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E-raamat: Economic Dynamics in Discrete Time, second edition

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  • Ilmumisaeg: 03-Mar-2020
  • Kirjastus: MIT Press
  • Keel: eng
  • ISBN-13: 9780262357333
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  • Formaat: EPUB+DRM
  • Sari: The MIT Press
  • Ilmumisaeg: 03-Mar-2020
  • Kirjastus: MIT Press
  • Keel: eng
  • ISBN-13: 9780262357333
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A unified and comprehensive introduction to the analytical and numerical tools for solving dynamic economic problems; substantially revised for the second edition.

A unified and comprehensive introduction to the analytical and numerical tools for solving dynamic economic problems; substantially revised for the second edition.

This book offers a unified, comprehensive, and up-to-date treatment of analytical and numerical tools for solving dynamic economic problems. The focus is on introducing recursive methods—an important part of every economist's set of tools—and readers will learn to apply recursive methods to a variety of dynamic economic problems. The book is notable for its combination of theoretical foundations and numerical methods. Each topic is first described in theoretical terms, with explicit definitions and rigorous proofs; numerical methods and computer codes to implement these methods follow. Drawing on the latest research, the book covers such cutting-edge topics as asset price bubbles, recursive utility, robust control, policy analysis in dynamic New Keynesian models with the zero lower bound on interest rates, and Bayesian estimation of dynamic stochastic general equilibrium (DSGE) models.

This second edition has been substantially updated. Responding to renewed interest in modeling with multiple equilibria, it incorporates new material on this topic throughout. It offers an entirely new chapter on deterministic nonlinear systems, and provides new material on such topics as linear planar systems, chaos, bifurcations, indeterminacy and sunspot solutions, pruning nonlinear solutions, the bandit problem, rational inattention models, bequests, self-fulfilling prophecies, the cyclical behavior of unemployment and vacancies, and the long-run risk model. The exposition of each chapter has been revised and improved, and many new figures, Matlab codes, and exercises have been added. A student solutions manual can be purchased separately.

Preface to the Second Edition xvii
Acknowledgments xix
I Dynamical Systems 1(164)
1 Deterministic Linear Systems
3(28)
1.1 Some Basic Concepts
3(3)
1.2 Scalar First-Order Linear Difference Equations
6(4)
1.3 Lag Operators
10(1)
1.4 Scalar Second-Order Linear Difference Equations
11(2)
1.5 Planar Linear Systems
13(3)
1.5.1 Distinct Real Eigenvalues
14(1)
1.5.2 Repeated Real Eigenvalues
15(1)
1.5.3 Complex Eigenvalues
16(1)
1.6 Phase Diagrams
16(2)
