Foundations for the New Keynesian Model. Lawrence J. Christiano
|
|
- Lily Robinson
- 5 years ago
- Views:
Transcription
1 Foundations for the New Keynesian Model Lawrence J. Christiano
2 Objective Describe a very simple model economy with no monetary frictions. Describe its properties. markets work well Modify the model dlto include price setting frictions. Now markets won t necessarily work so well, unless monetary policy is good.
3 Model Household preferences: E 0 t0 t logc t exp t N t, t t t, t ~iidn0, 2
4 Production Final output requires lots of intermediate inputs: Y t Yi,t 0 Production of intermediate inputs: di, Y a t a a ~iidn0, 2 i,t e N i,t, Δa t Δa t t, t a Constraint on allocation of labor: N it di N t 0
5 Efficient Allocation of Total Labor Suppose total labor,, is fixed. N t What is the best way to allocate N t among the various activities, 0 i? Answer: allocate labor equally across all the activities N it N t, all i
6 Suppose Labor Not Allocated Equally Example: N it 2N t i 0, 2 2 N t i,,0. 2 Note that this is a particular distribution of labor across activities: N di 2N it t 2 N N 2 2 t t 0
7 Labor Not Allocated Equally, cnt d Y t Y i,t 0 di 0 2 Y i,t e a t 0 2 di N i,t Yi,t 2 di 2 di Ni,t di e a 2 t 2N t di 0 2 Nt 2 e a t N t di 2 2 a t e N t di di e a t N t f
8 f Efficient Resource Allocation Means Equal Labor Across All Sectors f α
9 Economy with Efficient N Allocation Efficiency dictates N it N t all i So, with efficient production: Y a t e t N t Resource constraint: Preferences: C t Y t E 0 t0 N t logc t t exp t, ~iid, t t, t
10 Efficient Determination of Labor Lagrangian: max E 0 C t,n t t0 t logc t exp t N t uc t,n t, t t e a t N t C t First order conditions: or: u c C t,n t, t t, u n C t,n t, t t e a t 0 marginal cost of labor in consumption units u n,t u c,t a t u n,t u c,t e 0 du dnt du dct dc t dnt marginal product of labor e a t
11 Efficient Determination of Labor, cont d Solving the fonc s: u n,t u c,t e a t C t exp t N e a t t e a t N t exp t N t e a t N t exp t Note: C t exp a t t Labor responds to preference shock, not to tech shock
12 Response to a Jump in a consumption Higher a Indifference curve Budget constraint Leisure, -N
13 Decentralizing the Model Give households budget constraints and place them in markets. Give the production functions to firms and suppose that they seek to maximize i profits.
14 Solve: Subject to: Households t N t maxe 0 logc t exp t, t0 bonds purchases in t wage rate profits (real) interest on bonds C t B t w t N t t r t B t First order conditions: u n,t u c,t C t exp t N t w t marginal cost of working equals marginal benefit u c,t E t u c,t r t marginal cost of saving equals marginal benefit
15 Final Good Firms Final good firms buy Y i,t, i 0,, at given prices,, to maximize profits: P i,t Y t P i,t Y i,t di 0 Subject to Y t Yi,t 0 di Fonc s: P i,t Y t Y i,t Y i,t P i,t Y t, Pi,t di 0
16 Intermediate Good Firms Y i,t For each there is a single producer who is a monopolist in the product market and hires labor, in competitive labor markets. N i,t Marginal cost of production: (real) marginal costs t dcost dwor ker doutput dwor ker subsidy payment to firm expa t wt t Subsidy will be required to ensure markets work efficiently.
