Transcript of June 2009Rationality, Behaviour and Experiments Moscow 1 Building Public Infrastructure in a...
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- June 2009Rationality, Behaviour and Experiments Moscow 1
Building Public Infrastructure in a Representative Democracy Marco
Battaglini Princeton University and CEPR Salvatore Nunnari Caltech
Thomas Palfrey Caltech
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- June 2009Rationality, Behaviour and Experiments Moscow 2 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 Public Infrastructure
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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 Government and Public Infrastructure
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- June 2009Rationality, Behaviour and Experiments Moscow 4 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 Theoretical
Approach
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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 Empirical Approach
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districts, i=1,,n each of equal size Infinite horizon. Discrete
time Two goods Private good x Public good g (durable). Initial
level g 0 Public policy in period t: z t =(x t,g t ) where x t =(x
t 1,,x t n ) Each district endowment in each period t i =W/n
Societal endowment W Endowment can be consumed (x t ) or invested
(I t ) Public good technology. Depreciation rate d The Model
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Feasibility The Model Budget balance Can rewrite Budget balance as:
Preferences u () < 0 u() > 0 u(0) = u() = 0
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Planners Problem (optimum) Notice y0 constraint not binding because
of Inada conditions Hence rewrite optimization problem as: Denote:
value function v p (.) aggregate consumption X=x i
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- June 2009Rationality, Behaviour and Experiments Moscow 9 Denote
optimal policy by y^(g). Optimal steady state y p * Three phases:
Rapid growth I t = W Maintenance of steady state 0 < I t < W
Decline I t 0 Depends on whether nonnegativity constraint on
consumption is binding Optimal Policy
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- June 2009Rationality, Behaviour and Experiments Moscow 10 Case
1: Constraint binding Rapid growth I = W y t = W + (1-d)g t-1 Case
2: Constraint not binding. Steady state: y* = W + (1-d)g t-1
Solves: nu(y*) + v(y*) = 1 Corresponds to two phases Maintenance of
steady state 0 < I t < W Decline I t 0 Optimal Path
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Switch from growth to maintenance phase at g p Optimal Path
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Optimal Path
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Optimal Path Summary of optimal policy:
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Planners solution 1 y*py*p gpgp W 1-d g p /(1-d) y(g) g
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Planners solution 2 y*py*p gpgp W g p /(1-d) y(g) g
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Optimal Path: Example u(y) = y /
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- June 2009Rationality, Behaviour and Experiments Moscow 17 The
Legislative Mechanism Legislature decides policy in each period
Non-negative transfers, x 1,,x n Level of public good y= (1-d)g + W
x i Random recognition rule Proposer offers proposal (x,y)
Committee votes using qualified majority rule (q) If proposal
fails, then y = 0, x i = i = W/n for all i
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- June 2009Rationality, Behaviour and Experiments Moscow 18 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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- June 2009Rationality, Behaviour and Experiments Moscow 19 The
Legislative Mechanism Proposers Maximization Problem: Several
cases, depending on state, g=y t-1, and on whether IC is
binding.
