consumer chooses the contract if
u(2c)+1/2 u (λc) ≥ u (c) Hypothesis: expected utility maximization, u is CRRA
Rejection of contract C
Acceptance of contract C
Rejection of contract B
Relative risk aversion 3.76=<γ 2=<γ<3.76 1=<γ<2
France 1998 (total sample) % 43,1 39,4 11,2
France 2004 (total sample) % 58,4 26,5 10,3 4,8
Rejection of Contract A
γ<1
Acceptance of Contract A
Acceptance of contract B
6,3
6 Liege, June 2, 2009
Our alternative approach (1) : objective
We try only to build in small touches the psychological profile of the saver with respect to risk and time… We ask various questions : lotteries, opinions and intentions, real-life
choices & actual behaviors, possible scenarios, self-reported scales…
…on different areas of life: consumption, leisure, health, investments, work, retirement, family…
by multiplying the number of simple, direct, “ad hoc" questions
by considering different kinds of risks (big, small, gains, losses…) and different time-horizons
Individual scores as “averages” of the responses given, on a purely ordinal basis, to the questions concerning her preferences towards risk, time and family
7 Liege, June 2, 2009
Our alternative approach (2) : building the scores
2007 scores: 65 items for risk, 34 for time, 16 for impatience, 14 for altruism
A priori attribution of questions to preference parameters: the issue of possibly multiple interpretations
Coding the questions (-1, 0, 1): the scores are the sum of the answers given (such “aggregation” diminishes framing effects and endogeneity biases)
Validation and measure of the consistency of ordinal measures (PCA, Cronbach alpha, correlation of “sub-scores” in different life domains)
Decide how many different scores for each preference
8 Liege, June 2, 2009
Our alternative approach (3) : virtues of aggregation
Aggregation in synthetic, relative scores could be the answer Score = context-free measure Score = summary measure (e.g. risk : large & small risks, gains &
losses…)
Score = partly a collection of natural instruments Score = significant explanatory power of wealth amount & composition
Data have the final word as to the number of scores to be introduced…
Conclusion : our approach is at the same time… Piecemeal (how many questions should be asked?)
Empirical (number of scores)
Agnostic (which parameter of preference is measured?)
Problem : no one question is fully satisfactory (see below)
9 Liege, June 2, 2009
Which scores of preferences ?
Only one risk parameter aimed at representing: Risk-aversion Prudence
Temperance Loss-aversion
And many others (pessimism/optimism, ambiguity aversion…)
3 preferences concerning the horizon Short-term impatience Time preference for the present over the life-cycle
Altruistic behavior (towards children)
10 Liege, June 2, 2009
No one question is fully satisfactory (1)
Only a few questions have no problem of interpretation…
A way to present some questions…
11 Liege, June 2, 2009
Lotteries
You are offered to buy for 500 Francs a lottery ticket that has one chance in a thousand to win 1 million Francs. Do you buy it ?
8%
11%
33% No, it is too risky
Yes, may be
Yes, certainly
No, I never play 48%
Absolute risk aversion
Too abstract
12 Liege, June 2, 2009
“ Following a peak, your employer asks employees whether some would like to volunteer to postpone a week’s holidays to the following year. Volunteers will benefit from negotiable extra holidays besides the week itself. You have no previous commitment. Would you accept the principle of this offer? (yes/no, what is the threshold of extra holidays you would consider appropriate?) «
20% (19% in 2004) refuse (strong preference for the present)
11% (10% in 2004) accept with less than two days bonus (weak preference for the present)
Delaying holidays
Time preference
Between “utils” but too many qualifications & only ordinal measure
13 Liege, June 2, 2009
No one question is fully satisfactory (2)
We know which type (risk, time or altruism) of preference is involved, but not :
which parameter of preference exactly, nor whether it is rational or not…
14 Liege, June 2, 2009
The Family
18% 28% 42%
12% Perfectly agree Rather agree
Not really agree Utterly disagree
To choose a partner is to take risks
Perfectly agree Rather agree
Not really agree Utterly disagree
32% 36% 18% 14%
27%
22%
29% 22%
Marriage is an insurance
76% 15% 6%
3%
To decide to have children is to take risks
To decide to have children is to take a life-time commitment
Risk
Risk
Time preference Risk
15 Liege, June 2, 2009
The French and the « Mad Cow »
14%
14%
1% I used the price reduction to increase my beef consumption
Yes, I chose other kinds of meat
Yes, I reduced it
I don’t eat meat 4%
“Have you modified or reduced your meat consumption after learning about the disease?”
