Manager’s reputation
”Worldly wisdom teaches that it is better for reputation to
fail conventionally than to succeed unconventionally.”
John Maynard Keynes, The General Theory, Ch. 12.
• The manager makes decisions on behalf of the owners
- collects information about investments
- chooses investment projects
- runs the projects
• The manager is concerned about his future career
• Could it be that the manager, in his investment decisions,
behaves more risk aversely than the owners would like?
• Can a manager impose too much risk on the owners?
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 1
Suppose the manager does not know whether he is talented
or not
- in picking investment projects
- in running the projects
Could it be that his decisions are governed by a desire not
to find out?
Two models:
1) How uncertainty about the ability to run projects may
make risk averse managers too careful and stay away
from new investments.
2) How uncertainty about the ability to find good projects
may make managers do as other managers do rather than
as their own information implies.
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 2
1) Uncertainty about ability to run projects
(Holmström, Review of Economic Studies 1999 [1982])
Model: manager vs. owner
Neither manager nor owner knows whether the manager is
talented. The probability of him being talented is: η
The manager observes a pool of investment projects and
picks one of them as his advice to the owner. The owner
takes the final decision whether or not to proceed with the
project put before him.
An investment project, I, is described by four
characteristics:
I = (H, L, pT, pN),
where:
H = project value if it is a success
L = project value if it is a failure; L < H.
pT = probability of success if the manager is
talented
pN = probability of success if the manager is not
talented; pN < pT.
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 3
Unconditional probability that the project I is a success:
π = pTη + pN(1 - η)
Conditional probabilities:
η+ = Pr(Manager is talented | Investment success) =
Pr(talented ∩ success) η pT
=
π
Pr(success)
η− = Pr(Manager is talented | Investment failure) =
η (1− pT )
(1−π )
The manager’s salary is a function of the owner’s belief
that he is talented.
Simple case: Salary = Owner’s belief.
The manager maximizes:
πu(η+) + (1 – π)u(η−)
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 4
A risk neutral manager maximizes:
πη+ + (1 – π)η− = π
η pT
η (1− pT )
+ (1−π )
= η.
1−π
π
A risk neutral manager is indifferent between all
investment projects, and between investing and not.
A risk averse manager will prefer the owner’s initial belief
to be unaltered and strictly prefers no investment at all.
u
η−
η
η+
It may be necessary to make the manager more interested in
taking risk.
- stock options
- golden parachutes
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 5
2) Uncertainty about ability to find projects
(Scharfstein & Stein, American Economic Review 1990.)
Herd behaviour among managers
• A talented manager is good at collecting information.
• Because they are good at collecting information, talented
managers will often have similar information.
• When you are not sure about your own talent as
manager, it may be best to do as other managers, in case
they are talented.
Model:
Two managers, A and B.
Stage 1: A collects information and makes an investment
decision (Yes/No).
Stage 2: B observes A’s decision, collects information, and
makes his own investment decision (Yes/No).
Stage 3: Payoff is disclosed (the same for both projects):
Either
xH > 0
(prob. ½)
or
xL < 0
(prob. ½)
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 6
The value of the information the manager collects before
making his decision depends on his talent: smart vs. dumb.
Probability of a manager being smart = θ ∈ (0, 1).
• Collected information: sG or sB
• sG is sign of a profitable investment, but only if the
manager is smart.
Pr(sG | xH, smart) = p ∈ (½, 1),
Pr(sG | xL, smart) = (1 – p) ∈ (0, ½).
• If the manager is dumb, then the collected information
will be uninformative.
Pr(sG | xH, dumb) = Pr(sG | xL, dumb) = ½.
• The collected information does not in itself provide the
manager with a hint on whether or not he is smart.
Pr(sG | smart) = Pr(sG | dumb) = ½.
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 7
Having observed the collected information, the manager
updates the probability of having a high payoff:
Pr(xH | sG) =
=
Pr(xH | sB)=
Pr(sG ∩ xH ) Pr(xH )⋅Pr(sG | xH )
=
Pr(sG )
Pr(sG )
[
1
θp +
2
(1−θ )12 ]
1
2
1 ⎛ 1⎞
= + θ ⎜ p − ⎟ ≡ µG
2 ⎝ 2⎠
1 ⎛ 1⎞
−θ ⎜ p − ⎟ ≡ µ B
2 ⎝ 2⎠
Assumption: θ (2 p −1) >
xH + xL
xH − xL
Implication: The investment is profitable if and only if the
manager has collected the information sG:
µGxH + (1 – µG)xL > 0 > µBxH + (1 – µB)xL
Assumption: If both managers are smart, then they collect
the same information. If at least one of them is dumb, then
their information is independently distributed.
More generally: positive correlation among smart managers
– creates scope for herd behaviour.
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 8
Manager B wants potential future employers in the market
for managers to believe he is smart.
θˆ = outsiders’ updated probability that B is smart.
Assumption: Manager B’s objective is to maximize θˆ .
Efficient decisions:
Stage 1: Manager A invests if and only if he observes sG.
Stage 2: Manager B is able to infer A’s information. If B
has the same information as A, he does the same as A. What
if he has the opposite information?
