June 2009 Rationality, Behaviour and Experi ments 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 1 Building Public Infrastructure in a Representative Democracy Marco Battaglini Princeton University.
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Slide 1
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
Slide 2
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
Slide 3
June 2009Rationality, Behaviour and Experiments Moscow 3 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 Government and Public Infrastructure
Slide 4
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
Slide 5
June 2009Rationality, Behaviour and Experiments Moscow 5
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
Slide 6
June 2009Rationality, Behaviour and Experiments Moscow 6 n
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
Slide 7
June 2009Rationality, Behaviour and Experiments Moscow 7
Feasibility The Model Budget balance Can rewrite Budget balance as:
Preferences u () < 0 u() > 0 u(0) = u() = 0
Slide 8
June 2009Rationality, Behaviour and Experiments Moscow 8
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
Slide 9
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
Slide 10
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
Slide 11
June 2009Rationality, Behaviour and Experiments Moscow 11
Switch from growth to maintenance phase at g p Optimal Path
Slide 12
June 2009Rationality, Behaviour and Experiments Moscow 12
Optimal Path
Slide 13
June 2009Rationality, Behaviour and Experiments Moscow 13
Optimal Path Summary of optimal policy:
Slide 14
June 2009Rationality, Behaviour and Experiments Moscow 14
Planners solution 1 y*py*p gpgp W 1-d g p /(1-d) y(g) g
Slide 15
June 2009Rationality, Behaviour and Experiments Moscow 15
Planners solution 2 y*py*p gpgp W g p /(1-d) y(g) g
Slide 16
June 2009Rationality, Behaviour and Experiments Moscow 16
Optimal Path: Example u(y) = y /
Slide 17
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
Slide 18
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.
Slide 19
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.
Slide 20
June 2009Rationality, Behaviour and Experiments Moscow 20
Slide 21
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 *)
Slide 22
June 2009Rationality, Behaviour and Experiments Moscow 22
Slide 23
June 2009Rationality, Behaviour and Experiments Moscow 23 IC
Binding s > 0 CASE
Slide 24
June 2009Rationality, Behaviour and Experiments Moscow 24 IC
Binding s = 0 CASE
Slide 25
June 2009Rationality, Behaviour and Experiments Moscow 25
LEGISLATIVE MECHANISM INVESTMENT FUNCTION Note: Investment function
is not monotonically decreasing! Investment is increasing in third
region g 2 < g < g 3
Slide 26
June 2009Rationality, Behaviour and Experiments Moscow 26
y*1y*1 g1g1 1 g3g3 g2g2 y*2y*2 y * 2 /(1-d) 45 o Legislative
Mechanism 1
Slide 27
June 2009Rationality, Behaviour and Experiments Moscow 27
y*1y*1 g1g1 1 g3g3 g2g2 y*2y*2 y * 2 /(1-d) q>q Legislative
Mechanism 1
Slide 28
June 2009Rationality, Behaviour and Experiments Moscow 28
y*1y*1 g1g1 1 g3g3 g2g2 y*2y*2 y * 2 /(1-d) 45 o Legislative
Mechanism 2
Slide 29
June 2009Rationality, Behaviour and Experiments Moscow 29
y*1y*1 g1g1 1 g3g3 g2g2 y*2y*2 y * 2 /(1-d) 45 o Legislative
Mechanism 3
Slide 30
June 2009Rationality, Behaviour and Experiments Moscow 30
LEGISLATIVE MECHANISM VALUE FUNCTION Note: Value function is
monotonically increasing! Investment is increasing in third region
g 2 < g < g 3
Slide 31
June 2009Rationality, Behaviour and Experiments Moscow 31
