Equality of Opportunity

Transcription

1 Equality of Opportunity and School Financing Structure Juan Rios January 4, 2017 Juan Rios Equality of Opportunity January 4, / 20

2 Motivation (I) 1 Normative Principles: Compensation Principle: Allocation is intended to compensate individuals for their disadvantageous circumstances (Roemer, 2012) Liberal Reward Principle: Particular Inequalities due to responsibilities should be left untouched (Fleurbaey, 2008) Juan Rios Equality of Opportunity January 4, / 20

3 Motivation (I) 1 Normative Principles: Compensation Principle: Allocation is intended to compensate individuals for their disadvantageous circumstances (Roemer, 2012) Liberal Reward Principle: Particular Inequalities due to responsibilities should be left untouched (Fleurbaey, 2008) 2 Crucial distinction Circumstances: Responsibility: Juan Rios Equality of Opportunity January 4, / 20

4 Motivation (I) 1 Normative Principles: Compensation Principle: Allocation is intended to compensate individuals for their disadvantageous circumstances (Roemer, 2012) Liberal Reward Principle: Particular Inequalities due to responsibilities should be left untouched (Fleurbaey, 2008) 2 Crucial distinction Circumstances: Affect opportunity sets Responsibility: Affect preferences Juan Rios Equality of Opportunity January 4, / 20

5 Motivation (II) It is, of course, a deep philosophical question, with psychological and neurophysiological components, to determine exactly what constitutes the complete set of circumstances for any given social problem. In practice, we choose some circumstances for the purpose of the computation, and define the partition of types with respect to those. We then arbitrarily attribute the variation in the acquisition of the objective among those within a type entirely to differential effort. (Roemer, 2003) Juan Rios Equality of Opportunity January 4, / 20

6 Motivation (III) Equality of Opportunity: force to equalize school investment Transfers from Central Government Property Taxes are efficient to finance local public schools (Tiebout) Juan Rios Equality of Opportunity January 4, / 20

7 Motivation (III) Equality of Opportunity: force to equalize school investment Transfers from Central Government Property Taxes are efficient to finance local public schools (Tiebout) Efficiency vs Equality of Opportunity Property Taxes vs Central Transfers Juan Rios Equality of Opportunity January 4, / 20

8 The Research Question What is the optimal public school financing structure? Equality of Opportunity vs Efficiency Central Government Transfers vs Property Taxes Juan Rios Equality of Opportunity January 4, / 20

9 The Research Question What is the optimal public school financing structure? Equality of Opportunity vs Efficiency Central Government Transfers vs Property Taxes Optimal Policy depends on Elasticities of house prices wrt to scholl investments House price distribution Elasticity of children wages wrt public sch. inv. Juan Rios Equality of Opportunity January 4, / 20

10 Related Literature 1 Equality of Opportunity: Fleurbaey (2008), Roemer (2012), Saez and Stancheva (2016), Jacquet et al (2015), Lockwood and Weinzierl (2015), Bergstrom and Dodds (2016). Juan Rios Equality of Opportunity January 4, / 20

11 Related Literature 1 Equality of Opportunity: Fleurbaey (2008), Roemer (2012), Saez and Stancheva (2016), Jacquet et al (2015), Lockwood and Weinzierl (2015), Bergstrom and Dodds (2016). Consider EOp in Education Juan Rios Equality of Opportunity January 4, / 20

12 Related Literature 1 Equality of Opportunity: Fleurbaey (2008), Roemer (2012), Saez and Stancheva (2016), Jacquet et al (2015), Lockwood and Weinzierl (2015), Bergstrom and Dodds (2016). Consider EOp in Education 2 Local Public Economics: Tiebout (1956), Benabou (1996). Juan Rios Equality of Opportunity January 4, / 20

13 Related Literature 1 Equality of Opportunity: Fleurbaey (2008), Roemer (2012), Saez and Stancheva (2016), Jacquet et al (2015), Lockwood and Weinzierl (2015), Bergstrom and Dodds (2016). Consider EOp in Education 2 Local Public Economics: Tiebout (1956), Benabou (1996). Take EOp into account Juan Rios Equality of Opportunity January 4, / 20

14 Related Literature 1 Equality of Opportunity: Fleurbaey (2008), Roemer (2012), Saez and Stancheva (2016), Jacquet et al (2015), Lockwood and Weinzierl (2015), Bergstrom and Dodds (2016). Consider EOp in Education 2 Local Public Economics: Tiebout (1956), Benabou (1996). Take EOp into account 3 Optimal School Financing Structure: Feldstein (1975), Fleuerbaey et al (2002), De Fraja (2002), Gottlieb and Moreira (2002), Kranich (2016) Juan Rios Equality of Opportunity January 4, / 20

