Robust Optimal Taxation and Environmental Externalities
|
|
- Bertha Armstrong
- 5 years ago
- Views:
Transcription
1 Robust Optimal Taxation and Environmental Externalities Xin Li Borghan Narajabad Ted Loch-Temzelides Department of Economics Rice University
2 Outline Outline 1 Introduction 2 One-Energy-Sector Model 3 Complete Model 4 Numerical Results
3 Introduction Outline 1 Introduction 2 One-Energy-Sector Model 3 Complete Model 4 Numerical Results
4 Introduction Research Question Environmental Externality: CO 2 Emission Global Temperature output. Model Uncertainty: Our knowledge is limited regarding how CO 2 emission affects future global mean temperature and output. Robust Control: The fear of catastrophic events alters the optimal path of energy extraction and thereby production and consumption. We want to find out: Robust vesion of optimal energy extraction How to achieve it in a decentralized economy
5 Introduction Literature Review Golosov, Hassler, Krusell, and Tsyvinski (GHKT, 2012): 1. Assume that the mapping from carbon concentration to output damages is subject to a risk γ: y = e γs ỹ (the true distribution of γ is known). 2. Obtain analytical expressions for carbon externality. 3. Assess optimal use of energy based on average performance (w.r.t. the know distribution) 4. Optimal taxation: A Pigouvian tax on carbon emission with a rate equal to the marginal externality of carbon.
6 Introduction Literature Review Hansen and Sargent (2002, 2008) Robust Control: 1. Decision maker does not know the true distribution of γ, but has an approximating one in his mind. 2. Only concerns about social (individual) walfare in the worst case scenario. 3. Chooses the worst case distribution of γ around a neighborhood centered at the approximating one. 4. Uses entropy as a measure of the deviation from the approximating model. 5. Linear-Quadratic-Gaussian world.
7 Introduction Our Contribution To the Literature of Environmental Externality: 1. Incorporate model uncertainty into GHKT (2012) and characterize optimal allocation and tax as functions of the size of model uncertainty. 2. The concern of robustness matters both qualitatively and qnantatively. To the Literature of Robust Control: 1. Study a dynamic model outside the LQG world. 2. Develop a simple method which divide the model into two parts and solve them separately.
8 One-Energy-Sector Model Outline 1 Introduction 2 One-Energy-Sector Model 3 Complete Model 4 Numerical Results
9 One-Energy-Sector Model Basic Setup Preference: Final Good Production: E 0 β t u(c t ) t=0 F (K, E) = K θ E ν, θ + ν 1 where E denotes energy input measured in its carbon content. In addition, the extraction cost of E is zero. Capital Accumulation (with 100 percent depreciation): K = F (K, E) + (1 δ)k C Law of motion of atmospheric carbon concentration: S = S + φ 0 E
10 One-Energy-Sector Model Externality and Uncertainty (elaborate) Introducing a stochastic variable γ, which reduces the end-of-period capital stock K by a factor of h(s, γ) = e S γ to K. That is, K = h(s, γ) K, The approximating distribution of γ is π(γ) = λe λγ. Let ˆπ(γ) be an alternative distribution, and m(γ) = ˆπ(γ) π(γ) be the likelihood ratio. The distance between ˆπ(γ) and π(γ) is measured by relative entropy ρ(ˆπ(γ), π(γ)) [m(γ) log m(γ)]π(γ)dγ.
11 One-Energy-Sector Model A Zero-Sum Dynamic Game We first focus on a robust version of social planner s problem and then show that the robust social optimal allocation is implemented via a Pigouvian tax in a decentralized economy. Two-person zero-sum dynamic game: In any period, The beginning-of-the-period capital K is given. The planner chooses E, production takes place and the planner chooses C. K and S evolve according to K = F (K, E) + (1 δ)k C and S = S + φ 0 E, respectively. The malevolent player chooses an alternative distribution ˆπ(γ) or, equivalently, m(γ), to minimize welfare. Accordingly, the next period K = h(s, γ) K.
