Economic Growth : Theory and Numerical Solution Methods
by Novales, Alfonso; Fernandez, Esther; Ruiz, JesusFormat: Hardcover
Pub. Date: 2009-02-28
Publisher(s): Springer Verlag
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Summary
"This is a book on deterministic and stochastic Growth Theory and the computational methods needed to produce numerical solutions. The book is self contained and it is designed so that the student advances in the theoretical and the computational issues in parallel. EXCEL and Matlab files are provided on an accompanying website to illustrate theoretical results as well as to simulate the effects of economic policy interventions."--BOOK JACKET.
Author Biography
ALFONSO NOVALES is Professor of Economics at the Department of Quantitative Economics at Universidad Complutense (Madrid). He holds a Ph.D. in Economics from University of Minnesota and a Ph.D. in Mathematics from Universidad del Pais Vasco. After graduation, he was Assistant Professor at State University of New York (Stony Brook). He has been President of the Spanish Economic Association and chairman of FEDEA (Fundaci+¦n de Estudios de Econom+¡a Aplicada, Madrid). He has published in Econometrica, Journal of Economic Dynamics and Control, Journal of Macroeconomics, International Journal of Forecasting, Journal of Forecasting, Journal of Time Series Analysis, Journal of Banking and Finance, Economic Modelling, Computational Economics, Journal of International Financial Institutions, Markets and Money, International Journal of Money and Finance, Applied Financial Economics, Applied Economics Letters, and International Journal of Finance, and he has contributed with chapters to books on Macroeconomics and Econometrics. He is the author of Econometria and Estadistica y Econometr+¡a, both textbooks edited by McGrawHill in Spanish. His research interests include Economic Policy Evaluation and Financial Econometrics. JESUS RUIZ is Associate Professor of Economics at the Department of Quantitative Economics at Universidad Complutense (Madrid). He obtained his Ph.D. in Economics from Universidad Complutense in 1997. He has published in Journal of Economic Dynamics and Control, Economic Modelling, Applied Financial Economics, Spanish Economic Review and other Spanish journals, and he has contributed with chapters to books on Computational Economics. His research interests include Economic Policy Evaluation in Dynamic Macroeconomic Models and Environmental Economics. ESTHER FERN+üNDEZ is Associate Professor of Economics at the Department of Quantitative Economics at Universidad Complutense (Madrid). Her Ph.D. dissertation was selected as the best doctoral dissertation in Economics at Universidad Complutense in 1999. Her research interests include Monetary Theory, Economic Growth and Environmental Economics. She has published at Economic Modelling and Spanish academic journals.
Table of Contents
| Introduction | p. 1 |
| A Few Time Series Concepts | p. 2 |
| Some Simple Stochastic Processes | p. 3 |
| Stationarity, Mean Reversion, Impulse Responses | p. 6 |
| Numerical Exercise: Simulating Simple Stochastic Processes | p. 9 |
| Structural Macroeconomic Models | p. 12 |
| Static Structural Models | p. 12 |
| Dynamic Structural Models | p. 16 |
| Stochastic, Dynamic Structural Models | p. 21 |
| Stochastic Simulation | p. 23 |
| Numerical Exercise - Simulating Dynamic, Structural Macroeconomic Models | p. 24 |
| Why are Economic Growth Models Interesting? | p. 27 |
| Microeconomic Foundations of Macroeconomics | p. 27 |
| Lucas' Critique on Economic Policy Evaluation | p. 33 |
| A Brief Overview of Developments on Growth Theory | p. 35 |
| The Use of Growth Models for Actual Policy Making | p. 39 |
| Numerical Solution Methods | p. 40 |
| Why do we Need to Compute Numerical Solutions to Growth Models? | p. 40 |
| Stability | p. 42 |
| Indeterminacy | p. 43 |
| The Type of Questions We Ask and the Conclusions We Reach | p. 44 |
| Synopsis of the Book | p. 48 |
| The Neoclassical Growth Model Under a Constant Savings Rate | p. 53 |
| Introduction | p. 53 |
| Returns to Scale and Sustained Growth | p. 54 |
| The Neoclassical Growth Model of Solow and Swan | p. 59 |
