Equality of Opportunity
|
|
- Bryan Phillips
- 6 years ago
- Views:
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
Optimal Income Taxation: Mirrlees Meets Ramsey
Optimal Income Taxation: Mirrlees Meets Ramsey Jonathan Heathcote Minneapolis Fed Hitoshi Tsujiyama University of Minnesota and Minneapolis Fed ASSA Meetings, January 2012 The views expressed herein are
More informationproblem. max Both k (0) and h (0) are given at time 0. (a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming
1. Endogenous Growth with Human Capital Consider the following endogenous growth model with both physical capital (k (t)) and human capital (h (t)) in continuous time. The representative household solves
More informationLecture 2 Optimal Indirect Taxation. March 2014
Lecture 2 Optimal Indirect Taxation March 2014 Optimal taxation: a general setup Individual choice criterion, for i = 1,..., I : U(c i, l i, θ i ) Individual anonymous budget constraint Social objective
More informationEconomics 2450A: Public Economics Section 8: Optimal Minimum Wage and Introduction to Capital Taxation
Economics 2450A: Public Economics Section 8: Optimal Minimum Wage and Introduction to Capital Taxation Matteo Paradisi November 1, 2016 In this Section we develop a theoretical analysis of optimal minimum
More informationA Theory of Optimal Inheritance Taxation
A Theory of Optimal Inheritance Taxation Thomas Piketty, Paris School of Economics Emmanuel Saez, UC Berkeley July 2013 1 1. MOTIVATION Controversy about proper level of inheritance taxation 1) Public
More informationRedistributive Taxation in a Partial-Insurance Economy
Redistributive Taxation in a Partial-Insurance Economy Jonathan Heathcote Federal Reserve Bank of Minneapolis and CEPR Kjetil Storesletten Federal Reserve Bank of Minneapolis and CEPR Gianluca Violante
More informationEconomic Policy and Equality of Opportunity
Economic Policy and Equality of Opportunity Sang Yoon (Tim) Lee 1 Ananth Seshdari 2 1 University of Mannheim 2 University of Wisconsin October 25, 2014 Normative Ethics and Welfare Economics Redistributive
More informationOptimal Income, Education and Bequest Taxes in an Intergenerational Model
38 Optimal Income, Education and Bequest Taxes in an Intergenerational Model Stefanie Stantcheva (Harvard Society of Fellows) May 1, 2015 2 38 Introduction Parents can transfer resources to children through
More informationComprehensive Exam. Macro Spring 2014 Retake. August 22, 2014
Comprehensive Exam Macro Spring 2014 Retake August 22, 2014 You have a total of 180 minutes to complete the exam. If a question seems ambiguous, state why, sharpen it up and answer the sharpened-up question.
More information(a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming
1. Government Purchases and Endogenous Growth Consider the following endogenous growth model with government purchases (G) in continuous time. Government purchases enhance production, and the production
More informationHandout: Competitive Equilibrium
1 Competitive equilibrium Handout: Competitive Equilibrium Definition 1. A competitive equilibrium is a set of endogenous variables (Ĉ, N s, N d, T, π, ŵ), such that given the exogenous variables (G, z,
More informationAPPENDIX Should the Private Sector Provide Public Capital?
APPENIX Should the Private Sector Provide Public Capital? Santanu Chatterjee epartment of Economics Terry College of Business University of eorgia Appendix A The appendix describes the optimization problem
More informationEconomic Growth: Lecture 8, Overlapping Generations
14.452 Economic Growth: Lecture 8, Overlapping Generations Daron Acemoglu MIT November 20, 2018 Daron Acemoglu (MIT) Economic Growth Lecture 8 November 20, 2018 1 / 46 Growth with Overlapping Generations
More informationEconomic Growth: Lecture 7, Overlapping Generations
14.452 Economic Growth: Lecture 7, Overlapping Generations Daron Acemoglu MIT November 17, 2009. Daron Acemoglu (MIT) Economic Growth Lecture 7 November 17, 2009. 1 / 54 Growth with Overlapping Generations
More informationHOMEWORK #3 This homework assignment is due at NOON on Friday, November 17 in Marnix Amand s mailbox.
