Economic growth: theory and numerical solution methods
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 517 - 520 |
| Physical Description: | XX, 528 S. graph. Darst. |
| ISBN: | 9783540686651 |
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| 100 | 1 | |a Novales, Alfonso |d 1952- |e Verfasser |0 (DE-588)136495370 |4 aut | |
| 245 | 1 | 0 | |a Economic growth |b theory and numerical solution methods |c Alfonso Novales ; Esther Fernández ; Jesús Ruiz |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XX, 528 S. |b graph. Darst. | ||
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| 500 | |a Literaturverz. S. 517 - 520 | ||
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Wirtschaftsentwicklung | |
| 650 | 4 | |a Business cycles |x Mathematical models | |
| 650 | 4 | |a Economic development |x Mathematical models | |
| 650 | 4 | |a Monetary policy |x Mathematical models | |
| 650 | 4 | |a Stochastic processes | |
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Record in the Search Index
| _version_ | 1804137813043576832 |
|---|---|
| adam_text | Contents
Introduction
................................................... 1
1.1
A Few Time Series Concepts
................................. 2
1.1.1
Some Simple Stochastic Processes
...................... 3
1.1.2
Stationarity, Mean Reversion, Impulse Responses
......... 6
1.1.3
Numerical Exercise: Simulating Simple
Stochastic Processes
.................................. 9
1.2
Structural Macroeconomic Models
............................ 12
1.2.1
Static Structural Models
.............................. 12
1.2.2
Dynamic Structural Models
............................ 16
1.2.3
Stochastic, Dynamic Structural Models
.................. 21
1.2.4
Stochastic Simulation
................................. 23
1.2.5
Numerical Exercise
-
Simulating Dynamic, Structural
Macroeconomic Models
.............................. 24
1.3
Why are Economic Growth Models Interesting?
................. 27
1.3.1
Microeconomic Foundations of Macroeconomics
......... 27
1.3.2
Lucas Critique on Economic Policy Evaluation
.......... 33
1.3.3
A Brief Overview of Developments on Growth Theory
..... 35
1.3.4
The Use of Growth Models for Actual Policy Making
...... 39
1.4
Numerical Solution Methods
................................. 40
1.4.1
Why do we Need to Compute Numerical Solutions
to Growth Models?
................................... 40
1.4.2
Stability
............................................ 42
1.4.3
Indeterminacy
....................................... 43
1.4.4
The Type of Questions We Ask and the Conclusions
We Reach
.......................................... 44
1.5
Synopsis of the Book
....................................... 48
The Neoclassical Growth Model Under a Constant Savings Rate
..... 53
2.1
Introduction
............................................... 53
2.2
Returns to Scale and Sustained Growth
........................ 54
Contents
2.3
The Neoclassical Growth Model of Solow and Swan
............. 59
2.3.1
Description of the Model
.............................. 60
2.3.2
The Dynamics of the Economy
......................... 61
2.3.3
Steady-State
........................................ 64
2.3.4
The Transition Towards Steady-State
.................... 68
2.3.5
The Duration of the Transition to Steady-State
............ 69
2.3.6
The Growth Rate of Output and Consumption
............ 69
2.3.7
Convergence in the Neoclassical Model
................. 71
2.3.8
A Special Steady-State: The Golden Rule of Capital
Accumulation
....................................... 73
2.4
Solving the Continuous-Time Solow-Swan Model
............... 76
2.4.1
Solution to the Exact Model
........................... 76
2.4.2
The Linear Approximation to the Solow-Swan Model
..... 77
2.4.3
Changes in Structural Parameters
....................... 79
2.4.4
Dynamic Inefficiency
................................. 82
2.5
The Deterministic, Discrete-Time Solow Swan Model
............ 85
2.5.1
The Exact Solution
................................... 85
2.5.2
Approximate Solutions to the Discrete-Time Model
....... 87
2.5.3
Numerical Exercise
-
Solving the Deterministic
Solow-Swan Model
.................................. 89
2.5.4
Numerical Exercise
-
A Permanent Change
in the Savings Rate
................................... 91
2.5.5
Numerical Exercise
-
Dynamic Inefficiency
.............. 93
2.6
The Stochastic, Discrete Time Version of the Solow-Swan Model
.. 95
2.6.1
Numerical Exercise
-
Solving the Stochastic
Solow-Swan Model
.................................. 96
2.7
Exercises
................................................. 98
Optimal Growth. Continuous Time Analysis
......................101
3.1
The Continuous-Time Version of the Cass-Koopmans Model
......101
3.1.1
Optimality Conditions for the Cass-Koopmans Model
.....103
3.1.2
The Instantaneous Elasticity of Substitution
of Consumption
(IES)
................................104
3.1.3
Risk Aversion and the
Intertemporal
Substitution
of Consumption
.....................................106
3.1.4
Keynes-Ramsey Condition
............................107
3.1.5
The Optimal Steady-State
