Building Public Infrastructure in a Representative Democracy

1. Building Public Infrastructure in a Representative Democracy Marco Battaglini Princeton University and CEPR Salvatore Nunnari Caltech Thomas Palfrey Caltech Rationality, Behaviour and Experiments Moscow

2. 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 Rationality, Behaviour and Experiments Moscow

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 Rationality, Behaviour and Experiments Moscow

4. Theoretical Approach • Simple infinite horizon model of building public infrastructure. Similar to capital accumulation models • Characterize the planner’s (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 Rationality, Behaviour and Experiments Moscow

5. 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 Rationality, Behaviour and Experiments Moscow

6. The Model • n districts, i=1,…,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 ωti=W/n • Societal endowment W • Endowment can be consumed (xt ) or invested (It) • Public good technology. Depreciation rate d Rationality, Behaviour and Experiments Moscow

7. The Model Feasibility Budget balance Can rewrite Budget balance as: Preferences u´´ () < 0 u´() > 0 u´(0) = ∞ u´(∞) = 0 Rationality, Behaviour and Experiments Moscow

8. Planner’s Problem (optimum) Denote: value function vp(.) aggregate consumption X=Σxi Notice y≥0 constraint not binding because of Inada conditions Hence rewrite optimization problem as: Rationality, Behaviour and Experiments Moscow

9. Optimal Policy • Denote optimal policy by y^(g). Optimal steady state yp* • Three phases: • Rapid growth It = W • Maintenance of steady state 0 < It < W • Decline It≤ 0 • Depends on whether nonnegativity constraint on consumption is binding Rationality, Behaviour and Experiments Moscow

10. 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 < It < W • Decline It≤ 0 Rationality, Behaviour and Experiments Moscow

11. Optimal Path • Switch from growth to maintenance phase at gp Rationality, Behaviour and Experiments Moscow

12. Optimal Path Rationality, Behaviour and Experiments Moscow

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

14. Planner’s solution 1 y(g) y*p 1-d W gp gp/(1-d) g Rationality, Behaviour and Experiments Moscow

15. Planner’s solution 2 y(g) y*p W gp gp/(1-d) g Rationality, Behaviour and Experiments Moscow

16. Optimal Path: Example u(y) = yα/ α Rationality, Behaviour and Experiments Moscow

17. The Legislative Mechanism Legislature decides policy in each period • Non-negative transfers, x1,…,xn • Level of public good y= (1-d)g + W – Σxi • Random recognition rule • Proposer offers proposal (x,y) • Committee votes using qualified majority rule (q) • If proposal fails, then y = 0, xi = ωi = W/n for all i Rationality, Behaviour and Experiments Moscow

18. The Legislative Mechanism Proposer’s 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. Rationality, Behaviour and Experiments Moscow

19. The Legislative Mechanism Proposer’s Maximization Problem: Several cases, depending on state, g=yt-1, and on whether IC is binding. Rationality, Behaviour and Experiments Moscow

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21. In the other case, we have W-y(g)+(1-d)g=0, i.e., x(g)=0. This occurs when g < g1(y1*) Rationality, Behaviour and Experiments Moscow

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23. IC Binding s > 0 CASE Rationality, Behaviour and Experiments Moscow

24. IC Binding s = 0 CASE Rationality, Behaviour and Experiments Moscow

25. LEGISLATIVE MECHANISM INVESTMENT FUNCTION Note: Investment function is not monotonically decreasing! Investment is increasing in third region g2 < g < g3 Rationality, Behaviour and Experiments Moscow

26. Legislative Mechanism 1 y*2 y*1 1 45o g1 g2 g3 y*2/(1-d) Rationality, Behaviour and Experiments Moscow

27. Legislative Mechanism 1 q’>q y*2 y*1 1 g1 g2 g3 y*2/(1-d) Rationality, Behaviour and Experiments Moscow

28. Legislative Mechanism 2 y*2 y*1 1 45o g1 g2 g3 y*2/(1-d) Rationality, Behaviour and Experiments Moscow

29. Legislative Mechanism 3 y*2 y*1 1 45o g1 g2 g3 y*2/(1-d) Rationality, Behaviour and Experiments Moscow

30. LEGISLATIVE MECHANISM VALUE FUNCTION Note: Value function is monotonically increasing! Investment is increasing in third region g2 < g < g3 Rationality, Behaviour and Experiments Moscow

31. LEGISLATIVE MECHANISM VALUE FUNCTION Relationship between v and (y1*,y2*) Rationality, Behaviour and Experiments Moscow

32. Illustration of Legislative Bargaining Equilibrium u=2y1/2 n=3 q=2 W=15 δ=.75 d=0 Rationality, Behaviour and Experiments Moscow

33. COMPUTING THE EQUILIBRIUM Exploit the relationship between v and (y1*,y2*) Rationality, Behaviour and Experiments Moscow

34. The Autarky Mechanism In each period, each district simultaneously decides it’s own policy for how to divide ωi = W/n between private consumption and public good investment. District can disinvest up to 1/n share of g Symmetric Markov perfect equilibrium Rationality, Behaviour and Experiments Moscow

35. The Autarky Mechanism District’s 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) Rationality, Behaviour and Experiments Moscow

36. The Autarky Mechanism Rationality, Behaviour and Experiments Moscow

37. The Autarky Mechanism Rationality, Behaviour and Experiments Moscow

38. The Autarky Mechanism Example with power utility function u = Byα/α: [Typo: Exponent Should be 1/(1-α)] In planner’s solution, the denominator equals 1-(1-d)δ Rationality, Behaviour and Experiments Moscow

39. Autarky Mechanism y*v 1-d 1 gV Rationality, 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 Rationality, Behaviour and Experiments Moscow

41. Experimental Design Rationality, Behaviour and Experiments Moscow

42. Experimental Design Rationality, 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 Rationality, Behaviour and Experiments Moscow

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

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

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