Lecture VI: PrincipalAgent Models

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Lecture VI Principal-Agent Models

• Recommended Reading (beyond syllabus)
• Milgrom Roberts, Economics, Organization
  Management, Chs 6, 7, 12.

2
Lecture VI Principal-Agent Models

• The Problem
• Delegation leads to agency loss
• Undercuts efficiency, offsets gains from trade or
  specialization
• Sources
• Divergent preferences
• Information Asymmetry expertise,
• In Stroms (2000) terms
• Ex ante Hidden Information (adverse selection)
• See Akerlof (1970)
• Ex post Hidden Action (moral hazard)
• See Grossman Hart (1983)

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Lecture VI Principal-Agent Models

• Solutions (again, Strom)
• Screening
• Revelation of type
• Contract Design
• Incentive compatibility
• Monitoring
• Reduce information asymmetry
• Institutional checks
• veto power
• competition

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Akerloff The Market For Lemons

• Information asymmetry undercuts efficient
  exchange
• Creates divergence between price quality
• Bad quality drives out good until market
  collapses
• Example market for used cars
• Some fraction, q, cars are good, 1-q are lemons
• People prefer good cars to lemons
• Only know if you own a lemon after sale driving
  it
• Thus, we expect used car market to have gt 1-q
  lemons. If a used car were good, why is it for
  sale. at that price?

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Akerloff The Market For Lemons

• Two types of traders, with utility functions
• U1 M ?xi
• U2 M ?3/2xi
• where,
• xi is utility from the quality of the ith car
• M is utility from other goods
• M costs 1 unit (say 1)
• Type 1s own all N cars
• Car quality, x U0, 2 observed only by type
  1s

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Akerloff The Market For Lemons

• Type 2s get more utility from cars than type 1s
• A type 1 could sell a car to a type 2 for a
  price, p ?(1, 3/2)
• Type 1 surrenders 1 unit of x, but can afford gt 1
  unit of M
• Type 2 surrenders p units of M, buts gets more
  utility from x
• But as Type 1s MRS between M x 1, type 1s
  sell only x lt 1p

x lt 1 put up for sale ? µx-used 1/2
x 1 not put up for sale
0
2
µx 1
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Akerloff The Market For Lemons

• Average quality of cars on market is p/2
• Type 2s willing to trade up to p 3/2 p/2
  3p/4
• This price does not compensate Type 1s enough
• Bad quality good drive out good market collapses

x lt 1 put up for sale ? µx-used 1/2
x 1 not put up for sale
0
2
µx 1
8
Akerloff The Market For Lemons

• Bad quality good drive out good market
  collapses adverse selection
• More realistically
• (Low) Price of used good reflects information
  asymmetry as well as wear tear
• Given low resale price, less of good offered for
  resale inefficient

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Adverse Selection Politics

• How do voters know if politician is honest?
• How does PM know if Cabinet Minister is loyal?
• How do party delegates know which leadership
  contestant is a winner?
• Is applicant to civil service competent,
  discrete, non-partisan?

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Technology of Adverse Selection

• Already introduced Signalling game
• Agent (type 1, 2, N) send costly signal
• Principal updates on type via Bayes Rule (if
  possible)
• Pooling
• Separating
• Semi-separating
• Low quality agents want to pool principal wants
  agents to separate
• Incentive compatibility Principal can structure
  contract (i.e. payoffs) to compensate high
  quality but not low quality agents for costly
  signalling.

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Moral Hazard

• No types here, but information asymmetry still a
  problem
• Agent has incentives for ex post opportunism
  shirking, sabotage
• Political Examples
• Ministers prefer to coast (i.e., shirk) rather
  than advance potentially controversial policies
  (Dewan Myatt 2007)
• Bureaucrats undermine political initiatives that
  upset a comfortable status quo or maximize
  budgets not efficiency (Niskanen 1971)
• Coalition partners alter pre-election policy
  agreements

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Moral Hazard Typical Game Structure

• Principal delegates production of a good x to
  agent in exchange for some payment, p
• e.g., Cabinet delegates policy implementation to
  civil service provides ministries with budgets
  to do so
• Production of x is costly to agent
• Political science analog moving policy from sq
  to x requires civil servants to exert effort (e)
  or move policy from their ideal point
• ?UP/?x gt 0, ?UP/?p lt 0 ?UA/?e lt 0, ?UA/?p gt 0

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Moral Hazard Typical Game Structure

• Agent knows more about production process than
  principal
• Example 1 x effort ?, ? N (µ,s2)
• Example 2 x (1-?)(effort) ?budget, ?
  N(µ,s2)
• Agent observes ? higher ? allows less effort,
  can maintain effort and obtain larger budget
  keep surplus, etc. depending on UA
• Principal knows f(x) ? N(µ,s2), but sees
  only x
• Can Principal structure payment scheme to limit
  Agents opportunism enhance efficiency?