.............................108
3.1.6
Numerical Exercise: The Sensitivity of Steady-State
Levels to Changes in Structural Parameters
...............110
3.1.7
Existence, Uniqueness and Stability of Long-Run
Equilibrium
-
A Graphical Discussion
..................112
3.1.8
Suboptimality of the Golden Rule
......................114
3.2
Stability and Convergence
...................................115
3.2.1
The Trajectory for Income
.............................119
Contents
3.2.2
Numerical Exercise
-
Characterizing the Transition
after a Change in a Structural Parameter
.................120
3.3
Interpreting the Central Planners s Model as a Competitive
Equilibrium Economy
.......................................126
3.3.1
The Efficiency of Competitive Equilibrium
...............129
3.4
A Competitive Equilibrium with Government
...................131
3.4.1
The Structure of the Economy
.........................131
3.4.2
Feasible Stationary Public Expenditure and Financing
Policies
............................................135
3.4.3
Competitive Equilibrium
..............................135
3.4.4
Global Constraint of Resources
........................136
3.4.5
The Representative Agent Problem
.....................136
3.5
On the Efficiency of Equilibrium with Government
..............138
3.5.1
On the Efficiency of Equilibrium Under Lump-Sum Taxes
and Debt
...........................................138
3.5.2
The Inefficiency of the Competitive Equilibrium
Allocation Under
Distorti
onary Taxes
...................140
3.6
The Ricardian Doctrine
......................................146
3.6.1
The Ricardian Doctrine Under Non-Distorting Taxes
......146
3.6.2
Failure of the Ricardian Doctrine Under Distorting Taxes
... 147
3.7
Appendix
.................................................149
3.7.1
Appendix
1 -
Log-linear Approximation to the Continuous
Time Version of Cass-Koopmans Model
.................149
3.7.2
Appendix
2 -
An Alternative Presentation
of the Equivalence Between the Planner s
and the Competitive Equilibrium Mechanisms
in an Economy Without Government
....................150
3.8
Exercises
.................................................153
Optimal Growth. Discrete Time Analysis
.........................155
4.1
Discrete-Time, Deterministic Cass-Koopmans Model
............155
4.1.1
The Global Constraint of Resources
.....................155
4.1.2
Discrete-Time Formulation of the Planner s Problem
......157
4.1.3
The Optimal Steady-State
.............................158
4.1.4
The Dynamics of the Model: The Phase Diagram
.........159
4.1.5
Transversality Condition in Discrete Time
...............161
4.1.6
Competitive Equilibrium with Government
...............162
4.2
Fiscal Policy in the Cass-Koopmans Model
....................167
4.2.1
The Deterministic Case
...............................167
4.2.2
Numerical Exercise
-
Solving the Deterministic
Competitive Equilibrium with Taxes
....................176
4.2.3
Numerical Exercise
-
Fiscal Policy Evaluation
............179
4.3
Appendices
................................................185
4.3.1
A Reformulation of the Stability Condition
for the Deterministic Version of the Model
...............185
Contents
4.3.2 The
Intertemporal Government Budget
Constraint
.........187
4.4
Appendix
2:
The Ricardian Proposition Under Non-Distortionary
Taxes in Discrete Time
......................................190
4.5
Exercises
.................................................191
Numerical Solution Methods
....................................195
5.1
Numerical Solutions and Simulation Analysis
...................195
5.2
Analytical Solutions to Simple Growth Models
..................197
5.2.1
A Model with Full Depreciation
........................197
5.2.2
A Model with Leisure in the Utility Function
.............200
5.2.3
Numerical Solutions of the Growth Model
Under Full Depreciation
..............................202
5.3
Solving a Simple, Stochastic Version of the Planner s Problem
.....203
5.3.1
Solving the Linear-Quadratic Approximation
to the Planner s Problem
..............................204
5.3.2
The Log-Linear Approximation to the Model
.............210
5.3.3
The Blanchard-Kahn Solution Method for the Stochastic
Planner s Problem. Log-Linear Approximation
...........212
5.3.4
Uhlig
s
Undetermined Coefficients Approach.
Log-Linear Approximation
............................215
5.3.5
Sims Eigenvalue-Eigenvector Decomposition Method
Using a Linear Approximation to the Model
..............217
5.4
Solving the Stochastic Representative Agent s Problem
with Taxes
................................................225
5.4.1
The Log-Linear Approximation
........................227
5.4.2
Numerical Exercise: Solving the Stochastic Representative
Agent s Model with Taxes Through
Blanchard
and
Kahn
s
Approach. Log-Linear Approximation
...................228
5.4.3
Numerical Exercise: Computing Impulse Responses
to a Technology Shock. Log-Linear Approximation
.......232
5.4.4
Numerical Exercise: Solving the Stochastic Representative
Agent s Model with Taxes Through the Eigenvector
and Eigenvalue Decomposition Approach.