Econ 50a second half) Yale University Fall 2006 Prof. Tony Smith HOMEWORK #3 This homework assignment is due at NOON on Friday, November 7 in Marnix Amand s mailbox.. This problem introduces wealth inequality
More informationRedistributive Taxation in a Partial Insurance Economy
Redistributive Taxation in a Partial Insurance Economy Jonathan Heathcote Federal Reserve Bank of Minneapolis Kjetil Storesletten Federal Reserve Bank of Minneapolis, and Oslo University Gianluca Violante
More informationOptimal Tax Progressivity: An Analytical Framework
Optimal Tax Progressivity: An Analytical Framework Jonathan Heathcote Federal Reserve Bank of Minneapolis Kjetil Storesletten Oslo University and Federal Reserve Bank of Minneapolis Gianluca Violante New
More informationBequest Motives, Estate Taxes, and Wealth Distributions in Becker-Tomes Models with Investment Risk
Bequest Motives, Estate Taxes, and Wealth Distributions in Becker-Tomes Models with Investment Risk Shenghao Zhu Department of Economics, NUS This draft: June 2013 Abstract I introduce investment risk
More informationProper Welfare Weights for Social Optimization Problems
Proper Welfare Weights for Social Optimization Problems Alexis Anagnostopoulos (Stony Brook University) Eva Cárceles-Poveda (Stony Brook University) Yair Tauman (IDC and Stony Brook University) June 24th
More informationA Theory of Optimal Inheritance Taxation
A Theory of Optimal Inheritance Taxation Thomas Piketty, Paris School of Economics Emmanuel Saez, UC erkeley and NER March 22, 2013 Abstract This paper derives optimal inheritance tax formulas that capture
More informationAdvanced Macroeconomics
Advanced Macroeconomics The Ramsey Model Marcin Kolasa Warsaw School of Economics Marcin Kolasa (WSE) Ad. Macro - Ramsey model 1 / 30 Introduction Authors: Frank Ramsey (1928), David Cass (1965) and Tjalling
More informationOptimal Tax Progressivity: An Analytical Framework
Optimal Tax Progressivity: An Analytical Framework Jonathan Heathcote Federal Reserve Bank of Minneapolis Kjetil Storesletten Oslo University Gianluca Violante New York University Midwest Macro Meetings,
More informationOPTIMAL TAXATION: LESSONS FOR TAX POLICY
OPTIMAL TAXATION: LESSONS FOR TAX POLICY Special Lectures at the University of Tokyo International Program in Economics and Center for International Research on the Japanese Economy by Robin Boadway, Queen
More informationA Theory of Income Taxation under Multidimensional Skill Heterogeneity
A Theory of Income Taxation under Multidimensional Skill Heterogeneity Casey Rothschild Wellesley and Radcliffe Florian Scheuer Stanford and NBER November 2014 Casey Rothschild, Florian Scheuer Taxation
More informationOptimal Insurance of Search Risk
Optimal Insurance of Search Risk Mikhail Golosov Yale University and NBER Pricila Maziero University of Pennsylvania Guido Menzio University of Pennsylvania and NBER November 2011 Introduction Search and
More informationNegative Income Taxes, Inequality and Poverty
Negative Income Taxes, Inequality and Poverty Constantine Angyridis Brennan S. Thompson Department of Economics Ryerson University July 8, 2011 Overview We use a dynamic heterogeneous agents general equilibrium
More informationChapter 4. Applications/Variations