15 Related Literature 1 Equality of Opportunity: Fleurbaey (2008), Roemer (2012), Saez and Stancheva (2016), Jacquet et al (2015), Lockwood and Weinzierl (2015), Bergstrom and Dodds (2016). Consider EOp in Education 2 Local Public Economics: Tiebout (1956), Benabou (1996). Take EOp into account 3 Optimal School Financing Structure: Feldstein (1975), Fleuerbaey et al (2002), De Fraja (2002), Gottlieb and Moreira (2002), Kranich (2016) EOp vs Efficiency of Local Taxes Optimality as function of elasticities Juan Rios Equality of Opportunity January 4, / 20

16 Outline 1 Normative Criteria Juan Rios Equality of Opportunity January 4, / 20

17 Outline 1 Normative Criteria 2 Model Juan Rios Equality of Opportunity January 4, / 20

18 Outline 1 Normative Criteria 2 Model 3 Optimal Policy Juan Rios Equality of Opportunity January 4, / 20

19 Outline 1 Normative Criteria 2 Model 3 Optimal Policy 4 Future Directions Juan Rios Equality of Opportunity January 4, / 20

20 Normative Criteria Equality of Opportunity Function u(α, γ, x) α: Circumstances γ: Responsibility x: Policy Juan Rios Equality of Opportunity January 4, / 20

21 Normative Criteria Equality of Opportunity Function u(α, γ, x) α: Circumstances γ: Responsibility x: Policy EOp(x) = min α u(α, γ, x)df (γ) Link to General EOp Juan Rios Equality of Opportunity January 4, / 20

22 Example Normative Criteria Table : Economy with 4 Types Responsibility γ Circumstances α Low High min α Selfish Parents Altruistic Parents EOp u(α, γ)df (γ) min α u(α, γ) Prob(γ = High) Juan Rios Equality of Opportunity January 4, / 20

23 Example Normative Criteria Table : Economy with 4 Types Responsibility γ Circumstances α Low High min α Selfish Parents Altruistic Parents EOp u(α, γ)df (γ) min α u(α, γ) Prob(γ = High) EOp reconciled with Welfarism If all heterogeneity is α: EOp = min u(α, x) If all heterogeneity is γ: EOp = u(γ, x)df (γ) Link to Optimal Tax Results Juan Rios Equality of Opportunity January 4, / 20

24 First Best Normative Criteria 1 EOp: Planner observes parents altruism u(α, γ) = u(γ), α No equality of outcome even in the first best Juan Rios Equality of Opportunity January 4, / 20

25 First Best Normative Criteria 1 EOp: Planner observes parents altruism u(α, γ) = u(γ), α No equality of outcome even in the first best 2 Mirrlees: Planner observes ability u(θ) = u θ Equality of outcome Juan Rios Equality of Opportunity January 4, / 20

26 Model Assumptions 1 2 generations 2 Parents are heterogeneous only on altruism 3 Planner observes house prices 4 Uniform property tax rate across districts 5 Uniform house quality within district Juan Rios Equality of Opportunity January 4, / 20

27 Model Assumptions 1 2 generations 2 Parents are heterogeneous only on altruism 3 Planner observes house prices 4 Uniform property tax rate across districts 5 Uniform house quality within district Tractability 1 Housing supply totally inelastic 2 Single crossing of parents consumption and school investments with respect to their altruism parameter. Juan Rios Equality of Opportunity January 4, / 20

28 Model Assumptions 1 2 generations 2 Parents are heterogeneous only on altruism 3 Planner observes house prices 4 Uniform property tax rate across districts 5 Uniform house quality within district Tractability 1 Housing supply totally inelastic 2 Single crossing of parents consumption and school investments with respect to their altruism parameter. What is in the model Focus on trade off between the efficiency of property taxes and redistribution of central transfers. Juan Rios Equality of Opportunity January 4, / 20

29 Children s Problem Model v k (α, γ, x) max u k (c, e; γ) s.t. c,e c w k( ) e, α, x u k ( ): Kids utility α: Parents Preferences γ: Responsibility x: School District investment c: Consumption e: Effort in education w k ( ): Endogenous children income Juan Rios Equality of Opportunity January 4, / 20

30 Parents Problem Model { v p (α) max u p( ) x h, l; α s.t. h,l ) } (1 + t)p (x h l u p ( ): Parents utility h: District index t: Property tax rate P(x h ): Price of a house in h with x h l: Parents labor supply (w p 1) u p l (α) 1 α No need to redistribute across parents: ) ux p (α) = (1 + t)p (x h (α) Juan Rios Equality of Opportunity January 4, / 20