Linear Approximation
................................234
5.5
Nonlinear Numerical Solution Methods
........................238
5.5.1
Parameterized Expectations
...........................238
5.5.2
Projection Methods
..................................241
5.6
Appendix
-
Solving the Planner s Model Under Full Depreciation
.. 251
5.7
Exercises
.................................................253
Endogenous Growth Models
.....................................257
6.1
TheAřModel
.............................................257
6.1.1
Balanced Growth Path
................................259
6.1.2
Transitional Dynamics
................................259
6.1.3
Boundedness of Time-Aggregate Utility
.................261
Contents
6.2
The Discrete Time Version of the Model
.......................262
6.2.1
The Transversality Condition and Bounded Utility
........265
6.2.2
Absence of Transitional Dynamics: Relationship
Between the Stock of Physical Capital and Consumption
... 266
6.3
Stability in the AK Model
....................................267
6.4
Effects from Transitory Changes in Policy Parameters
............271
6.4.1
A Policy Intervention
.................................272
6.4.2
A Comparison with the Cass-Koopmans Economy
........273
6.5
Dynamic
Laffer
Curves
.....................................275
6.5.1
Numerical Exercise on Dynamic
Laffer
Curves
...........278
6.6
Solving the Stochastic, Discrete Time Version of the AK Model
___280
6.6.1
A Linear Approximation to the Stochastic AK Model
......282
6.6.2
Numerical Exercise: Solving the Stochastic AK Model
.....285
6.7
An Endogenous Growth Model with Productive Public
Expenditures: Barro s Model
.................................286
6.8
Transitional Dynamics in Endogenous Growth: The Jones
and Manuelli Model
........................................288
6.8.1
Steady-State
........................................290
6.8.2
Solving the Deterministic Version of Jones and Manuelli s
Model Through a Linear Approximation
.................291
6.9
The Stochastic Version of Jones and Manuelli Model
.............294
6.9.1
Deterministic Balanced Growth Path
....................295
6.9.2
Transforming the Model in Stationary Ratios
.............295
6.9.3
The Phase Diagram of the Deterministic Version
of the Jones-Manuelli Model: Transitional Dynamics
......296
6.9.4
Computing the Dynamics: Log-Linear Approximation
.....298
6.9.5
Numerical Exercise: Solving the Jones
and Manuelli Model
..................................301
6.9.6
The Stochastic AK Model as a Special Case
..............301
6.10
Exercises
.................................................302
Additional Endogenous Growth Models
..........................305
7.1
Introduction
...............................................305
7.2
A Variety of Producer Products
...............................306
7.2.1
The Economy
.......................................306
7.2.2
The Inefficiency of the Equilibrium Allocation
............314
7.2.3
A Stochastic Version of the Economy with a Variety
of Intermediate Goods
................................316
7.3
Technological Diffusion and Growth
..........................323
7.3.1
The Problem of the Follower Country
...................324
7.3.2
Deterministic Steady-State
............................326
7.3.3
Computing the Numerical Solution by Log-Linear
Approximations and Numerical Derivatives
..............328
Contents
7.3.4
Numerical Exercise: Solving the Model with Varieties
of Intermediate Goods, and the Diffusion Growth Model
... 332
7.4
Schumpeterian Growth
......................................333
7.4.1
The Economy
.......................................334
7.4.2
Computing Equilibrium Trajectories
....................338
7.4.3
Deterministic Steady-State
............................341
7.5
Endogenous Growth with Accumulation of Human Capital
........342
7.5.1
The Economy
.......................................343
7.5.2
The Competitive Equilibrium
..........................347
7.5.3
Analyzing the Deterministic Steady-State
................349
7.5.4
Numerical Exercise: Steady-State Effects of Fiscal Policy
.. 352
7.5.5
Computing Equilibrium Trajectories in a Stochastic Setup
Under the Assumption of Rational Expectations
..........353
7.5.6
Indeterminacy of Equilibria
............................363
7.5.7
Numerical Exercise: The Correlation
Between Productivity and Hours Worked in the Human
Capital Accumulation Model
..........................374
7.6
Exercises
.................................................376
Growth in Monetary Economies: Steady-State Analysis
of Monetary Policy
.............................................377
8.1
Introduction
...............................................377
8.2
Optimal Growth in a Monetary Economy: The Sidrauski Model
.... 378
8.2.1
The Representative Agent s Problem
....................380
8.2.2
Steady-State in the Monetary Growth Economy
...........384
8.2.3
Golden Rule
........................................387
8.3
Steady-State Policy Analysis
.................................388
8.3.1
Optimal Steady-State Rate of Inflation
..................389
8.3.2
The Welfare Cost of Inflation
..........................392
8.4
Two Modelling Issues: Nominal Bonds and the Timing of Real
Balances
..................................................394
8.4.1
Nominal Bonds: The Relationship Between Real
and Nominal Interest Rates
............................395
8.4.2
Real Balances in the Utility Function: At the Beginning
or at the End of the Period?