17 Intermediate Good Firms Demand curve P i,t Y i,t P i,t Y t Marginal cost, s t Marginal revenue Y i,t
18 ith Intermediate Good Firm Problem: max Nit P it Y it s t Y it Subject to demand for : Problem: max N it Y i,t Y i,t P i,t Y t P it P i,t Y t s t P i,t Y t fonc : P it Y t s t P i,t Y t 0 P it s t price is markup over marginal cost Note: all prices are the same, so resources allocated efficiently across intermediate good firms. P i,t P j,t, because Pi,t di 0
19 Equilibrium Pulling things together: w s t t expa t household fonc if u n,t u c,t expa t. u n,t u c,t expa t If proper subsidy is provided to monopolists, employment is efficient: if, then u n,t u c,t expa t
20 Equilibrium Allocations With efficient subsidy, u n,t u c,t functional form Ct exp t N t resource constraint expat exp t N t expa t N t exp t t C a t t e N t exp ep a t Bond marketclearing implies: B t 0 always
21 Interest Rate in Equilibrium Interest rate backed out of household intertemporal Euler equation: u c,t E t u c,t r t C E t r t C t t r t C E t t E t expc t c t C t E t exp a t a t t t exp E Δa t t, V t 2 a ep t a t V logr t log E t c t c t Δa t t t 2 V
22 Dynamic Properties of the Model Response to.0 Technology Shock in Period x 0-3 Response to.0 Preference Shock in Period log C t (a t - a t- ) = 0.75(a t- - a t-2 ) + epsa t log C t τ t = 0.5τ t- + epstau t t t interest rate x 0-3 interest rate r t log, r log r t = -logβ a t- 9 t t- r t log, r log r t = -logβ - (0.5 - )τ t /( + ) t t
23 Key Features of Equilibrium Allocations Allocations efficient (as long as monopoly power neutralized) Employment does not respond to technology Improvement in technology raises marginal product of labor and marginal cost of labor by same amount. First best consumption not a function of intertemporal considerations Discount rate irrelevant. Anticipated future values of shocks irrelevant. Natural rate of interest steers consumption and p employment towards their natural levels.
24 Introducing Price Setting Frictions (Clarida Gali Gertler Gertler Model) Households maximize: E 0 t0 Subject to: logc t exp t N t, t t t, t ~iid, P t C t B t W t N t R t B t T t Intratemporal first order condition: C N W t C t exp t N t W t P t
25 Household Intertemporal FONC Condition: or E t u c,t u c,t R t t C t E R t t C t t E t explogr t log t Δc t explogr t E t t E t Δc t, c t logc t take log of both sides: or 0 log r t E t t E t Δc t, r t logr t or c t log r t E t t c t
26 Final Good Firms Buy at prices and sell for Y i,t, i 0, P i,t Y t P t Take all prices as given (competitive) Profits: Production function: P t Y t P i,t Y i,t di 0 Y t Yi,t 0 di,, First order condition: Y i,t Y t P i,t P t P t Pi,t di 0
27 Intermediate Good Firms Each ith good produced by a single monopoly producer. Demand curve: Technology: Y i,t Y t P i,t P t Calvo Price setting Friction Y i,t expa t N i,t, Δa t Δa t t a, P i,t P t P i,t with probability with probability,
28 Marginal Cost real marginal cost s t dcost dwor ker doutput dwor ker W t/p t expa t in efficient setting C t exp t N t expa t
29 The Intermediate Firm s Decisions ith firm is required to satisfy whatever demand shows up at its posted price. It s only real decision is to adjust price whenever the opportunity arises.
30 Intermediate Good Firm Present tdiscounted d value of firm profits: period tj profits sent to household E t j0 j marginal value of dividends to householdu c,tj /P tj tj revenues P i,tj Y i,tj totalt cost P tj s tj Y i,tj Each of the firms that can optimize price choose P to optimize P t in selecting price, firm only cares about future states in which it can t reoptimize E t j j tj P ty t i,tj P tj s tj Y i,tj. j0
31 Intermediate Good Firm Problem Substitute t out the demand dcurve: E t j tj P ty i,tj P tj s tj Y i,tj j0 j0 E t j tj Y tj P tj P t P tj s tj P t. Differentiate with respect to : or E t j0 j tj Y tj P tj P t P tj s tj P t 0, j P t E t tj Y tj P tj s Ptj tj 0. j0 P t
32 Intermediate Good Firm Problem Objective: E t j u C tj Y tj P P t tj s tj 0. P tj P tj j0 or j P t E t P tj Ptj s tj 0. j0 E t j0 j X t,j p tx t,j s tj 0, p t P t, X P t,j t tj tj t, j tj tj t, j 0., X t,j X t,j, j 0 t
33 Intermediate Good Firm Problem Want p t in: E t j0 j X t,j p tx t,j s tj 0 Solution: p t E t j0 j X t,j E t j X t,j j0 s tj K t F t But, still need expressions for K t, F t.
