PROPERTY RIGHTS IN GROWTH THEORY

Transcription

1 PROPERTY RIGHTS IN GROWTH THEORY Costas Azariadis Washington University and Federal Reserve Bank of St. Louis Preliminary Draft May 2013

2 1. CONTENTS 1. Issues and Goals 2. Main Results 3. Related Literature 4. Production, Extraction, Deterrence 5. Social Optima 6. Equilibrium with Given Property Rights 7. Endogenizing Deterrence 8. Conclusions and Extensions

3 2. ISSUES AND GOALS (a) Leading role of institutions in growth Adam Smith(1776): importance of tolerable administration of justice

4 2. ISSUES AND GOALS (a) Leading role of institutions in growth Adam Smith(1776): importance of tolerable administration of justice North & Thomas(1973): property rights foster growth by aligning private benets and costs with public ones

5 2. ISSUES AND GOALS (a) Leading role of institutions in growth Adam Smith(1776): importance of tolerable administration of justice North & Thomas(1973): property rights foster growth by aligning private benets and costs with public ones Acemoglu, Robinson & Johnson(2005): - strong correlation of growth with institutional quality/measures of social discord - causality chain: wealth distribution political power institutions growth future wealth distribution

6 2. ISSUES AND GOALS (a) Leading role of institutions in growth Adam Smith(1776): importance of tolerable administration of justice North & Thomas(1973): property rights foster growth by aligning private benets and costs with public ones Acemoglu, Robinson & Johnson(2005): - strong correlation of growth with institutional quality/measures of social discord - causality chain: wealth distribution political power institutions growth future wealth distribution Large literature exploring interaction of property rights with occupational choices and growth - property rights typically a strategic / individual choice - mostly idiosyncratic growth models - labor-intensive appropriation - no public deterence of theft

7 2. ISSUES AND GOALS (b) This paper Collective choice of property rights p [0, 1]

8 2. ISSUES AND GOALS (b) This paper Collective choice of property rights p [0, 1] 1 p =tax imposed by extraction on production

9 2. ISSUES AND GOALS (b) This paper Collective choice of property rights p [0, 1] 1 p =tax imposed by extraction on production Use (k, p) as state variables with k = K/L

10 2. ISSUES AND GOALS (b) This paper Collective choice of property rights p [0, 1] 1 p =tax imposed by extraction on production Use (k, p) as state variables with k = K/L explain joint evolution of (k t, p t ): ( kt+1 p t+1 ) = Q ( kt p t ) (1)

11 3. RESULTS (a) Setting Lifecycle growth model: Diamond(1965)

12 3. RESULTS (a) Setting Lifecycle growth model: Diamond(1965) Heterogeneously endowed workers - individual choice: saving, occupation - collective choice: property rights p

13 3. RESULTS (a) Setting Lifecycle growth model: Diamond(1965) Heterogeneously endowed workers - individual choice: saving, occupation - collective choice: property rights p Occupations - deterrence (part-time compulsory draft) - production - extraction (appropriation/predation)

14 3. RESULTS (a) Setting Lifecycle growth model: Diamond(1965) Heterogeneously endowed workers - individual choice: saving, occupation - collective choice: property rights p Occupations - deterrence (part-time compulsory draft) - production - extraction (appropriation/predation) p = 0 GDP = 0 (chaos)

15 3. RESULTS (a) Setting Lifecycle growth model: Diamond(1965) Heterogeneously endowed workers - individual choice: saving, occupation - collective choice: property rights p Occupations - deterrence (part-time compulsory draft) - production - extraction (appropriation/predation) p = 0 GDP = 0 (chaos) Simple politics - property rights chosen one period in advance (same as capital) - p maximizes after-tax capital yield

16 3. RESULTS (b) Planning optimum (p, k ) maximizes steady state consumption

17 3. RESULTS (b) Planning optimum (p, k ) maximizes steady state consumption p < 1: - completely secure property. too expensive

18 3. RESULTS (b) Planning optimum (p, k ) maximizes steady state consumption p < 1: - completely secure property. too expensive k < golden rule: - capital intensity compromised by allowance for unproductive labor