Chapter 4 Applications/Variations 149 4.1 Consumption Smoothing 4.1.1 The Intertemporal Budget Economic Growth: Lecture Notes For any given sequence of interest rates {R t } t=0, pick an arbitrary q 0
More informationAdvanced Macroeconomics
Advanced Macroeconomics The Ramsey Model Micha l Brzoza-Brzezina/Marcin Kolasa Warsaw School of Economics Micha l Brzoza-Brzezina/Marcin Kolasa (WSE) Ad. Macro - Ramsey model 1 / 47 Introduction Authors:
More informationA Theory of Optimal Inheritance Taxation
A Theory of Optimal Inheritance Taxation Thomas Piketty, Paris School of Economics Emmanuel Saez, UC Berkeley and NBER November 19, 2012 Abstract This paper derives optimal inheritance tax formulas that
More informationSelf-test for applicants M.Sc. Economics
Self-test for applicants M.Sc. Economics First of all, we thank you for considering the Friedrich Schiller University Jena, and in particular this master program in economics, for your future academic
More informationAggregate Demand, Idle Time, and Unemployment
Aggregate Demand, Idle Time, and Unemployment Pascal Michaillat (LSE) & Emmanuel Saez (Berkeley) September 2014 1 / 44 Motivation 11% Unemployment rate 9% 7% 5% 3% 1974 1984 1994 2004 2014 2 / 44 Motivation
More informationSeminario de Investigación. Life-Cycle Models. Jorge Mondragón Minero ITAM. March 25, 2015
Life-Cycle Models Jorge Mondragón Minero ITAM March 25, 2015 Introduction Evidence Wages across USA and Europe have been increasing since 1970 Differences in TFP between USA and Europe affect the return
More informationA Modern Equilibrium Model. Jesús Fernández-Villaverde University of Pennsylvania
A Modern Equilibrium Model Jesús Fernández-Villaverde University of Pennsylvania 1 Household Problem Preferences: max E X β t t=0 c 1 σ t 1 σ ψ l1+γ t 1+γ Budget constraint: c t + k t+1 = w t l t + r t
More informationA Variational Approach to the Analysis of Tax Systems
A Variational Approach to the Analysis of Tax Systems Mikhail Golosov, Aleh Tsyvinski, and Nicolas Werquin December 12, 2014 Abstract We develop a general method to study the effects of non-linear taxation
More informationAggregate Demand, Idle Time, and Unemployment
Aggregate Demand, Idle Time, and Unemployment Pascal Michaillat (LSE) & Emmanuel Saez (Berkeley) July 2014 1 / 46 Motivation 11% Unemployment rate 9% 7% 5% 3% 1974 1984 1994 2004 2014 2 / 46 Motivation
More informationu(c t, x t+1 ) = c α t + x α t+1
Review Questions: Overlapping Generations Econ720. Fall 2017. Prof. Lutz Hendricks 1 A Savings Function Consider the standard two-period household problem. The household receives a wage w t when young
More informationMacroeconomic Theory and Analysis Suggested Solution for Midterm 1
Macroeconomic Theory and Analysis Suggested Solution for Midterm February 25, 2007 Problem : Pareto Optimality The planner solves the following problem: u(c ) + u(c 2 ) + v(l ) + v(l 2 ) () {c,c 2,l,l
More informationEstate Taxation with Altruism Heterogeneity
Estate Taxation with Altruism Heterogeneity Emmanuel Farhi Harvard University Iván Werning MIT We develop a theory of optimal estate taxation in a model where bequest inequality is driven by differences
More informationIn the Name of God. Sharif University of Technology. Microeconomics 1. Graduate School of Management and Economics. Dr. S.