34 K t E t j X t,j j00 s tj s t E t j X t,j t j t s tj s t E t j X t,j s tj t t j0 E t by LIME s t E t E t t j X t,j s tj j0 exactly K t! s t E t t E t j X t,j j0 0 s tj s t E t t Kt
35 From previous slide: Kt K t s t E t K t. t Substituting out for marginal cost: dcost/dlabor s t W t /P t doutput/dlabor expa t W t Pt by household optimization exp t N t C t expa t.
36 In Sum solution: Where: p t E t j0 j X t,j E t j0 j X t,j s tj K t, F t F t K t t exp t N t C t expa t E t t Kt. F F j t E t X t,j E t F t t j0
37 To Characterize Equilibrium Have equations characterizing optimization by firms and households. Still need: Expression for all the prices. Prices, P i,t,0 i, will all be different because of the price setting frictions. i Relationship between aggregate employment and aggregate output not simple becauseof price distortions: Y a t t e N t, in general This part of the analysis is the reason why it made Cl Calvo famous it s not easy.
38 Going for Prices Aggregate price relationship P t P i,t di 0 P di i,t firms that reoptimize price P i,t firms that don t reoptimize price di all reoptimizers choose same price P t P i,t di firms that don t reoptimize price In principle, to solve the model need all the prices, P t, P i,t,, 0 i Fortunately, that won t be necessary.
39 Key insight firms that don t reoptimize price in t P i,t di add over prices, weighted by # of firms posting that price number of firms thatt hd had price, P, in t and were not able to reoptimize i in t f t,t P d
40 Applying the Insight By Calvo randomization assumption total number of firms with price P in t f t,t f t, for all Substituting: P i,t di firms that don t reoptimize price f t,t P d f t P d P t Something hard got very simple!
41 p t Expression for in terms of aggregate inflation Conclude that this relationship holds between prices: P t P t P t. Only two variables here! Divide by P : P t Rearrange: p t t t p t t
42 Relation Between Aggregate Output and Aggregate Inputs Technically, there is no aggregate production function in this model If you know how many people are working, N, and the state of technology, a, you don t have enough information to know what Y is. Price frictions imply that resources will not be efficiently allocated among different inputs. Implies Y low for given a and N. How low? Tak Yun (JME) gave a simple answer.
43 Tak Yun Algebra Y t 0 Yi,t di 0 At N i,t di labor market clearing At N t demand curve Y P i,t Yt di 0 P t Y t P t Pi,t di 0 Calvo insight Y t P t P t Where: P t Pi,t 0 di P t P t
44 Relationship Between Agg Inputs and Agg Output Rewriting previous equation: Y t P t P t Yt p t e a t N t, efficiency distortion : p t : P i,t P j,t,, all i,j
45 Example of Efficiency Distortion P j,t P P 0 j 2 P 2 j. p P t t P P t 0.5, 0 P 2 P logp /P 2
46 Collecting Equilibrium Conditions Price setting: K t exp t N t C t A t E t t K t () F t E t t F t (2) Intermediate good firm optimality and restriction across prices: p t by firm optimality Kt F t p t by restriction across prices t (3)
47 Equilibrium Conditions Law of motion of (Tak Yun) distortion: p t t t (4) p t Household IntertemporalCondition: E C t t C t R t t (5) Aggregate inputs and output: C t p t e a t N t (6) 6 equations, 8 unknowns:, C t, p t,nn t, t, K t, F t, R t System under determined!
48 Underdetermined System Not surprising: we added a variable, the nominal rate of interest. Also, we re counting subsidy as among the unknowns. Have two extra policy variables. One way to pin them down: compute optimal policy.
49 Ramsey Optimal Policy 6 equations in 8 unknowns.. Many configurations i of the 8 unknowns that satisfy the 6 equations. Look kfor the best configurations (Ramsey optimal) Value of tax subsidy and of R represent optimal policy Finding the Ramsey optimal setting of the 6 variables ibl involves solving li a simple Lagrangian optimization problem.