19 3. RESULTS (c) Equilibria Intensive variables (k, factor prices) - p < 1 equivalent to lower TFP - costly deterrence with property rights p and technology f (k), equivalent to costless deterrence with full property rights and technology pf (k)

20 3. RESULTS (c) Equilibria Intensive variables (k, factor prices) - p < 1 equivalent to lower TFP - costly deterrence with property rights p and technology f (k), equivalent to costless deterrence with full property rights and technology pf (k) Extensive variables - p initially boosts productive employment; eventually harms it - (conjecture) output increases with p until p = p, declines beyond that point

21 3. RESULTS (c) Equilibria Intensive variables (k, factor prices) - p < 1 equivalent to lower TFP - costly deterrence with property rights p and technology f (k), equivalent to costless deterrence with full property rights and technology pf (k) Extensive variables - p initially boosts productive employment; eventually harms it - (conjecture) output increases with p until p = p, declines beyond that point Choice of p - High p if MPK relatively insensitive to k; low otherwise

22 3. RESULTS (c) Equilibria Intensive variables (k, factor prices) - p < 1 equivalent to lower TFP - costly deterrence with property rights p and technology f (k), equivalent to costless deterrence with full property rights and technology pf (k) Extensive variables - p initially boosts productive employment; eventually harms it - (conjecture) output increases with p until p = p, declines beyond that point Choice of p - High p if MPK relatively insensitive to k; low otherwise Key questions: - How does the collective choice of p depend on wealth? - Do poor societies choose low p?

23 4. LITERATURE (a) Voting models Emphasize political power (b) Static economies

24 4. LITERATURE (a) Voting models Emphasize political power Power sharing within qualied elite (Acemoglu et al, 2005) (b) Static economies

25 4. LITERATURE (a) Voting models Emphasize political power Power sharing within qualied elite (Acemoglu et al, 2005) Voting over strategic policy platforms (Auerbach, 2013) (b) Static economies

26 4. LITERATURE (a) Voting models Emphasize political power Power sharing within qualied elite (Acemoglu et al, 2005) Voting over strategic policy platforms (Auerbach, 2013) (b) Static economies Ignoring growth

27 4. LITERATURE (a) Voting models Emphasize political power Power sharing within qualied elite (Acemoglu et al, 2005) Voting over strategic policy platforms (Auerbach, 2013) (b) Static economies Ignoring growth Skapedas(1991): choosing how much to invest in oensive/defensive weapons when p = 0

28 4. LITERATURE (a) Voting models Emphasize political power Power sharing within qualied elite (Acemoglu et al, 2005) Voting over strategic policy platforms (Auerbach, 2013) (b) Static economies Ignoring growth Skapedas(1991): choosing how much to invest in oensive/defensive weapons when p = 0 Murphy et al(1991): allocation of talent between production and rent-seeking

29 4. LITERATURE (a) Voting models Emphasize political power Power sharing within qualied elite (Acemoglu et al, 2005) Voting over strategic policy platforms (Auerbach, 2013) (b) Static economies Ignoring growth Skapedas(1991): choosing how much to invest in oensive/defensive weapons when p = 0 Murphy et al(1991): allocation of talent between production and rent-seeking Dal Bo & Dal Bo(2011): multi-sector international trade model with xed input stocks; labor intensive extraction; response to sectoral TFP shocks

30 4. LITERATURE (c) Growth models Grossman & Kim(1996) - builds on Skaperdas(1991) - AK technology - OLG with bequest motive - private deterrence (oensive/defensive weapons) - key role for wealth distribution among prey and predator

31 4. LITERATURE (c) Growth models Grossman & Kim(1996) - builds on Skaperdas(1991) - AK technology - OLG with bequest motive - private deterrence (oensive/defensive weapons) - key role for wealth distribution among prey and predator Benhabib & Rustichini(1996) - redistribution distorts growth - no direct cost; weakens incentives to save - equality vs. growth trade-o

32 4. LITERATURE (c) Growth models Grossman & Kim(1996) - builds on Skaperdas(1991) - AK technology - OLG with bequest motive - private deterrence (oensive/defensive weapons) - key role for wealth distribution among prey and predator Benhabib & Rustichini(1996) - redistribution distorts growth - no direct cost; weakens incentives to save - equality vs. growth trade-o Tornell(1997) - focus on tragedy of the commons - strategic interactions of two groups - possibility of regime switch at xed cost - regime menu: common property, private property, intermediate regime