12 One-Energy-Sector Model A Zero-Sum Dynamic Game (Continued) (elaborate) V (K, S) = max {C,E, K,S } min {u(c) m(γ) +β [m(γ)v (K, S ) + αm(γ) log m(γ) ] π(γ)dγ} s.t. K = F (K, E) C K = h(s, γ) K S = S + φ 0 E 1 = m(γ)π(γ)dγ
13 One-Energy-Sector Model A Zero-Sum Dynamic Game (Continued) αm(γ) log m(γ)π(γ)dγ = αρ(ˆπ(γ), π(γ)): Deviation from the approximating distribution will be penalized by adding αρ(ˆπ(γ), π(γ)) to the objective function. A greater α means a greater penalty associated with the deviation of γ from its approximating distribution, thus, a less concern about robustness.
14 One-Energy-Sector Model Robustness (the inner minimization problem) (Skip) Define the robustness part of the problem by [m(γ)v R(V )( K, S ) = min (K, S ) + αm(γ) log m(γ) ] π(γ)dγ m(γ) s.t. K = e S γ K 1 = m(γ)π(γ)dγ
15 One-Energy-Sector Model Robustness (Continued) (Skip) Suppose V ( ) takes the form V (K, S ) = f(s ) + Ā log(k ) + D, and subsititute it into the above problem, we obtain: and m (γ) = (1 S )e λs γ R(V )( K, S ) = f(s ) + Ā log( K ) + D + H(S ; α, Ā) where = Ā αλ and H(S ; α, Ā) = α log(1 S ) is the robust version externality of carbon.
16 One-Energy-Sector Model Optimal Choice (the outer maximization problem) (Skip) With the above results, the maximization problem can be written as V (K, S) = max {C,E, K,S } {log(c) + βr(v )( K, S )} or equivalently, f(s) + Ā log(k) + D = max C,E β[f(s ) + Ā log( K ) + D + H(S ; α, Ā)]} s.t. K = F (K, E) C S = S + φ 0 E
17 One-Energy-Sector Model Equilibrium Proposition 1: The two-person zero-sum dynamic game described by admits a unique feedback (Markov perfect) equilibrium, in which the equilibrium strategies are given by: C = (1 βθ)k θ E ν = (1 βθ)k θ [c E (1 S)] ν E = c E (1 S) S = S + φ 0 c E (1 S) ˆπ (γ) = m (γ)π(γ) = λ e λ γ where λ = λ(1 S ) = λ(1 φ 0 c E )(1 S) and ν(1 β) c E = [βα(1 βθ)+ν]φ 0 and = Ā αλ.
18 One-Energy-Sector Model Remarks V (K, S) is increasing in K, decreasing in S, and jointly concave in K and S. A greater concern of robustness (α ) is going to lower E, C and S. The worst case distribution is also exponential, ˆπ (γ) = λ e λ γ. Since λ < λ, the worst case mean of γ, (λ ) 1, is strictly greatly than the approximating mean, λ 1.
19 One-Energy-Sector Model Remarks (Continued) The marginal externality of Carbon emission, measured in the unit of utility and evaluated at E, is given by λ s = β V (K, S ) K E,S = ν c E (1 βθ)(1 S) = The marginal externality of Carbon emission, measured in the unit of comsuption goods and evaluated at E, is given by Λ s = λs u (C t ) = νkθ E ν 1. The marginal externality of Carbon emission, measured as a percentage of output and evaluated at E, is given by ˆΛ s = Λ s F (K, E) = ν E. ν (1 βθ)e.
20 One-Energy-Sector Model Decentralization We now turn to the decentralized problem. Suppose the government imposes a percentage tax τ t on emissions, E t. [ {u(c) + βêγ V (k, K, S ) + α log V (k, K, S) = max min c, k ˆπ(γ) s.t. c + k = r(k, S)k + τ(k, S)E(τ) + π profit K = G(K, S) k = k γs k K = K γs K S = S + φ 0E(S) ( ˆπ(γ) π(γ) )]}
21 One-Energy-Sector Model Decentralization (Continued) Proposition 2 Suppose the government sets E = c E (1 S) or, equivalently, τ t = Λ s, and the tax proceeds are rebated lump-sum to the representative consumer. Then the competitive equilibrium allocation coincides with the solution to the robust planner s problem. That is, c = C = (1 βθ)k θ [c E (1 S)] ν.