LEGISLATIVE MECHANISM VALUE FUNCTION Relationship between v and (y
1 *,y 2 *)
Slide 32
June 2009Rationality, Behaviour and Experiments Moscow 32
Illustration of Legislative Bargaining Equilibrium u=2y 1/2 n=3 q=2
W=15 =.75 d=0
Slide 33
June 2009Rationality, Behaviour and Experiments Moscow 33
COMPUTING THE EQUILIBRIUM Exploit the relationship between v and (y
1 *,y 2 *)
Slide 34
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
Slide 35
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)
Slide 36
June 2009Rationality, Behaviour and Experiments Moscow 36 The
Autarky Mechanism
Slide 37
June 2009Rationality, Behaviour and Experiments Moscow 37 The
Autarky Mechanism
Slide 38
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-)]
Slide 39
June 2009Rationality, Behaviour and Experiments Moscow 39
y*vy*v gVgV 1 1-d Autarky Mechanism
Slide 40
June 2009Rationality, Behaviour and Experiments Moscow 40
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
Slide 41
June 2009Rationality, Behaviour and Experiments Moscow 41
Experimental Design
Slide 42
June 2009Rationality, Behaviour and Experiments Moscow 42
Experimental Design
Slide 43
June 2009Rationality, Behaviour and Experiments Moscow 43
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
Slide 44
June 2009Rationality, Behaviour and Experiments Moscow 44
Sample Screens: Legislative Mechanism
Slide 45
June 2009Rationality, Behaviour and Experiments Moscow 45
Slide 46
June 2009Rationality, Behaviour and Experiments Moscow 46
Slide 47
June 2009Rationality, Behaviour and Experiments Moscow 47
Slide 48
June 2009Rationality, Behaviour and Experiments Moscow 48
Slide 49
June 2009Rationality, Behaviour and Experiments Moscow 49
Sample Screens: Autarky Mechanism
Slide 50
June 2009Rationality, Behaviour and Experiments Moscow 50
Slide 51
June 2009Rationality, Behaviour and Experiments Moscow 51
Slide 52
June 2009Rationality, Behaviour and Experiments Moscow 52
Slide 53
June 2009Rationality, Behaviour and Experiments Moscow 53
RESULTS
Slide 54
June 2009Rationality, Behaviour and Experiments Moscow 54 L5
ALL COMMITTEE PATHS. PERIOD 1
Slide 55
June 2009Rationality, Behaviour and Experiments Moscow 55 L5
ALL COMMITTEE PATHS. PERIOD 2
Slide 56
June 2009Rationality, Behaviour and Experiments Moscow 56 L5
ALL COMMITTEE PATHS. PERIOD 3
Slide 57
June 2009Rationality, Behaviour and Experiments Moscow 57 L5
ALL COMMITTEE PATHS. PERIOD 4
Slide 58
June 2009Rationality, Behaviour and Experiments Moscow 58 L5
ALL COMMITTEE PATHS. PERIOD 5
Slide 59
June 2009Rationality, Behaviour and Experiments Moscow 59 L5
ALL COMMITTEE PATHS. PERIOD 6
Slide 60
June 2009Rationality, Behaviour and Experiments Moscow 60 L5
ALL COMMITTEE PATHS. ALL PERIODS
Slide 61
June 2009Rationality, Behaviour and Experiments Moscow 61 A5
ALL COMMITTEE PATHS. PERIOD 1
Slide 62
June 2009Rationality, Behaviour and Experiments Moscow 62 A5
ALL COMMITTEE PATHS. PERIOD 2
Slide 63
June 2009Rationality, Behaviour and Experiments Moscow 63 A5
ALL COMMITTEE PATHS. PERIOD 3
Slide 64
June 2009Rationality, Behaviour and Experiments Moscow 64 A5
ALL COMMITTEE PATHS. PERIOD 4
Slide 65
June 2009Rationality, Behaviour and Experiments Moscow 65 A5
ALL COMMITTEE PATHS. PERIOD 5
Slide 66
June 2009Rationality, Behaviour and Experiments Moscow 66
Slide 67
June 2009Rationality, Behaviour and Experiments Moscow 67 A3
ALL COMMITTEE PATHS. PERIOD 1
Slide 68
June 2009Rationality, Behaviour and Experiments Moscow 68 A3
ALL COMMITTEE PATHS. PERIOD 2
Slide 69
June 2009Rationality, Behaviour and Experiments Moscow 69 A3
