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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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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

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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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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

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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

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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

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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

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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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June 2009Rationality, Behaviour and Experiments Moscow 11 Switch from growth to maintenance phase at g p Optimal Path

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June 2009Rationality, Behaviour and Experiments Moscow 12 Optimal Path

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June 2009Rationality, Behaviour and Experiments Moscow 13 Optimal Path Summary of optimal policy:

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June 2009Rationality, Behaviour and Experiments Moscow 14 Planners solution 1 y*py*p gpgp W 1-d g p /(1-d) y(g) g

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June 2009Rationality, Behaviour and Experiments Moscow 15 Planners solution 2 y*py*p gpgp W g p /(1-d) y(g) g

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June 2009Rationality, Behaviour and Experiments Moscow 16 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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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

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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

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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

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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

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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

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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

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June 2009Rationality, Behaviour and Experiments Moscow 31 LEGISLATIVE MECHANISM VALUE FUNCTION Relationship between v and (y 1 *,y 2 *)

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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

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June 2009Rationality, Behaviour and Experiments Moscow 33 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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June 2009Rationality, Behaviour and Experiments Moscow 39 y*vy*v gVgV 1 1-d Autarky Mechanism

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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

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June 2009Rationality, Behaviour and Experiments Moscow 41 Experimental Design

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June 2009Rationality, Behaviour and Experiments Moscow 42 Experimental Design

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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

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June 2009Rationality, Behaviour and Experiments Moscow 44 Sample Screens: Legislative Mechanism

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June 2009Rationality, Behaviour and Experiments Moscow 49 Sample Screens: Autarky Mechanism

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June 2009Rationality, Behaviour and Experiments Moscow 53 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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June 2009Rationality, Behaviour and Experiments Moscow 63 A5 ALL COMMITTEE PATHS. PERIOD 3

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June 2009Rationality, Behaviour and Experiments Moscow 64 A5 ALL COMMITTEE PATHS. PERIOD 4

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June 2009Rationality, Behaviour and Experiments Moscow 65 A5 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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June 2009Rationality, Behaviour and Experiments Moscow 68 A3 ALL COMMITTEE PATHS. PERIOD 2

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June 2009Rationality, Behaviour and Experiments Moscow 69 A3 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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June 2009Rationality, Behaviour and Experiments Moscow 71 A3 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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June 2009Rationality, Behaviour and Experiments Moscow 74 L3 ALL COMMITTEE PATHS. PERIOD 2

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June 2009Rationality, Behaviour and Experiments Moscow 75 L3 ALL COMMITTEE PATHS. PERIOD 3

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June 2009Rationality, Behaviour and Experiments Moscow 76 L3 ALL COMMITTEE PATHS. PERIOD 4

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June 2009Rationality, Behaviour and Experiments Moscow 77 L3 ALL COMMITTEE PATHS. PERIOD 5

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June 2009Rationality, Behaviour and Experiments Moscow 78 L3 ALL COMMITTEE PATHS. PERIOD 6

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June 2009Rationality, Behaviour and Experiments Moscow 80 Median Time Paths

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June 2009Rationality, Behaviour and Experiments Moscow 81 Autarky Median Time Paths

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June 2009Rationality, Behaviour and Experiments Moscow 82 5 person committees Legislative vs. Autarky

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June 2009Rationality, Behaviour and Experiments Moscow 83 3 person committees Legislative vs. Autarky

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June 2009Rationality, Behaviour and Experiments Moscow 84 Legislative Median Time Paths

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June 2009Rationality, Behaviour and Experiments Moscow 85 Median Time Paths of g

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June 2009Rationality, Behaviour and Experiments Moscow 86 Investment Paths (includes conditional and failed proposals)

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June 2009Rationality, Behaviour and Experiments Moscow 87 Investment function for L3

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June 2009Rationality, Behaviour and Experiments Moscow 88 Investment function for L5

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June 2009Rationality, Behaviour and Experiments Moscow 89 Investment function for A3

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June 2009Rationality, Behaviour and Experiments Moscow 90 Investment function for A5

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June 2009Rationality, Behaviour and Experiments Moscow 91 Investment Paths as a function of the State

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June 2009Rationality, Behaviour and Experiments Moscow 92 Investment function L3

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June 2009Rationality, Behaviour and Experiments Moscow 96 L5 ALL COMMITTEE PATHS. ALL PERIODS

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June 2009Rationality, Behaviour and Experiments Moscow 97 Voting Behavior

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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

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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

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June 2009Rationality, Behaviour and Experiments Moscow 100 VOTING BEHAVIOR ACCEPTANCE RATES

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June 2009Rationality, Behaviour and Experiments Moscow 101 VOTING BEHAVIOR ACCEPTANCE RATES Test for stationary behavior

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June 2009Rationality, Behaviour and Experiments Moscow 102 PROPOSAL BEHAVIOR: PORK TO PREVIOUS PROPOSER Test for stationary behavior PUNISHMENT AND REWARD

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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

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June 2009Rationality, Behaviour and Experiments Moscow 104 Investment function L5 Some outliers excluded