22 Complete Model Outline 1 Introduction 2 One-Energy-Sector Model 3 Complete Model 4 Numerical Results
23 Complete Model Complete Model In this section, we extend the analytical one-sector model as follows: Three Energy Sectors: 1. The oil sector produces oil (E 1 ) at zero cost but is subject to a resource feasibility constraint, R 0 > The coal and the green energy sector use linear technologies E i = A i N i ; i = 2, 3. The stock of coal is assumed to be infinity. 3. A 2 N 2 and A 3 N 3 grow at a rate of two percent per year.
24 Complete Model Complete Model The composite energy is produced by E = (κ 1 E ρ 1 + κ 2E ρ 2 + κ 3E ρ 3 )1/ρ. As in GHTK, suppose S = P + T where P and T are the permanent and temporary components of S, respectively. P = P + φ L (E 1 + E 2 ) and T = (1 φ)t + (1 φ L )φ 0 (E 1 + E 2 ).
25 Complete Model Complete Model Now assume that the approximating distribution of γ is normal with mean γ and variance σ 2 ; i.e., π N ( γ, σ 2 ). It follows from the inner-minimization problem that H(S ; α, ˆπ (γ) N ( γ + Āσ2 α S 2, σ 2 ) Āσ2 Ā) = ( γ + S )ĀS 2α
26 Complete Model Social Planner f(n, P, T, R) = max E 1,E 2,E 3,E,P,T,S,R s.t. 1 { 1 βθ log[(1 E 2 A 2 N E 3 A 3 N )1 θ ν E ν ] +β[f(n, P, T, R ) + H(S ; α, Ā)]} E = (κ 1 E ρ 1 + κ 2E ρ 2 + κ 3E ρ 3 )1/ρ N = (1 + g)n R = R E 1 0 P = P + φ L (E 1 + E 2 ) T = (1 φ)t + (1 φ L )φ 0 (E 1 + E 2 ) S = P + T
27 Complete Model FONC and Externalities (skip) We calculate the marginal externalities caused by P and T respectively, and show that the externality caused by Carbon emission is a weighted sum of the two. ˆΛ P = (1 βθ) f P = θ γ + j=1 ˆΛ T = (1 βθ) f T = θ γ + j=1 ˆΛ S = φ ˆΛP L + (1 φ L)φ 0 ˆΛ T 1 φ [ lim ˆΛ S φl β α + t = θ γ 1 β + (1 φ ] L)φ 0 β 1 (1 φ)β β j 1 S t+j [β(1 φ)] j 1 S t+j
28 Complete Model FONC and Externalities (skip) FONC s: νκ 1 E 1 ρ 1 E ˆΛ S ρ = β νκ 2 E 1 ρ [ ] νκ 1 (E 1 )1 ρ (E ) ρ (ˆΛ S ), ( E 1 ) 2 E ˆΛ S = 1 θ ν, ρ A 2 N 0 ( E 2 ) νκ 3 E 1 ρ = 1 θ ν. 3 E ρ A 3 N 0 ( E 3 )
29 Numerical Results Outline 1 Introduction 2 One-Energy-Sector Model 3 Complete Model 4 Numerical Results
30 Numerical Results Calibration Table: Calibration Summary Parameter φ φ L φ 0 θ Value Parameter ν β ρ 1 + g Value Parameter P 0 T 0 R 0 κ 1 Value Parameter κ 2 A 2,0 A 3,0 λ 1 Value ,693 1,
31 Numerical Results Optimal Energy Path when R 0 = 253.8GtC (The same as in GHKT) Figure: Optimal Use of Energy when R 0 = 253.8
32 Numerical Results Optimal Energy Path when R 0 = 8000GtC (Including Methane) Figure: Optimal Use of Energy when R 0 = 8000
