Self-Control in Peer Groups

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Building Public Infrastructure in a
Representative Democracy
Marco Battaglini Princeton University and
CEPR Salvatore Nunnari Caltech Thomas
Palfrey Caltech
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Public Infrastructure

• New dynamic approach to the political economy of
  public investment
• Many public goods are durable and cannot be
  produced overnight. Call this Public
  Infrastructure
• Examples
• Transportation networks
• Defense infrastructure
• Three key features of public infrastructure
• Public good
• Durability current investment has lasting value
  
• Dynamics takes time to build

3
Government and Public Infrastructure

• A major function of governments is the
  development and maintenance of lasting public
  goods.
• How do political institutions affect provision?
• Federalist systems Decentralized
• Provinces, States, Counties, etc.
• Centralized/Representative Legislatures and
  Parliaments

4
Theoretical Approach

• Simple infinite horizon model of building public
  infrastructure. Similar to capital accumulation
  models
• Characterize the planners (optimal) solution as
  benchmark
• Compare Institutions for making these decisions
• Two models
• Centralized (Representative Legislature)
• Legislative bargaining model
• Decentralized (Autarky)
• Simultaneous independent decision making at
  district level

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Empirical Approach

• Laboratory Experiments
• Control the driving parameters (environment) of
  model
• Preferences, Technology, Endowments
• Mechanism Rules of the game
• Incentivize behavior with money
• Theory gives us predictions
• Equilibrium behavior and Time paths of investment
• Differences across mechanisms and environments
• Experiments give us data
• Compare theory and data

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The Model

• n districts, i1,,n each of equal size
• Infinite horizon. Discrete time
• Two goods
• Private good x
• Public good g (durable). Initial level g0
• Public policy in period t zt(xt,gt) where
  xt(xt1,,xtn)
• Each district endowment in each period ?tiW/n
• Societal endowment W
• Endowment can be consumed (xt ) or invested (It)
• Public good technology. Depreciation rate d

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The Model
Feasibility
Budget balance
Can rewrite Budget balance as
Preferences
u () lt 0 u() gt 0 u(0) 8 u(8) 0
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Planners Problem (optimum)
Denote value function vp(.) aggregate
consumption XSxi
Notice y0 constraint not binding because of
Inada conditions Hence rewrite optimization
problem as
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Optimal Policy

• Denote optimal policy by y(g). Optimal steady
  state yp
• Three phases
• Rapid growth It W
• Maintenance of steady state 0 lt It lt W
• Decline It 0
• Depends on whether nonnegativity constraint on
  consumption is binding

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Optimal Path

• Case 1 Constraint binding Rapid growth
• I W
• yt W (1-d)gt-1
• Case 2 Constraint not binding. Steady state y
  W (1-d)gt-1
• Solves nu(y) v(y) 1
• Corresponds to two phases
• Maintenance of steady state 0 lt It lt W
• Decline It 0

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Optimal Path

• Switch from growth to maintenance phase at gp

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Optimal Path
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Optimal Path
Summary of optimal policy
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Planners solution 1
y(g)
yp
1-d
W
gp
gp/(1-d)
g
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Planners solution 2
y(g)
yp
W
gp
gp/(1-d)
g
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Optimal Path Example
u(y) ya/ a
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The Legislative Mechanism

• Legislature decides policy in each period
• Non-negative transfers, x1,,xn
• Level of public good y (1-d)g W Sxi
• Random recognition rule
• Proposer offers proposal (x,y)
• Committee votes using qualified majority rule (q)
• If proposal fails, then y 0, xi ?i W/n for
  all i

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The Legislative Mechanism

• Proposers Maximization Problem

Note (1) Proposal is (x,s,y) (2) s is
the private allocation offered to each of the
(q-1) other members of the coalition.
(3) x is the private allocation to the proposer
(4) First constraint is IC Other members
of the coalition are willing to vote for the
proposal. (5) v() is the value function
for continuing next period at state y.
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The Legislative Mechanism

• Proposers Maximization Problem

Several cases, depending on state, gyt-1, and
on whether IC is binding.
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In the other case, we have W-y(g)(1-d)g0, i.e.,
x(g)0. This occurs when g lt g1(y1)
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IC Binding s gt 0 CASE
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IC Binding s 0 CASE
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LEGISLATIVE MECHANISM INVESTMENT FUNCTION
Note Investment function is not monotonically
decreasing! Investment is increasing in third
region g2 lt g lt g3
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Legislative Mechanism 1
y2
y1
1
45o
g1
g3
g2
y2/(1-d)
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Legislative Mechanism 1
qgtq
y2
y1
1
g1
g3
g2
y2/(1-d)
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Legislative Mechanism 2
y2
y1
1
45o
g1
g3
g2
y2/(1-d)
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Legislative Mechanism 3
y2
y1
1
45o
g1
g3
g2
y2/(1-d)
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LEGISLATIVE MECHANISM VALUE FUNCTION
Note Value function is monotonically
increasing! Investment is increasing in third
region g2 lt g lt g3
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LEGISLATIVE MECHANISM VALUE FUNCTION
Relationship between v and (y1,y2)
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Illustration of Legislative Bargaining Equilibrium

• u2y1/2
• n3
• q2
• W15
• d.75
• d0

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COMPUTING THE EQUILIBRIUM
Exploit the relationship between v and (y1,y2)
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The Autarky Mechanism

• In each period, each district simultaneously
  decides its own policy for how to divide ?i
  W/n between private consumption and public good
  investment.
• District can disinvest up to 1/n share of g
• Symmetric Markov perfect equilibrium

