Modeling self-control problems II:
Dual-self models
Lectures in Behavioral economics
Fall 2011, Part 4
(Based on notes by Kjell Arne Brekke)
13 September 2011
G.B. Asheim, ECON4260, #4
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Dual self models of impulse control

Thaler and Sherfin (1981)
● Consider each individual as an organization
● Consist of a planner and doers
● The planner is concerned with lifetime utility
● The doers exists only one period and is completely selfish

Current interpretation
● Planner is prefrontal cortex
● Doers are the rest of the brain (reptilian brain)

Fudenberg and Levine (2006)
● Equivalent formulation: Planner control doers at a cost.
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Using new insight from neurology—Neuroeconomics

The importance for economics discussed

“Economics needs brains”


“The case for a mindless economics”


Gul and Pesendorfer (2008)
New knowledge about the brain has made the dual self
model much more plausible


Some argue as if such evidence is almost conclusive
Others insist that econ
econ. th.
th should be tested on econ.
econ data



Camerer,, Loewenstein and Prelec (2004,
(
, 2005))
Consumer theory makes no claims about the brain
Nor about underlying psychology
Neurology can inspire new theory building

To be tested on economic data
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The prefrontal cortex


Phineas Gage survived a pole
through frontal lobe
After the damage, the doctor
described him: “.. devising many
plans for future operation which
are no sooner arranged than they
are abandoned. … Ladies were
advised not to stay in his
presence. The hallmark of Gage’s
new condition was his complete
inability to direct or control himself”
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Choices under cognitive load



Shiv and Fedorikhin (1999)
S bj t were instructed
Subjects
i t t d to
t memorize
i 2 (7) digits
di it
inducing low (high) cognitive load
Then walk from one room to another, in-between
choosing between a cake and a fruit salad
Choice
Memorize
37 (5274657)
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Recall
G.B. Asheim, ECON4260, #4
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Choices under cognitive load (cont.)

Results



High load: 59 percent chose cake
Low load: 37 percent chose cake
Interpretation

Prefrontal cortex cares about the long run (health)




Prefer the fruit salad
Sugar (the cake) is tempting to reptilian brain (the
crocodile within)
High cognitive load reduces the prefrontal cortex’s ability
to control the impulses from the reptilian brain
Cognitive load; short term memory has 7 slots
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3
The dual self model


Thaler and Shefrin (1981) do not talk about
prefrontal
f
l cortex andd reptilian
ili brain,
b i b
but this
hi h
how
the model is often interpreted today. (And this is
this interpretation that we will use here).
Their motivation: “The idea of self-control is
paradoxical unless it is assumed that the psyche
contains more than one energy system, and that
these energy systems have some degree of
independence from each other” (McIntosh, 1969).
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The dual self model (cont.)

A planner
l
(th
(the prefrontal
f t l cortex;
t frontal
f t l lobe)
l b )

A sequence of doers (the reptilian brain)

Setting

Income stream: y  (y1, y2, … , yT)

Consumption plan: c  (c1, c2, … , cT)

The utility of the doer at time t: Zt(ct)

The utility of the planner: V(Z1, Z2, … , ZT)
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4
Alter incentives
Utility
Unaltered pref.
The planner can alter the
Cost of impulse control
doer' s incentive s through  t .
Doer' s utility : Z t (ct ; t ).
Altered
preferences
Such altering of the doer' s
preferences induces costs.
If  t is chosen such that
arg max Z t (ct ; t )  cˆ,
then Z t (cˆ; t )  Z t (cˆ;0).
13 September 2011
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G.B. Asheim, ECON4260, #4
c
Consumption
9
Equivalent formulation:
Fudenberg and Levine (2006)
Doer' s utilityy u (ct ) is strictlyy increasing.
g
Maximum feasible consumption ct .
Cost of self control : C (c, c*)   (u (c*)  u (c)).
The more the doer sacrifices the more effort required.
Total utility : Z t  u (ct )  C (ct , ct *).
Planner maximizes V ( Z1 , Z 2 ,..., ZT ).
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Application: Immediate money

First choice problem (in 1000 $):


Second choice problem (in 1000 $):






A: 1 in year 1,
1 or B: 1.5
1 5 in year 2
C: 1 in year 2, or D: 1.5 in year 3
Basic income stream: 10 each year.
Doer’s utility: u(ct)  lnct
May save, but no borrowing.
Cost of self control: 0.5ln ct  ln ct 
Planner’s utility: V ( Z1 , Z 2 , Z 3 )  Z1  Z 2  Z 3
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G.B. Asheim, ECON4260, #4
No saving due to control costs—B as an example

Income stream: 10, 11.5, 10

In year 2, c2  11.5

dV 1.5
1


dc2 c2 21.5  c2
 dV 



dc
Saving some of the additional income  2  c2 11.5
1.5 1
would induce cost of self control:
 0