50 Ramsey Problem max E 0,p t,c t,n t,r t, t,f t,k t t0 0 t logc t exp t N t t E R t t Ct C t C t t C t 2t pt t t p t 3t E t t F t F t 4t C t exp t N t a t e 5t F t t Kt E t t K t K t 6t C t p t e a t N t
51 Solving the Ramsey Problem (surprisingly easy in this case) First, substitute out consumption everywhere defines R defines F defines tax defines K max E 0 t logn t logp exp t N t t,p t,n t,r t, t,f t,k t 0 t0 e t p E at R t t N t t e a t Nt p t 2t pt t t t p t 3t E t t F t F t 4t exp t N t p t E t t K t K t 5t F t t Kt
52 Solving the Ramsey Problem, cnt d Simplified problem: max E 0 t logn t logp exp t N t t t,p t,n t t0 2t pt t t p t First order conditions with respect to p t, t, N t p t 2,t t 2t, t p t p t, Nt exp t Substituting the solution for inflation into law of motion for price distortion: p t p t.
53 Solution to Ramsey Problem Eventually, price distortions eliminated, regardless of shocks p t When price distortions t p gone, so is inflation. t p t p t p t t N t exp Efficient ( first best ) allocations in real economy C t p t e a t N t. Consumption corresponds to efficient allocations in real economy, eventually when price distortions gone
54 Eventually, Optimal (Ramsey) Equilibrium and Efficient i Allocations in Real Economy Coincide id Convergence of price distortion , 0 r p-star p t p t
55 The Ramsey allocations are eventually the best allocations in the economy without price frictions (i.e., first best allocations ) Rf Refer to the Ramsey allocations as the natural allocations. Natural consumption, natural rate of interest, etc.
56 Preceding provides important foundations for Preceding provides important foundations for the construction of the New Keynesian model.
Foundations for the New Keynesian Model. Lawrence J. Christiano
Foundations for the New Keynesian Model Lawrence J. Christiano Objective Describe a very simple model economy with no monetary frictions. Describe its properties. markets work well Modify the model to
More informationSimple New Keynesian Model without Capital. Lawrence J. Christiano
Simple New Keynesian Model without Capital Lawrence J. Christiano Outline Formulate the nonlinear equilibrium conditions of the model. Need actual nonlinear conditions to study Ramsey optimal policy, even
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 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 informationSimple New Keynesian Model without Capital
Simple New Keynesian Model without Capital Lawrence J. Christiano Gerzensee, August 27 Objective Review the foundations of the basic New Keynesian model without capital. Clarify the role of money supply/demand.
More informationEquilibrium Conditions for the Simple New Keynesian Model
Equilibrium Conditions for the Simple New Keynesian Model Lawrence J. Christiano August 4, 04 Baseline NK model with no capital and with a competitive labor market. private sector equilibrium conditions
More informationThe Basic New Keynesian Model, the Labor Market and Sticky Wages
The Basic New Keynesian Model, the Labor Market and Sticky Wages Lawrence J. Christiano August 25, 203 Baseline NK model with no capital and with a competitive labor market. private sector equilibrium
More informationThe Labor Market in the New Keynesian Model: Incorporating a Simple DMP Version of the Labor Market and Rediscovering the Shimer Puzzle
The Labor Market in the New Keynesian Model: Incorporating a Simple DMP Version of the Labor Market and Rediscovering the Shimer Puzzle Lawrence J. Christiano April 1, 2013 Outline We present baseline
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 informationThe Labor Market in the New Keynesian Model: Foundations of the Sticky Wage Approach and a Critical Commentary
The Labor Market in the New Keynesian Model: Foundations of the Sticky Wage Approach and a Critical Commentary Lawrence J. Christiano March 30, 2013 Baseline developed earlier: NK model with no capital
More informationDeviant Behavior in Monetary Economics
Deviant Behavior in Monetary Economics Lawrence Christiano and Yuta Takahashi July 26, 2018 Multiple Equilibria Standard NK Model Standard, New Keynesian (NK) Monetary Model: Taylor rule satisfying Taylor
More informationMonetary Economics. Lecture 15: unemployment in the new Keynesian model, part one. Chris Edmond. 2nd Semester 2014
Monetary Economics Lecture 15: unemployment in the new Keynesian model, part one Chris Edmond 2nd Semester 214 1 This class Unemployment fluctuations in the new Keynesian model, part one Main reading:
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 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 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 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 informationThe Basic New Keynesian Model. Jordi Galí. June 2008
The Basic New Keynesian Model by Jordi Galí June 28 Motivation and Outline Evidence on Money, Output, and Prices: Short Run E ects of Monetary Policy Shocks (i) persistent e ects on real variables (ii)
More informationADVANCED MACROECONOMICS I
Name: Students ID: ADVANCED MACROECONOMICS I I. Short Questions (21/2 points each) Mark the following statements as True (T) or False (F) and give a brief explanation of your answer in each case. 1. 2.