............................397
8.4.3
Numerical Exercise: Optimal Rate of Inflation
Under Alternative Assumptions on Preferences
...........400
8.5
Monetary Policy Analysis Under Consumption and Income Taxes
.. 401
8.5.1
Steady-State
........................................403
8.5.2
Numerical Exercise: Computation of Steady-State Levels
Under Alternative Policy Choices
.......................405
8.6
Monetary Policy Under Endogenous Labor Supply
..............406
8.6.1
The Neutrality of Monetary Policy Under Endogenous
Labor Supply
.......................................406
8.6.2
Numerical Exercise: Evaluation of Steady-State Policies
with an Endogenous Labour Supply
.....................411
Contents xix
8.7 Optimal
Monetary Policy Under Distortionary Taxation
and Endogenous Labor
......................................413
8.7.1
The Model
..........................................414
8.7.2
Implementability Condition
...........................417
8.7.3
The Ramsey Problem
.................................418
8.8
Exercises
.................................................419
9
Transitional Dynamics in Monetary Economies:
Numerical Solutions
............................................423
9.1
Introduction
...............................................423
9.2
Stability of Public Debt
.....................................424
9.3
Alternative Strategies for Monetary Policy: Control of Nominal
Rates vs. Money Growth Control
.............................426
9.4
Deterministic Monetary Model with the Monetary Authority
Choosing Money Growth
....................................427
9.4.1
Steady-State
........................................429
9.4.2
Solution Through a Log-Linear Approximation
..........430
9.4.3
Complex Eigenvalues
.................................433
9.5
Deterministic Monetary Model with the Monetary Authority
Choosing Nominal Interest Rates
.............................437
9.6
Transitional Effects of Policy Interventions
.....................441
9.6.1
Solving the Model with Nominal Interest Rates as Control
Variable, Using a Linear Approximation
.................442
9.6.2
Numerical Exercise: Changes in Nominal Interest Rates
.... 444
9.6.3
Solving the Model with Money Growth as Control
Variable, Using a Linear Approximation
.................445
9.6.4
Numerical Exercise: Gradual vs. Drastic Changes
in Money Growth
....................................448
9.7
The Stochastic Version of the Monetary Model
..................450
9.7.1
The Monetary Authority Chooses Nominal Interest Rates
.. 452
9.7.2
The Monetary Authority Chooses Money Supply Growth
... 463
9.8
A New Keynesian Monetary Model
...........................469
9.8.1
A Model Without Capital Accumulation: Ireland s
(2004) .. 470
9.8.2
A New Keynesian Monetary Model with Capital
Accumulation
.......................................477
9.9
Appendix: In a Log-Linear Approximation, Etiit+
=к~ћ.......
491
9.10
Exercises
.................................................492
10
Mathematical Appendix
........................................495
10.1
The Deterministic Control Problem in Continuous Time
..........495
10.1.1
Transversality Condition
..............................496
10.1.2
The Discounted Problem
..............................496
10.1.3
Calculus of Variations
................................498
10.2
The Deterministic Control Problem in Discrete Time
.............499
10.3
First Order Differential Equations
.............................501
xx Contents
10.3.1 1. First Order Differential
Equations
with Constant
Coefficients
.........................................501
10.3.2 2.
First Order Differential Equations with Variable
Coefficients
.........................................504
10.4
Matrix Algebra
............................................506
10.4.1
The
2
χ
2
Case
......................................508
10.4.2
Systems with a Saddle Path Property
....................510
10.4.3
Imposing Stability Conditions Over Time
................510
10.5
Some Notes on Complex Numbers
............................513
10.6
Solving a Dynamic Two-Equation System with Complex Roots
.... 514
References
.........................................................517
Index
.............................................................521
|
| adam_txt |
Contents
Introduction
. 1
1.1
A Few Time Series Concepts
. 2
1.1.1
Some Simple Stochastic Processes
. 3
1.1.2
Stationarity, Mean Reversion, Impulse Responses
. 6
1.1.3
Numerical Exercise: Simulating Simple
Stochastic Processes
. 9
1.2
Structural Macroeconomic Models
. 12
1.2.1
Static Structural Models
. 12
1.2.2
Dynamic Structural Models
. 16
1.2.3
Stochastic, Dynamic Structural Models
. 21
1.2.4
Stochastic Simulation
. 23
1.2.5
Numerical Exercise
-
Simulating Dynamic, Structural
Macroeconomic Models
. 24
1.3
Why are Economic Growth Models Interesting?
. 27
1.3.1
Microeconomic Foundations of Macroeconomics
. 27
1.3.2
Lucas' Critique on Economic Policy Evaluation
. 33
1.3.3
A Brief Overview of Developments on Growth Theory
. 35
1.3.4
The Use of Growth Models for Actual Policy Making
. 39
1.4
Numerical Solution Methods
. 40
1.4.1
Why do we Need to Compute Numerical Solutions
to Growth Models?