1.7 Higher-Dimensional Linear Systems
18(11)
1.7.1 Nonsingular Systems
20(6)
1.7.2 Singular Systems
26(3)
1.8 Exercises
29(2)
2 Deterministic Nonlinear Systems
31(34)
2.1 Linear Approximation
31(2)
2.2 Local Stability
33(5)
2.3 Lyapunov Function
38(3)
2.4 Cycles and Chaos
41(14)
2.4.1 Periodic Solutions
41(2)
2.4.2 Bifurcations
43(6)
2.4.3 Chaos
49(6)
2.5 Numerical Solutions Using Dynare
55(7)
2.6 Exercises
62(3)
3 Stochastic Difference Equations
65(38)
3.1 First-Order Linear Systems
65(2)
3.2 Scalar Linear Rational Expectations Models
67(4)
3.2.1 Lag Operators
67(3)
3.2.2 Method of Undetermined Coefficients
70(1)
3.3 Multivariate Linear Rational Expectations Models
71(10)
3.3.1 Blanchard-Kahn Method
71(2)
3.3.2 Klein Method
73(2)
3.3.3 Sims Method
75(6)
3.4 Nonlinear Rational Expectations Models
81(4)
3.5 Numerical Solutions Using Dynare
85(9)
3.6 Indeterminacy and Sunspot Equilibria
94(2)
3.7 Pruning Nonlinear Solutions
96(3)
3.8 Exercises
99(4)
4 Markov Processes
103(44)
4.1 Markov Chains
104(24)
4.1.1 Classification of States
108(3)
4.1.2 Stationary Distribution: Finite State Space
111(7)
4.1.3 Countable-State Markov Chains
118(10)
4.2 General Markov Processes
128(4)
4.3 Convergence
132(8)
4.3.1 Strong Convergence
132(5)
4.3.2 Weak Convergence
137(3)
4.4 Markov Chain Monte Carlo Algorithms
140(3)
4.5 Exercises
143(4)
5 Ergodic Theory and Stationary Processes
147(18)
5.1 Ergodic Theorem
147(5)
5.2 Application to Stationary Processes
152(7)
5.3 Application to Stationary Markov Processes
159(5)
5.4 Exercises
164(1)
II Dynamic Optimization 165(248)
6 Markov Decision Process Model
167(16)
6.1 Model Setup
167(6)
6.2 Examples
173(8)
6.2.1 Discrete Choice
173(1)
6.2.2 Optimal Stopping
174(3)
6.2.3 Bandit Model
177(3)
6.2.4 Optimal Control
180(1)
6.3 Exercises
181(2)
7 Finite-Horizon Dynamic Programming
183(28)
7.1 A Motivating Example
183(4)
7.2 Measurability Problem
187(2)
7.3 Principle of Optimality
189(7)
7.4 Optimal Control
196(6)
7.5 Maximum Principle
202(4)
7.6 Applications
206(3)
7.6.1 Secretary Problem
206(1)
7.6.2 A Consumption-Saving Problem
207(2)
7.7 Exercises
209(2)
8 Infinite-Horizon Dynamic Programming
211(36)
8.1 Principle of Optimality
211(9)
8.2 Bounded Rewards
220(2)
8.3 Unbounded Rewards
222(7)
8.3.1 Negative Dynamic Programming
222(3)
8.3.2 Weighted Contraction Approach
225(4)
8.4 Optimal Control
229(4)
8.5 The Maximum Principle and Transversality Conditions
233(3)
8.6 Euler Equations and Transversality Conditions
236(7)
8.7 Exercises
243(4)
9 Applications
247(54)
9.1 Option Exercise
247(3)
9.2 Discrete Choice
250(2)
9.3 Multi-Armed Bandit
252(6)
9.4 Consumption and Saving
258(18)
9.4.1 Deterministic Income
261(7)
9.4.2 Stochastic Income
268(8)
9.5 Consumption/Portfolio Choice
276(2)
9.6 Inventory
278(11)
9.6.1 Finite-Horizon Problem
280(4)
9.6.2 Infinite-Horizon Problem
284(5)
9.7 Investment
289(10)
9.7.1 Neoclassical Theory
289(2)
9.7.2 Q Theory
291(2)
9.7.3 Augmented Adjustment Costs
293(6)
