Economic dynamics in discrete time:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Massachusetts ; London, England
The MIT Press
[2020]
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| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xviii, 825 Seiten Diagramme |
| ISBN: | 9780262043625 |
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| 100 | 1 | |a Miao, Jianjun |d 1969- |e Verfasser |0 (DE-588)133541398 |4 aut | |
| 245 | 1 | 0 | |a Economic dynamics in discrete time |c Jianjun Miao |
| 250 | |a Second edition | ||
| 264 | 1 | |a Cambridge, Massachusetts ; London, England |b The MIT Press |c [2020] | |
| 300 | |a xviii, 825 Seiten |b Diagramme | ||
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Contents Preface to the Second Edition Acknowledgments xix xvii I Dynamical Systems 1 1 Deterministic Linear Systems 3 1.1 Some Basic Concepts 3 1.2 Scalar First-Order Linear Difference Equations 6 1.3 Lag Operators 10 1.4 Scalar Second-Order Linear Difference Equations 1.5 Planar Linear Systems 13 1.5.1 Distinct Real Eigenvalues 14 1.5.2 Repeated Real Eigenvalues 15 1.5.3 Complex Eigenvalues 16 1.6 Phase Diagrams 16 1.7 Higher-Dimensional Linear Systems 18 1.7.1 Nonsingular Systems 20 1.7.2 Singular Systems 26 1.8 Exercises 29 2 Deterministic Nonlinear Systems 31 2.1 Linear Approximation 31 2.2 Local Stability 33 2.3 Lyapunov Function 38 2.4 Cycles and Chaos 41 2.4.1 Periodic Solutions 41 2.4.2 Bifurcations 43 2.4.3 Chaos 49
Contents 2.5 2.6 3 Stochastic Difference Equations 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 4 4.2 4.3 4.4 4.5 65 103 Markov Chains 104 4.1.1 Classification of States 108 4.1.2 Stationary Distribution: Finite State Space 4.1.3 Countable-State Markov Chains 118 General Markov Processes 128 Convergence 132 4.3.1 Strong Convergence 132 4.3.2 Weak Convergence 137 Markov Chain Monte Carlo Algorithms 140 Exercises 143 Ergodic Theory and Stationary Processes 5.1 5.2 5.3 5.4 147 Ergodic Theorem 147 Application to Stationary Processes 152 Application to Stationary Markov Processes Exercises 164 II Dynamic Optimization 6 Markov Decision Process Model 6.1 55 First-Order Linear Systems 65 Scalar Linear Rational Expectations Models 67 3.2.1 Lag Operators 67 3.2.2 Method of Undetermined Coefficients 70 Multivariate Linear Rational Expectations Models 71 3.3.1 Blanchard-Kahn Method 71 3.3.2 Klein Method 73 3.3.3 Sims Method 75 Nonlinear Rational Expectations Models 81 Numerical Solutions Using Dynare 85 Indeterminacy and Sunspot Equilibria 94 Pruning Nonlinear Solutions 96 Exercises 99 Markov Processes 4.1 5 Numerical Solutions Using Dynare Exercises 62 Model Setup 167 165 167 159 111
Contents 6.2 6.3 7 8 9 ix Examples 173 6.2.1 Discrete Choice 173 6.2.2 Optimal Stopping 174 6.2.3 Bandit Model 177 6.2.4 Optimal Control 180 Exercises 181 Finite-Horizon Dynamic Programming 183 7.1 A Motivating Example 183 7.2 Measurability Problem 187 7.3 Principle of Optimality 189 7.4 Optimal Control 196 7.5 Maximum Principle 202 7.6 Applications 206 7.6.1 Secretary Problem 206 7.6.2 A Consumption-Saving Problem 7.7 Exercises 209 207 Infinite-Horizon Dynamic Programming 211 8.1 Principle of Optimality 211 8.2 Bounded Rewards 220 8.3 Unbounded Rewards 222 8.3.1 Negative Dynamic Programming 222 8.3.2 Weighted Contraction Approach 225 8.4 Optimal Control 229 8.5 The Maximum Principle and Transversality Conditions 8.6 Euler Equations and Transversality Conditions 236 8.7 Exercises 243 Applications 247 9.1 Option Exercise 247 9.2 Discrete Choice 250 9.3 Multi-Armed Bandit 252 9.4 Consumption and Saving 258 9.4.1 Deterministic Income 261 9.4.2 Stochastic Income 268 9.5 Consumption/Portfolio Choice 276 9.6 Inventory 278 9.6.1 Finite-Horizon Problem 280 9.6.2 Infinite-Horizon Problem 284 233