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Moral Hazard Typical Game Structure

• Typical modelling trick
• Principal is risk neutral in p, Agent is risk
  averse in p
• Mathematically, UP is linear in p, UA quadratic
  in p

UA
Utility
p
UP
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An Example Indridason Kam (2007)

• Puzzle
• Why do PMs reshuffle ministers frequently if
  reshuffling only serves to undercut ministerial
  experience amplify civil servants
  informational advantage?
• Argument
• Ministers have incentives to use their portfolios
  in manner that runs contrary to PM cabinets
  collective interests, e.g., run up budgets to
  boost their own profile, make a leadership run,
  etc.
• By reshuffling ministers, PM can rein in
  ministers propensity to deviate from cabinet
  PM.

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An Example Indridason Kam (2007)

• PM sets status quo policy, x ??2 w.l.o.g. set
  x (0,0)
• Mi Mj spend , s0 ? -?, ? where ? is PMs
  oversight
• s0 alters policy x ? x0 (s0i, s0j)
• PM reshuffles (r 1) or not (r 0)
• Mi Mj spend again, s1 ? -?, ?
• x0 ? x1 (s0i (1-r)s1i rs1j, s0j rs1i
  (1-r)s1j)
• Payoffs

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An Example Indridason Kam (2007)

• PM utility tied to governments policy
• UPM(x0, x1) -x02 - x12
• Mis policy tied to government policy spending
  in portfolio
• UMi(x0, x1) -x02 - x12 ?ix0i (1-r)
  ?ix1i r?ix1I
• where ?i represents Mis preference for spending
  over policy

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A Reshuffle Equilibrium
Reshuffle r 1

• Mj is within ? of ?/2
• if Mj can obtain ?/2 in t1, she does so else
  Mj spends ?
• So would Mi ever spend s0 lt ??

?
s1j
?j 2
s0i
UMj
Shift
t0
t1
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A Reshuffle Equilibrium
In restraining spending at t0, Mi
?
?

• Forgoes spending utility at t0
• Depends on ?

s1j
s1j

• Avoids policy disutility by limiting Mjs
  spending at t1
• Depends on ?

s0i
UMi
s0i
Shift

• In equilibrium when
• ? ? (?/6, ?/(2 2/3?6))

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Calvert, McCubbins, Weingast (1989)

• Theme Another look at the agency drift model set
  out by McNollgast.
• Question To what extent can bureaucracy
  substitute its own discretion for political
  instructions ex post?
• Argument Political institutions allow
  bureaucrats discretion only within limits allowed
  by politicians

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Calvert, McCubbins, Weingast (1989)

• L E bargain over selection of A (Nash
  Cooperative Solution)
• Policy setting is delegated to A
• A sets policy xA on contract curve normalized to
  L 0, E 1
• Either L or E may veto xA

E
A
L
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Calvert, McCubbins, Weingast (1989)
Utility Functions UA ?A - x xA UE ?E -
1 x UL ?L - x i.e., the higher ?i, the
more the actor is willing to give up in terms of
agency discretion to get some policy
E
A
L
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Calvert, McCubbins, Weingast (1989)

• Full Information Game
• xA must be closer to both principals than their
  respective reservation values, ?E and ?L
• Any x further away ?i than provides ui lt 0 veto

?L
xA
L 0
?E
E 1
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Calvert, McCubbins, Weingast (1989)

• Add uncertainty
• xA xA ?, where ? is a r.v. such that xA ?
  0, 1
• Does this change game?
• Not much Within ? ? of veto points, A has some
  wriggle room

??
?L
xA
?E
L 0
E 1
??
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Calvert, McCubbins, Weingast (1989)

• Principals capacity to veto, i.e., exert ex post
  correct limits agency discretion even in presence
  of uncertainty

??
?L
xA
?E
L 0
E 1
??