9.8 Exercises
299(2)
10 Linear-Quadratic Models
301(34)
10.1 Controlled Linear State-Space System
301(4)
10.2 Finite-Horizon Problems
305(3)
10.3 Infinite-Horizon Limits
308(6)
10.3.1 Value Function Iteration
312(1)
10.3.2 Policy Improvement Algorithm
312(1)
10.3.3 Lagrange Method
313(1)
10.4 Optimal Policy under Commitment
314(6)
10.5 Optimal Discretional Policy
320(4)
10.6 Robust Control
324(7)
10.6.1 Belief Distortions and Entropy
324(2)
10.6.2 Two Robust Control Problems
326(1)
10.6.3 Recursive Formulation
327(1)
10.6.4 Linear-Quadratic Model with Gaussian Disturbances
328(2)
10.6.5 Relative Entropy and Normal Distributions
330(1)
10.6.6 Modified Certainty Equivalence Principle
330(1)
10.7 Exercises
331(4)
11 Control under Partial Information
335(26)
11.1 Filters
335(12)
11.1.1 Kalman Filter
335(9)
11.1.2 Smoothing
344(1)
11.1.3 Hidden Markov Chain
344(2)
11.1.4 Hidden Markov-Switching Model
346(1)
11.2 Control Problems
347(4)
11.3 Linear-Quadratic Control
351(2)
11.4 Rational Inattention
353(5)
11.4.1 Information Theory
353(2)
11.4.2 Linear-Quadratic-Gaussian Models
355(3)
11.5 Exercises
358(3)
12 Numerical Methods
361(32)
12.1 Numerical Integration
361(3)
12.1.1 Gaussian Quadrature
361(2)
12.1.2 Multidimensional Quadrature
363(1)
12.2 Discretizing AR(1) Processes
364(3)
12.2.1 Tauchen (1986) Method
364(1)
12.2.2 Tauchen-Hussey (1991) Method
365(1)
12.2.3 Simulating a Markov Chain
366(1)
12.3 Interpolation
367(10)
12.3.1 Orthogonal Polynomials
369(3)
12.3.2 Splines
372(3)
12.3.3 Multidimensional Approximation
375(2)
12.4 Perturbation Methods
377(3)
12.5 Projection Methods
380(5)
12.6 Numerical Dynamic Programming
385(6)
12.6.1 Discrete Approximation Methods
386(2)
12.6.2 Smooth Approximation Methods
388(3)
12.7 Exercises
391(2)
13 Structural Estimation
393(20)
13.1 Generalized Method of Moments
393(8)
13.1.1 Estimation
394(2)
13.1.2 Asymptotic Properties
396(2)
13.1.3 Weighting Matrix and Covariance Matrix Estimation
398(1)
13.1.4 Overidentifying Restrictions
399(1)
13.1.5 Implementation
400(1)
13.1.6 Relation to Other Estimation Methods
401(1)
13.2 Maximum Likelihood
401(3)
13.2.1 Estimation
401(1)
13.2.2 Asymptotic Properties
402(1)
13.2.3 Hypothesis Testing
403(1)
13.3 Simulation-Based Methods
404(7)
13.3.1 Simulated Method of Moments
405(2)
13.3.2 Simulated Maximum Likelihood
407(1)
13.3.3 Indirect Inference
408(3)
13.4 Exercises
411(2)
III Equilibrium Analysis 413(238)
14 Complete Markets Exchange Economies
415(34)
14.1 Uncertainty, Preferences, and Endowments
415(1)
14.2 Pareto Optimum
416(1)
14.3 Time 0 Trading
417(6)
14.3.1 Equilibrium Computation
419(1)
14.3.2 Two Welfare Theorems
420(2)
14.3.3 Asset Pricing
422(1)
14.4 Sequential Trading
423(8)
14.4.1 Investment Opportunities
423(1)
14.4.2 Ponzi Scheme and Portfolio Constraints
424(1)
14.4.3 Radner Equilibrium
425(1)
14.4.4 Arbitrage and State Prices
426(2)
14.4.5 Complete Markets
428(1)
14.4.6 Equilibrium with Transversality Condition