33 Numerical Results Optimal Energy Path when R 0 = Figure: Optimal Use of Energy when R 0 =
34 Numerical Results More Graphs for R 0 = Figure: Global Average Temperature when R 0 =
35 Numerical Results More Graphs for R 0 = (Continued) Figure: The Path of Output and Capital when R 0 =
36 Numerical Results Thank You!
Robust Optimal Taxation and Environmental Externalities
Robust Optimal Taxation and Environmental Externalities Xin Li Borghan Narajabad Ted Loch-Temzelides Department of Economics Rice University Outline Outline 1 Introduction 2 One-Energy-Sector Model 3 Complete
More informationRobust Dynamic Energy Use and Climate Change
Working Paper Robust Dynamic Energy Use and Climate Change Xin Li, Ph.D. Economist, International Monetary Fund Borghan Narajabad, Ph.D. Economist, Federal Reserve Board Ted Temzelides, Ph.D. Professor
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 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 informationEconomic Growth: Lecture 9, Neoclassical Endogenous Growth
14.452 Economic Growth: Lecture 9, Neoclassical Endogenous Growth Daron Acemoglu MIT November 28, 2017. Daron Acemoglu (MIT) Economic Growth Lecture 9 November 28, 2017. 1 / 41 First-Generation Models
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 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 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 informationRamsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path
Ramsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path Ryoji Ohdoi Dept. of Industrial Engineering and Economics, Tokyo Tech This lecture note is mainly based on Ch. 8 of Acemoglu
More informationA simple macro dynamic model with endogenous saving rate: the representative agent model
A simple macro dynamic model with endogenous saving rate: the representative agent model Virginia Sánchez-Marcos Macroeconomics, MIE-UNICAN Macroeconomics (MIE-UNICAN) A simple macro dynamic model with
More informationHomework 3 - Partial Answers
Homework 3 - Partial Answers Jonathan Heathcote Due in Class on Tuesday February 28th In class we outlined two versions of the stochastic growth model: a planner s problem, and an Arrow-Debreu competitive
More informationNews Driven Business Cycles in Heterogenous Agents Economies
News Driven Business Cycles in Heterogenous Agents Economies Paul Beaudry and Franck Portier DRAFT February 9 Abstract We present a new propagation mechanism for news shocks in dynamic general equilibrium
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 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 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 informationA Global Economy-Climate Model with High Regional Resolution
A Global Economy-Climate Model with High Regional Resolution Per Krusell IIES, University of Göteborg, CEPR, NBER Anthony A. Smith, Jr. Yale University, NBER March 2014 WORK-IN-PROGRESS!!! Overall goals
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 informationCapital Structure and Investment Dynamics with Fire Sales
Capital Structure and Investment Dynamics with Fire Sales Douglas Gale Piero Gottardi NYU April 23, 2013 Douglas Gale, Piero Gottardi (NYU) Capital Structure April 23, 2013 1 / 55 Introduction Corporate
More informationLecture 15. Dynamic Stochastic General Equilibrium Model. Randall Romero Aguilar, PhD I Semestre 2017 Last updated: July 3, 2017
Lecture 15 Dynamic Stochastic General Equilibrium Model Randall Romero Aguilar, PhD I Semestre 2017 Last updated: July 3, 2017 Universidad de Costa Rica EC3201 - Teoría Macroeconómica 2 Table of contents
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 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 informationThe economy is populated by a unit mass of infinitely lived households with preferences given by. β t u(c Mt, c Ht ) t=0
Review Questions: Two Sector Models Econ720. Fall 207. Prof. Lutz Hendricks A Planning Problem The economy is populated by a unit mass of infinitely lived households with preferences given by β t uc Mt,
More informationSuggested Solutions to Homework #3 Econ 511b (Part I), Spring 2004