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The Autarky Mechanism

• Districts Maximization Problem

A symmetric equilibrium is a district-consumption
function x(g)
For each g, a district chooses the
district-optimal feasible xi taking as given that
other districts current decision is given by
x(g), and assuming that all districts future
decisions in the future are given by x(g)
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The Autarky Mechanism
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The Autarky Mechanism
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The Autarky Mechanism
Example with power utility function u Bya/a
Typo Exponent Should be 1/(1-a)
In planners solution, the denominator equals
1-(1-d)d
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Autarky Mechanism
yv
1-d
1
gV
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• Summary of theory and possible extensions
• New Approach to the Political Economy of Public
  Investment.
• Applies equally as a model of capital
  accumulation
• Centralized representative system much better
  than decentralized
• Still significant inefficiencies with majority
  rule
• Higher q leads to greater efficiency
  theoretically
• Why not qn?
• Model can be extended to other political
  institutions
• Elections
• Regional aggregation (subnational)
• Different legislative institutions (parties,
  etc.)
• Model can be extended to allow for more complex
  economic institutions
• Debt and taxation, Multiple projects,
  Heterogeneity

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Experimental Design
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Experimental Design
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Experiment Implementation

• Discount factor implemented by random stopping
  rule. (prcontinue.75)
• Game durations from 1 period to 13 periods in our
  data
• Multiple committees simultaneously processed (5x3
  and 3x4)
• Payoffs rescaled to allow fractional decisions
• Caltech subjects. Experiments conducted at SSEL
• Multistage game software package
• 10 matches in each session
• Subjects paid the sum of earnings in all periods
  of all matches
• Total earnings ranged from 20 to 50
• Sessions lasted between 1 and 2 hours

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Sample ScreensLegislative Mechanism
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Sample ScreensAutarky Mechanism
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RESULTS
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L5 ALL COMMITTEE PATHS. PERIOD 1
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L5 ALL COMMITTEE PATHS. PERIOD 2
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L5 ALL COMMITTEE PATHS. PERIOD 3
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L5 ALL COMMITTEE PATHS. PERIOD 4
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L5 ALL COMMITTEE PATHS. PERIOD 5
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L5 ALL COMMITTEE PATHS. PERIOD 6
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L5 ALL COMMITTEE PATHS. ALL PERIODS
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A5 ALL COMMITTEE PATHS. PERIOD 1
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A5 ALL COMMITTEE PATHS. PERIOD 2
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A5 ALL COMMITTEE PATHS. PERIOD 3
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A5 ALL COMMITTEE PATHS. PERIOD 4
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A5 ALL COMMITTEE PATHS. PERIOD 5
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A3 ALL COMMITTEE PATHS. PERIOD 1
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A3 ALL COMMITTEE PATHS. PERIOD 2
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A3 ALL COMMITTEE PATHS. PERIOD 3
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A3 ALL COMMITTEE PATHS. PERIOD 4
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A3 ALL COMMITTEE PATHS. PERIOD 5
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L3 ALL COMMITTEE PATHS. PERIOD 1
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L3 ALL COMMITTEE PATHS. PERIOD 2
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L3 ALL COMMITTEE PATHS. PERIOD 3
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L3 ALL COMMITTEE PATHS. PERIOD 4
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L3 ALL COMMITTEE PATHS. PERIOD 5
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L3 ALL COMMITTEE PATHS. PERIOD 6
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Median Time Paths
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Autarky Median Time Paths
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5 person committeesLegislative vs. Autarky
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3 person committeesLegislative vs. Autarky
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Legislative Median Time Paths
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Median Time Paths of g
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Investment Paths(includes conditional and failed
proposals)
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Investment function for L3
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Investment function for L5
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Investment function for A3
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Investment function for A5
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Investment Pathsas a function of the State
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Investment function L3
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L5 ALL COMMITTEE PATHS. ALL PERIODS
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Voting Behavior
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L5 PROPOSAL ACCEPTANCE RATES

• InvW is common
• Pork to all is common with investment
• MWC most common with no investment
• Rejection declines over first six rounds
• Negative investment only with high g
• Types commonly rejected
• Pork only to proposer
• Negative investment
• Even with pork to all

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L3 PROPOSAL ACCEPTANCE RATES
low
low
low

• InvW is common
• Pork to all is common (often token)
• MWC less common
• Rejection declines over first six rounds
• Negative investment only with high g
• Types commonly rejected
• Pork only to proposer
• Negative investment
• Even with pork to all

low
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VOTING BEHAVIOR ACCEPTANCE RATES
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VOTING BEHAVIOR ACCEPTANCE RATES Test for
stationary behavior
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PROPOSAL BEHAVIOR PORK TO PREVIOUS PROPOSER Test
for stationary behavior
PUNISHMENT AND REWARD
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• Summary
• New Approach to Political Economy of Public
  Investment.
• Centralized system theoretically better than
  decentralized
• Important role for centralized representative
  government
• Still, significant inefficiencies with majority
  rule
• Higher q leads to greater efficiency
  theoretically
• Laboratory trajectories of public good close to
  theoretical model
• Centralized representative voting mechanism leads
  to big efficiency gains
• Suggests value of applying framework to a much
  wider variety of institutions and environments.
• Role of repeated game effects non-Markov
  behavior
• Statistically significant. Affects a few
  committees (higher investment)
• Economically significant? Not much. Small in
  these experiments

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Investment function L5
Some outliers excluded