In the Name of God Sharif University of Technology Graduate School of Management and Economics Microeconomics 1 44715 (1396-97 1 st term) - Group 1 Dr. S. Farshad Fatemi Chapter 10: Competitive Markets
More informationEmpirical approaches in public economics
Empirical approaches in public economics ECON4624 Empirical Public Economics Fall 2016 Gaute Torsvik Outline for today The canonical problem Basic concepts of causal inference Randomized experiments Non-experimental
More informationProblem 1 (30 points)
Problem (30 points) Prof. Robert King Consider an economy in which there is one period and there are many, identical households. Each household derives utility from consumption (c), leisure (l) and a public
More informationCompetitive Equilibrium and the Welfare Theorems
Competitive Equilibrium and the Welfare Theorems Craig Burnside Duke University September 2010 Craig Burnside (Duke University) Competitive Equilibrium September 2010 1 / 32 Competitive Equilibrium and
More informationTrade, Inequality and Costly Redistribution
Trade, Inequality and Costly Redistribution Pol Antràs Alonso de Gortari Oleg Itskhoki Harvard Harvard Princeton ILO Symposium September 2015 1 / 30 Introduction International trade raises real income
More informationLecture 2: Firms, Jobs and Policy
Lecture 2: Firms, Jobs and Policy Economics 522 Esteban Rossi-Hansberg Princeton University Spring 2014 ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring 2014 1 / 34 Restuccia and Rogerson
More informationOptimal age-dependent income taxation in a dynamic extensive model: The case for negative participation tax to the young people
Optimal age-dependent income taxation in a dynamic extensive model: The case for negative participation tax to the young people Takao Kataoka and Yoshihiro Takamatsu July 25, 207 Abstract We consider an
More informationOptimal Mirrleesian Income Taxation with Tax Avoidance
Optimal Mirrleesian Income Taxation with Tax Avoidance Daniel Moncayo January 30, 2014 Introduction People have more than one way to respond to taxation. The labor supply elasticity alone can t explain
More informationMacroeconomic Theory and Analysis V Suggested Solutions for the First Midterm. max
Macroeconomic Theory and Analysis V31.0013 Suggested Solutions for the First Midterm Question 1. Welfare Theorems (a) There are two households that maximize max i,g 1 + g 2 ) {c i,l i} (1) st : c i w(1
More informationNeoclassical Growth Model: I
Neoclassical Growth Model: I Mark Huggett 2 2 Georgetown October, 2017 Growth Model: Introduction Neoclassical Growth Model is the workhorse model in macroeconomics. It comes in two main varieties: infinitely-lived
More informationOnline Appendix for Investment Hangover and the Great Recession
ONLINE APPENDIX INVESTMENT HANGOVER A1 Online Appendix for Investment Hangover and the Great Recession By MATTHEW ROGNLIE, ANDREI SHLEIFER, AND ALP SIMSEK APPENDIX A: CALIBRATION This appendix describes
More informationMonetary Economics: Solutions Problem Set 1
Monetary Economics: Solutions Problem Set 1 December 14, 2006 Exercise 1 A Households Households maximise their intertemporal utility function by optimally choosing consumption, savings, and the mix of
More information1 The Basic RBC Model
IHS 2016, Macroeconomics III Michael Reiter Ch. 1: Notes on RBC Model 1 1 The Basic RBC Model 1.1 Description of Model Variables y z k L c I w r output level of technology (exogenous) capital at end of
More informationFoundations of Neoclassical Growth
Foundations of Neoclassical Growth Ömer Özak SMU Macroeconomics II Ömer Özak (SMU) Economic Growth Macroeconomics II 1 / 78 Preliminaries Introduction Foundations of Neoclassical Growth Solow model: constant
More informationTaxation, Time Allocation and Externalities
Taxation, Time Allocation and Externalities Jens Eri Nielsen Danish Transport Research Institute and University of Copenhagen Ninette Pilegaard Danish Transport Research Institute September 2004 Preliminary
More informationThe Ramsey Model. (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 2013)
The Ramsey Model (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 213) 1 Introduction The Ramsey model (or neoclassical growth model) is one of the prototype models in dynamic macroeconomics.
More informationIntroduction to second order approximation. SGZ Macro Week 3, Day 4 Lecture 1
Introduction to second order approximation 1 Outline A. Basic concepts in static models 1. What are first and second order approximations? 2. What are implications for accuracy of welfare calculations
More informationShould Robots Be Taxed?