429(2)
14.4.7 Natural Debt Limit
431(1)
14.5 Equivalence of Equilibria
431(3)
14.6 Asset Price Bubbles
434(5)
14.7 Recursive Formulation
439(1)
14.8 Asset Pricing
440(5)
14.8.1 Capital Asset-Pricing Model
442(1)
14.8.2 Factor-Pricing Model
442(1)
14.8.3 Consumption-Based Capital Asset-Pricing Model
443(2)
14.9 Exercises
445(4)
15 Neoclassical Growth Models
449(44)
15.1 Deterministic Models
449(12)
15.1.1 A Basic Ramsey Model
449(9)
15.1.2 Incorporating Fiscal Policy
458(3)
15.2 A Basic RBC Model
461(13)
15.2.1 Steady State
463(1)
15.2.2 Calibration
463(1)
15.2.3 Log-Linearized System
464(5)
15.2.4 Business Cycle Statistics and Model Results
469(2)
15.2.5 Impact of a Permanent TFP Shock
471(1)
15.2.6 Impact of a Temporary TFP Shock
472(1)
15.2.7 Effects of Persistence and Critiques of the RBC Model
473(1)
15.3 Extensions of the Basic RBC Model
474(17)
15.3.1 Various Utility Functions
474(5)
15.3.2 Capacity Utilization
479(1)
15.3.3 Capital or Investment Adjustment Costs
480(5)
15.3.4 Stochastic Trends
485(2)
15.3.5 Other Sources of Shocks
487(4)
15.4 Exercises
491(2)
16 Bayesian Estimation of DSGE Models Using Dynare
493(18)
16.1 Principles of Bayesian Estimation
494(1)
16.2 Bayesian Estimation of DSGE Models
495(8)
16.2.1 Numerical Solution and State-Space Representation
496(1)
16.2.2 Evaluating the Likelihood Function
497(2)
16.2.3 Computing the Posterior
499(2)
16.2.4 Identification
501(1)
16.2.5 Model Comparison
502(1)
16.2.6 Model Diagnosis: Predictive Checks
502(1)
16.3 An Example
503(6)
16.3.1 Dynare Codes
503(4)
16.3.2 Dynare Output
507(1)
16.3.3 Stochastic Trends
508(1)
16.4 Exercises
509(2)
17 Overlapping Generations Models
511(40)
17.1 Exchange Economies
511(13)
17.1.1 A Special Case and Multiple Equilibria
513(5)
17.1.2 Existence and Efficiency
518(6)
17.2 Production Economies
524(18)
17.2.1 Multiple Equilibria
526(3)
17.2.2 Dynamic Efficiency
529(11)
17.2.3 Altruism, Bequests, and Infinite Horizons
540(2)
17.3 Asset Price Bubbles
542(4)
17.4 Sunspots and Self-Fulfilling Prophecies
546(2)
17.5 Exercises
548(3)
18 Incomplete Markets Models
551(22)
18.1 Production Economies
551(8)
18.1.1 Income Fluctuation Problem
552(1)
18.1.2 Production
553(1)
18.1.3 Stationary Recursive Equilibrium
554(1)
18.1.4 Computation and Implications
555(4)
18.2 Endowment Economies
559(7)
18.2.1 Risk-Free Rate
559(2)
18.2.2 Fiat Money
561(1)
18.2.3 Interest on Currency
561(3)
18.2.4 Seigniorage
564(2)
18.3 Aggregate Shocks
566(3)
18.3.1 Recursive Equilibrium
566(1)
18.3.2 Krusell-Smith Method
567(2)
18.4 Uninsured Idiosyncratic Investment Risk
569(1)
18.5 Exercises
570(3)
19 Search and Matching Models of Unemployment
573(28)
19.1 A Basic DMP Model
574(10)
19.1.1 Steady State
577(2)
19.1.2 Transitional Dynamics
579(2)
19.1.3 Large Firms
581(2)
19.1.4 Efficiency
583(1)
19.2 Cyclical Volatilities of Unemployment and Vacancies
584(3)
19.3 Endogenous Job Destruction
587(6)
19.3.1 Steady State
590(3)
19.3.2 Transitional Dynamics