More informationAdvanced Macroeconomics II. Monetary Models with Nominal Rigidities. Jordi Galí Universitat Pompeu Fabra April 2018
Advanced Macroeconomics II Monetary Models with Nominal Rigidities Jordi Galí Universitat Pompeu Fabra April 208 Motivation Empirical Evidence Macro evidence on the e ects of monetary policy shocks (i)
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 informationGali (2008), Chapter 3
Set 4 - The Basic New Keynesian Model Gali (28), Chapter 3 Introduction There are several key elements of the baseline model that are a departure from the assumptions of the classical monetary economy.
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 informationThe Basic New Keynesian Model. Jordi Galí. November 2010
The Basic New Keynesian Model by Jordi Galí November 2 Motivation and Outline Evidence on Money, Output, and Prices: Short Run E ects of Monetary Policy Shocks (i) persistent e ects on real variables (ii)
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 informationNeoclassical Business Cycle Model
Neoclassical Business Cycle Model Prof. Eric Sims University of Notre Dame Fall 2015 1 / 36 Production Economy Last time: studied equilibrium in an endowment economy Now: study equilibrium in an economy
More informationLecture 3, November 30: The Basic New Keynesian Model (Galí, Chapter 3)
MakØk3, Fall 2 (blok 2) Business cycles and monetary stabilization policies Henrik Jensen Department of Economics University of Copenhagen Lecture 3, November 3: The Basic New Keynesian Model (Galí, Chapter
More informationWORKING PAPER NO INTEREST RATE VERSUS MONEY SUPPLY INSTRUMENTS: ON THE IMPLEMENTATION OF MARKOV-PERFECT OPTIMAL MONETARY POLICY
WORKING PAPER NO. 07-27 INTEREST RATE VERSUS MONEY SUPPLY INSTRUMENTS: ON THE IMPLEMENTATION OF MARKOV-PERFECT OPTIMAL MONETARY POLICY Michael Dotsey Federal Reserve Bank of Philadelphia Andreas Hornstein
More informationStagnation Traps. Gianluca Benigno and Luca Fornaro
Stagnation Traps Gianluca Benigno and Luca Fornaro May 2015 Research question and motivation Can insu cient aggregate demand lead to economic stagnation? This question goes back, at least, to the Great
More informationEquilibrium in a Production Economy
Equilibrium in a Production Economy Prof. Eric Sims University of Notre Dame Fall 2012 Sims (ND) Equilibrium in a Production Economy Fall 2012 1 / 23 Production Economy Last time: studied equilibrium in
More informationNew Keynesian DSGE Models: Building Blocks
New Keynesian DSGE Models: Building Blocks Satya P. Das @ NIPFP Satya P. Das (@ NIPFP) New Keynesian DSGE Models: Building Blocks 1 / 20 1 Blanchard-Kiyotaki Model 2 New Keynesian Phillips Curve 3 Utility
More informationDSGE-Models. Calibration and Introduction to Dynare. Institute of Econometrics and Economic Statistics
DSGE-Models Calibration and Introduction to Dynare Dr. Andrea Beccarini Willi Mutschler, M.Sc. Institute of Econometrics and Economic Statistics willi.mutschler@uni-muenster.de Summer 2012 Willi Mutschler
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 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 informationLecture 6, January 7 and 15: Sticky Wages and Prices (Galí, Chapter 6)
MakØk3, Fall 2012/2013 (Blok 2) Business cycles and monetary stabilization policies Henrik Jensen Department of Economics University of Copenhagen Lecture 6, January 7 and 15: Sticky Wages and Prices (Galí,
More informationSession 4: Money. Jean Imbs. November 2010
Session 4: Jean November 2010 I So far, focused on real economy. Real quantities consumed, produced, invested. No money, no nominal in uences. I Now, introduce nominal dimension in the economy. First and
More informationGetting to page 31 in Galí (2008)
Getting to page 31 in Galí 2008) H J Department of Economics University of Copenhagen December 4 2012 Abstract This note shows in detail how to compute the solutions for output inflation and the nominal
More informationThe New Keynesian Model
The New Keynesian Model Basic Issues Roberto Chang Rutgers January 2013 R. Chang (Rutgers) New Keynesian Model January 2013 1 / 22 Basic Ingredients of the New Keynesian Paradigm Representative agent paradigm
More informationMacroeconomics Theory II
Macroeconomics Theory II Francesco Franco Nova SBE March 9, 216 Francesco Franco Macroeconomics Theory II 1/29 The Open Economy Two main paradigms Small Open Economy: the economy trades with the ROW but
