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E-raamat: Introduction to Quantitative Macroeconomics Using Julia: From Basic to State-of-the-Art Computational Techniques

(Institute for Economic Forecasting, Romanian Academy, Bucharest, Romania)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 29-Aug-2018
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128135129
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Introduction to Quantitative Macroeconomics Using Julia: From Basic to State-of-the-Art Computational TechniquesSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 29-Aug-2018
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128135129
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Its modelling challenges make quantitative macroeconomics dynamic, yet few books provide macroeconomists with the basic tools to build, solve, and simulate macroeconomic models. Introduction to Quantitative Macroeconomics Using Julia facilitates access to fundamental techniques in computational and quantitative macroeconomics. One of its most appealing elements is its focus on the recent and very promising software Julia, which offers a MATLAB-like language at speeds comparable to C/Fortran. It neatly fills the gap between intermediate macroeconomic books and modern DSGE models used in research.

  • Combines an introduction to Julia with the specific needs of macroeconomic students who are interested in DSGE models and PhD students and researchers interested in building DSGE models
  • Teaches fundamental techniques in quantitative macroeconomics by introducing theoretical elements of key macroeconomic models and their potential algorithmic implementations
  • Exposes researchers working in macroeconomics to staate-of-the-art computational techniques for simulating and solving DSGE models

Arvustused

"The book is one of the few books written for economists having expertise in mathematics. The book focuses mainly on computational aspects of macroeconomics from the perspective of Julia. In this book the author has left a long lasting impact on important mathematical foundations of macroeconomics. This process makes the book self sufficient to use Julia in macroeconomics.... Now, if I have to write about the weakness of the book, then I suggest to include a few separate chapters on basic macroeconomics in this book. These chapters will make this book self sufficient from the perspective of mathematicians, statisticians, computer scientists, etc. Moreover, these basic chapters will also attract their attentions on macroeconomics from the perspective of Julia and the book will have readers from interdisciplinary areas. At the end, I would like to congratulate the author for writing a book on a programming language Julia which has been gaining its applicability slowly. The book will have long run impact in the area of computational macroeconomics. Thus, this book is highly recommended for undergraduate students, graduate students, researchers, etc. those who want to learn and apply new programming language Julia in their research activities of macroeconomics and allied areas. Overall, this book must be considered as an extraordinary and most useful book for Julia." --zbMath/European Mathematical Society and the Heidelberg Academy of Sciences and Humanities "A concise and elegant introduction to many of the topics involved in the solution of dynamic macroeconomic models. Caraiani 's use of Julia is a fantastic choice for teaching modern numerical methods." --Jesus Fernandez-Villaverde, University of Pennsylvania

"Julia is a computer language that is taking economics by storm. In this book, Petre Caraiani takes the reader by their hands and introduce them to a wide variety of numerical methods that are then applied to recent macroeconomic models. The book explains these methods and applies them in Julia not only those models with representative-agent (RBC and DSGE models), but also to heterogeneous-agents models. Therefore, the book is a valuable source for readers interested in numerical methods and in Julia." --Pedro Garcia Duarte, University of São Paulo

"Petre Caraianis book guides the readers into the sophisticated and innovative field of quantitative macroeconomics with the aim of bridging the gap between theoretical models and modern computational techniques. Caraiani provides an outstandingly clear exposition of the numerical methods by which researchers and graduate students can approach the complex problems of solving DSGE models or setting up heterogeneous agents models. This book is a must for all those who are interested in making theoretical macroeconomics an empirical discipline." --Peter Galbács, Budapest Business School

"This book provides an excellent overview of key numerical tools to study macroeconomic models and provides supporting programs using Julia, a frontier programming language." --Wouter den Haan, London School of Economics

"This book provides a clear and comprehensive introduction to the numerical techniques that every student that aims at doing quantitative economics should know. Not only the book provides with a minimal introduction to the theory underlying these methods, but it also offers many examples, all coded in a modern language, Julia. This book is definitely a good reference for whoever needs a quick and nice introduction to these techniques." --Fabrice Collard, University of Bern