. 40
1.4.2
Stability
. 42
1.4.3
Indeterminacy
. 43
1.4.4
The Type of Questions We Ask and the Conclusions
We Reach
. 44
1.5
Synopsis of the Book
. 48
The Neoclassical Growth Model Under a Constant Savings Rate
. 53
2.1
Introduction
. 53
2.2
Returns to Scale and Sustained Growth
. 54
Contents
2.3
The Neoclassical Growth Model of Solow and Swan
. 59
2.3.1
Description of the Model
. 60
2.3.2
The Dynamics of the Economy
. 61
2.3.3
Steady-State
. 64
2.3.4
The Transition Towards Steady-State
. 68
2.3.5
The Duration of the Transition to Steady-State
. 69
2.3.6
The Growth Rate of Output and Consumption
. 69
2.3.7
Convergence in the Neoclassical Model
. 71
2.3.8
A Special Steady-State: The Golden Rule of Capital
Accumulation
. 73
2.4
Solving the Continuous-Time Solow-Swan Model
. 76
2.4.1
Solution to the Exact Model
. 76
2.4.2
The Linear Approximation to the Solow-Swan Model
. 77
2.4.3
Changes in Structural Parameters
. 79
2.4.4
Dynamic Inefficiency
. 82
2.5
The Deterministic, Discrete-Time Solow Swan Model
. 85
2.5.1
The Exact Solution
. 85
2.5.2
Approximate Solutions to the Discrete-Time Model
. 87
2.5.3
Numerical Exercise
-
Solving the Deterministic
Solow-Swan Model
. 89
2.5.4
Numerical Exercise
-
A Permanent Change
in the Savings Rate
. 91
2.5.5
Numerical Exercise
-
Dynamic Inefficiency
. 93
2.6
The Stochastic, Discrete Time Version of the Solow-Swan Model
. 95
2.6.1
Numerical Exercise
-
Solving the Stochastic
Solow-Swan Model
. 96
2.7
Exercises
. 98
Optimal Growth. Continuous Time Analysis
.101
3.1
The Continuous-Time Version of the Cass-Koopmans Model
.101
3.1.1
Optimality Conditions for the Cass-Koopmans Model
.103
3.1.2
The Instantaneous Elasticity of Substitution
of Consumption
(IES)
.104
3.1.3
Risk Aversion and the
Intertemporal
Substitution
of Consumption
.106
3.1.4
Keynes-Ramsey Condition
.107
3.1.5
The Optimal Steady-State
.108
3.1.6
Numerical Exercise: The Sensitivity of Steady-State
Levels to Changes in Structural Parameters
.110
3.1.7
Existence, Uniqueness and Stability of Long-Run
Equilibrium
-
A Graphical Discussion
.112
3.1.8
Suboptimality of the Golden Rule
.114
3.2
Stability and Convergence
.115
3.2.1
The Trajectory for Income
.119
Contents
3.2.2
Numerical Exercise
-
Characterizing the Transition
after a Change in a Structural Parameter
.120
3.3
Interpreting the Central Planners's Model as a Competitive
Equilibrium Economy
.126
3.3.1
The Efficiency of Competitive Equilibrium
.129
3.4
A Competitive Equilibrium with Government
.131
3.4.1
The Structure of the Economy
.131
3.4.2
Feasible Stationary Public Expenditure and Financing
Policies
.135
3.4.3
Competitive Equilibrium
.135
3.4.4
Global Constraint of Resources
.136
3.4.5
The Representative Agent Problem
.136
3.5
On the Efficiency of Equilibrium with Government
.138
3.5.1
On the Efficiency of Equilibrium Under Lump-Sum Taxes
and Debt
.138
3.5.2
The Inefficiency of the Competitive Equilibrium
Allocation Under
Distorti
onary Taxes
.140
3.6
The Ricardian Doctrine
.146
3.6.1
The Ricardian Doctrine Under Non-Distorting Taxes
.146
3.6.2
Failure of the Ricardian Doctrine Under Distorting Taxes
. 147
3.7
Appendix
.149
3.7.1
Appendix
1 -
Log-linear Approximation to the Continuous
Time Version of Cass-Koopmans Model
.149
3.7.2
Appendix
2 -
An Alternative Presentation
of the Equivalence Between the Planner's
and the Competitive Equilibrium Mechanisms
in an Economy Without Government
.150
3.8
Exercises
.153
Optimal Growth. Discrete Time Analysis
.155
4.1
Discrete-Time, Deterministic Cass-Koopmans Model
.155
4.1.1
The Global Constraint of Resources
.155
4.1.2
Discrete-Time Formulation of the Planner's Problem
.157
4.1.3
The Optimal Steady-State
.158
4.1.4
The Dynamics of the Model: The Phase Diagram
.159
4.1.5
Transversality Condition in Discrete Time
.161
4.1.6
Competitive Equilibrium with Government
.162
4.2
Fiscal Policy in the Cass-Koopmans Model
.167
4.2.1
The Deterministic Case
.167
4.2.2
Numerical Exercise
-
Solving the Deterministic
Competitive Equilibrium with Taxes
.176
4.2.3
Numerical Exercise
-
Fiscal Policy Evaluation
.179
4.3
Appendices
.185
4.3.1
A Reformulation of the Stability Condition
for the Deterministic Version of the Model
.185
Contents
4.3.2 The
Intertemporal Government Budget
Constraint
.187
4.4
Appendix
2:
The Ricardian Proposition Under Non-Distortionary
Taxes in Discrete Time
.190
4.5
Exercises
.191
Numerical Solution Methods
.195
5.1
Numerical Solutions and Simulation Analysis
.195
5.2
Analytical Solutions to Simple Growth Models
.197
5.2.1
A Model with Full Depreciation
.197
5.2.2
A Model with Leisure in the Utility Function
.200
5.2.3
Numerical Solutions of the Growth Model
Under Full Depreciation
.202
5.3
Solving a Simple, Stochastic Version of the Planner's Problem
.203
5.3.1
Solving the Linear-Quadratic Approximation
to the Planner's Problem
.204
5.3.2
The Log-Linear Approximation to the Model
.210
5.3.3
The Blanchard-Kahn Solution Method for the Stochastic
Planner's Problem. Log-Linear Approximation
.212
5.3.4
Uhlig'
s
Undetermined Coefficients Approach.