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 informationMonetary Policy and Unemployment: A New Keynesian Perspective
Monetary Policy and Unemployment: A New Keynesian Perspective Jordi Galí CREI, UPF and Barcelona GSE April 215 Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment April 215 1 / 16
More informationImperfect Information and Optimal Monetary Policy
Imperfect Information and Optimal Monetary Policy Luigi Paciello Einaudi Institute for Economics and Finance Mirko Wiederholt Northwestern University March 200 Abstract Should the central bank care whether
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 informationTopic 8: Optimal Investment
Topic 8: Optimal Investment Yulei Luo SEF of HKU November 22, 2013 Luo, Y. SEF of HKU) Macro Theory November 22, 2013 1 / 22 Demand for Investment The importance of investment. First, the combination of
More informationInference. Jesús Fernández-Villaverde University of Pennsylvania
Inference Jesús Fernández-Villaverde University of Pennsylvania 1 A Model with Sticky Price and Sticky Wage Household j [0, 1] maximizes utility function: X E 0 β t t=0 G t ³ C j t 1 1 σ 1 1 σ ³ N j t
More informationToulouse School of Economics, M2 Macroeconomics 1 Professor Franck Portier. Exam Solution
Toulouse School of Economics, 2013-2014 M2 Macroeconomics 1 Professor Franck Portier Exam Solution This is a 3 hours exam. Class slides and any handwritten material are allowed. You must write legibly.
More informationFinancial Factors in Economic Fluctuations. Lawrence Christiano Roberto Motto Massimo Rostagno
Financial Factors in Economic Fluctuations Lawrence Christiano Roberto Motto Massimo Rostagno Background Much progress made on constructing and estimating models that fit quarterly data well (Smets-Wouters,
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 information1. Constant-elasticity-of-substitution (CES) or Dixit-Stiglitz aggregators. Consider the following function J: J(x) = a(j)x(j) ρ dj
Macro II (UC3M, MA/PhD Econ) Professor: Matthias Kredler Problem Set 1 Due: 29 April 216 You are encouraged to work in groups; however, every student has to hand in his/her own version of the solution.
More informationNew Keynesian Model Walsh Chapter 8
New Keynesian Model Walsh Chapter 8 1 General Assumptions Ignore variations in the capital stock There are differentiated goods with Calvo price stickiness Wages are not sticky Monetary policy is a choice
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 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 informationToulouse School of Economics, Macroeconomics II Franck Portier. Homework 1. Problem I An AD-AS Model
Toulouse School of Economics, 2009-2010 Macroeconomics II Franck Portier Homework 1 Problem I An AD-AS Model Let us consider an economy with three agents (a firm, a household and a government) and four
More informationMonetary Policy Design in the Basic New Keynesian Model. Jordi Galí. October 2015
Monetary Policy Design in the Basic New Keynesian Model by Jordi Galí October 2015 The E cient Allocation where C t R 1 0 C t(i) 1 1 1 di Optimality conditions: max U (C t ; N t ; Z t ) subject to: C t
More informationFiscal Multipliers in a Nonlinear World
Fiscal Multipliers in a Nonlinear World Jesper Lindé Sveriges Riksbank Mathias Trabandt Freie Universität Berlin November 28, 2016 Lindé and Trabandt Multipliers () in Nonlinear Models November 28, 2016
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 informationResolving the Missing Deflation Puzzle. June 7, 2018
Resolving the Missing Deflation Puzzle Jesper Lindé Sveriges Riksbank Mathias Trabandt Freie Universität Berlin June 7, 218 Motivation Key observations during the Great Recession: Extraordinary contraction
More informationGraduate Macro Theory II: Business Cycle Accounting and Wedges
Graduate Macro Theory II: Business Cycle Accounting and Wedges Eric Sims University of Notre Dame Spring 2017 1 Introduction Most modern dynamic macro models have at their core a prototypical real business
More informationMonetary Economics Notes
Monetary Economics Notes Nicola Viegi 2 University of Pretoria - School of Economics Contents New Keynesian Models. Readings...............................2 Basic New Keynesian Model...................