Suggested Solutions to Homework #3 Econ 5b (Part I), Spring 2004. Consider an exchange economy with two (types of) consumers. Type-A consumers comprise fraction λ of the economy s population and type-b
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 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 informationHigh-dimensional Problems in Finance and Economics. Thomas M. Mertens
High-dimensional Problems in Finance and Economics Thomas M. Mertens NYU Stern Risk Economics Lab April 17, 2012 1 / 78 Motivation Many problems in finance and economics are high dimensional. Dynamic Optimization:
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 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 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 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 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 informationReal Business Cycle Model (RBC)
Real Business Cycle Model (RBC) Seyed Ali Madanizadeh November 2013 RBC Model Lucas 1980: One of the functions of theoretical economics is to provide fully articulated, artificial economic systems that
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 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 informationslides chapter 3 an open economy with capital
slides chapter 3 an open economy with capital Princeton University Press, 2017 Motivation In this chaper we introduce production and physical capital accumulation. Doing so will allow us to address two
More informationEC487 Advanced Microeconomics, Part I: Lecture 5
EC487 Advanced Microeconomics, Part I: Lecture 5 Leonardo Felli 32L.LG.04 27 October, 207 Pareto Efficient Allocation Recall the following result: Result An allocation x is Pareto-efficient if and only
More informationEcon 204A: Section 3
Econ 204A: Section 3 Ryan Sherrard University of California, Santa Barbara 18 October 2016 Sherrard (UCSB) Section 3 18 October 2016 1 / 19 Notes on Problem Set 2 Total Derivative Review sf (k ) = (δ +
More informationLecture 3: Growth with Overlapping Generations (Acemoglu 2009, Chapter 9, adapted from Zilibotti)
Lecture 3: Growth with Overlapping Generations (Acemoglu 2009, Chapter 9, adapted from Zilibotti) Kjetil Storesletten September 5, 2014 Kjetil Storesletten () Lecture 3 September 5, 2014 1 / 56 Growth
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 informationIntroduction to Continuous-Time Dynamic Optimization: Optimal Control Theory
Econ 85/Chatterjee Introduction to Continuous-ime Dynamic Optimization: Optimal Control heory 1 States and Controls he concept of a state in mathematical modeling typically refers to a specification of
More informationSecond-Best Environmental Taxation In Dynamic Models Without Commitment
Second-Best Environmental Taxation In Dynamic Models Without Commitment Alex Schmitt July 10, 2013 WORK IN PROGRESS Abstract This paper analyzes the interaction between optimal environmental regulation
More information2. What is the fraction of aggregate savings due to the precautionary motive? (These two questions are analyzed in the paper by Ayiagari)
University of Minnesota 8107 Macroeconomic Theory, Spring 2012, Mini 1 Fabrizio Perri Stationary equilibria in economies with Idiosyncratic Risk and Incomplete Markets We are now at the point in which
More informationOrganizational Equilibrium with Capital
Organizational Equilibrium with Capital Marco Bassetto, Zhen Huo, and José-Víctor Ríos-Rull FRB of Chicago, Yale University, University of Pennsylvania, UCL, CAERP Fiscal Policy Conference Mar 20, 2018
More informationSimple New Keynesian Model without Capital
Simple New Keynesian Model without Capital Lawrence J. Christiano March, 28 Objective Review the foundations of the basic New Keynesian model without capital. Clarify the role of money supply/demand. Derive
More informationDynamic stochastic general equilibrium models. December 4, 2007
Dynamic stochastic general equilibrium models December 4, 2007 Dynamic stochastic general equilibrium models Random shocks to generate trajectories that look like the observed national accounts. Rational
More information4- Current Method of Explaining Business Cycles: DSGE Models. Basic Economic Models