Log-Linear Approximation
.215
5.3.5
Sims' Eigenvalue-Eigenvector Decomposition Method
Using a Linear Approximation to the Model
.217
5.4
Solving the Stochastic Representative Agent's Problem
with Taxes
.225
5.4.1
The Log-Linear Approximation
.227
5.4.2
Numerical Exercise: Solving the Stochastic Representative
Agent's Model with Taxes Through
Blanchard
and
Kahn'
s
Approach. Log-Linear Approximation
.228
5.4.3
Numerical Exercise: Computing Impulse Responses
to a Technology Shock. Log-Linear Approximation
.232
5.4.4
Numerical Exercise: Solving the Stochastic Representative
Agent's Model with Taxes Through the Eigenvector
and Eigenvalue Decomposition Approach.
Linear Approximation
.234
5.5
Nonlinear Numerical Solution Methods
.238
5.5.1
Parameterized Expectations
.238
5.5.2
Projection Methods
.241
5.6
Appendix
-
Solving the Planner's Model Under Full Depreciation
. 251
5.7
Exercises
.253
Endogenous Growth Models
.257
6.1
TheAřModel
.257
6.1.1
Balanced Growth Path
.259
6.1.2
Transitional Dynamics
.259
6.1.3
Boundedness of Time-Aggregate Utility
.261
Contents
6.2
The Discrete Time Version of the Model
.262
6.2.1
The Transversality Condition and Bounded Utility
.265
6.2.2
Absence of Transitional Dynamics: Relationship
Between the Stock of Physical Capital and Consumption
. 266
6.3
Stability in the AK Model
.267
6.4
Effects from Transitory Changes in Policy Parameters
.271
6.4.1
A Policy Intervention
.272
6.4.2
A Comparison with the Cass-Koopmans Economy
.273
6.5
Dynamic
Laffer
Curves
.275
6.5.1
Numerical Exercise on Dynamic
Laffer
Curves
.278
6.6
Solving the Stochastic, Discrete Time Version of the AK Model
_280
6.6.1
A Linear Approximation to the Stochastic AK Model
.282
6.6.2
Numerical Exercise: Solving the Stochastic AK Model
.285
6.7
An Endogenous Growth Model with Productive Public
Expenditures: Barro's Model
.286
6.8
Transitional Dynamics in Endogenous Growth: The Jones
and Manuelli Model
.288
6.8.1
Steady-State
.290
6.8.2
Solving the Deterministic Version of Jones and Manuelli's
Model Through a Linear Approximation
.291
6.9
The Stochastic Version of Jones and Manuelli Model
.294
6.9.1
Deterministic Balanced Growth Path
.295
6.9.2
Transforming the Model in Stationary Ratios
.295
6.9.3
The Phase Diagram of the Deterministic Version
of the Jones-Manuelli Model: Transitional Dynamics
.296
6.9.4
Computing the Dynamics: Log-Linear Approximation
.298
6.9.5
Numerical Exercise: Solving the Jones
and Manuelli Model
.301
6.9.6
The Stochastic AK Model as a Special Case
.301
6.10
Exercises
.302
Additional Endogenous Growth Models
.305
7.1
Introduction
.305
7.2
A Variety of Producer Products
.306
7.2.1
The Economy
.306
7.2.2
The Inefficiency of the Equilibrium Allocation
.314
7.2.3
A Stochastic Version of the Economy with a Variety
of Intermediate Goods
.316
7.3
Technological Diffusion and Growth
.323
7.3.1
The Problem of the Follower Country
.324
7.3.2
Deterministic Steady-State
.326
7.3.3
Computing the Numerical Solution by Log-Linear
Approximations and Numerical Derivatives
.328
Contents
7.3.4
Numerical Exercise: Solving the Model with Varieties
of Intermediate Goods, and the Diffusion Growth Model
. 332
7.4
Schumpeterian Growth
.333
7.4.1
The Economy
.334
7.4.2
Computing Equilibrium Trajectories
.338
7.4.3
Deterministic Steady-State
.341
7.5
Endogenous Growth with Accumulation of Human Capital
.342
7.5.1
The Economy
.343
7.5.2
The Competitive Equilibrium
.347
7.5.3
Analyzing the Deterministic Steady-State
.349
7.5.4
Numerical Exercise: Steady-State Effects of Fiscal Policy
. 352
7.5.5
Computing Equilibrium Trajectories in a Stochastic Setup
Under the Assumption of Rational Expectations
.353
7.5.6
Indeterminacy of Equilibria
.363
7.5.7
Numerical Exercise: The Correlation
Between Productivity and Hours Worked in the Human
Capital Accumulation Model
.374
7.6
Exercises
.376
Growth in Monetary Economies: Steady-State Analysis
of Monetary Policy
.377
8.1
Introduction
.377
8.2
Optimal Growth in a Monetary Economy: The Sidrauski Model
. 378
8.2.1
The Representative Agent's Problem
.380
8.2.2
Steady-State in the Monetary Growth Economy
.384
8.2.3
Golden Rule
.387
8.3
Steady-State Policy Analysis
.388
8.3.1
Optimal Steady-State Rate of Inflation
.389
8.3.2
The Welfare Cost of Inflation
.392
8.4
Two Modelling Issues: Nominal Bonds and the Timing of Real
Balances
.394
8.4.1
Nominal Bonds: The Relationship Between Real
and Nominal Interest Rates
.395
8.4.2
Real Balances in the Utility Function: At the Beginning
or at the End of the Period?
