DSGE Models for Real Business Cycle and New Keynesian Macroeconomics : Theoretical Methods and Numerical Solutions with DYNARE

Preface
Contents
List of Figures
List of Tables
Chapter 1: Introduction
	References
Chapter 2: Finite-Difference Equations and Systems of Difference Equations in Rational Expectations
	2.1 Review of Solutions of Linear First-Order Difference Equations
	2.2 Solution by Factorization Method
	2.3 First-Order Difference Equation in Rational Expectations
	2.4 Forward Solution for the Case |a| < 1
		2.4.1 Method of Iterated Forward Substitution of Expectations
		2.4.2 Factorization Method
		2.4.3 Method of Indeterminate Coefficients
		2.4.4 A Simple Example of a Forward Solution with the Method of Indeterminate Coefficients
	2.5 Case |a| > 1 and Solution with the Backward Iteration Method
	2.6 Bubbles
	2.7 Second-Order Finite-Difference Equations and Related Equations with Expectations
	2.8 Properties of Characteristic Equation Associated with a Second-Order Difference Equation
	2.9 Stability Conditions for Second-Order Finite-Difference Equation
	2.10 Solution Method by Factorization
	2.11 Sargent´s Approach to Solution Method by Factorization
	2.12 Method for Reduction of a Rational Polynomial to Partial Fractions
	2.13 Partial Fractions and Discussion of Solutions of Finite-Difference Equation of Second Order
	2.14 Second-Order Difference Equations with Expectations
		2.14.1 Method of Solution of Indeterminate Coefficients
		2.14.2 Solution Method by Factorization
	2.15 Solution to Second-Order Finite-Difference Equation with the Matrix Approach
	2.16 Systems of Finite-Difference Equations
	2.17 Systems of Finite-Difference Equations with Rational Expectations
	2.18 Analytical Solution of Systems of Rational Expectations
	2.19 Saddle Point Path
	2.20 Solving System with the Blanchard-Kahn Procedure
	2.21 The Case of Indeterminacy
	2.22 The Case of Singular Problems: Outlines
	2.23 An Elaborate Example of Economic Theory
		2.23.1 Solution with the Method of Factorization
		2.23.2 Solution with the Method of Indeterminate Coefficients
		2.23.3 Solution with the Matrix Method and Application of the Blanchard-Kahn Procedure
	Appendix
		A.1 Introduction
			A.1.1 Review of Quadratic Equations
			A.1.2 Relations Between Roots and Coefficients of Quadratic Equation
			A.1.3 Comparison Between Roots of Quadratic Equation and Two Given Real Numbers
			A.1.4 Some Review on Complex Numbers and Trigonometric Identities
	References
Chapter 3: Models of Representative Agents and Real Business Cycle Models
	3.1 Use of the Lagrangian in Intertemporal Maximization
	3.2 A Discussion of the Transversality Condition
	3.3 An Application of the Intertemporal Maximization: The Case of Adjustment Costs of Capital and the Relationship with ``Tobi...
	3.4 From Micro to Macro: A Simple Dynamic General Equilibrium Model (DGE) of Representative Agents (Ramsey) for a Decentralize...
	3.5 Discussion of Solution of Simple DGE Macroeconomic Model
	3.6 Log-Linear Approximation of DGE Macroeconomic Model
	3.7 Methods of Solution of a Log-Linearized System: Indeterminate Coefficients
	3.8 A Model of a Decentralized Economy, with Inelastic Labor Supply, as a Basic Model of Real Business Cycle
	3.9 The Blanchard-Kahn Method for Solving Systems with Rational Expectations
	3.10 Solution of the Basic Real Business Cycle Model with Blanchard-Kahn Method
	3.11 Jordan Transformation Applied to System in Expectations in the Basic Real Business Cycle Model
	3.12 Basic RBC Model of Centralized Economy with (a) Flexible Labor Supply and (b) Stochastic Shocks to Technology and Aggrega...
		3.12.1 Steady-State Variables as Functions of Parameters
	3.13 An Application of the Blanchard-Kahn Method to Hansen´s DSGE Model
	3.14 The Model of a Decentralized Economy, with Flexible Labor Supply and Exogenous Public Spending
	3.15 A Complete Analysis of the RBC Model of the Centralized Economy, with Log-CRRA Utility Function in Consumption and Labor
		3.15.1 Steady-State Solution
		3.15.2 Log-Linearization of the Model
		3.15.3 The State-Space Representation of the Log-Linear System
		3.15.4 Transformation of the Real Cycle Model into a System of Rational Expectations
		3.15.5 The Blanchard-Kahn Transformation of the RBC Model of the Centralized Economy
	Appendix
		A.1 Bellman and Dynamic Programming
		A.2 An Economic Example of the Application of Bellman´s Principle: Aggregate Savings in an Intertemporal Context Under Conditi...
	References
Chapter 4: A Simplified Illustration of Numerical Solution Methods of DSGE Models with DYNARE Software
	4.1 DYNARE Coding as a Method for Numerical Solving DSGE Models
	4.2 Three Different Ways of Writing Model Block Equations
	4.3 The Code of the Centralized Economy Model, with Flexible Labor Supply, in the Form of Levels
	4.4 A Comment on DYNARE´s Numerical Simulation of the Model of the Centralized Economy in Level Form, with a Flexible Labor Su...