Should Robots Be Taxed? Joao Guerreiro, Sergio Rebelo, and Pedro Teles January 2018 Abstract We use a model of automation to show that with the current U.S. tax system, a fall in automation costs could
More informationPublic Economics Ben Heijdra Chapter 9: Introduction to Normative Public Economics
Public Economics: Chapter 9 1 Public Economics Ben Heijdra Chapter 9: Introduction to Normative Public Economics Objectives of this chapter Public Economics: Chapter 9 2 Read Atkinson & Stiglitz (1980,
More informationGeneral Equilibrium and Welfare
and Welfare Lectures 2 and 3, ECON 4240 Spring 2017 University of Oslo 24.01.2017 and 31.01.2017 1/37 Outline General equilibrium: look at many markets at the same time. Here all prices determined in the
More informationOPTIMAL CATEGORICAL TRANSFER PAYMENTS: THE WELFARE ECONOMICS OF LIMITED LUMP-SUM REDISTRIBUTION
OPTIMAL CATEGORICAL TRANSFER PAYMENTS: THE WELFARE ECONOMICS OF LIMITED LUMP-SUM REDISTRIBUTION A central component of most countries' tax-transfer systems is the provision of transfer payments to categories
More informationGovernment The government faces an exogenous sequence {g t } t=0
Part 6 1. Borrowing Constraints II 1.1. Borrowing Constraints and the Ricardian Equivalence Equivalence between current taxes and current deficits? Basic paper on the Ricardian Equivalence: Barro, JPE,
More informationThe New Keynesian Model: Introduction
The New Keynesian Model: Introduction Vivaldo M. Mendes ISCTE Lisbon University Institute 13 November 2017 (Vivaldo M. Mendes) The New Keynesian Model: Introduction 13 November 2013 1 / 39 Summary 1 What
More informationPractice Questions for Mid-Term I. Question 1: Consider the Cobb-Douglas production function in intensive form:
Practice Questions for Mid-Term I Question 1: Consider the Cobb-Douglas production function in intensive form: y f(k) = k α ; α (0, 1) (1) where y and k are output per worker and capital per worker respectively.
More informationStructural change in a multi-sector model of the climate and the economy
Structural change in a multi-sector model of the climate and the economy Gustav Engström The Beijer Institute of Environmental Economics Stockholm, December 2012 G. Engström (Beijer) Stockholm, December
More informationPerfect Competition in Markets with Adverse Selection
Perfect Competition in Markets with Adverse Selection Eduardo Azevedo and Daniel Gottlieb (Wharton) Presented at Frontiers of Economic Theory & Computer Science at the Becker Friedman Institute August
More informationFoundations of Modern Macroeconomics Second Edition
Foundations of Modern Macroeconomics Second Edition Chapter 5: The government budget deficit Ben J. Heijdra Department of Economics & Econometrics University of Groningen 1 September 2009 Foundations of
More informationSimple New Keynesian Model without Capital
Simple New Keynesian Model without Capital Lawrence J. Christiano January 5, 2018 Objective Review the foundations of the basic New Keynesian model without capital. Clarify the role of money supply/demand.
More informationSources of Income Inequality: Productivities vs. Preferences
Sources of Income Inequality: Productivities vs. Preferences Katy Bergstrom William Dodds JOB MARKET PAPER CLICK HERE FOR LATEST VERSION December 19, 2018 Abstract This paper develops a new method to understand
More informationLabour Supply Responses and the Extensive Margin: The US, UK and France
Labour Supply Responses and the Extensive Margin: The US, UK and France Richard Blundell Antoine Bozio Guy Laroque UCL and IFS IFS INSEE-CREST, UCL and IFS January 2011 Blundell, Bozio and Laroque ( )
More informationHousing with overlapping generations
Housing with overlapping generations Chiara Forlati, Michael Hatcher, Alessandro Mennuni University of Southampton Preliminary and Incomplete May 16, 2015 Abstract We study the distributional and efficiency
More informationTax avoidance and the design of the tax structure
University of Toulouse I From the SelectedWorks of Georges Casamatta 2011 Tax avoidance and the design of the tax structure Georges Casamatta, Toulouse School of Economics Available at: https://works.bepress.com/georges_casamatta/19/
More informationOptimal Insurance of Search Risk
Optimal Insurance of Search Risk Mikhail Golosov Yale University and NBER Pricila Maziero University of Pennsylvania Guido Menzio University of Pennsylvania and NBER May 27, 2011 Introduction Search and
More informationInequality, Costly Redistribution and Welfare in an Open Economy
Inequality, Costly Redistribution and Welfare in an Open Economy Pol Antràs Alonso de Gortari Oleg Itskhoki Harvard Harvard Princeton TRISTAN Workshop University of Bayreuth June 2016 1 / 29 Introduction
More informationAggregate Implications of Innovation Policy
Aggregate Implications of Innovation Policy Andrew Atkeson University of California, Los Angeles, Federal Reserve Bank of Minneapolis, and National Bureau of Economic Research Ariel T. Burstein University
More informationTechnological Spillovers and Dynamics of Comparative Advantage
Technological Spillovers and Dynamics of Comparative Advantage Yury Yatsynovich University of California, Berkeley January 21, 2015 MOTIVATION Comparative advantage is dynamic: Korea from rice to microchips.