More informationDemand Shocks with Dispersed Information
Demand Shocks with Dispersed Information Guido Lorenzoni (MIT) Class notes, 06 March 2007 Nominal rigidities: imperfect information How to model demand shocks in a baseline environment with imperfect info?
More informationEquilibrium Conditions and Algorithm for Numerical Solution of Kaplan, Moll and Violante (2017) HANK Model.
Equilibrium Conditions and Algorithm for Numerical Solution of Kaplan, Moll and Violante (2017) HANK Model. January 8, 2018 1 Introduction This document describes the equilibrium conditions of Kaplan,
More informationFoundation of (virtually) all DSGE models (e.g., RBC model) is Solow growth model
THE BASELINE RBC MODEL: THEORY AND COMPUTATION FEBRUARY, 202 STYLIZED MACRO FACTS Foundation of (virtually all DSGE models (e.g., RBC model is Solow growth model So want/need/desire business-cycle models
More informationThe Smets-Wouters Model
The Smets-Wouters Model Monetary and Fiscal Policy 1 1 Humboldt Universität zu Berlin uhlig@wiwi.hu-berlin.de Winter 2006/07 Outline 1 2 3 s Intermediate goods firms 4 A list of equations Calibration Source
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 informationMonetary Policy and Exchange Rate Volatility in a Small Open Economy. Jordi Galí and Tommaso Monacelli. March 2005
Monetary Policy and Exchange Rate Volatility in a Small Open Economy by Jordi Galí and Tommaso Monacelli March 2005 Motivation The new Keynesian model for the closed economy - equilibrium dynamics: simple
More informationDemand Shocks, Monetary Policy, and the Optimal Use of Dispersed Information
Demand Shocks, Monetary Policy, and the Optimal Use of Dispersed Information Guido Lorenzoni (MIT) WEL-MIT-Central Banks, December 2006 Motivation Central bank observes an increase in spending Is it driven
More informationTopic 9. Monetary policy. Notes.
14.452. Topic 9. Monetary policy. Notes. Olivier Blanchard May 12, 2007 Nr. 1 Look at three issues: Time consistency. The inflation bias. The trade-off between inflation and activity. Implementation and
More informationFluctuations. Shocks, Uncertainty, and the Consumption/Saving Choice
Fluctuations. Shocks, Uncertainty, and the Consumption/Saving Choice Olivier Blanchard April 2002 14.452. Spring 2002. Topic 2. 14.452. Spring, 2002 2 Want to start with a model with two ingredients: ²
More informationThe Natural Rate of Interest and its Usefulness for Monetary Policy
The Natural Rate of Interest and its Usefulness for Monetary Policy Robert Barsky, Alejandro Justiniano, and Leonardo Melosi Online Appendix 1 1 Introduction This appendix describes the extended DSGE model
More informationMAGYAR NEMZETI BANK MINI-COURSE
MAGYAR NEMZETI BANK MINI-COURSE LECTURE 3. POLICY INTERACTIONS WITH TAX DISTORTIONS Eric M. Leeper Indiana University September 2008 THE MESSAGES Will study three models with distorting taxes First draws
More informationSignaling Effects of Monetary Policy
Signaling Effects of Monetary Policy Leonardo Melosi London Business School 24 May 2012 Motivation Disperse information about aggregate fundamentals Morris and Shin (2003), Sims (2003), and Woodford (2002)
More informationModelling Czech and Slovak labour markets: A DSGE model with labour frictions
Modelling Czech and Slovak labour markets: A DSGE model with labour frictions Daniel Němec Faculty of Economics and Administrations Masaryk University Brno, Czech Republic nemecd@econ.muni.cz ESF MU (Brno)
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 informationPublic Economics The Macroeconomic Perspective Chapter 2: The Ramsey Model. Burkhard Heer University of Augsburg, Germany
Public Economics The Macroeconomic Perspective Chapter 2: The Ramsey Model Burkhard Heer University of Augsburg, Germany October 3, 2018 Contents I 1 Central Planner 2 3 B. Heer c Public Economics: Chapter
More informationChapter 7. Endogenous Growth II: R&D and Technological Change
Chapter 7 Endogenous Growth II: R&D and Technological Change 225 Economic Growth: Lecture Notes 7.1 Expanding Product Variety: The Romer Model There are three sectors: one for the final good sector, one
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 informationTopic 2. Consumption/Saving and Productivity shocks
14.452. Topic 2. Consumption/Saving and Productivity shocks Olivier Blanchard April 2006 Nr. 1 1. What starting point? Want to start with a model with at least two ingredients: Shocks, so uncertainty.