| Description of the Model | p. 60 |
| The Dynamics of the Economy | p. 61 |
| Steady-State | p. 64 |
| The Transition Towards Steady-State | p. 68 |
| The Duration of the Transition to Steady-State | p. 69 |
| The Growth Rate of Output and Consumption | p. 69 |
| Convergence in the Neoclassical Model | p. 71 |
| A Special Steady-State: The Golden Rule of Capital Accumulation | p. 73 |
| Solving the Continuous-Time Solow-Swan Model | p. 76 |
| Solution to the Exact Model | p. 76 |
| The Linear Approximation to the Solow-Swan Model | p. 77 |
| Changes in Structural Parameters | p. 79 |
| Dynamic Inefficiency | p. 82 |
| The Deterministic, Discrete-Time Solow Swan Model | p. 85 |
| The Exact Solution | p. 85 |
| Approximate Solutions to the Discrete-Time Model | p. 87 |
| Numerical Exercise - Solving the Deterministic Solow-Swan Model | p. 89 |
| Numerical Exercise - A Permanent Change in the Savings Rate | p. 91 |
| Numerical Exercise - Dynamic Inefficiency | p. 93 |
| The Stochastic, Discrete Time Version of the Solow-Swan Model | p. 95 |
| Numerical Exercise - Solving the Stochastic Solow-Swan Model | p. 96 |
| Exercises | p. 98 |
| Optimal Growth. Continuous Time Analysis | p. 101 |
| The Continuous-Time Version of the Cass-Koopmans Model | p. 101 |
| Optimality Conditions for the Cass-Koopmans Model | p. 103 |
| The Instantaneous Elasticity of Substitution of Consumption (IES) | p. 104 |
| Risk Aversion and the Intertemporal Substitution of Consumption | p. 106 |
| Keynes-Ramsey Condition | p. 107 |
| The Optimal Steady-State | p. 108 |
| Numerical Exercise: The Sensitivity of Steady-State Levels to Changes in Structural Parameters | p. 110 |
| Existence, Uniqueness and Stability of Long-Run Equilibrium - A Graphical Discussion | p. 112 |
| Suboptimality of the Golden Rule | p. 114 |
| Stability and Convergence | p. 115 |
| The Trajectory for Income | p. 119 |
| Numerical Exercise - Characterizing the Transition after a Change in a Structural Parameter | p. 120 |
| Interpreting the Central Planners's Model as a Competitive Equilibrium Economy | p. 126 |
| The Efficiency of Competitive Equilibrium | p. 129 |
| A Competitive Equilibrium with Government | p. 131 |
| The Structure of the Economy | p. 131 |
| Feasible Stationary Public Expenditure and Financing Policies | p. 135 |
| Competitive Equilibrium | p. 135 |
| Global Constraint of Resources | p. 136 |
| The Representative Agent Problem | p. 136 |
| On the Efficiency of Equilibrium with Government | p. 138 |
| On the Efficiency of Equilibrium Under Lump-Sum Taxes and Debt | p. 138 |
| The Inefficiency of the Competitive Equilibrium Allocation Under Distortionary Taxes | p. 140 |
| The Ricardian Doctrine | p. 146 |
| The Ricardian Doctrine Under Non-Distorting Taxes | p. 146 |
| Failure of the Ricardian Doctrine Under Distorting Taxes | p. 147 |
| Appendix | p. 149 |
| Appendix 1 - Log-linear Approximation to the Continuous Time Version of Cass-Koopmans Model | p. 149 |
| Appendix 2 - An Alternative Presentation of the Equivalence Between the Planner's and the Competitive Equilibrium Mechanisms in an Economy Without Government | p. 150 |
| Exercises | p. 153 |
| Optimal Growth. Discrete Time Analysis | p. 155 |
| Discrete-Time, Determinstic Cass-Koopmans Model | p. 155 |
| The Global Constraint of Resources | p. 155 |
| Discrete-Time Formulation of the Planner's Problem | p. 157 |
| The Optimal Steady-State | p. 158 |
| The Dynamics of the Model: The Phase Diagram | p. 159 |
| Transversality Condition in Discrete Time | p. 161 |
| Competitive Equilibrium with Government | p. 162 |
| Fiscal Policy in the Cass-Koopmans Model | p. 167 |
| The Deterministic Case | p. 167 |
| Numerical Exercise - Solving the Deterministic Competitive Equilibrium with Taxes | p. 176 |
| Numerical Exercise - Fiscal Policy Evaluation | p. 179 |
| Appendices | p. 185 |
| A Reformulation of the Stability Condition for the Deterministic Version of the Model | p. 185 |
| The Intertemporal Government Budget Constraint | p. 187 |
| Appendix 2: The Ricardian Proposition Under Non-Distortionary Taxes in Discrete Time | p. 190 |
| Exercises | p. 191 |
| Numerical Solution Methods | p. 195 |
| Numerical Solutions and Simulation Analysis | p. 195 |