Pr(xH | sG, sB) = ½
⇒
Expected payoff given (sG, sB) = ½xH + ½xL
⇒
B invests, when information differs, if and only if
xH + xL > 0
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 9
What is B’s decision when he is concerned with his
reputation?
First: Could it be that B invests if and only if he collects
information sG?
(This is efficient only if xH + xL > 0, and/or if A already has
invested.)
In such a case, both managers reveal their collected
information through their investment decisions, and
outsiders’ beliefs are consistent with this.
Calculating outsiders’ beliefs
Consider the case where both managers invest and the
outcome of the investments is positive.
θˆ(sG , sG , xH ) =
=
Pr({B smart} ∩ {(sG , sG , xH )})
Pr(sG , sG , xH )
θ 2 p+(1−θ )θ 12 p
2
()
2
2
θN
p +(1−θ )θ 12 p+θ(1−θ ) p 12 +(1−θ ) 1
2
A is smart
A is dumb
A is smart
=
2 pθ(1+θ )
A is dumb
B is smart
2
4 pθ +(1−θ )
B is dumb
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 10
This cannot be an equilibrium.
To see this, it is sufficient to consider one case where
equilibrium conditions are not satisfied:
Suppose A observes sG and invests, and B observes sB.
Should B refrain from investing and this way reveal his
information sB, or should he invest, pretending he observed
sG? In this equilibrium, he should refrain from investing.
The equilibrium condition is:
Pr(xH | sG, sB)θˆ (sG, sB, xH) + Pr(xL | sG, sB)θˆ (sG, sB, xL) ≥
Pr(xH | sG, sB)θˆ (sG, sG, xH) + Pr(xL | sG, sB)θˆ (sG, sG, xL)
⇔
1 2θ (1− p ) 1 2θ p 1 2 pθ (1+θ ) 1 2θ (1− p )(1+θ )
+
≥
+
2 1+θ
2 1+θ 2 4 pθ + (1−θ )2 2 4θ (1− p )+ (1−θ )2
(
)
p(1− p )θ 1+θ 2
⇔
≤ 0 ; not possible.
2
(1−θ )
The equilibrium condition is never satisfied. Therefore,
there does not exist an equilibrium in which B always
makes his investment decision according to his own
collected information.
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 11
On the other hand: Suppose A behaves efficiently. Does an
equilibrium exist where B thereafter invests if and only if A
has already invested? – Herd behaviour.
Reasonable beliefs among outsiders, in case B makes a
decision ”out of equilibrium”:
i)
If B invests when A has not invested first, then
outsiders believe B has observed sG.
ii)
If B refrains from investing even if A has already
invested, then outsiders believe B has observed sB.
Example: A has invested. There are two cases to consider.
(i)
B observes sG. The equilibrium condition is:
θ ≥ Pr(xH | sG, sG)θˆ (sG, sB, xH) + Pr(xL | sG, sG)θˆ (sG, sB, xL)
• In this equilibrium, where B does not use his own
observations, the outsiders are unable to update their
beliefs, and so θˆ = θ.
• If B deviates from equilibrium by not investing, then
the outsiders believe this is because he observed sB.
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 12
Pr(sG, sG, xH) = θp +
1
(1 - θ)2;
4
Pr(sG, sG, xL) = θ(1 – p) +
Pr(sG, sG) = Pr(sG, sG, xH) + Pr(sG, sG, xL) = θ +
Pr ( sG , sG , xH ) 4 pθ + (1 − θ )
Pr(xH | sG, sG) =
=
Pr ( sG , sG )
2 (1 + θ 2 )
1
(1 - θ)2
4
1
1
(1 - θ)2 = (1 + θ2)
2
2
2
⇒ The equilibrium condition can be written as:
4 pθ + (1−θ ) 2θ (1− p ) 4θ (1− p )+ (1−θ ) 2θ p
θ≥
+
2
1+θ
1+θ
2 1+θ
2 1+θ 2
2
(
)
2
(
)
3+θ 2
⇔ p(1 – p) ≤
; always satisfied, since p(1 – p) < ¼.
8
(ii)
B observes sB. The equilibrium condition is:
θ ≥ Pr(xH | sG, sB)θˆ (sG, sB, xH) + Pr(xL | sG, sB)θˆ (sG, sB, xL)
=
1 2θ (1− p ) 1 2θ p θ
+
=
⇔ θ ≥ 0; always satisfied.
2 1+θ
2 1+θ 1+θ
What is left to show is that manager A takes best care of his
own reputation by investing efficiently (if and only if he
observes sG), knowing that manager B does the same as he;
and in equilibrium, this is what manager A does.
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 13
• Herding behaviour among managers
- An unstable situation: First one in the sequence says
Yes; thereafter, all others also say Yes.
- Application: the Norwegian banking crisis
• Reputational herding vs. statistical herding
- Statistical herding: information cascades
- herding without career concerns
- late-comers using others’ information
Grant, King & Polak, “Information Externalities, SharePrice Based Incentives, and Managerial Behaviour”,
Journal of Economic Surveys 1996, Sec. 4.
- Combining reputational and statistical herding:
herding without correlation
Ottaviani & Sørensen, American Economic
Review 2000.
Economics of the firm – Tore Nilssen – Lecture 11 - Managing the firm: Reputations - 14