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 informationMonetary Policy and Unemployment: A New Keynesian Perspective
Monetary Policy and Unemployment: A New Keynesian Perspective Jordi Galí CREI, UPF and Barcelona GSE May 218 Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy and Unemployment May 218 1 / 18 Introducing
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 informationMA Advanced Macroeconomics: 7. The Real Business Cycle Model
MA Advanced Macroeconomics: 7. The Real Business Cycle Model Karl Whelan School of Economics, UCD Spring 2016 Karl Whelan (UCD) Real Business Cycles Spring 2016 1 / 38 Working Through A DSGE Model We have
More informationSolutions to Problem Set 4 Macro II (14.452)
Solutions to Problem Set 4 Macro II (14.452) Francisco A. Gallego 05/11 1 Money as a Factor of Production (Dornbusch and Frenkel, 1973) The shortcut used by Dornbusch and Frenkel to introduce money in
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 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 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 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 informationNonlinearity. Exploring this idea and what to do about it requires solving a non linear model.
The Zero Bound Based on work by: Eggertsson and Woodford, 2003, The Zero Interest Rate Bound and Optimal Monetary Policy, Brookings Panel on Economic Activity. Christiano, Eichenbaum, Rebelo, When is the
More informationMacroeconomics I. University of Tokyo. Lecture 12. The Neo-Classical Growth Model: Prelude to LS Chapter 11.
Macroeconomics I University of Tokyo Lecture 12 The Neo-Classical Growth Model: Prelude to LS Chapter 11. Julen Esteban-Pretel National Graduate Institute for Policy Studies The Cass-Koopmans Model: Environment
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 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 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 information"0". Doing the stuff on SVARs from the February 28 slides
Monetary Policy, 7/3 2018 Henrik Jensen Department of Economics University of Copenhagen "0". Doing the stuff on SVARs from the February 28 slides 1. Money in the utility function (start) a. The basic
More informationEconomic transition following an emission tax in a RBC model with endogenous growth. EC-IILS JOINT DISCUSSION PAPER SERIES No. 17
International Labour Organization European Union International Institute for Labour Studies Economic transition following an emission tax in a RBC model with endogenous growth EC-IILS JOINT DISCUSSION
More informationMacroeconomics Theory II
Macroeconomics Theory II Francesco Franco FEUNL February 2011 Francesco Franco Macroeconomics Theory II 1/34 The log-linear plain vanilla RBC and ν(σ n )= ĉ t = Y C ẑt +(1 α) Y C ˆn t + K βc ˆk t 1 + K
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 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 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 informationThe TransPacific agreement A good thing for VietNam?
The TransPacific agreement A good thing for VietNam? Jean Louis Brillet, France For presentation at the LINK 2014 Conference New York, 22nd 24th October, 2014 Advertisement!!! The model uses EViews The
More informationGold Rush Fever in Business Cycles
Gold Rush Fever in Business Cycles Paul Beaudry, Fabrice Collard & Franck Portier University of British Columbia & Université de Toulouse UAB Seminar Barcelona November, 29, 26 The Klondike Gold Rush of
More informationAdvanced Macroeconomics II. Real Business Cycle Models. Jordi Galí. Universitat Pompeu Fabra Spring 2018
Advanced Macroeconomics II Real Business Cycle Models Jordi Galí Universitat Pompeu Fabra Spring 2018 Assumptions Optimization by consumers and rms Perfect competition General equilibrium Absence of a
More information