.397
8.4.3
Numerical Exercise: Optimal Rate of Inflation
Under Alternative Assumptions on Preferences
.400
8.5
Monetary Policy Analysis Under Consumption and Income Taxes
. 401
8.5.1
Steady-State
.403
8.5.2
Numerical Exercise: Computation of Steady-State Levels
Under Alternative Policy Choices
.405
8.6
Monetary Policy Under Endogenous Labor Supply
.406
8.6.1
The Neutrality of Monetary Policy Under Endogenous
Labor Supply
.406
8.6.2
Numerical Exercise: Evaluation of Steady-State Policies
with an Endogenous Labour Supply
.411
Contents xix
8.7 Optimal
Monetary Policy Under Distortionary Taxation
and Endogenous Labor
.413
8.7.1
The Model
.414
8.7.2
Implementability Condition
.417
8.7.3
The Ramsey Problem
.418
8.8
Exercises
.419
9
Transitional Dynamics in Monetary Economies:
Numerical Solutions
.423
9.1
Introduction
.423
9.2
Stability of Public Debt
.424
9.3
Alternative Strategies for Monetary Policy: Control of Nominal
Rates vs. Money Growth Control
.426
9.4
Deterministic Monetary Model with the Monetary Authority
Choosing Money Growth
.427
9.4.1
Steady-State
.429
9.4.2
Solution Through a Log-Linear Approximation
.430
9.4.3
Complex Eigenvalues
.433
9.5
Deterministic Monetary Model with the Monetary Authority
Choosing Nominal Interest Rates
.437
9.6
Transitional Effects of Policy Interventions
.441
9.6.1
Solving the Model with Nominal Interest Rates as Control
Variable, Using a Linear Approximation
.442
9.6.2
Numerical Exercise: Changes in Nominal Interest Rates
. 444
9.6.3
Solving the Model with Money Growth as Control
Variable, Using a Linear Approximation
.445
9.6.4
Numerical Exercise: Gradual vs. Drastic Changes
in Money Growth
.448
9.7
The Stochastic Version of the Monetary Model
.450
9.7.1
The Monetary Authority Chooses Nominal Interest Rates
. 452
9.7.2
The Monetary Authority Chooses Money Supply Growth
. 463
9.8
A New Keynesian Monetary Model
.469
9.8.1
A Model Without Capital Accumulation: Ireland's
(2004) . 470
9.8.2
A New Keynesian Monetary Model with Capital
Accumulation
.477
9.9
Appendix: In a Log-Linear Approximation, Etiit+\
=к~ћ.
491
9.10
Exercises
.492
10
Mathematical Appendix
.495
10.1
The Deterministic Control Problem in Continuous Time
.495
10.1.1
Transversality Condition
.496
10.1.2
The Discounted Problem
.496
10.1.3
Calculus of Variations
.498
10.2
The Deterministic Control Problem in Discrete Time
.499
10.3
First Order Differential Equations
.501
xx Contents
10.3.1 1. First Order Differential
Equations
with Constant
Coefficients
.501
10.3.2 2.