More informationAdvanced Macroeconomics
Advanced Macroeconomics Endogenous Growth Marcin Kolasa Warsaw School of Economics Marcin Kolasa (WSE) Ad. Macro - Endogenous growth 1 / 18 Introduction The Solow and Ramsey models are exogenous growth
More informationEco Spring 2002 Chris Sims OLG EXERCISES
Eco 504.2 Spring 2002 Chris Sims OLG EXERCISES (1) Suppose in our overlapping generations model the utility function is U ( C 1 (t), ) = log ( C 1 (t) ). Suppose also that instead of being endowed with
More informationECON 582: The Neoclassical Growth Model (Chapter 8, Acemoglu)
ECON 582: The Neoclassical Growth Model (Chapter 8, Acemoglu) Instructor: Dmytro Hryshko 1 / 21 Consider the neoclassical economy without population growth and technological progress. The optimal growth
More informationTOBB-ETU - Econ 532 Practice Problems II (Solutions)
TOBB-ETU - Econ 532 Practice Problems II (Solutions) Q: Ramsey Model: Exponential Utility Assume that in nite-horizon households maximize a utility function of the exponential form 1R max U = e (n )t (1=)e
More informationPROPERTY RIGHTS IN GROWTH THEORY
PROPERTY RIGHTS IN GROWTH THEORY Costas Azariadis Washington University and Federal Reserve Bank of St. Louis Preliminary Draft May 2013 1. CONTENTS 1. Issues and Goals 2. Main Results 3. Related Literature
More informationIncentives and Nutrition for Rotten Kids: Intrahousehold Food Allocation in the Philippines
Incentives and Nutrition for Rotten Kids: Intrahousehold Food Allocation in the Philippines Pierre Dubois and Ethan Ligon presented by Rachel Heath November 3, 2006 Introduction Outline Introduction Modification
More informationThe Real Business Cycle Model
The Real Business Cycle Model Macroeconomics II 2 The real business cycle model. Introduction This model explains the comovements in the fluctuations of aggregate economic variables around their trend.
More informationPart A: Answer question A1 (required), plus either question A2 or A3.
Ph.D. Core Exam -- Macroeconomics 5 January 2015 -- 8:00 am to 3:00 pm Part A: Answer question A1 (required), plus either question A2 or A3. A1 (required): Ending Quantitative Easing Now that the U.S.
More informationShould Robots Be Taxed?
Should Robots Be Taxed? Joao Guerreiro, Sergio Rebelo, and Pedro Teles August 2017 (revised September 2017) Abstract We use a model of automation to show that with the current U.S. tax system, a fall in
More informationTutorial 2: Comparative Statics
Tutorial 2: Comparative Statics ECO42F 20 Derivatives and Rules of Differentiation For each of the functions below: (a) Find the difference quotient. (b) Find the derivative dx. (c) Find f (4) and f (3)..
More informationGlobalization, Inequality and Welfare
Globalization, Inequality and Welfare Pol Antràs Harvard University Alonso de Gortari Harvard University Oleg Itskhoki Princeton University Harvard - September 7, 2016 Antràs, de Gortari and Itskhoki Globalization,
More informationHow to Model Household Decisions?
