How can we show that Utility
is Relative?
Andrew Clark. Paris School of Economics.
http://www.pse.ens.fr/clark/
There is great, and growing, interest in the idea of “relative utility”,
where some components of the utility function are evaluated relative to
some comparison level.
U = U(x, x*). Where du/dx > 0, du/dx* < 0.
see: Clark, A.E., Frijters, P., & Shields, M. (2008). "Relative Income,
Happiness and Utility: An Explanation for the Easterlin Paradox and
Other Puzzles". Journal of Economic Literature, Forthcoming.
However much we like the idea of relative utility, it’s actually not that easy to
demonstrate. A number of approaches:
1)
2)
3)
4)
Survey data on Behaviour: x=f(x*,….).
Survey data on Utility: U=U(x, x*). Is Satisfaction Utility?
NeuroEconomics. Look at brain reactions.
Experimental.
Probably the two most important problems to be faced in this literature are those of
the Manski critique and definition of the reference group.
Manski critique.
Observation of two individuals behaving similarly (i.e. of x=f(x*,….)) does NOT
prove social interactions, as individuals could face similar constraints (incomes,
prices, availability), or have similar preferences (birds of a feather stick together).
Who’s in the reference group? We have no idea. Here are some ideas.
* Peer group/people like me
* Others in the same household
* Spouse/partner
* Myself in the past
* Friends
* Neighbours
* Work colleagues
* “Expectations”
Our results re: relative utility will be wrong if we have the wrong reference group.
How can we be sure that we have the right reference group?
- Ask individuals to whom they compare (European Social Survey, Wave 3, 2007).
An Aside: Is Modelling Behaviour Really a Panacea?
Behaviour often reflects the intersection of supply and
demand, whereas we are interested in individuals’
preferences.
Under certain technical restrictions (think separability for
example), your behaviour may affect my utility, but will
not affect my behaviour. This happens if my utility
function writes out as Ui = f(xi) + g(xj), where f’(.)>0 and
g’(.)<0.
Note that both problems (the Manski critique and the definition of the reference
group) can be circumvented in an Experimental approach, where the reference group
is defined exogenously (via revelation of information). Thus it is a) not chosen
endogenously by individuals, and b) we control the revelation of information so that
we are sure which reference group is pertinent.
Neuroeconomics is one way of revealing evidence of relative utility experimentally:
here our outcome measure is brain activity.
Fließbach, K., Weber, B., Trautner, P., Dohmen, T., Sunde, U., Elger, C., & Falk, A.
(2007). "Social comparison affects reward-related brain activity in the human ventral
striatum". Science, 318, 1305-1308.
MRI techniques used to measure the brain activity of pairs of individuals engaged in
identical tasks (guessing the number of dots on a screen). Each individual’s ensuing
monetary reward is announced to both subjects, and both absolute and relative
payments were varied.
The results with respect to the ventral striatum show that relative
income is significantly correlated with blood oxygenation in the
brain. In fact, brain activity is completely relative in this respect, as
there is no significant role for absolute income levels once relative
income is introduced.
A more common approach is experiments where the outcome
measure is some kind of behaviour or decision. This is the approach
taken in the paper I’ll discuss here.
However, I’m not really an experimentalist, and I like survey data.
So our paper combines the analysis of experimental and survey data.
Amazingly enough, they produce the same results.
Effort and Comparison Income
Experimental and Survey Evidence
Andrew Clark (CNRS, PSE)
David Masclet (CNRS, CREM)
Marie-Claire Villeval (CNRS, GATE)
1. Motivation
Impact of comparisons on behavior on financial markets (Campbell and
Cochrane 99), criminal activity (Glaeser, Sacerdote and Sheinkman 96),
well-being (Ferrer-i-Carbonell 05, Luttmer 05, Brown, Oswald et al. 05)
Impact of comparisons on labor market behavior (Galizzi and Lang 98,
Neumark and Postlewaite 98, Stark and Taylor, 91)….
… But little is known about their impact on effort behavior (Frank 84)
Our hypothesis: effort does not only depend on the absolute wage but also on
wage comparisons
Idea of social comparisons seductive but conclusive empirical proof of
their existence has been elusive due to (at least) two difficulties:
To whom does the individual compare?