67% (68% en 2004) No I changed nothing
(31%)
2004
1998
Risk aversion, aversion to ambiguity, or irrational fears ?
16 Liege, June 2, 2009
Children and risk
37% No
Yes, absolutely 6%
«Towards your younger or teen-age children are you (or would you be) the kind of parents encouraging them to take risks? »
57% Other
Risk aversion or aversion to ambiguity ?
17 Liege, June 2, 2009
«As regards your young or teenaged children, are you (or would you be) the type to inculcate a savings mentality in them ?»
82% Yes
No 18%
Time preference and education
Time preference or taste for saving ?
18 Liege, June 2, 2009
No one question is fully satisfactory (3)
Some questions could reveal more than one type of preference, e.g. both towards risk and time (future is uncertain)…
19 Liege, June 2, 2009
The French and being in good shape
“Do you worry about being in good shape (exercises, weight and diet watching…)”
13%
27% Not at all
Yes, a lot
A little 61%
Risk and time preference
20 Liege, June 2, 2009
« Do you believe it is worth, for gaining a few more years of life, to give up what you may consider your pleasures of life (eating well, drink, smoke, have an exciting life ?... »
« Cigarettes, whisky… »
65% (57% in 2004) No (strong preference for the present)
34% (43% in 2004) Yes (weak preference for the present)
Risk and time preference
21 Liege, June 2, 2009
Retirement
“As an alternative to the present retirement system you are offered the following option : a greater annuity until age 85, but, in exchange, only a minimum after 85. How would you, a priori, evaluate this offer ?”
19%
19%
26% This system is interesting though quite bold
This system is not interesting
This proposition is scandalous
This system is very interesting
36%
Risk and time preference
22 Liege, June 2, 2009
No one question is fully satisfactory (4)
There is a lot of framing and other effects that cannot be controlled…
23 Liege, June 2, 2009
The French and their car
46 %
36 %
18 % No car
No
Yes
« Does it happen to you to park your car for a short period of time in a pay zone without having put your coins in the machine, or to park out of the authorized zone? »
Risk attitudes or/and civic feeling ?
24 Liege, June 2, 2009
No one question is fully satisfactory (5)
Most questions show, alone, little explanatory power of wealth behaviour …
25 Liege, June 2, 2009
The French and the « weather forecast »
63% Yes
No 37%
« When you leave home and the weather forecast is uncertain do you take your measures (umbrella, raincoat…)? »
Risk
26 Liege, June 2, 2009
No one question is fully satisfactory (6)
The causation may run in the opposite direction : wealth explaining the answer given…
27 Liege, June 2, 2009
Protecting the partner
86% Yes
No 14%
« In a couple where there is only one breadwinner, do you think it is important to cover financially the risk of his (or her) death (through life-insurance, appropriate savings…) ? »
Life insurance is a luxury good
Risk and time preference and altruism
28 Liege, June 2, 2009
Budgeting consumption
78%
Yes
No
22%
« Have you ever run into difficulties in balancing your budget because of debts contracted to acquire household goods (Hi-Fi, car...) or to pay for your holidays, etc. ? »
Impatience and Time preference
1
2
Risk Insee 1998 Sofres 2002 Sofres 2007
Cronbach's alpha 0.65 0.51 0.67
Items retained / Total Items 54/56 27/32 57/65
3
0
1
2
3
4
5
6
-21 -19 -17 -15 -13 -11 -9 -7 -5 -3 -1 1 3 5 7 9 11 13 15 17 19 21 23 25 27
Mean=Median
Source : Sofres 2007
More risk Averse
4 Source : Sofres 2007
Axe 1 : Everyday life or family choices
Axe 2 : Long-term choices (survival)