Contents x 9.7 9.8 10 Investment 289 9.7.1 Neoclassical Theory 289 9.7.2 Q Theory 291 9.7.3 Augmented Adjustment Costs Exercises 299 293 Linear-Quadratic Models 301 10.1 Controlled Linear State-Space System 301 10.2 Finite-Horizon Problems 305 10.3 Infinite-Horizon Limits 308 10.3.1 Va!ue Function Iteration 312 10.3.2 Policy Improvement Algorithm 312 10.3.3 Lagrange Method 313 10.4 Optimal Policy under Commitment 314 10.5 Optimal Discretional Policy 320 10.6 Robust Control 324 10.6.1 Belief Distortions and Entropy 324 10.6.2 Two Robust Control Problems 326 10.6.3 Recursive Formulation 327 10.6.4 Linear-Quadratic Model with Gaussian Disturbances 10.6.5 Relative Entropy and Normal Distributions 330 10.6.6 Modified Certainty Equivalence Principle 330 10.7 Exercises 331 11 Control under Partial Information 335 11.1 Filters 335 11.1.1 Kalman Filter 335 11.1.2 Smoothing 344 11.1.3 Hidden Markov Chain 344 11.1.4 Hidden Markov-Switching Model 346 11.2 Control Problems 347 11.3 Linear-Quadratic Control 351 11.4 Rational Inattention 353 11.4.1 Information Theory 353 11.4.2 Linear-Quadra tic-Gaussian Models 355 11.5 Exercises 358 12 Numerical Methods 361 12.1 Numerical Integration 361 12.1.1 Gaussian Quadrature 361 12.1.2 Multidimensional Quadrature 363 328
Contents xi 12.2 Discretizing AR(1) Processes 364 12.2.1 Tauchen (1986) Method 364 12.2.2 Tauchen-Hussey (1991) Method 365 12.2.3 Simulating a Markov Chain 366 12.3 Interpolation 367 12.3.1 Orthogonal Polynomials 369 12.3.2 Splines 372 12.3.3 Multidimensional Approximation 375 12.4 Perturbation Methods 377 12.5 Projection Methods 380 12.6 Numerical Dynamic Programming 385 12.6.1 Discrete Approximation Methods 386 12.6.2 Smooth Approximation Methods 388 12.7 Exercises 391 13 Structural Estimation 393 13.1 Generalized Method of Moments 393 13.1.1 Estimation 394 13.1.2 Asymptotic Properties 396 13.1.3 Weighting Matrix and Covariance Matrix Estimation 398 13.1.4 Overidentifying Restrictions 399 13.1.5 Implementation 400 13.1.6 Relation to Other Estimation Methods 401 13.2 Maximum Likelihood 401 13.2.1 Estimation 401 13.2.2 Asymptotic Properties 402 13.2.3 Hypothesis Testing 403 13.3 Simulation-Based Methods 404 13.3.1 Simulated Method of Moments 405 13.3.2 Simulated Maximum Likelihood 407 13.3.3 Indirect Inference 408 13.4 Exercises 411 III Equilibrium Analysis 14 Complete Markets Exchange Economies 415 14.1 Uncertainty, Preferences, and Endowments 14.2 Pareto Optimum 416 413 415
Contents xii 14.3 Time 0 Trading 417 14.3.1 Equilibrium Computation 419 14.3.2 Two Welfare Theorems 420 14.3.3 Asset Pricing 422 14.4 Sequential Trading 423 14.4.1 Investment Opportunities 423 14.4.2 Ponzi Scheme and Portfolio Constraints 424 14.4.3 Rådner Equilibrium 425 14.4.4 Arbitrage and State Prices 426 14.4.5 Complete Markets 428 14.4.6 Equilibrium with Transversality Condition 429 14.4.7 Natural Debt Limit 431 14.5 Equivalence of Equilibria 431 14.6 Asset Price Bubbles 434 14.7 Recursive Formulation 439 14.8 Asset Pricing 440 14.8.1 Capital Asset-Pricing