| Analytical Solutions to Simple Growth Models | p. 197 |
| A Model with Full Depreciation | p. 197 |
| A Model with Leisure in the Utility Function | p. 200 |
| Numerical Solutions of the Growth Model Under Full Depreciation | p. 202 |
| Solving a Simple, Stochastic Version of the Planner's Problem | p. 203 |
| Solving the Linear-Quadratic Approximation to the Planner's Problem | p. 204 |
| The Log-Linear Approximation to the Model | p. 210 |
| The Blanchard-Kahn Solution Method for the Stochastic Planner's Problem. Log-Linear Approximation | p. 212 |
| Uhlig's Undetermined Coefficients Approach. Log-Linear Approximation | p. 215 |
| Sims' Eigenvalue-Eigenvector Decomposition Method Using a Linear Approximation to the Model | p. 217 |
| Solving the Stochastic Representative Agent's Problem with Taxes | p. 225 |
| The Log-Linear Approximation | p. 227 |
| Numerical Exercise: Solving the Stochastic Representative Agent's Model with Taxes Through Blanchard and Kahn's Approach. Log-Linear Approximation | p. 228 |
| Numerical Exercise: Computing Impulse Responses to a Technology Shock. Log-Linear Approximation | p. 232 |
| Numerical Exercise: Solving the Stochastic Representative Agent's Model with Taxes Through the Eigenvector and Eigenvalue Decomposition Approach. Linear Approximation | p. 234 |
| Nonlinear Numerical Solution Methods | p. 238 |
| Parameterized Expectations | p. 238 |
| Projection Methods | p. 241 |
| Appendix - Solving the Planner's Model Under Full Depreciation | p. 251 |
| Exercises | p. 253 |
| Endogenous Growth Models | p. 257 |
| The AK Model | p. 257 |
| Balanced Growth Path | p. 259 |
| Transitional Dynamics | p. 259 |
| Boundedness of Time-Aggregate Utility | p. 261 |
| The Discrete Time Version of the Model | p. 262 |
| The Transversality Condition and Bounded Utility | p. 265 |
| Absence of Transitional Dynamics: Relationship Between the Stock of Physical Capital and Consumption | p. 266 |
| Stability in the AK Model | p. 267 |
| Effects from Transitory Changes in Policy Parameters | p. 271 |
| A Policy Intervention | p. 272 |
| A Comparison with the Cass-Koopmans Economy | p. 273 |
| Dynamic Laffer Curves | p. 275 |
| Numerical Exercise on Dynamic Laffer Curves | p. 278 |
| Solving the Stochastic, Discrete Time Version of the AK Model | p. 280 |
| A Linear Approximation to the Stochastic AK Model | p. 282 |
| Numerical Exercise: Solving the Stochastic AK Model | p. 285 |
| An Endogenous Growth Model with Productive Public Expenditures: Barro's Model | p. 286 |
| Transitional Dynamics in Endogenous Growth: The Jones and Manuelli Model | p. 288 |
| Steady-State | p. 290 |
| Solving the Deterministic Version of Jones and Manuelli's Model Through a Linear Approximation | p. 291 |
| The Stochastic Version of Jones and Manuelli Model | p. 294 |
| Deterministic Balanced Growth Path | p. 295 |
| Transforming the Model in Stationary Ratios | p. 295 |
| The Phase Diagram of the Deterministic Version of the Jones-Manuelli Model: Transitional Dynamics | p. 296 |
| Computing the Dynamics: Log-Linear Approximation | p. 298 |
| Numerical Exercise: Solving the Jones and Manuelli Model | p. 301 |
| The Stochastic AK Model as a Special Case | p. 301 |
| Exercises | p. 302 |
| Additional Endogenous Growth Models | p. 305 |
| Introduction | p. 305 |
| A Variety of Producer Products | p. 306 |
| The Economy | p. 306 |
| The Inefficiency of the Equilibrium Allocation | p. 314 |
| A Stochastic Version of the Economy with a Variety of Intermediate Goods | p. 316 |
| Technological Diffusion and Growth | p. 323 |
| The Problem of the Follower Country | p. 324 |
| Deterministic Steady-State | p. 326 |
| Computing the Numerical Solution by Log-Linear Approximations and Numerical Derivatives | p. 328 |
| Numerical Exercise: Solving the Model with Varieties of Intermediate Goods, and the Diffusion Growth Model | p. 332 |
| Schumpeterian Growth | p. 333 |
| The Economy | p. 334 |
| Computing Equilibrium Trajectories | p. 338 |
| Deterministic Steady-State | p. 341 |
| Endogenous Growth with Accumulation of Human Capital | p. 342 |
| The Economy | p. 343 |
| The Competitive Equilibrium | p. 347 |
| Analyzing the Deterministic Steady-State | p. 349 |