11.5 10
For c2  c2  11.5, utility equals
ln10  ln c2  ln(10  11.5  c2 )  0.5(ln11.5  ln c2 )
 1.5 ln c2  ln(10  11.5  c2 )  ln10  0.5 ln11.5

Optimal consumption stream: 10, 11.5, 10
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Choosing A or B
 
B : ln10  ln11.5  ln10  0.5ln11  ln10  ln 1150
 ln1096
1.1


Additional income in A or B will be cons. immediately.
y
Without problems of self control, B is best:
 A: ln11 + ln10 + ln10
 ln1100




B: ln10 + ln11.5 + ln10
But with A as an option, c1  11 , while choosing B
i li c1  10 .
implies
The cost of self control exceed additional utility.
The planner will choose A.
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Choosing C or D



Additional income in C or D will be cons. immediately.
With no cost of self-control, D is best:
 C: ln10 + ln11 + ln10
 ln1100
 D: ln10 + ln10 + ln11.5
 ln1150
With cost of self control




Onlyy 10 available to the doer in year
y 1 in both C and D.
Choice made before doer in year 2 or 3 may influence it.
No cost of self control.
The planner will choose D.
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Compared to Gul and Pesendorfer (2001, 2004)

With onlyy A available,, utilityy is
ln11 + ln10 + ln10

With only B available, utility is
ln10 + ln11.5 + ln10

With a choice between A and B, the planner will
choose A dduee to the cost of self control.
control Thus:
Th s
{ A} ~ { A, B}  {B}
ln 1100  ln 1100  ln 1150
13 September 2011
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.
Compared
to Gul and Pesendorfer (2001, 2004) (cont.)

B: 2 in year 2

With onlyy A available,, utilityy is
ln11 + ln10 + ln10

With only B available, utility is
ln10 + ln12 + ln10

With a choice between A and B, the planner will
choose
h s B in spite
spit off self
s lf control
ntr l costs.
sts Th
Thus:
s
{ A}  { A, B}  {B}
ln 1100  ln 1144  ln 1200
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Control methods

Alter preferences


Alter opportunities: Rules




Thi corresponds
This
d to the
h approach
h studied
di d
Precommitment, (e.g. non-liquid assets)
Limiting choices (avoid Las Vegas)
Rules of thumb (ban on borrowing)
Why would rules of thumb work?


Public announcement (“I’ve stopped smoking”)
Other?
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Applications in Thaler and Shefrin (1981)


Rich in ideas; weak in formal proofs.
The effect of mandatory pension saving




A person saves a share s of income
Saving p < s becomes mandatory
Does total saving change?
Bonus-payments and saving

Two person with annual income 84 (thousand),



one get 7 per month
the other gets 6 per month + a bonus of 12 once a year.
Who saves most?
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Bonus payment

B gets the bonus, A does not





A saves 0.4 per month.


Cost of impulse control: 12(ln7 – ln6.6)  0.71
B saves 4.8
4 8 in one month.
month


A earns 7 p
per month
B earns 6 except one month with 12
Both have doer utility lnc
Both save 4.8, what are their cost of impulse control?
Cost of impulse control : (ln18 – ln13.2) = 0.31
Least cost of self control for B, since marginal utility
the one month is lower.
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Conclusion

Dual self model




“Planner” (p
(prefrontal cortex)) controllingg
“Doer” (reptilian brain)
Equivalent to a cost of self control if deviating from
short run optimum.
Explains



Choosing 1 now over 11.55 in one year
year, while also choosing
1.5 in two years over 1 in one year.
Demand for commitment.
Consumption correlating with income.
13 September 2011
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Additional references





Colin Camerer, George Loewenstein and Drazen Prelec (2004):
Neuroeconomics: Why Economics Needs Brains. Scandinavian
Journal of Economics, 106, 555-579
C li Camerer,
Colin
C
G
George
L
Loewenstein
t i andd Drazen
D
P l
Prelec
(2005):Neuroeconomics: How Neuroscience Can Inform
Economics, Journal of Economic Literature, Vol XLIII, pp. 9-64
Faruk Gul and Wolfgang Pesendorfer (2008): The Case for
Mindless Economics, in The Foundations of Positive and Normative
Economics, by A. Caplin and A. Shotter (eds.). Oxford Univ Press
http://www.princeton.edu/~pesendor/mindless.pdf
p //
p
/ p
/
p
Baba Shiv and Alexander Fedorikhin (1999): Heart and Mind in
Conflict: The interplay of Affect and Cognition in Consumer
Decision Making, Journal of Consumer Research, 26, 127-90.
Rita Carter (1998): Mapping the Mind. University of California Press
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