Model 442 14.8.2 Factor-Pricing Model 442 14.8.3 Consumption-Based Capital Asset-Pricing Model 14.9 Exercises 445 15 443 Neoclassical Growth Models 449 15.1 Deterministic Models 449 15.1.1 A Basic Ramsey Model 449 15.1.2 Incorporating Fiscal Policy 458 15.2 A Basic RBC Model 461 15.2.1 Steady State 463 15.2.2 Calibration 463 15.2.3 Log-Linearized System 464 15.2.4 Business Cycle Statistics and Model Results 469 15.2.5 Impact of a Permanent TFP Shock 471 15.2.6 Impact of a Temporary TFP Shock 472 15.2.7 Effects of Persistence and Critiques of the RBC Model 15.3 Extensions of the Basic RBC Model 474 15.3.1 Various Utility Functions 474 15.3.2 Capacity Utilization 479 15.3.3 Capital or Investment Adjustment Costs 480 15.3.4 Stochastic Trends 485 15.3.5 Other Sources of Shocks 487 15.4 Exercises 491 473
Contents 16 Bayesian Estimation of DSGE Models Using Dynare 493 16.1 Principles of Bayesian Estimation 494 16.2 Bayesian Estimation of DSGE Models 495 16.2.1 Numerical Solution and State-Space Representation 496 16.2.2 Evaluating the Likelihood Function 497 16.2.3 Computing the Posterior 499 16.2.4 Identification 501 16.2.5 Model Comparison 502 16.2.6 Model Diagnosis: Predictive Checks 502 16.3 An Example 503 16.3.1 Dynare Codes 503 16.3.2 Dynare Output 507 16.3.3 Stochastic Trends 508 16.4 Exercises 509 17 Overlapping Generations Models 511 17.1 Exchange Economies 511 17.1.1 A Special Case and Multiple Equilibria 513 17.1.2 Existence and Efficiency 518 17.2 Production Economies 524 17.2.1 Multiple Equilibria 526 17.2.2 Dynamic Efficiency 529 17.2.3 Altruism, Bequests, and Infinite Horizons 540 17.3 Asset Price Bubbles 542 17.4 Sunspots and Self-Fulfilling Prophecies 546 17.5 Exercises 548 18 Incomplete Markets Models 551 18.1 Production Economies 551 18.1.1 Income Fluctuation Problem 552 18.1.2 Production 553 18.1.3 Stationary Recursive Equilibrium 554 18.1.4 Computation and Implications 555 18.2 Endowment Economies 559 18.2.1 Risk-Free Rate 559 18.2.2 Fiat Money 561 18.2.3 Interest on Currency 561 18.2.4 Seigniorage 564 xiii
Contents XIV 18.3 Aggregate Shocks 566 18.3.1 Recursive Equilibrium 566 18.3.2 Krusell-Smith Method 567 18.4 Uninsured Idiosyncratic Investment Risk 18.5 Exercises 570 19 20 569 Search and Matching Models of Unemployment 573 19.1 A Basic DMP Model 574 19.1.1 Steady State 577 19.1.2 Transitional Dynamics 579 19.1.3 Large Firms 581 19.1.4 Efficiency 583 19.2 Cyclical Volatilities of Unemployment and Vacancies 19.3 Endogenous Job Destruction 587 19.3.1 Steady State 590 19.3.2 Transitional Dynamics 593 19.4 Unemployment and Business Cycles 593 19.4.1 Households 593 19.4.2 Firms 595 19.4.3 Nash Bargained Wages 597 19.4.4 Equilibrium 598 19.5 Exercises 598 Dynamic New Keynesian Models 601 20.1 A Basic DNK Model 601 20.1.1 Households 602 20.1.2 Final Goods Firms 603 20.1.3 Intermediate Goods Firms 604 20.1.4 Central Bank 606 20.1.5 Sticky-Price Equilibrium 607 20.1.6 Flexible-Price Equilibrium 607 20.1.7 Log-Linearized System 608 20.2 Monetary Policy Design 614 20.2.1 Efficient Allocation 614 20.2.2 Quadratic Approximation to Utility 616 20.2.3 Commitment versus Discretion 620 20.3 Fiscal Stimulus 624 20.3.1 A Neoclassical Model 624 20.3.2 Monopolistic Competition 625 20.3.3 A DNK Model 627 584