31 Model Parents Problem: Reduced Form ( ) ũ x, P; α = u p( ) x, (1 + t)p; α Juan Rios Equality of Opportunity January 4, / 20

32 Model Parents Problem: Reduced Form ( ) ũ x, P; α = u p( ) x, (1 + t)p; α x P

33 Model Parents Problem: Reduced Form ( ) ũ x, P; α = u p( ) x, (1 + t)p; α x x(p) P

34 Model Parents Problem: Reduced Form ( ) ũ x, P; α = u p( ) x, (1 + t)p; α x α M x(p) Decreasing - ũp ũ x (α) P 1 P 2 P

35 Model Parents Problem: Reduced Form ( ) ũ x, P; α = u p( ) x, (1 + t)p; α x α L α M x(p) Decreasing - ũp ũ x (α) P 1 P 2 P

36 Model Parents Problem: Reduced Form ( ) ũ x, P; α = u p( ) x, (1 + t)p; α x α L α M α H x(p) Decreasing - ũp ũ x (α) P 1 P 2 P

37 Model Parents Problem: Reduced Form ( ) ũ x, P; α = u p( ) x, (1 + t)p; α x α L α M α H x(p) Decreasing - ũp ũ x (α) Sorted Equilibrium Link to Competitive Equilibrium Definition P 1 P 2 P Juan Rios Equality of Opportunity January 4, / 20

38 Planner s Problem Model max x( ) { v p (α)df (α) + β α min α 0 v k (α, γ, x)df (γ) s.t. x(p) tpdh(p) R } β: Discount factor P H( ) R: Exogenous Revenue Juan Rios Equality of Opportunity January 4, / 20

39 Elasticities Model P(ξ, I ) = argmax P ( ) ũ x(p) + ξp + I, P; α Juan Rios Equality of Opportunity January 4, / 20

40 Elasticities Model P(ξ, I ) = argmax P ( ) ũ x(p) + ξp + I, P; α 1 ε(p) = x (P) P(ξ,I ) P ξ : Elasticity of house prices with respect to ξ=i =0 the marginal public school resources 2 η(p) = x (P) P(ξ,I ) I : Level Effect Parameter ξ=i =0 3 ε c (P) = ε(p) + η(p): Slutsky Equation Juan Rios Equality of Opportunity January 4, / 20

41 Optimal Policy Optimal Policy x opt(p) ( t x opt(p) = εc (P)h(P)P P 1 g(p) βeop(p) t x opt(p) x opt(p) and 0 ) 1 η(p)dh(p) x opt (p) tpdh(p) = R for P P t Observations Larger x opt(p) implies less redistribution. Juan Rios Equality of Opportunity January 4, / 20

42 Optimal Policy x P

43 Optimal Policy x tp t P

44 Optimal Policy x tp x(p) t P

45 Optimal Policy x x(p) dx (P )dp dx (P ) P P + dp P Juan Rios Equality of Opportunity January 4, / 20

46 Intuition Optimal Policy x x(p) dx (P )dp Consider a perturbation dx (P ) at P dx (P ) t P P Juan Rios Equality of Opportunity January 4, / 20

47 Intuition Optimal Policy x x(p) dx (P )dp Consider a perturbation dx (P ) at P 1 BE: [t x (P )]ε c (P P ) x (P ) h(p )dp dx (P ) dx (P ) t P BE P Juan Rios Equality of Opportunity January 4, / 20

48 Intuition Optimal Policy Consider a perturbation dx (P ) at P 1 BE: [t x (P )]ε c (P P ) x (P ) h(p )dp dx (P ) 2 ME: P dh(p)dx (P )dp 3 EopE: P g(p) + βeop(p)dh(p)dx (P )dp 4 LE: t x (p) P x η(p)dh(p)dx (p) (P )dp t P P ME+EopE+LE x dx (P ) x(p) dx (P )dp Juan Rios Equality of Opportunity January 4, / 20

49 Intuition Optimal Policy Consider a perturbation dx (P ) at P 1 BE: [t x (P )]ε c (P P ) x (P ) h(p )dp dx (P ) 2 ME: P dh(p)dx (P )dp 3 EopE: P g(p) + βeop(p)dh(p)dx (P )dp 4 LE: P t x (p) x η(p)dh(p)dx (p) (P )dp At the optimum the sum of these effects is zero. x dx (P ) t P x(p) dx (P )dp P Juan Rios Equality of Opportunity January 4, / 20

50 Planner s weights Optimal Policy 1 g(p) = 1 λũx(α(p)) Lump-sum transfers if this is the only concern (Tiebout) Link to Details Juan Rios Equality of Opportunity January 4, / 20