| Numerical Exercise: Steady-State Effects of Fiscal Policy | p. 352 |
| Computing Equilibrium Trajectories in a Stochastic Setup Under the Assumption of Rational Expectations | p. 353 |
| Indeterminacy of Equilibria | p. 363 |
| Numerical Exercise: The Correlation Between Productivity and Hours Worked in the Human Capital Accumulation Model | p. 374 |
| Exercises | p. 376 |
| Growth in Monetary Economies: Steady-State Analysis of Monetary Policy | p. 377 |
| Introduction | p. 377 |
| Optimal Growth in a Monetary Economy: The Sidrauski Model | p. 378 |
| The Representative Agent's Problem | p. 380 |
| Steady-State in the Monetary Growth Economy | p. 384 |
| Golden Rule | p. 387 |
| Steady-State Policy Analysis | p. 388 |
| Optimal Steady-State Rate of Inflation | p. 389 |
| The Welfare Cost of Inflation | p. 392 |
| Two Modelling Issues: Nominal Bonds and the Timing of Real Balances | p. 394 |
| Nominal Bonds: The Relationship Between Real and Nominal Interest Rates | p. 395 |
| Real Balances in the Utility Function: At the Beginning or at the End of the Period? | p. 397 |
| Numerical Exercise: Optimal Rate of Inflation Under Alternative Assumptions on Preferences | p. 400 |
| Monetary Policy Analysis Under Consumption and Income Taxes | p. 401 |
| Steady-State | p. 403 |
| Numerical Exercise: Computation of Steady-State Levels Under Alternative Policy Choices | p. 405 |
| Monetary Policy Under Endogenous Labor Supply | p. 406 |
| The Neutrality of Monetary Policy Under Endogenous Labor Supply | p. 406 |
| Numerical Exercise: Evaluation of Steady-State Policies with an Endogenous Labour Supply | p. 411 |
| Optimal Monetary Policy Under Distortionary Taxation and Endogenous Labor | p. 413 |
| The Model | p. 414 |
| Implementability Condition | p. 417 |
| The Ramsey Problem | p. 418 |
| Exercises | p. 419 |
| Transitional Dynamics in Monetary Economies: Numerical Solutions | p. 423 |
| Introduction | p. 423 |
| Stability of Public Debt | p. 424 |
| Alternative Strategies for Monetary Policy: Control of Nominal Rates vs. Money Growth Control | p. 426 |
| Deterministic Monetary Model with the Monetary Authority Choosing Money Growth | p. 427 |
| Steady-State | p. 429 |
| Solution Through a Log-Linear Approximation | p. 430 |
| Complex Eigenvalues | p. 433 |
| Deterministic Monetary Model with the Monetary Authority Choosing Nominal Interest Rates | p. 437 |
| Transitional Effects of Policy Interventions | p. 441 |
| Solving the Model with Nominal Interest Rates as Control Variable, Using a Linear Approximation | p. 442 |
| Numerical Exercise: Changes in Nominal Interest Rates | p. 444 |
| Solving the Model with Money Growth as Control Variable, Using a Linear Approximation | p. 445 |
| Numerical Exercise: Gradual vs. Drastic Changes in Money Growth | p. 448 |
| The Stochastic Version of the Monetary Model | p. 450 |
| The Monetary Authority Chooses Nominal Interest Rates | p. 452 |
| The Monetary Authority Chooses Money Supply Growth | p. 463 |
| A New Keynesian Monetary Model | p. 469 |
| A Model Without Capital Accumulation: Ireland's (2004) | p. 470 |
| A New Keynesian Monetary Model with Capital Accumulation | p. 477 |
| Appendix: In a Log-Linear Approximation, E[subscript t phi subscript t+1] = i[subscript t] - r[subscript t] | p. 491 |
| Exercises | p. 492 |
| Mathematical Appendix | p. 495 |
| The Deterministic Control Problem in Continuous Time | p. 495 |
| Transversality Condition | p. 496 |
| The Discounted Problem | p. 496 |
| Calculus of Variations | p. 498 |
| The Deterministic Control Problem in Discrete Time | p. 499 |
| First Order Differential Equations | p. 501 |
| 1. First Order Differential Equations with Constant Coefficients | p. 501 |
| 2. First Order Differential Equations with Variable Coefficients | p. 504 |
| Matrix Algebra | p. 506 |
| The 2 x 2 Case | p. 508 |
| Systems with a Saddle Path Property | p. 510 |
| Imposing Stability Conditions Over Time | p. 510 |
| Some Notes on Complex Numbers | p. 513 |
| Solving a Dynamic Two-Equation System with Complex Roots | p. 514 |
| References | p. 517 |
| Index | p. 521 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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