Contents XV 20.3.4 Zero-Interest-Rate Lower Bound 630 20.3.5 Duration of Fiscal Stimulus 635 20.3.6 Government Purchases and Welfare 636 20.4 A Medium-Scale DSGE Model 640 20.4.1 Households 641 20.4.2 Firms 644 20.4.3 Monetary and Fiscal Policies 646 20.4.4 Aggregation and Equilibrium 646 20.5 Exercises 647 IV Further Topics 651 21 Recursive Utility 653 21.1 Deterministic Case 654 21.1.1 Koopmans's Utility 654 21.1.2 Construction 656 21.2 Stochastic Case 659 21.2.1 Epstein-Zin Preferences 659 21.2.2 Ambiguity Aversion 665 21.2.3 Temporal Resolution of Uncertainty 673 21.3 Properties of Recursive Utility 675 21.3.1 Concavity 676 21.3.2 Risk Aversion 676 21.3.3 Utility Gradients and Pricing Kernels 677 21.4 Portfolio Choice and Asset Pricing 680 21.4.1 Optimality and Equilibrium 681 21.4.2 Log-Linear Approximation 684 21.4.3 Long-Run Risk 692 21.5 Pareto Optimality 698 21.5.1 Lucas-Stokey Approach 699 21.5.2 Dumas-Uppal-Wang Approach 702 21.6 Exercises 703 22 Dynamic Games 705 22.1 Repeated Games 706 22.1.1 Perfect Monitoring 706 22.1.2 Equilibrium Payoff Set 708 22.1.3 Computation 711 22.1.4 Simple Strategies 712 22.1.5 Imperfect Public Monitoring 713
xvi Contents 22.2 Dynamic Stochastic Games 716 22.3 Application: The Great Fish War 718 22.4 Credible Government Policies 720 22.4.1 One-Period Economy 721 22.4.2 Infinitely Repeated Economy 723 22.4.3 Equilibrium Value Set 725 22.4.4 Best and Worst SPE Values 727 22.4.5 Recursive Strategies 729 22.5 Exercises 731 23 Recursive Contracts 733 23.1 Limited Commitment 734 23.1.1 A Dynamic Programming Method 735 23.1.2 A Lagrangian Method 737 23.1.3 An Alternative Characterization 738 23.2 Hidden Action 739 23.3 Hidden Information 745 23.3.1 Characterizations 746 23.3.2 Long-Run Poverty 751 23.4 Exercises 752 Mathematical Appendixes A В C D 755 Linear Algebra 757 Real and Functional Analysis 763 Convex Analysis 771 Measure and Probability Theory 779 References 787 Matlab Index 811 Name Index 813 Subject Index 819 |
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| spelling | Miao, Jianjun 1969- Verfasser (DE-588)133541398 aut Economic dynamics in discrete time Jianjun Miao Second edition Cambridge, Massachusetts ; London, England The MIT Press [2020] xviii, 825 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Diskrete Optimierung (DE-588)4150179-2 gnd rswk-swf Dynamisches Modell (DE-588)4150932-8 gnd rswk-swf Dynamisches Modell (DE-588)4150932-8 s Diskrete Optimierung (DE-588)4150179-2 s DE-604 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032047330&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Miao, Jianjun 1969- Economic dynamics in discrete time Diskrete Optimierung (DE-588)4150179-2 gnd Dynamisches Modell (DE-588)4150932-8 gnd |
| subject_GND | (DE-588)4150179-2 (DE-588)4150932-8 |
| title | Economic dynamics in discrete time |
| title_auth | Economic dynamics in discrete time |
| title_exact_search | Economic dynamics in discrete time |
| title_exact_search_txtP | Economic dynamics in discrete time |
| title_full | Economic dynamics in discrete time Jianjun Miao |
| title_fullStr | Economic dynamics in discrete time Jianjun Miao |
| title_full_unstemmed | Economic dynamics in discrete time Jianjun Miao |
| title_short | Economic dynamics in discrete time |
| title_sort | economic dynamics in discrete time |
| topic | Diskrete Optimierung (DE-588)4150179-2 gnd Dynamisches Modell (DE-588)4150932-8 gnd |
| topic_facet | Diskrete Optimierung Dynamisches Modell |
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