Identification problem – common unobserved environmental factors
(Manski, 93)
2 strands in the literature on social interactions:
Utility: Ui=U(ai,aj,…) for ji estimated by an indirect utility function:
Vi=V(yi,yj,…) for ji (Clark and Oswald, 1996, Clark, 2003)
Behavior: ai*=f(aj,…)
(Sacerdote 01; Aronsson et al. 99; Fortin, Lacroix et al. 04, Arcidiano
et al 05)
Our approach brings these two together by considering behavior as a
function of both absolute and relative income
ai=a(yi,yj,…), estimated by
ai   0   yi   y j   ' X i   i
Our questions
Q1 : Does worker’s effort depend on how much other workers earn?
Q1’: Does it depend on their rank in the distribution of income?
ei=e(yi, y*,…)
+ Little evidence of the influence of others’ incomes on effort (Charness and
Kuhn, 2005; Güth et al. 2001; Gächter and Thoeni, 2005): wage
compression despite a weak effect of others’ incomes on agents’ behavior
Q2: Are comparisons horizontal (to others) or also vertical (intertemporal; to oneself in the past)?
2. Empirical strategy
Joint use of a lab experiment based on a gift-exchange game and
survey data from the 1997 International Social Survey Program
Experimental data: A direct measure of the willingness to contribute
Better control of the reference group
Survey data: Questions related to the willingness to exert effort
Large sample size with employed people
Possibility of cross-country comparisons
Offers a potential check of the external validity of experimental data
Still unusual (Fehr et al. 03; Brown et al. 05, Carpenter and Seki 05,
Cummings et al. 05)
A lab experiment with between-firm comparisons
Benchmark Treatment: Gift-Exchange Game
N=20 subjects, with 10 firms and 10 a priori similar employees
Stage 1: After being randomly matched with an employee, the firm offers
w  20,21,...,120
a contract
Stage 2: The employee accepts or rejects
In case of rejection, both earn 0
In case of an acceptance, choice of level of effort
ei   0.1,0.2,...,1
Convex cost function
Effort e 0.1
Cost c(e) 0
0.2
1
0.3
2
0.4
4
0.5
6
0.6
8
0.7
10
0.8
12
0.9
15
1
18
Firm’s payoff:
  v  we
Employee’s payoff:
with ‘transportation costs’=20
 iE  w  c(ei )  20
F
i
with v=120

Feedback to the employee:
own payoff
Information Treatment
End of stage 1: employees (not firms) receive information on their
reference group’s incomes before accepting the contract
Information set: income levels of 4 other employees
Theoretical predictions
Same SPNE in both treatments:
e*=0.1 => w*=20
Experimental procedures
Regate software, GATE Lyon
120 participants from undergraduate classes in engineering and business
schools
6 sessions (with 20 participants each): 2 sessions in the Benchmark
Treatment (200 obs.) + 4 sessions in the Information Treatment (400 obs.)
10 repetitions with a Perfect Stranger matching protocol
At each of the 10 periods, in the Info Treatment, the set of 5 incomes
come from randomly chosen firms
80 different income distributions
60 minutes
Average earnings: € 14. Show-up fee: € 5
Survey data: 1997 Work Orientations module of the International Social
Survey Program (ISSP: http://www.issp.org)
11,987 individuals aged 16-65 in full or part-time jobs
17 countries
Key variables:
 Earnings: individual, yearly earnings
 Weekly hours of work
 Discretionary effort at work (scaled from 1 to 5):
“I am willing to work harder than I have to in order to help
the firm or organization I work in to succeed”
= Equivalent to effort in the experiment
Country
USA
Canada
Portugal
Switzerland
Denmark
Great Britain
Japan
Hungary
Czech Republic
Norway
East Germany
West Germany
Sweden
Spain
Poland
Italy
France
Total
Employees
interviewed
No.