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- June 2009Rationality, Behaviour and Experiments Moscow 21 In
the other case, we have W-y(g)+(1-d)g=0, i.e., x(g)=0. This occurs
when g < g1(y 1 *)
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- June 2009Rationality, Behaviour and Experiments Moscow 23 IC
Binding s > 0 CASE
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- June 2009Rationality, Behaviour and Experiments Moscow 24 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 g 2 < g < g 3
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y*1y*1 g1g1 1 g3g3 g2g2 y*2y*2 y * 2 /(1-d) 45 o Legislative
Mechanism 1
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y*1y*1 g1g1 1 g3g3 g2g2 y*2y*2 y * 2 /(1-d) q>q Legislative
Mechanism 1
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y*1y*1 g1g1 1 g3g3 g2g2 y*2y*2 y * 2 /(1-d) 45 o Legislative
Mechanism 2
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y*1y*1 g1g1 1 g3g3 g2g2 y*2y*2 y * 2 /(1-d) 45 o Legislative
Mechanism 3
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LEGISLATIVE MECHANISM VALUE FUNCTION Note: Value function is
monotonically increasing! Investment is increasing in third region
g 2 < g < g 3
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LEGISLATIVE MECHANISM VALUE FUNCTION Relationship between v and (y
1 *,y 2 *)
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Illustration of Legislative Bargaining Equilibrium u=2y 1/2 n=3 q=2
W=15 =.75 d=0
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COMPUTING THE EQUILIBRIUM Exploit the relationship between v and (y
1 *,y 2 *)
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- June 2009Rationality, Behaviour and Experiments Moscow 34 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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- June 2009Rationality, Behaviour and Experiments Moscow 35 The
Autarky Mechanism Districts Maximization Problem: For each g, a
district chooses the district-optimal feasible x i 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) A symmetric equilibrium is a district-consumption
function x(g)
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- June 2009Rationality, Behaviour and Experiments Moscow 36 The
Autarky Mechanism
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- June 2009Rationality, Behaviour and Experiments Moscow 37 The
Autarky Mechanism
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- June 2009Rationality, Behaviour and Experiments Moscow 38 The
Autarky Mechanism Example with power utility function u = By /: In
planners solution, the denominator equals 1-(1-d) [Typo: Exponent
Should be 1/(1-)]
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y*vy*v gVgV 1 1-d Autarky Mechanism
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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 q=n? 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. (pr{continue}=.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 Screens: Legislative Mechanism
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Sample Screens: Autarky Mechanism
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RESULTS
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- June 2009Rationality, Behaviour and Experiments Moscow 54 L5
ALL COMMITTEE PATHS. PERIOD 1
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- June 2009Rationality, Behaviour and Experiments Moscow 55 L5
ALL COMMITTEE PATHS. PERIOD 2
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- June 2009Rationality, Behaviour and Experiments Moscow 56 L5
ALL COMMITTEE PATHS. PERIOD 3
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- June 2009Rationality, Behaviour and Experiments Moscow 57 L5
ALL COMMITTEE PATHS. PERIOD 4
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- June 2009Rationality, Behaviour and Experiments Moscow 58 L5
ALL COMMITTEE PATHS. PERIOD 5
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- June 2009Rationality, Behaviour and Experiments Moscow 59 L5
ALL COMMITTEE PATHS. PERIOD 6
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- June 2009Rationality, Behaviour and Experiments Moscow 60 L5
ALL COMMITTEE PATHS. ALL PERIODS
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- June 2009Rationality, Behaviour and Experiments Moscow 61 A5
ALL COMMITTEE PATHS. PERIOD 1
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- June 2009Rationality, Behaviour and Experiments Moscow 62 A5
ALL COMMITTEE PATHS. PERIOD 2
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ALL COMMITTEE PATHS. PERIOD 3
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ALL COMMITTEE PATHS. PERIOD 4
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ALL COMMITTEE PATHS. PERIOD 5
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- June 2009Rationality, Behaviour and Experiments Moscow 67 A3
ALL COMMITTEE PATHS. PERIOD 1
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ALL COMMITTEE PATHS. PERIOD 2
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ALL COMMITTEE PATHS. PERIOD 3
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- June 2009Rationality, Behaviour and Experiments Moscow 70 A3
ALL COMMITTEE PATHS. PERIOD 4
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ALL COMMITTEE PATHS. PERIOD 5
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- June 2009Rationality, Behaviour and Experiments Moscow 73 L3
ALL COMMITTEE PATHS. PERIOD 1
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ALL COMMITTEE PATHS. PERIOD 2
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ALL COMMITTEE PATHS. PERIOD 3
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ALL COMMITTEE PATHS. PERIOD 4
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ALL COMMITTEE PATHS. PERIOD 5
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ALL COMMITTEE PATHS. PERIOD 6
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Median Time Paths
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Autarky Median Time Paths
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person committees Legislative vs. Autarky
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person committees Legislative 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 Paths as a function of the State
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Investment function L3
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- June 2009Rationality, Behaviour and Experiments Moscow 96 L5
ALL COMMITTEE PATHS. ALL PERIODS
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Voting Behavior
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PROPOSAL ACCEPTANCE RATES Inv=W 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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PROPOSAL ACCEPTANCE RATES low Inv=W 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
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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