How to Model? Based on Chiappori and Mazzocco (2017) Universidad Carlos III de Madrid March, 20 1/17 Plan 1 2 3 4 5 2/17 : decisions Browning et al. (2014) and Mazzocco et al. (2017) Static models 1 Unitary
More informationSGZ Macro Week 3, Lecture 2: Suboptimal Equilibria. SGZ 2008 Macro Week 3, Day 1 Lecture 2
SGZ Macro Week 3, : Suboptimal Equilibria 1 Basic Points Effects of shocks can be magnified (damped) in suboptimal economies Multiple equilibria (stationary states, dynamic paths) in suboptimal economies
More informationUNIVERSITY OF MARYLAND Department of Economics Economics 754 Topics in Political Economy Fall 2005 Allan Drazen. Exercise Set I
UNIVERSITY OF MARYLAND Department of Economics Economics 754 Topics in Political Economy Fall 005 Allan Drazen Exercise Set I The first four exercises are review of what we did in class on 8/31. The next
More informationPolitico Economic Consequences of Rising Wage Inequality
Politico Economic Consequences of Rising Wage Inequality Dean Corbae Pablo D Erasmo Burhan Kuruscu University of Texas at Austin and University of Maryland February 8, 2010 Increase in Wage Inequality
More informationLecture 1: Labour Economics and Wage-Setting Theory
ecture 1: abour Economics and Wage-Setting Theory Spring 2015 ars Calmfors iterature: Chapter 1 Cahuc-Zylberberg (pp 4-19, 28-29, 35-55) 1 The choice between consumption and leisure U = U(C,) C = consumption
More informationA Policy Lesson from an Overlapping Generations Model of Habit Persistence
A Policy Lesson from an Overlapping Generations Model of Habit Persistence Ronald Wendner Department of Economics, Graz University, Austria and Department of Economics, University of California, Berkeley,
More informationSecond Welfare Theorem
Second Welfare Theorem Econ 2100 Fall 2015 Lecture 18, November 2 Outline 1 Second Welfare Theorem From Last Class We want to state a prove a theorem that says that any Pareto optimal allocation is (part
More informationDevelopment Economics
Development Economics Slides 2 Debraj Ray Columbia, Fall 2013 Development traps [1] Self-fulfilling failure of expectations. [2] History-dependence Development Traps I: Self-Fulfilling Prophecies Origins:
More informationEconomics 210B Due: September 16, Problem Set 10. s.t. k t+1 = R(k t c t ) for all t 0, and k 0 given, lim. and
Economics 210B Due: September 16, 2010 Problem 1: Constant returns to saving Consider the following problem. c0,k1,c1,k2,... β t Problem Set 10 1 α c1 α t s.t. k t+1 = R(k t c t ) for all t 0, and k 0
More informationECON 581: Growth with Overlapping Generations. Instructor: Dmytro Hryshko
ECON 581: Growth with Overlapping Generations Instructor: Dmytro Hryshko Readings Acemoglu, Chapter 9. Motivation Neoclassical growth model relies on the representative household. OLG models allow for
More informationAAEC 6524: Environmental Theory and Policy Analysis. Outline. Theory of Externalities and Public Goods. Klaus Moeltner Spring 2019.
AAEC 6524: Theory and Policy Analysis Theory of Externalities and Public Goods Klaus Moeltner Spring 2019 January 21, 2019 Outline Overarching and Related Fields and Microeconomics (consumer, firm, s)
More informationMacroeconomics Theory II
Macroeconomics Theory II Francesco Franco FEUNL February 2016 Francesco Franco (FEUNL) Macroeconomics Theory II February 2016 1 / 18 Road Map Research question: we want to understand businesses cycles.
More informationMacroeconomics Theory II
Macroeconomics Theory II Francesco Franco Novasbe February 2016 Francesco Franco (Novasbe) Macroeconomics Theory II February 2016 1 / 8 The Social Planner Solution Notice no intertemporal issues (Y t =
More information1 Recursive Competitive Equilibrium
Feb 5th, 2007 Let s write the SPP problem in sequence representation: max {c t,k t+1 } t=0 β t u(f(k t ) k t+1 ) t=0 k 0 given Because of the INADA conditions we know that the solution is interior. So
More informationThe Origin Principle, Tax Harmonization and Public Goods
The Origin Principle, Tax Harmonization and Public Goods Christos Kotsogiannis Unviersity of Exeter Miguel-Angel Lopez-Garcia Universidad Autonoma de Barcelona Gareth D. Myles University of Exeter and
More information