%
775
546
843
1 727
600
545
607
626
526
1 366
261
648
793
387
564
475
698
11 987
6.47
4.55
7.03
14.41
5.01
4.55
5.06
5.22
4.39
11.40
2.18
5.41
6.62
3.23
4.71
3.96
5.82
100.00
Mean Effort
3.93
3.75
3.71
3.65
3.64
3.63
3.62
3.60
3.60
3.59
3.59
3.52
3.42
3.35
3.26
2.96
2.85
3.55
ei=f(yi,y*, hi)
Reference group income y* = average values by broad demographic groups
(Leyden School- see van Praag and Frijters, 1999)
Average earnings calculated by
- Country (17)
- Sex
- Education: 3 groups (10 or fewer years of education / 11 to 13 /
over 13 years education)
- Age groups: 3 groups (16 to 29 / 30 to 44 / 45 to 65)
 306 reference group income cells (= y*)
Normalized earnings rank = 1- (rank in cell / #obs. in the cell)
3. Results
Effort and Comparison Income
In the experiment, employers do not care about social comparisons
Average income = 53.56 (SD: 19.75) in the Benchmark Treatment
53.09 (SD: 20.04)
Information
The income - effort relationship is positive and steeper in the Information
Treatment (Mann Whitney Tests)
0,9
0,8
Mean effort
0,7
0,6
0,5
Benchmark Treatment
0,4
Info Treatment
0,3
0,2
0,1
0
20-25
26-35
36-45
46-55
56-65
Wage
66-75
76-85
86-95
96-120
The rank-dependence of effort (Random-effect Tobit model)
Effort is strongly correlated with own absolute income
Effort increases with the rank in the income distribution
Experiment: a rise in rank of 1 position increases effort as much as
an income increase of 9.7%. Rank/income elasticity=0.49
ISSP: a 20% rank increase is worth $ 606 per month on
average. Rank/income elasticity=1.6
Average reference group income has a significant influence only in
the experiment
=> Comparisons are more ordinal than cardinal
Effort and Comparisons over time
Hypothesis: past exposure to higher incomes may reduce the utility
associated with current income and decrease the current level of effort
Not easy to test with field data because of the difficulty to ensure that
ceteris paribus holds over long time-periods between waves.
Experimental data ideally suited to test models of habituation: same
environment over time
Test: we estimate the influence of the running minimum and running
maximum incomes and ranks on the current level of effort
Inspired by the peak-end transformation in psychology
(Redelmeier and Kahneman 96)
Past income matters! (Random-effect Tobit on experimental data only)
4. Conclusion
Both the experimental evidence and the ISSP data analysis show the
importance of income comparisons on observable behavior
Effort at work depends both on own income and on what others earn
Income rank is a better predictor than average reference group income
Income profile over time matters in itself; higher influence of
relative demotions than promotions. Past best rank matters more than
past best absolute income => Implications on mergers
1) Interpretation: Status seeking (Frank 85) drives effort behavior
Alternative interpretations:
-> Inequality aversion (Fehr and Schmidt 99, Bolton and Ockenfels 00)?
(but why a stronger role for rank? Why an influence of the past?)
-> Search for the fair wage
(but why not more rejections over time? Why not care about worse
wages in the past?)
2) Implications: comparisons blur the relationship between incentives
and effort
Incentive, selection and reciprocity effects
vs. Crowding-out of intrinsic motivation (Frey, Gneezy and Rustichini),
choking under pressure (Ariely, Loewenstein), threshold effects
(Camerer)
=> we suggest to add wage comparisons as an additional vector
Implications for the no. of ladders in a hierarchy and wage secrecy
3) Survey data and experimental evidence tell the same story
A good signal for both the credibility of subjective measures and the
external validity of lab experiments
4) Extensions
Information on the distribution of contributions instead of income
Information for firms about the income policy of other firms
Other Implications:
1) Firms can trade off wages and status.
2) U=U(y, y*) or U=U(R(y))? A mean-preserving-spread in income
has no effect on rank, but will affect relative income (rank-utility
functions are less directly affected by inequality).
3) U=U(y, y*) or U=U(R(y))? Bilancini, E., & Boncinelli, L.
(2007). "Ordinal vs Cardinal Status: Two Examples". University
of Siena, Working Paper No. 512. Frank (AER, 1985) suggests
that savings rise with income when rank income comparisons
matter. Clark and Oswald (JPubEc, 1998) show that conformity
in behaviour results from concave utility functions where
relative outcomes matter. Neither result continues to hold when
ordinal are swapped for cardinal utility functions.