33 5. PRODUCTION, EXTRACTION, DETERRENCE (a) Economic environment Lifecycle growth model

34 5. PRODUCTION, EXTRACTION, DETERRENCE (a) Economic environment Lifecycle growth model cohorts with mass 1

35 5. PRODUCTION, EXTRACTION, DETERRENCE (a) Economic environment Lifecycle growth model cohorts with mass 1 heterogeneous workers indexed h [0, 1] with cdf G, mean µ

36 5. PRODUCTION, EXTRACTION, DETERRENCE (a) Economic environment Lifecycle growth model cohorts with mass 1 heterogeneous workers indexed h [0, 1] with cdf G, mean µ lifespan L=2

37 5. PRODUCTION, EXTRACTION, DETERRENCE (a) Economic environment Lifecycle growth model cohorts with mass 1 heterogeneous workers indexed h [0, 1] with cdf G, mean µ lifespan L=2 common payos: v t = u (c t t ) + βu homothetic ( c t t+1), with u (c)

38 5. PRODUCTION, EXTRACTION, DETERRENCE (a) Economic environment Lifecycle growth model cohorts with mass 1 heterogeneous workers indexed h [0, 1] with cdf G, mean µ lifespan L=2 common payos: v t = u (c t t ) + βu homothetic ( c t t+1), with u (c) { time labor endowment ω t = (1, 0), h, split into draft service for public deterrence θ time supplied to gainful work 1 θ

39 5. PRODUCTION, EXTRACTION, DETERRENCE (a) Economic environment Lifecycle growth model cohorts with mass 1 heterogeneous workers indexed h [0, 1] with cdf G, mean µ lifespan L=2 common payos: v t = u (c t t ) + βu homothetic ( c t t+1), with u (c) { time labor endowment ω t = (1, 0), h, split into draft service for public deterrence θ time supplied to gainful work 1 θ endowment { of ecient labor per unit time, (h, 0) if producer e (h) = (1, 0) if extractor

40 5. PRODUCTION, EXTRACTION, DETERRENCE (a) Economic environment Lifecycle growth model cohorts with mass 1 heterogeneous workers indexed h [0, 1] with cdf G, mean µ lifespan L=2 common payos: v t = u (c t t ) + βu homothetic ( c t t+1), with u (c) { time labor endowment ω t = (1, 0), h, split into draft service for public deterrence θ time supplied to gainful work 1 θ endowment { of ecient labor per unit time, (h, 0) if producer e (h) = (1, 0) if extractor producer/extractor mutually exclusive acts [cf. Bethencourt & Perera-Tallo(2011)]

41 5. PRODUCTION, EXTRACTION, DETERRENCE Saving

42 5. PRODUCTION, EXTRACTION, DETERRENCE Saving if s = argmax s y [u (y s) + βu (Rs)], then s = yz (R) (2) where z = R + [0, 1] is an increasing function

43 5. PRODUCTION, EXTRACTION, DETERRENCE Saving if s = argmax s y [u (y s) + βu (Rs)], then Sectors s = yz (R) (2) where z = R + [0, 1] is an increasing function

44 5. PRODUCTION, EXTRACTION, DETERRENCE Saving if s = argmax s y [u (y s) + βu (Rs)], then s = yz (R) (2) where z = R + [0, 1] is an increasing function Sectors production Y = F (K, N) extraction X = F e (K e, N e ) deterrence A = A (θ)

45 5. PRODUCTION, EXTRACTION, DETERRENCE Saving if s = argmax s y [u (y s) + βu (Rs)], then s = yz (R) (2) where z = R + [0, 1] is an increasing function Sectors production Y = F (K, N) extraction X = F e (K e, N e ) deterrence A = A (θ) (F, F e ) are standard neoclassic CRS technologies

46 5. PRODUCTION, EXTRACTION, DETERRENCE Saving if s = argmax s y [u (y s) + βu (Rs)], then s = yz (R) (2) where z = R + [0, 1] is an increasing function Sectors production Y = F (K, N) extraction X = F e (K e, N e ) deterrence A = A (θ) (F, F e ) are standard neoclassic CRS technologies extraction income imposes a uniform tax on all capital and labor income (extraction not tax exempt)