	4.5 The Code of Model of the Centralized Economy with Flexible Labor Supply, in Exp-Log Form
	4.6 The Code of the Model of the Centralized Economy in (Log) Linear Form, i.e., in the Form of Percentage Deviations from the...
	4.7 An Alternative Way of Encoding Model Block
	4.8 Code of the Basic RBC Model with a CRRA Utility Function and Government Spending as a Shock
		4.8.1 Steady-State Variables as Functions of Parameters of the Model
	4.9 The Complete DYNARE Code of the Log-Linearized Model with Public Expenditure
	4.10 A Note on CALIBRATION, i.e., Assigning Numerical Values to Parameters
	4.11 Different Ways for Calculating the Steady State in DYNARE
		4.11.1 Method 1: steady_state_model Block
		4.11.2 Method 2: steady_state with the steady state_helper Function
		4.11.3 Method 3: Assigning Initial Values in the initval Block
		4.11.4 A Focus on External Steady-State File
	4.12 Another DYNARE Focus: Model with Different Parameter Values
	References
Chapter 5: A Basic Version of the Micro-founded Neo-Keynesian Model
	5.1 A Decentralized Economy: Choices of Representative Household
	5.2 Firms´ Choices in the Case of Linear Production Technology and Flexible Prices
	5.3 Firm Choices in the Case of Cobb-Douglas Production Technology
	5.4 Firm Choices in the Case of Production Technology CES for Final Goods, Cobb-Douglas Technology for Intermediate Goods, and...
		5.4.1 Choices of Firm Producing Final Good
		5.4.2 Choices of Firm Producing Intermediate Goods
	5.5 Firms´ Pricing in the Presence of Price Stickiness: (a) The Case of Costs of Price Adjustment
	5.6 Firm´s Pricing in the Presence of Price Stickiness: (b) Price Stickiness a-la-Calvo in a Model of Linear Production Techno...
	5.7 Firm´s Pricing in the Presence of Price Stickiness: (c) Price Stickiness a-la-Calvo and Nonlinear Production Technology
	5.8 Differences Between Rotemberg and Calvo Price Stickiness
	5.9 Implications for the Inflation Rate of Firm´s Way of Setting Prices
	5.10 The Aggregate Economic System with Price Stickiness a-la-Calvo and Linear Production Technology: The Demand Side
	5.11 The Aggregate Economic System with Price Stickiness a-la-Calvo and Linear Production Technology: The Supply Side
	5.12 General Equilibrium of NKE Model with Linear Technology
		5.12.1 The Log-Linear Version of Model
	5.13 Dynamics of the Equilibrium Inflation
	5.14 The Notion of GDP Gap and the New Keynesian Phillips´ Curve
	5.15 The Definitive Basic Model of the New Keynesian Economics (NKE)
	5.16 Blanchard-Kahn Conditions for Stability and Uniqueness of Solutions of the Basic NKE Model
	5.17 Numerical Solution of the Basic NKE Model and the DYNARE Code
	References
Chapter 6: More Complex NKE Models: Stickiness in Money Wages, Real Stickiness, and Extensions to a Medium-Size Model
	6.1 Complex Model of the NKE with (a) Nonlinear Production Technology and Capital Accumulation; (b) Money Wages Setting by Hou...
		6.1.1 The Representative Firm Producing Final Good
		6.1.2 Firms Producing Intermediate Goods
		6.1.3 Households
		6.1.4 General Wage Index
	6.2 Nominal Wage´s Setting for Labor Service by the Representative Household
	6.3 The Aggregate Labor Supply and Representative Trade Union
	6.4 The Public Administration and the Central Bank
	6.5 Equilibrium of Model with Rotemberg Price Stickiness and Flexible Wages
	6.6 The Phillips Curve with Rotemberg Price Adjustment Costs
	6.7 Steady State and Details of Log-Linearization Algebra
	6.8 The Complete Log-Linearized NKE Model, with Physical Capital and Price Adjustment Costs
	6.9 DYNARE´s Code for the Numerical Solution of the NKE Model with Physical Capital and Price Adjustment Costs
	6.10 Some Specific Extensions of the NKE Model
		6.10.1 Calvo Stickiness in Wage Modifications
		6.10.2 Habit Persistence and Adjustment Costs of Capital and Labor
		6.10.3 ``Rules of Thumb´´ and Non-Ricardian Households
	6.11 The Medium-Sized Micro-founded Keynesian Model (E. Sims 2016)
	6.12 Labor´s Supply Aggregation and Representative Trade Union Choices
		6.12.1 Households
		6.12.2 Firm Producer of the Final Good
		6.12.3 Firm Producer of Intermediate Goods
		6.12.4 Public Administration and Central Bank
	6.13 Equilibrium and Aggregation
		6.13.1 Exogenous Stochastic Processes
	6.14 The Complete Set of Equilibrium Equations
		6.14.1 Calculation of the Steady-State Solution
		6.14.2 The Complete Set of Steady-State Equations
	6.15 DYNARE Code for the Numerical Solution of the Medium-Sized NK Model
	6.16 The Results of the DYNARE code for the Medium-Sized NK Model
	References
Untitled
Index