593(1)
19.4 Unemployment and Business Cycles
593(5)
19.4.1 Households
593(2)
19.4.2 Firms
595(2)
19.4.3 Nash Bargained Wages
597(1)
19.4.4 Equilibrium
598(1)
19.5 Exercises
598(3)
20 Dynamic New Keynesian Models
601(50)
20.1 A Basic DNK Model
601(13)
20.1.1 Households
602(1)
20.1.2 Final Goods Firms
603(1)
20.1.3 Intermediate Goods Firms
604(2)
20.1.4 Central Bank
606(1)
20.1.5 Sticky-Price Equilibrium
607(1)
20.1.6 Flexible-Price Equilibrium
607(1)
20.1.7 Log-Linearized System
608(6)
20.2 Monetary Policy Design
614(10)
20.2.1 Efficient Allocation
614(2)
20.2.2 Quadratic Approximation to Utility
616(4)
20.2.3 Commitment versus Discretion
620(4)
20.3 Fiscal Stimulus
624(16)
20.3.1 A Neoclassical Model
624(1)
20.3.2 Monopolistic Competition
625(2)
20.3.3 A DNK Model
627(3)
20.3.4 Zero-Interest-Rate Lower Bound
630(5)
20.3.5 Duration of Fiscal Stimulus
635(1)
20.3.6 Government Purchases and Welfare
636(4)
20.4 A Medium-Scale DSGE Model
640(7)
20.4.1 Households
641(3)
20.4.2 Firms
644(2)
20.4.3 Monetary and Fiscal Policies
646(1)
20.4.4 Aggregation and Equilibrium
646(1)
20.5 Exercises
647(4)
IV Further Topics 651(104)
21 Recursive Utility
653(52)
21.1 Deterministic Case
654(5)
21.1.1 Koopmans's Utility
654(2)
21.1.2 Construction
656(3)
21.2 Stochastic Case
659(16)
21.2.1 Epstein-Zin Preferences
659(6)
21.2.2 Ambiguity Aversion
665(8)
21.2.3 Temporal Resolution of Uncertainty
673(2)
21.3 Properties of Recursive Utility
675(5)
21.3.1 Concavity
676(1)
21.3.2 Risk Aversion
676(1)
21.3.3 Utility Gradients and Pricing Kernels
677(3)
21.4 Portfolio Choice and Asset Pricing
680(18)
21.4.1 Optimality and Equilibrium
681(3)
21.4.2 Log-Linear Approximation
684(8)
21.4.3 Long-Run Risk
692(6)
21.5 Pareto Optimality
698(5)
21.5.1 Lucas-Stokey Approach
699(3)
21.5.2 Dumas-Uppal-Wang Approach
702(1)
21.6 Exercises
703(2)
22 Dynamic Games
705(28)
22.1 Repeated Games
706(10)
22.1.1 Perfect Monitoring
706(2)
22.1.2 Equilibrium Payoff Set
708(3)
22.1.3 Computation
711(1)
22.1.4 Simple Strategies
712(1)
22.1.5 Imperfect Public Monitoring
713(3)
22.2 Dynamic Stochastic Games
716(2)
22.3 Application: The Great Fish War
718(2)
22.4 Credible Government Policies
720(11)
22.4.1 One-Period Economy
721(2)
22.4.2 Infinitely Repeated Economy
723(2)
22.4.3 Equilibrium Value Set
725(2)
22.4.4 Best and Worst SPE Values
727(2)
22.4.5 Recursive Strategies
729(2)
22.5 Exercises
731(2)
23 Recursive Contracts
733(22)
23.1 Limited Commitment
734(5)
23.1.1 A Dynamic Programming Method
735(2)
23.1.2 A Lagrangian Method
737(1)
23.1.3 An Alternative Characterization
738(1)
23.2 Hidden Action
739(6)
23.3 Hidden Information
745(7)
23.3.1 Characterizations
746(5)
23.3.2 Long-Run Poverty
751(1)
23.4 Exercises
752(3)
Mathematical Appendixes 755(32)
A Linear Algebra
757(6)
B Real and Functional Analysis
763(8)
C Convex Analysis
771(8)
D Measure and Probability Theory
779(8)
References 787(24)
Matlab Index 811(2)
Name Index 813
Subject Index 81