First Order Differential Equations with Variable
Coefficients
.504
10.4
Matrix Algebra
.506
10.4.1
The
2
χ
2
Case
.508
10.4.2
Systems with a Saddle Path Property
.510
10.4.3
Imposing Stability Conditions Over Time
.510
10.5
Some Notes on Complex Numbers
.513
10.6
Solving a Dynamic Two-Equation System with Complex Roots
. 514
References
.517
Index
.521 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Novales, Alfonso 1952- Fernández, Esther Ruíz, Jesús |
| author_GND | (DE-588)136495370 (DE-588)136495680 (DE-588)136415067 |
| author_facet | Novales, Alfonso 1952- Fernández, Esther Ruíz, Jesús |
| author_role | aut aut aut |
| author_sort | Novales, Alfonso 1952- |
| author_variant | a n an e f ef j r jr |
| building | Verbundindex |
| bvnumber | BV023420592 |
| callnumber-first | H - Social Science |
| callnumber-label | HD75 |
| callnumber-raw | HD75.5 |
| callnumber-search | HD75.5 |
| callnumber-sort | HD 275.5 |
| callnumber-subject | HD - Industries, Land Use, Labor |
| classification_rvk | QC 340 |
| ctrlnum | (OCoLC)269454498 (DE-599)DNB988747154 |
| dewey-full | 338.90015118 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 338 - Production |
| dewey-raw | 338.90015118 |
| dewey-search | 338.90015118 |
| dewey-sort | 3338.90015118 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| discipline_str_mv | Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV023420592 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:30:55Z |
| indexdate | 2024-07-09T21:18:15Z |
| institution | BVB |
| isbn | 9783540686651 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016603039 |
| oclc_num | 269454498 |
| open_access_boolean | |
| owner | DE-521 DE-703 DE-20 DE-945 DE-384 |
| owner_facet | DE-521 DE-703 DE-20 DE-945 DE-384 |
| physical | XX, 528 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| spelling | Novales, Alfonso 1952- Verfasser (DE-588)136495370 aut Economic growth theory and numerical solution methods Alfonso Novales ; Esther Fernández ; Jesús Ruiz Berlin [u.a.] Springer 2009 XX, 528 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 517 - 520 Economische groei gtt Economische modellen gtt Mathematisches Modell Wirtschaftsentwicklung Business cycles Mathematical models Economic development Mathematical models Monetary policy Mathematical models Stochastic processes Wachstumstheorie (DE-588)4128160-3 gnd rswk-swf Numerisches Modell (DE-588)4338132-7 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Allgemeines Gleichgewichtsmodell (DE-588)4210294-7 gnd rswk-swf Monetäre Wachstumstheorie (DE-588)4724050-7 gnd rswk-swf Wachstumstheorie (DE-588)4128160-3 s Numerisches Modell (DE-588)4338132-7 s DE-604 Monetäre Wachstumstheorie (DE-588)4724050-7 s Allgemeines Gleichgewichtsmodell (DE-588)4210294-7 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Fernández, Esther Verfasser (DE-588)136495680 aut Ruíz, Jesús Verfasser (DE-588)136415067 aut Erscheint auch als Online-Ausgabe 978-3-540-68669-9 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016603039&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Novales, Alfonso 1952- Fernández, Esther Ruíz, Jesús Economic growth theory and numerical solution methods Economische groei gtt Economische modellen gtt Mathematisches Modell Wirtschaftsentwicklung Business cycles Mathematical models Economic development Mathematical models Monetary policy Mathematical models Stochastic processes Wachstumstheorie (DE-588)4128160-3 gnd Numerisches Modell (DE-588)4338132-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Allgemeines Gleichgewichtsmodell (DE-588)4210294-7 gnd Monetäre Wachstumstheorie (DE-588)4724050-7 gnd |
| subject_GND | (DE-588)4128160-3 (DE-588)4338132-7 (DE-588)4128130-5 (DE-588)4210294-7 (DE-588)4724050-7 |
| title | Economic growth theory and numerical solution methods |
| title_auth | Economic growth theory and numerical solution methods |
| title_exact_search | Economic growth theory and numerical solution methods |
| title_exact_search_txtP | Economic growth theory and numerical solution methods |
| title_full | Economic growth theory and numerical solution methods Alfonso Novales ; Esther Fernández ; Jesús Ruiz |
| title_fullStr | Economic growth theory and numerical solution methods Alfonso Novales ; Esther Fernández ; Jesús Ruiz |
| title_full_unstemmed | Economic growth theory and numerical solution methods Alfonso Novales ; Esther Fernández ; Jesús Ruiz |
| title_short | Economic growth |
| title_sort | economic growth theory and numerical solution methods |
| title_sub | theory and numerical solution methods |
| topic | Economische groei gtt Economische modellen gtt Mathematisches Modell Wirtschaftsentwicklung Business cycles Mathematical models Economic development Mathematical models Monetary policy Mathematical models Stochastic processes Wachstumstheorie (DE-588)4128160-3 gnd Numerisches Modell (DE-588)4338132-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Allgemeines Gleichgewichtsmodell (DE-588)4210294-7 gnd Monetäre Wachstumstheorie (DE-588)4724050-7 gnd |
| topic_facet | Economische groei Economische modellen Mathematisches Modell Wirtschaftsentwicklung Business cycles Mathematical models Economic development Mathematical models Monetary policy Mathematical models Stochastic processes Wachstumstheorie Numerisches Modell Numerisches Verfahren Allgemeines Gleichgewichtsmodell Monetäre Wachstumstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016603039&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT novalesalfonso economicgrowththeoryandnumericalsolutionmethods AT fernandezesther economicgrowththeoryandnumericalsolutionmethods AT ruizjesus economicgrowththeoryandnumericalsolutionmethods |