47 5. PRODUCTION, EXTRACTION, DETERRENCE Sectors(continued)

48 5. PRODUCTION, EXTRACTION, DETERRENCE Sectors(continued) A : [ 0, θ ] [0, 1], decreasing convex, A (0) = 1, A (θ) = 0, for allθ [ θ, 1 ]

49 5. PRODUCTION, EXTRACTION, DETERRENCE Sectors(continued) A : [ 0, θ ] [0, 1], decreasing convex, A (0) = 1, A (θ) = 0, for allθ [ θ, 1 ] A (θ)= eciency units of N e per unit time

50 5. PRODUCTION, EXTRACTION, DETERRENCE Sectors(continued) A : [ 0, θ ] [0, 1], decreasing convex, A (0) = 1, A (θ) = 0, for allθ [ θ, 1 ] A (θ)= eciency units of N e per unit time

51 5. PRODUCTION, EXTRACTION, DETERRENCE Sectors(continued) A : [ 0, θ ] [0, 1], decreasing convex, A (0) = 1, A (θ) = 0, for allθ [ θ, 1 ] A (θ)= eciency units of N e per unit time perfect capital mobility: implies f (k) = f e (k e ) k = k e F = F e if

52 5. PRODUCTION, EXTRACTION, DETERRENCE Sectors(continued) A : [ 0, θ ] [0, 1], decreasing convex, A (0) = 1, A (θ) = 0, for allθ [ θ, 1 ] A (θ)= eciency units of N e per unit time perfect capital mobility: implies f (k) = f e (k e ) k = k e F = F e F e = F full factor-price equalization if

53 5. PRODUCTION, EXTRACTION, DETERRENCE Taxes and property rights

54 5. PRODUCTION, EXTRACTION, DETERRENCE Taxes and property rights time tax θ: collective choice and paid by all

55 5. PRODUCTION, EXTRACTION, DETERRENCE Taxes and property rights time tax θ: collective choice and paid by all extraction tax τ = N e [0, 1] e N + N

56 5. PRODUCTION, EXTRACTION, DETERRENCE Taxes and property rights time tax θ: collective choice and paid by all extraction tax τ = N e [0, 1] e N + N N property rights p = [0, 1] e N + N <FP equality tax rates proportional to employment shares>

57 5. PRODUCTION, EXTRACTION, DETERRENCE (b) Occupational choice Maximize after-tax { income (1 θ) (1 τ) wh if producer y (h, θ) = (1 θ) (1 τ) wa (θ) if extractor given (θ, τ)

58 5. PRODUCTION, EXTRACTION, DETERRENCE (b) Occupational choice Maximize after-tax { income (1 θ) (1 τ) wh if producer y (h, θ) = (1 θ) (1 τ) wa (θ) if extractor given (θ, τ) Extract if A (θ) > h, produce o.w.

59 5. PRODUCTION, EXTRACTION, DETERRENCE (b) Occupational choice Maximize after-tax { income (1 θ) (1 τ) wh if producer y (h, θ) = (1 θ) (1 τ) wa (θ) if extractor given (θ, τ) Extract if A (θ) > h, produce o.w. Employment and taxes

60 5. PRODUCTION, EXTRACTION, DETERRENCE (b) Occupational choice Maximize after-tax { income (1 θ) (1 τ) wh if producer y (h, θ) = (1 θ) (1 τ) wa (θ) if extractor given (θ, τ) Extract if A (θ) > h, produce o.w. Employment and taxes production N (θ) = (1 θ) 1 A(θ) hdg (concave)

61 5. PRODUCTION, EXTRACTION, DETERRENCE (b) Occupational choice Maximize after-tax { income (1 θ) (1 τ) wh if producer y (h, θ) = (1 θ) (1 τ) wa (θ) if extractor given (θ, τ) Extract if A (θ) > h, produce o.w. Employment and taxes production N (θ) = (1 θ) 1 A(θ) hdg (concave) total L (θ) = (1 θ) 1 max [h, A (θ)] dg (convex decreasing) 0