4- Current Method of Explaining Business Cycles: DSGE Models Basic Economic Models In Economics, we use theoretical models to explain the economic processes in the real world. These models de ne a relation
More informationPermanent Income Hypothesis Intro to the Ramsey Model
Consumption and Savings Permanent Income Hypothesis Intro to the Ramsey Model Lecture 10 Topics in Macroeconomics November 6, 2007 Lecture 10 1/18 Topics in Macroeconomics Consumption and Savings Outline
More informationGrowth Theory: Review
Growth Theory: Review Lecture 1.1, Exogenous Growth Topics in Growth, Part 2 June 11, 2007 Lecture 1.1, Exogenous Growth 1/76 Topics in Growth, Part 2 Growth Accounting: Objective and Technical Framework
More informationAssumption 5. The technology is represented by a production function, F : R 3 + R +, F (K t, N t, A t )
6. Economic growth Let us recall the main facts on growth examined in the first chapter and add some additional ones. (1) Real output (per-worker) roughly grows at a constant rate (i.e. labor productivity
More informationEconomic Growth: Lectures 5-7, Neoclassical Growth
14.452 Economic Growth: Lectures 5-7, Neoclassical Growth Daron Acemoglu MIT November 7, 9 and 14, 2017. Daron Acemoglu (MIT) Economic Growth Lectures 5-7 November 7, 9 and 14, 2017. 1 / 83 Introduction
More informationSuggested Solutions to Homework #6 Econ 511b (Part I), Spring 2004
Suggested Solutions to Homework #6 Econ 511b (Part I), Spring 2004 1. (a) Find the planner s optimal decision rule in the stochastic one-sector growth model without valued leisure by linearizing the Euler
More informationUNIVERSITY OF VIENNA
WORKING PAPERS Cycles and chaos in the one-sector growth model with elastic labor supply Gerhard Sorger May 2015 Working Paper No: 1505 DEPARTMENT OF ECONOMICS UNIVERSITY OF VIENNA All our working papers
More informationVolume 30, Issue 3. Ramsey Fiscal Policy and Endogenous Growth: A Comment. Jenn-hong Tang Department of Economics, National Tsing-Hua University
Volume 30, Issue 3 Ramsey Fiscal Policy and Endogenous Growth: A Comment Jenn-hong Tang Department of Economics, National Tsing-Hua University Abstract Recently, Park (2009, Economic Theory 39, 377--398)
More informationThe welfare cost of energy insecurity
The welfare cost of energy insecurity Baltasar Manzano (Universidade de Vigo) Luis Rey (bc3) IEW 2013 1 INTRODUCTION The 1973-1974 oil crisis revealed the vulnerability of developed economies to oil price
More information1. Using the model and notations covered in class, the expected returns are:
Econ 510a second half Yale University Fall 2006 Prof. Tony Smith HOMEWORK #5 This homework assignment is due at 5PM on Friday, December 8 in Marnix Amand s mailbox. Solution 1. a In the Mehra-Prescott
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 informationOptimal Simple And Implementable Monetary and Fiscal Rules
Optimal Simple And Implementable Monetary and Fiscal Rules Stephanie Schmitt-Grohé Martín Uribe Duke University September 2007 1 Welfare-Based Policy Evaluation: Related Literature (ex: Rotemberg and Woodford,
More informationSchumpeterian Growth Models
Schumpeterian Growth Models Yin-Chi Wang The Chinese University of Hong Kong November, 2012 References: Acemoglu (2009) ch14 Introduction Most process innovations either increase the quality of an existing
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 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 informationEquilibrium in the growth model with an endogenous labor-leisure choice
Equilibrium in the growth model with an endogenous labor-leisure choice Aditya Goenka Manh-Hung Nguyen April 6, 2011 Abstract We prove the existence of competitive equilibrium in an optimal growth model
More informationTechnical appendices: Business cycle accounting for the Japanese economy using the parameterized expectations algorithm
Technical appendices: Business cycle accounting for the Japanese economy using the parameterized expectations algorithm Masaru Inaba November 26, 2007 Introduction. Inaba (2007a) apply the parameterized