ALL COMMITTEE PATHS. PERIOD 3
Slide 70
June 2009Rationality, Behaviour and Experiments Moscow 70 A3
ALL COMMITTEE PATHS. PERIOD 4
Slide 71
June 2009Rationality, Behaviour and Experiments Moscow 71 A3
ALL COMMITTEE PATHS. PERIOD 5
Slide 72
June 2009Rationality, Behaviour and Experiments Moscow 72
Slide 73
June 2009Rationality, Behaviour and Experiments Moscow 73 L3
ALL COMMITTEE PATHS. PERIOD 1
Slide 74
June 2009Rationality, Behaviour and Experiments Moscow 74 L3
ALL COMMITTEE PATHS. PERIOD 2
Slide 75
June 2009Rationality, Behaviour and Experiments Moscow 75 L3
ALL COMMITTEE PATHS. PERIOD 3
Slide 76
June 2009Rationality, Behaviour and Experiments Moscow 76 L3
ALL COMMITTEE PATHS. PERIOD 4
Slide 77
June 2009Rationality, Behaviour and Experiments Moscow 77 L3
ALL COMMITTEE PATHS. PERIOD 5
Slide 78
June 2009Rationality, Behaviour and Experiments Moscow 78 L3
ALL COMMITTEE PATHS. PERIOD 6
Slide 79
June 2009Rationality, Behaviour and Experiments Moscow 79
Slide 80
June 2009Rationality, Behaviour and Experiments Moscow 80
Median Time Paths
Slide 81
June 2009Rationality, Behaviour and Experiments Moscow 81
Autarky Median Time Paths
Slide 82
June 2009Rationality, Behaviour and Experiments Moscow 82 5
person committees Legislative vs. Autarky
Slide 83
June 2009Rationality, Behaviour and Experiments Moscow 83 3
person committees Legislative vs. Autarky
Slide 84
June 2009Rationality, Behaviour and Experiments Moscow 84
Legislative Median Time Paths
Slide 85
June 2009Rationality, Behaviour and Experiments Moscow 85
Median Time Paths of g
Slide 86
June 2009Rationality, Behaviour and Experiments Moscow 86
Investment Paths (includes conditional and failed proposals)
Slide 87
June 2009Rationality, Behaviour and Experiments Moscow 87
Investment function for L3
Slide 88
June 2009Rationality, Behaviour and Experiments Moscow 88
Investment function for L5
Slide 89
June 2009Rationality, Behaviour and Experiments Moscow 89
Investment function for A3
Slide 90
June 2009Rationality, Behaviour and Experiments Moscow 90
Investment function for A5
Slide 91
June 2009Rationality, Behaviour and Experiments Moscow 91
Investment Paths as a function of the State
Slide 92
June 2009Rationality, Behaviour and Experiments Moscow 92
Investment function L3
Slide 93
June 2009Rationality, Behaviour and Experiments Moscow 93
Slide 94
June 2009Rationality, Behaviour and Experiments Moscow 94
Slide 95
June 2009Rationality, Behaviour and Experiments Moscow 95
Slide 96
June 2009Rationality, Behaviour and Experiments Moscow 96 L5
ALL COMMITTEE PATHS. ALL PERIODS
Slide 97
June 2009Rationality, Behaviour and Experiments Moscow 97
Voting Behavior
Slide 98
June 2009Rationality, Behaviour and Experiments Moscow 98 L5
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
Slide 99
June 2009Rationality, Behaviour and Experiments Moscow 99 L3
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
Slide 100
June 2009Rationality, Behaviour and Experiments Moscow 100
VOTING BEHAVIOR ACCEPTANCE RATES
Slide 101
June 2009Rationality, Behaviour and Experiments Moscow 101
VOTING BEHAVIOR ACCEPTANCE RATES Test for stationary behavior
Slide 102
June 2009Rationality, Behaviour and Experiments Moscow 102
PROPOSAL BEHAVIOR: PORK TO PREVIOUS PROPOSER Test for stationary
behavior PUNISHMENT AND REWARD
Slide 103
June 2009Rationality, Behaviour and Experiments Moscow 103
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
Slide 104
June 2009Rationality, Behaviour and Experiments Moscow 104
Investment function L5 Some outliers excluded