62 5. PRODUCTION, EXTRACTION, DETERRENCE (b) Occupational choice Maximize after-tax { income (1 θ) (1 τ) wh if producer y (h, θ) = (1 θ) (1 τ) wa (θ) if extractor given (θ, τ) Extract if A (θ) > h, produce o.w. Employment and taxes production N (θ) = (1 θ) 1 A(θ) hdg (concave) total L (θ) = (1 θ) 1 max [h, A (θ)] dg (convex decreasing) property rights: p (θ) = N (θ) L (θ) 0 (concave increasing)

63 5. PRODUCTION, EXTRACTION, DETERRENCE

64 6. SOCIAL OPTIMA Planner maximizes steady-state consumption

65 6. SOCIAL OPTIMA Planner maximizes steady-state consumption (k, θ ) = argmax c (θ, k) c (θ, k) := N (θ) f (k) L (θ) k, concave in (k, θ)

66 6. SOCIAL OPTIMA Planner maximizes steady-state consumption (k, θ ) = argmax c (θ, k) c (θ, k) := N (θ) f (k) L (θ) k, concave in (k, θ) FOC f (k) = L (θ) 1, = i θ = θ N (θ) L (θ) N (θ) = f (k) k ) for some θ ( θ, θ θ := argmax N (θ)

67 6. SOCIAL OPTIMA Planner maximizes steady-state consumption (k, θ ) = argmax c (θ, k) c (θ, k) := N (θ) f (k) L (θ) k, concave in (k, θ) FOC f (k) = L (θ) 1, = i θ = θ N (θ) L (θ) N (θ) = f (k) k ) for some θ ( θ, θ θ := argmax N (θ) Optimality features - interest rate above growth rate - imperfect property rights - too little capital per worker (relative to golden rule)

68 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (a) Dynamics Equate value of capital with private wealth

69 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (a) Dynamics Equate value of capital with private wealth Wage rate w (k) := f (k) kf (k)

70 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (a) Dynamics Equate value of capital with private wealth Wage rate w (k) := f (k) kf (k) Extractors and producers have identical saving patterns (except for income)

71 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (a) Dynamics Equate value of capital with private wealth Wage rate w (k) := f (k) kf (k) Extractors and producers have identical saving patterns (except for income) Aggregate wage income: W := N (θ) w (k)

72 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (a) Dynamics Equate value of capital with private wealth Wage rate w (k) := f (k) kf (k) Extractors and producers have identical saving patterns (except for income) Aggregate wage income: W := N (θ) w (k) After-tax return on capital R = p (θ) f (k)

73 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (a) Dynamics Equate value of capital with private wealth Wage rate w (k) := f (k) kf (k) Extractors and producers have identical saving patterns (except for income) Aggregate wage income: W := N (θ) w (k) After-tax return on capital R = p (θ) f (k) basic equation L (θ t+1) k t+1 = N (θ t ) w (k t ) z [p (θ t+1) f (k t+1)] (3)

74 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (a) Dynamics Equate value of capital with private wealth Wage rate w (k) := f (k) kf (k) Extractors and producers have identical saving patterns (except for income) Aggregate wage income: W := N (θ) w (k) After-tax return on capital R = p (θ) f (k) basic equation L (θ t+1) k t+1 = N (θ t ) w (k t ) z [p (θ t+1) f (k t+1)] (3) if θ t = constant, then eq.(4) illustrated in Figure 3 k t+1 z [p (θ) f (k t+1)] = p (θ) w (k t) (4)

75 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS

76 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS Theorem The equilibrium sequences of the intensive variables (k t, w t, R t ) are identical to those of an economy with technology p (θ) f (k) and costless enforcement of property rights. (Conjecture: this result extends beyond lifecycle economies)

77 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (b) Example: A Cobb-Douglas Economy Suppose f (k) = k α, 0 < α < 1; G (h) = h (uniform distribution { of skills); u (c) = log c; 1 θ/θ, θ θ A (θ) = 1, o.w.