51 Planner s weights Optimal Policy 1 g(p) = λũx(α(p)) 1 Lump-sum transfers if this is the only concern (Tiebout) { 1 2 eop(p) = λ u k w k c x df γ α(γ 0) if p = P(α = 0) 0 otherwise All weight on α = 0 under equality of opportunity Link to Details Juan Rios Equality of Opportunity January 4, / 20

52 Planner s weights Optimal Policy 1 g(p) = 1 λ u p v uc k w k x df γ α (γ α(p)) uc p p x Lump-sum transfers if this is the only concern (Tiebout) { 1 2 eop(p) = λ u k w k c x df γ α(γ 0) if p = P(α = 0) 0 otherwise All weight on α = 0 under equality of opportunity Link to Details Observations w k x (p) is relevant to compute parents weights Juan Rios Equality of Opportunity January 4, / 20

53 Planner s weights Optimal Policy 1 g(p) = 1 λ u p v uc k w k x df γ α (γ α(p)) uc p p x Lump-sum transfers if this is the only concern (Tiebout) { 1 2 eop(p) = λ u k w k c x df γ α(γ 0) if p = P(α = 0) 0 otherwise All weight on α = 0 under equality of opportunity Link to Details Observations w k x (p) is relevant to compute parents weights w k x (P(α = 0)) is relevant to compute children s weights Juan Rios Equality of Opportunity January 4, / 20

54 Planner s weights Optimal Policy 1 g(p) = 1 λ u p v uc k w k x df γ α (γ α(p)) uc p p x Lump-sum transfers if this is the only concern (Tiebout) { 1 2 eop(p) = λ u k w k c x d γ α(γ 0) if p = P(α = 0) 0 otherwise All weight on α = 0 under equality of opportunity Link to Details Observations w k x (p) is relevant to compute parents weights w k x (P(α = 0)) is relevant to compute children s weights Overlapping Generations + income tax fiscal externality on wages Juan Rios Equality of Opportunity January 4, / 20

55 Planner s weights Optimal Policy 1 g(p) = 1 λ u p v uc k w k x df γ α (γ α(p)) uc p p x Lump-sum transfers if this is the only concern (Tiebout) { 1 2 eop(p) = λ u k w k c x d F γ α (γ 0) if p = P(α = 0) 0 otherwise All weight on α = 0 under equality of opportunity Link to Details Observations w k x (p) is relevant to compute parents weights w k x (P(α = 0)) is relevant to compute children s weights Overlapping Generations + income tax fiscal externality on wages If γ is partially circumstances F becomes F Juan Rios Equality of Opportunity January 4, / 20

56 Future Directions Where to go? Endogenous human capital formation Bequests and access to credit Endogenous local taxes Overlapping generations + Endogenous R Heterogeneity of preferences for district quality Private schools and externalities Juan Rios Equality of Opportunity January 4, / 20

57 Generalized EOp m(γ, x) = min u(α, γ, x) M α EOp : M R + : Increasing Operator. ( ) EOp m(γ, x) : Equality of Opportunity Function Table : Generalized EOp Responsibility γ Social Criteria EOP Circumstances α Low High min m(γ) m(γ)df (γ) γ Selfish Parents Altruistic Parents m(γ) Prob(γ = High) Back to EOp Juan Rios Equality of Opportunity January 4, / 20

58 Income Taxation All weight on lower circumstances and equal weights over responsibilities justifies larger tax rates (Saez and Stancheva) All weight on circumstances with enough weight on high responsibility justifies EITC (Jacquet et al) Arbitrary weights on circumstances and equal weights on responsibilities optimal tax less progressive (Lockwood and Weinzierl) If planner can observe circumstances he could use tagging Back to Example Juan Rios Equality of Opportunity January 4, / 20

59 Competitive Equilibrium A CE is an allocation for the parents {c(α), h(α)}, for the children {c(h, γ), e(h, γ)} a price schedule P(h, x), a wage production function w(e, x, h) and a policy schedule x(p) such that. 1 {c(α), h(α)} solves the parents problem given P() and x() 2 {c(h, γ), e(h, γ)} solves the children problem given w(, x, h). 3 Good markets clear c(α) + (1 + t)p(h(α), x)df (α) = W 4 Housing markets clear F (α) = H(h(α)) Back to Reduced Form Juan Rios Equality of Opportunity January 4, / 20

60 Case without EOp concerns If eop(p) = 0 ũ x (α) = ũ x λ α Property taxes x (P) = t P ensure that LHS = 0 = RHS Tiebout Result Back to Planner s Weights Juan Rios Equality of Opportunity January 4, / 20