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 informationHousing in a two sector dynastic altruism model
Housing in a two sector dynastic altruism model Xavier Raurich Universitat de Barcelona Fernando Sanchez-Losada Universitat de Barcelona December 2008 Introduction Aims: 1. Study the e ects of housing
More informationLecture 2 The Centralized Economy
Lecture 2 The Centralized Economy Economics 5118 Macroeconomic Theory Kam Yu Winter 2013 Outline 1 Introduction 2 The Basic DGE Closed Economy 3 Golden Rule Solution 4 Optimal Solution The Euler Equation
More informationStructural change in a two-sector model of the climate and the economy
Structural change in a two-sector model of the climate and the economy Gustav Engström May 5, 202 Abstract This paper introduces issues concerning substitution possibilities among goods into a two-sector
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 informationAdvanced Economic Growth: Lecture 3, Review of Endogenous Growth: Schumpeterian Models
Advanced Economic Growth: Lecture 3, Review of Endogenous Growth: Schumpeterian Models Daron Acemoglu MIT September 12, 2007 Daron Acemoglu (MIT) Advanced Growth Lecture 3 September 12, 2007 1 / 40 Introduction
More informationEndogenous Growth. Lecture 17 & 18. Topics in Macroeconomics. December 8 & 9, 2008
Review: Solow Model Review: Ramsey Model Endogenous Growth Lecture 17 & 18 Topics in Macroeconomics December 8 & 9, 2008 Lectures 17 & 18 1/29 Topics in Macroeconomics Outline Review: Solow Model Review:
More informationMacroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PS 5, preliminary version
Macroeconomics I, UPF Professor ntonio Ciccone SOUTIONS PS 5, preliminary version 1 The Solow K model with transitional dynamics Consider the following Solow economy: production is determined by Y F (K,
More informationOptimal Taxation with Capital Accumulation and Wage Bargaining
ömmföäflsäafaäsflassflassflas ffffffffffffffffffffffffffffffffffff Discussion Papers Optimal Taxation with Capital Accumulation and Wage Bargaining Tapio Palokangas University of Helsinki and HECER Discussion
More informationLecture 15 Real Business Cycle Model. Noah Williams
Lecture 15 Real Business Cycle Model Noah Williams University of Wisconsin - Madison Economics 702/312 Real Business Cycle Model We will have a shock: change in technology. Then we will have a propagation
More informationMacro I - Practice Problems - Growth Models
Macro I - Practice Problems - Growth Models. Consider the infinitely-lived agent version of the growth model with valued leisure. Suppose that the government uses proportional taxes (τ c, τ n, τ k ) on
More informationEC9A2 Advanced Macro Analysis - Class #1
EC9A2 Advanced Macro Analysis - Class #1 Jorge F. Chávez University of Warwick October 29, 2012 Outline 1. Some math 2. Shocking the Solow model 3. The Golden Rule 4. CES production function (more math)
More informationPractical Dynamic Programming: An Introduction. Associated programs dpexample.m: deterministic dpexample2.m: stochastic
Practical Dynamic Programming: An Introduction Associated programs dpexample.m: deterministic dpexample2.m: stochastic Outline 1. Specific problem: stochastic model of accumulation from a DP perspective
More information1. Money in the utility function (start)
Monetary Economics: Macro Aspects, 1/3 2012 Henrik Jensen Department of Economics University of Copenhagen 1. Money in the utility function (start) a. The basic money-in-the-utility function model b. Optimal
More informationOptimal Inflation Stabilization in a Medium-Scale Macroeconomic Model
Optimal Inflation Stabilization in a Medium-Scale Macroeconomic Model Stephanie Schmitt-Grohé Martín Uribe Duke University 1 Objective of the Paper: Within a mediumscale estimated model of the macroeconomy
More informationMacroeconomics Qualifying Examination
Macroeconomics Qualifying Examination August 2015 Department of Economics UNC Chapel Hill Instructions: This examination consists of 4 questions. Answer all questions. If you believe a question is ambiguously
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 information14.452: Introduction to Economic Growth Problem Set 4