78 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (b) Example: A Cobb-Douglas Economy Suppose f (k) = k α, 0 < α < 1; G (h) = h (uniform distribution { of skills); u (c) = log c; 1 θ/θ, θ θ A (θ) = 1, o.w. Then z (R) = β/ (1 + β) := s in eq.(4)

79 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (b) Example: A Cobb-Douglas Economy Suppose f (k) = k α, 0 < α < 1; G (h) = h (uniform distribution { of skills); u (c) = log c; 1 θ/θ, θ θ A (θ) = 1, o.w. Then z (R) = β/ (1 + β) := s in eq.(4) Steady state: k = s (1 α) p (θ) k α

80 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (b) Example: A Cobb-Douglas Economy Suppose f (k) = k α, 0 < α < 1; G (h) = h (uniform distribution { of skills); u (c) = log c; 1 θ/θ, θ θ A (θ) = 1, o.w. Then z (R) = β/ (1 + β) := s in eq.(4) Steady state: k = s (1 α) p (θ) k α GDP at any θ [ 0, θ ] or property rights p [0, 1] Y (θ) = N (θ) k α = b [N α (θ) /L (θ)] 1/(1 α)

81 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (b) Example: A Cobb-Douglas Economy Suppose f (k) = k α, 0 < α < 1; G (h) = h (uniform distribution { of skills); u (c) = log c; 1 θ/θ, θ θ A (θ) = 1, o.w. Then z (R) = β/ (1 + β) := s in eq.(4) Steady state: k = s (1 α) p (θ) k α GDP at any θ [ 0, θ ] or property rights p [0, 1] Y (θ) = N (θ) k α = b [N α (θ) /L (θ)] 1/(1 α) b := [s (1 α)] α/(1 α)

82 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (b) Example: A Cobb-Douglas Economy Suppose f (k) = k α, 0 < α < 1; G (h) = h (uniform distribution { of skills); u (c) = log c; 1 θ/θ, θ θ A (θ) = 1, o.w. Then z (R) = β/ (1 + β) := s in eq.(4) Steady state: k = s (1 α) p (θ) k α GDP at any θ [ 0, θ ] or property rights p [0, 1] Y (θ) = N (θ) k α = b [N α (θ) /L (θ)] 1/(1 α) b := [s (1 α)] α/(1 α) N (θ) = (1 θ) 1 A2 (θ) 2 (productive work)

83 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS (b) Example: A Cobb-Douglas Economy Suppose f (k) = k α, 0 < α < 1; G (h) = h (uniform distribution { of skills); u (c) = log c; 1 θ/θ, θ θ A (θ) = 1, o.w. Then z (R) = β/ (1 + β) := s in eq.(4) Steady state: k = s (1 α) p (θ) k α GDP at any θ [ 0, θ ] or property rights p [0, 1] Y (θ) = N (θ) k α = b [N α (θ) /L (θ)] 1/(1 α) b := [s (1 α)] α/(1 α) N (θ) = (1 θ) 1 A2 (θ) 2 L (θ) = (1 θ) 1 + A2 (θ) 2 (productive work) (total work)

84 7. EQUILIBRIUM GIVEN PROPERTY RIGHTS Y (0) = 0, Y ( θ ) = b, Y maximal at planner's choice of θ 1 θ

85 8. ENDOGENOUS PROPERTY RIGHTS Assumptions: Young decide next period's property rights simultaneously with next period's capital

86 8. ENDOGENOUS PROPERTY RIGHTS Assumptions: Young decide next period's property rights simultaneously with next period's capital Pros: Simplied politics young maximize after-tax return on saving

87 8. ENDOGENOUS PROPERTY RIGHTS Assumptions: Young decide next period's property rights simultaneously with next period's capital Pros: Simplied politics young maximize after-tax return on saving Cons: Assumption rides hard in two-period lifecycle. Return on saving not a sucient statistic for welfare if longer lifecycles or longer workspans

88 8. ENDOGENOUS PROPERTY RIGHTS Choices

89 8. ENDOGENOUS PROPERTY RIGHTS Choices θt+1 = argmax {p (θ t+1) f (k t+1)} where k t+1 solves eq.(4), taking (k t, θ t ) as given

