How to measure risk and time preferences of savers: … to measure risk and time preferences of savers: France: 1998, 2002 and 2007 Luc Arrondel & André Masson CNRS-PSE Chaire Transition

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


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?


Measuring relative risk aversion : the lottery (first contract)

R : current (lifetime) income

Contract A

R

R

2/3R

R

1/2

1/2


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


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


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


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


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)


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)


No one question is fully satisfactory (1)

 Only a few questions have no problem of interpretation…

A way to present some questions…


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


“ 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



  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…


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


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 ?


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 ?


«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 ?



  Some questions could reveal more than one type of preference, e.g. both towards risk and time (future is uncertain)…


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


« 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)



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%




 There is a lot of framing and other effects that cannot be controlled…


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 ?



 Most questions show, alone, little explanatory power of wealth behaviour …


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



 The causation may run in the opposite direction : wealth explaining the answer given…


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


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


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


Less farsighted


Axe 1 : Want immediate consumption

Axe 2 : Little concern for the future

8

Familial altruism Insee 1998 Sofres 2002 Sofres 2007



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


More alltruist

10

Impatience Insee 1998 Sofres 2002 Sofres 2007



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


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


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


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


17

Marginal effects of a variation of one standard deviation on the probability of ownership


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


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

Documents

How to measure risk and time preferences of savers: … to measure risk and time preferences of savers: France: 1998, 2002 and 2007 Luc Arrondel & André Masson CNRS-PSE Chaire Transition