About the Author vii
Preface ix
Acknowledgments xi
1 Introduction to Julia
1.1 Overview
1(1)
1.2 Julia in a Nutshell
1(24)
1.2.1 Installing Julia
1(1)
1.2.2 Julia Packages
2(1)
1.2.3 Understanding REPL
2(1)
1.2.4 Variables and Operations
3(3)
1.2.5 Vectors
6(1)
1.2.6 Multidimensional Arrays
7(2)
1.2.7 Functions
9(3)
1.2.8 Control Flows
12(5)
1.2.9 Random Numbers
17(1)
1.2.10 Working With Data
18(1)
1.2.11 Working With Dates
19(2)
1.2.12 Data Frames
21(1)
1.2.13 Plotting in Julia
22(3)
1.3 Advanced Features
25(2)
1.3.1 Julia's Type System
25(1)
1.3.2 Multiple Dispatch
25(1)
1.3.3 Vectorization
26(1)
References
26(1)
2 Basic Numerical Techniques
2.1 Overview
27(1)
2.2 Linear Algebra
27(6)
2.2.1 Direct Methods
28(3)
2.2.2 Iterative Methods
31(1)
2.2.3 Eigenvalues and Eigenvectors
32(1)
2.3 Interpolation and Curve Fitting
33(8)
2.3.1 Polynomial Interpolation
33(2)
2.3.2 Spline Interpolation
35(1)
2.3.3 B-splines
36(1)
2.3.4 Interpolation in Julia
37(1)
2.3.5 Curve Fitting
38(2)
2.3.6 Curve Fitting In Julia
40(1)
2.4 Function Approximation
41(9)
2.4.1 Local Approximation
41(1)
2.4.2 Doing Approximations With Regression
42(1)
2.4.3 Orthogonal Polynomials
42(1)
2.4.4 Least Square Orthogonal Polynomials Approximation
43(2)
2.4.5 Chebyshev Approximation
45(1)
2.4.6 Shape-Preserving Approximation
45(2)
2.4.7 Multidimensional Approximations
47(2)
2.4.8 Doing Function Approximations in Julia
49(1)
2.5 Numerical Differentiation
50(4)
2.5.1 Finite Difference
51(2)
2.5.2 Richardson Extrapolation
53(1)
2.5.3 Using Interpolation to Approximate the Derivatives
54(1)
2.5.4 Numerical Differentiation in Julia
54(1)
2.6 Numerical Integration
54(14)
2.6.1 Newton-Cotes Methods
55(1)
2.6.2 The Simpson Rule
56(1)
2.6.3 Infinite Integration
57(1)
2.6.4 Gaussian Quadrature Methods
58(3)
2.6.5 Multivariate Integration
61(1)
2.6.6 Monte Carlo Integration
62(2)
2.6.7 Quasi Monte Carlo Integration
64(1)
2.6.8 Numerical Integration in Julia
65(3)
2.7 Root Finding and Nonlinear Equations
68(8)
2.7.1 The Bisection Method
68(1)
2.7.2 Newton's Method
69(1)
2.7.3 Function Iteration
70(1)
2.7.4 Quasi-Newton Methods
70(1)
2.7.5 Multivariate Methods
71(2)
2.7.6 Comparing Methods to Solve for Roots
73(1)
2.7.7 Solving for Roots of Polynomials
74(1)
2.7.8 Complementarity Problems in Julia
74(2)
2.7.9 Solving for Roots in Julia
76(1)
2.8 Optimization
76(11)
2.8.1 One-Dimensional Optimization
77(2)
2.8.2 Multidimensional Optimization
79(2)
2.8.3 The Nonlinear Least Square
81(2)
2.8.4 Constrained Optimization
83(2)
2.8.5 Optimization in Julia
85(2)
2.9 Computing the Accuracy of Approximations
87(4)
References
89(2)
3 Solving and Simulating DSGE Models
3.1 Introduction
91(1)
3.2 Deterministic Difference Equations
91(8)
3.2.1 First-Order Linear Equations
91(1)
3.2.2 Lag Operator
92(1)
3.2.3 Higher-Order Linear Equations
92(4)
3.2.4 Deterministic Linear Systems
96(3)
3.3 Stochastic Difference Equations
99(6)
3.3.1 Modeling the Rational Expectations
99(1)
3.3.2 First-Order Stochastic Linear Equations
99(3)
3.3.3 Multivariate Linear Rational Expectations Models
102(1)
3.3.4 The Blanchard-Kahn Approach
102(1)
3.3.5 The Klein Approach
103(1)
3.3.6 The Sims Approach
103(2)
3.4 Applications in Julia
105(14)
3.4.1 A Real Business Cycle Model
105(7)
3.4.2 A Basic New Keynesian Model
112(4)
3.4.3 DSGE Models in Julia
116(1)
References
117(2)
4 Dynamic Programming
4.1 Introduction
119(1)
4.2 Deterministic Dynamic Programming
119(10)
4.2.1 Theory
119(5)
4.2.2 Numerical Algorithms and Applications
124(5)
4.3 Stochastic Dynamic Programming
129(20)
4.3.1 Theory
129(14)
4.3.2 Numerical Algorithms and Applications
143(6)
4.4 Linear Quadratic Dynamic Programming
149(10)
4.4.1 The Deterministic Optimal Linear Regulator Problem
149(6)
4.4.2 The Stochastic Optimal Linear Regulator Problem
155(2)
References
157(2)
5 Advanced Numerical Techniques
5.1 Introduction
159(1)
5.2 Perturbation Methods
159(15)
5.2.1 The General Framework
159(2)
5.2.2 Solving DSGE Models With the Perturbation Method
161(3)
5.2.3 Applications in Julia
164(10)
5.3 Parameterized Expectations Algorithm
174(5)
5.3.1 The Theory
174(1)
5.3.2 An Example in Julia
175(4)
5.4 Projection Methods
179(22)
5.4.1 The Theory
179(2)
5.4.2 The Projection Method Algorithms and Applications
181(19)
References
200(1)
6 Heterogeneous Agents Models
6.1 Introduction
201(1)
6.2 Computing the Stationary Distribution
201(14)
6.2.1 The Baseline Model
201(1)
6.2.2 The Stationary Equilibrium
202(1)
6.2.3 A General Algorithm
203(1)
6.2.4 Examples in Julia
204(11)
6.3 Dynamics of the Distribution Function
215(8)
6.3.1 Introducing Dynamics in a Model Economy With Heterogeneous Agents
215(4)
6.3.2 Dynamic Heterogeneous Agents Models With Aggregate Uncertainty
219(2)
References
221(2)
Index 223
Petre Caraiani is a researcher at the Institute for Economic Forecasting at Romanian Academy. His principal research interests include DSGE modelling, business cycles, and forecasting. Petre has published numerous articles in major journals, including Journal of Macroeconomics, Economics Letters, Economic Modelling, Empirical Economics and International Review of Economics & Finance.
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