90 8. ENDOGENOUS PROPERTY RIGHTS Choices θt+1 = argmax {p (θ t+1) f (k t+1)} where k t+1 solves eq.(4), taking (k t, θ t ) as given In general θ t+1 = Q (k t, θ t ) (5) for some function Q : R + [ 0, θ ] [ 0, θ ]

91 8. ENDOGENOUS PROPERTY RIGHTS Choices θt+1 = argmax {p (θ t+1) f (k t+1)} where k t+1 solves eq.(4), taking (k t, θ t ) as given In general θ t+1 = Q (k t, θ t ) (5) for some function Q : R + [ 0, θ ] [ 0, θ ] Very little is known about properties of Q - general shape depends on politics and elasticity of f (k)

92 8. ENDOGENOUS PROPERTY RIGHTS Choices θt+1 = argmax {p (θ t+1) f (k t+1)} where k t+1 solves eq.(4), taking (k t, θ t ) as given In general θ t+1 = Q (k t, θ t ) (5) for some function Q : R + [ 0, θ ] [ 0, θ ] Very little is known about properties of Q - general shape depends on politics and elasticity of f (k) Questions: Does low θ persist at low k?

93 9. CONCLUSIONS AND EXTENSIONS (a) Building blocks 1. No production without property rights (b) Results

94 9. CONCLUSIONS AND EXTENSIONS (a) Building blocks 1. No production without property rights 2. Rights set by collective resources devoted to deterring extractive activity (b) Results

95 9. CONCLUSIONS AND EXTENSIONS (a) Building blocks 1. No production without property rights 2. Rights set by collective resources devoted to deterring extractive activity 3. Rights aect mutually exclusive occupational choice (produce or extract) (b) Results

96 9. CONCLUSIONS AND EXTENSIONS (a) Building blocks 1. No production without property rights 2. Rights set by collective resources devoted to deterring extractive activity 3. Rights aect mutually exclusive occupational choice (produce or extract) 4. Extractors and producers have dierent interests, except in retirement (b) Results

97 9. CONCLUSIONS AND EXTENSIONS (a) Building blocks 1. No production without property rights 2. Rights set by collective resources devoted to deterring extractive activity 3. Rights aect mutually exclusive occupational choice (produce or extract) 4. Extractors and producers have dierent interests, except in retirement (b) Results 1. Property rights are TFP shifter: from technology frontier to zero

98 9. CONCLUSIONS AND EXTENSIONS (a) Building blocks 1. No production without property rights 2. Rights set by collective resources devoted to deterring extractive activity 3. Rights aect mutually exclusive occupational choice (produce or extract) 4. Extractors and producers have dierent interests, except in retirement (b) Results 1. Property rights are TFP shifter: from technology frontier to zero 2. Example of maximal output at planner's choice of property rights

99 9. CONCLUSIONS AND EXTENSIONS (a) Building blocks 1. No production without property rights 2. Rights set by collective resources devoted to deterring extractive activity 3. Rights aect mutually exclusive occupational choice (produce or extract) 4. Extractors and producers have dierent interests, except in retirement (b) Results 1. Property rights are TFP shifter: from technology frontier to zero 2. Example of maximal output at planner's choice of property rights 3. Collective decision: maximal after-tax capital return

100 9. CONCLUSIONS AND EXTENSIONS (c) Extensions Result (1) is robust to modelling details: (2) and (3) probably not

101 9. CONCLUSIONS AND EXTENSIONS (c) Extensions Result (1) is robust to modelling details: (2) and (3) probably not Extending lifecycle (to innity?) - enriches politics - elites vs. democracy - producers vs. kleptocrats - veto players and other strategic interactions

102 9. CONCLUSIONS AND EXTENSIONS (c) Extensions Result (1) is robust to modelling details: (2) and (3) probably not Extending lifecycle (to innity?) - enriches politics - elites vs. democracy - producers vs. kleptocrats - veto players and other strategic interactions Permitting private deterrence - will bound output away from zero

103 9. CONCLUSIONS AND EXTENSIONS (c) Extensions Result (1) is robust to modelling details: (2) and (3) probably not Extending lifecycle (to innity?) - enriches politics - elites vs. democracy - producers vs. kleptocrats - veto players and other strategic interactions Permitting private deterrence - will bound output away from zero Overriding question: under what circumstances do societies choose weak property rights?