5
Time preference Insee 1998 Sofres 2002 Sofres 2007
Cronbach's alpha 0.53 0.40 0.54
Items retained/Total Items 25/34 16/18 27/34
6
0
1
2
3
4
5
6
7
8
9
10
-17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 13
Mean
Source : Sofres 2007
Less farsighted
7 Source : Sofres 2007
Axe 1 : Want immediate consumption
Axe 2 : Little concern for the future
8
Familial altruism Insee 1998 Sofres 2002 Sofres 2007
Cronbach's alpha 0.29 0.37 0.44
Items retained/Total Items 8/9 7/8 13/14
9
0
2
4
6
8
10
12
14
16
-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
Mean
Source : Sofres 2007
More alltruist
10
Impatience Insee 1998 Sofres 2002 Sofres 2007
Cronbach's alpha 0.27 0.28 0.47
Items retained/Total Items 8/13 3/3 16/16
11
0
2
4
6
8
10
12
14
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Mean
Source : Sofres 2007
More impatient
12
13
Time preference score Insee 1998 Sofres 2002 Sofres 2007
Income 0 - - Age - - - Gender : female 0 0 - Familial status Married : - Married : - Married : -
Social origin 0 0
Education - - -
Children at home 0 (+) (+) Children away from home (-) 0 Family transfers received (-) - -
Numbers of observations 1135 2460 3825
14
145
137
66 66
0
20
40
60
80
100
120
140
160
Financial wealth Gross wealth
Farsighted
Short-sighted
Time preference score between 1st and 4th quartiles
Source : Sofres 2007
15
109
113
87
95
0
20
40
60
80
100
120
Financial wealth Gross wealth
Altruiste
Egoist
Family altruism score between 1st and 4th quartiles
Source : Sofres 2007
16
Equities
Liquid saving
Annuities
Life insurance
Retirement saving arrangement
Housing saving arrangement
Mutual funds
Main residence
-4%
-3%
-2%
-1%
0%
1%
2%
3%
Marginal effects of a variation of one standard deviation on the probability of ownership
Source : Sofres 2007
17
Marginal effects of a variation of one standard deviation on the probability of ownership
18 Source : Sofres 2007
Correlations between risk and time preference
Scores Risk averse Preference for the present Impatient Familial
altruism
Risk averse 1.00 -0.44 -0.33 0.30
Preference for the present 1.00 0.26 -0.30
Impatient 1.00 -0.11
Familial altruism 1.00
19
19. Panel data : stability of preference measures between 2002 and 2007 Rank correlation – no risk or time scale in 2002 survey (a blunder)
Panel Risk Time preference
Score 0.54 0.40
Risk aversion measure (Barsky et al.)
0.28
Source : Sofres 2002 & 2007
Barsky et al.
France : Group IV (more risk averse) in 2002 : 39.2 % of group I in 2007 !!
USA : Group IV (more risk averse) in 1992 : 36.8 % of group I in 1994 !!
28% More risk averse
20% Less risk averse 52% Same
choice
Risk Score (in 3 groups for the two dates)
20
Distribution of the population according to time preference between 2002 and 2007 (rank correlation=0.40)
Column percentage (%)
2002
2007 I II III Number of observations
I 142 109 52 303
II 80 80 83 243
III 34 100 118 252
Number of observations 256 289 253 798
31% More farsighted 27% Less
farsighted 42% Same choice
Source : Survey Delta-TNS 2002. PSE-TNS 2007 (same individuals aged between 35 and 55 in 2002)
20. Panel data : stability of the time preference score between 2002 and 2007 Rank correlation = 0.40
21 Source : Sofres 2007
Couples Risk Preference for the present
Altruism Impatience
Score 0.52 0.45 0.42 0.32
Scales 0.19 0.25
Risk aversion question (Barsky et al.)
0.26
49.6% Same response
13.4% Women less risk averse than men
37.0% Women more risk averse than men
49.3% Same response
27.8% Women more farsighted than men
22.9% Women less farsighted than men
Risk score Time preference score
22 Source : Insee 1998