14.452: Introduction to Economic Growth Problem Set 4 Daron Acemoglu Due date: December 5, 12pm noon Please only hand in Question 3, which will be graded. The rest will be reviewed in the recitation but
More informationWelfare Equivalent NNP and Habit Formation
Welfare Equivalent NNP and Habit Formation Thomas Aronsson and Karl-Gustaf Löfgren Department of Economics, Umeå University, SE - 901 87 Umeå, Sweden April 2006 Abstract This note concerns the importance
More informationLecture notes on modern growth theory
Lecture notes on modern growth theory Part 2 Mario Tirelli Very preliminary material Not to be circulated without the permission of the author October 25, 2017 Contents 1. Introduction 1 2. Optimal economic
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 informationDeterministic Models
Deterministic Models Perfect foreight, nonlinearities and occasionally binding constraints Sébastien Villemot CEPREMAP June 10, 2014 Sébastien Villemot (CEPREMAP) Deterministic Models June 10, 2014 1 /
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 informationExpanding Variety Models
Expanding Variety Models Yin-Chi Wang The Chinese University of Hong Kong November, 2012 References: Acemoglu (2009) ch13 Introduction R&D and technology adoption are purposeful activities The simplest
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 informationErgodicity and Non-Ergodicity in Economics
Abstract An stochastic system is called ergodic if it tends in probability to a limiting form that is independent of the initial conditions. Breakdown of ergodicity gives rise to path dependence. We illustrate
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 informationThe Ramsey Model. Alessandra Pelloni. October TEI Lecture. Alessandra Pelloni (TEI Lecture) Economic Growth October / 61
The Ramsey Model Alessandra Pelloni TEI Lecture October 2015 Alessandra Pelloni (TEI Lecture) Economic Growth October 2015 1 / 61 Introduction Introduction Introduction Ramsey-Cass-Koopmans model: di ers
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 informationComputing risk averse equilibrium in incomplete market. Henri Gerard Andy Philpott, Vincent Leclère
Computing risk averse equilibrium in incomplete market Henri Gerard Andy Philpott, Vincent Leclère YEQT XI: Winterschool on Energy Systems Netherlands, December, 2017 CERMICS - EPOC 1/43 Uncertainty on
More informationGrowth Theory: Review
Growth Theory: Review Lecture 1, Endogenous Growth Economic Policy in Development 2, Part 2 March 2009 Lecture 1, Exogenous Growth 1/104 Economic Policy in Development 2, Part 2 Outline Growth Accounting
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 13, Stochastic Growth
14.452 Economic Growth: Lecture 13, Stochastic Growth Daron Acemoglu MIT December 10, 2013. Daron Acemoglu (MIT) Economic Growth Lecture 13 December 10, 2013. 1 / 52 Stochastic Growth Models Stochastic
More informationDepartment of Economics The Ohio State University Final Exam Questions and Answers Econ 8712
Prof. Peck Fall 20 Department of Economics The Ohio State University Final Exam Questions and Answers Econ 872. (0 points) The following economy has two consumers, two firms, and three goods. Good is leisure/labor.
More informationMarkov-Perfect Optimal Fiscal Policy: The Case of Unbalanced Budgets
Working Paper 2-30 Departamento de Economía Economic Series Universidad Carlos III de Madrid October, 202 Calle Madrid, 26 28903 Getafe (Spain) Fax (34) 96249875 Markov-Perfect Optimal Fiscal Policy: The
More informationMacroeconomics Field Exam. August 2007
Macroeconomics Field Exam August 2007 Answer all questions in the exam. Suggested times correspond to the questions weights in the exam grade. Make your answers as precise as possible, using graphs, equations,
More informationChapter 3 Task 1-4. Growth and Innovation Fridtjof Zimmermann
Chapter 3 Task 1-4 Growth and Innovation Fridtjof Zimmermann Recept on how to derive the Euler-Equation (Keynes-Ramsey-Rule) 1. Construct the Hamiltonian Equation (Lagrange) H c, k, t, μ = U + μ(side Condition)
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 information