Recursive models of dynamic linear economies:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton
Princeton University Press
2014
|
| Series: | The Gorman lectures in economics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references (p. 379-392) and index |
| Physical Description: | xv, 399 S. Diagramme |
| ISBN: | 9780691042770 |
Staff View
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| adam_text | RECURSIVE MODELS OF DYNAMIC LINEAR ECONOMIES
/ HANSEN, LARS
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
ACKNOWLEDGEMENTS
PREFACE
OVERVIEW
THEORY AND ECONOMETRICS
TOOLS
LINEAR STOCHASTIC DIFFERENCE EQUATIONS
EFFICIENT COMPUTATIONS
COMPONENTS OF ECONOMIES
ECONOMIC ENVIRONMENTS
OPTIMAL RESOURCE ALLOCATIONS
A COMMODITY SPACE
COMPETITIVE ECONOMIES
REPRESENTATIONS AND PROPERTIES
STATISTICAL REPRESENTATIONS
CANONICAL HOUSEHOLD TECHNOLOGIES
EXAMPLES
PERMANENT INCOME MODELS
GORMAN HETEROGENEOUS HOUSEHOLDS
COMPLETE MARKETS AGGREGATION
REFERENCES
SUBJECT INDEX
AUTHOR INDEX
MATLAB INDEX.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
Contents
Preface
xiii
Acknowledgments
xv
Part I: Overview
1. Theory and Econometrics 3
1.1. Introduction. 1.2. A Class of Economies. 1.3. Computer Programs.
1.4. Organization. 1.5. Recurring Mathematical Ideas.
Part II: Tools
2. Linear Stochastic Difference Equations 15
2.1. Introduction. 2.2. Notation and Basic Assumptions. 2.3. Predic-
tion Theory. 2.4. Transforming Variables to Uncouple Dynamics. 2.4.1.
Deterministic Seasonals. 2.4.2. Indeterministic Seasonals. 2.4.3. Uni-
variate Autoregressive Processes. 2.4.4. Vector Autoregressions. 2.4.5.
Polynomial Time Trends. 2.4.6. Martingales with Drift. 2.4.7. Covari-
ance Stationary Processes. 2.4.8. Multivariate ARMA Processes. 2.4.9.
Prediction of a Univariate First-Order ARMA. 2.4.10. Growth. 2.4.11.
A Rational Expectations Model. 2.4.12. Method of Undetermined Co-
efficients. 2.5. Concluding Remarks.
- Vll -
Contents
viii
3. Efficient Computations 33
3.1. Introduction. 3.2. The Optimal Linear Regulator Problem. 3.3.
Transformations to Eliminate Discounting and Cross-Products. 3.4. Sta-
bility Conditions. 3.5. Invariant Subspace Methods. 3.5.1. Px as La-
grange Multiplier. 3.5.2. Invariant Subspace Methods. 3.6. Doubling
Algorithm. 3.7. Partitioning the State Vector. 3.8. Periodic Optimal
Linear Regulator. 3.9. A Periodic Doubling Algorithm. 3.9.1. Parti-
tioning the State Vector. 3.10. Linear Exponential Quadratic Gaussian
Control. 3.10.1. Doubling Algorithm for a Risk-Sensitive Problem. A.
Concepts of Linear Control Theory. B. Symplectic Matrices. C. Alter-
native Forms of the Riccati Equation.
Part III: Components of Economies
4. Economic Environments 61
4.1. Information. 4.2. Taste and Technology Shocks. 4.3. Production
Technologies. 4.4. Examples of Production Technologies. 4.4.1. Other
Technologies. 4.5. Household Technologies. 4.6. Examples of Household
Technologies. 4.7. Square Summability. 4.8. Summary.
5. Optimal Resource Allocations 79
5.1. Planning Problem. 5.2. Lagrange Multipliers. 5.3. Dynamic Pro-
gramming. 5.4. Lagrange Multipliers as Gradients of Value Function.
5.5. Planning Problem as Linear Regulator. 5.6. Allocations for Five
Economies. 5.6.1. Brock-Mirman (1972) or Hall (1978) Model. 5.6.2.
A Growth Economy Fueled by Habit Persistence. 5.6.3. Lucas’s Pure
Exchange Economy. 5.6.4. An Economy with a Durable Consumption
Good. 5.6.5. Computed Examples. 5.7. Hall’s Model. 5.8. Higher Ad-
justment Costs. 5.9. Altered Growth Condition. 5.10. A Jones-Manuelli
(1990) Economy. 5.11. Durable Consumption Goods. 5.12. Summary.
A. Synthesizing a Linear Regulator. B. A Brock-Mirman (1972) or Hall
(1978) Model. 5.B.I. Uncertainty. 5.B.2. Optimal Stationary States.
Contents
IX
6. A Commodity Space 125
6.1. Valuation. 6.2. Price Systems as Linear Functionals. 6.3. A One-
Period Model under Certainty. 6.4. One Period under Uncertainty. 6.5.
An Infinite Number of Periods and Uncertainty. 6.5.1. Conditioning In-
formation. 6.6. Lagrange Multipliers. 6.7. Summary. A. Mathematical
Details.
7. Competitive Economies 131
7.1. Introduction. 7.2. Households. 7.3. Type I Firms. 7.4. Type II
Firms. 7.5. Competitive Equilibrium. 7.6. Lagrangians. 7.6.1. House-
hold Lagrangian. 7.6.2. Type I Firm Lagrangian. 7.6.3. Type II Firm
Lagrangian. 7.7. Equilibrium Price System. 7.8. Asset Pricing. 7.9.
Term Structure of Interest Rates. 7.10. Reopening Markets. 7.11. Non-
Gaussian Asset Prices. 7.12. Asset Pricing Example.
Part IV: Representations and Properties
8. Statistical Representations 153
8.1. The Kalman Filter. 8.2. Innovations Representation. 8.3. Con-
vergence. 8.3.1. Computation of Time-Invariant Kalman Filter. 8.4.
Factorization of Likelihood Function. 8.4.1. Initialization Assumptions.
8.4.2. Possible Nonexistence of Stationary Distribution. 8.5. Spectral
Factorization Identity. 8.6. Wold and Autoregressive Representations.
8.7. Frequency Domain Estimation. 8.8. Approximation Theory. 8.9.
Aggregation over Time. 8.10. Simulation Estimators. A. Initialization
of Kalman Filter. B. Zeros of Characteristic Polynomial. C. Serially
Correlated Measurement Errors. D. Innovations in yt+i as Functions of
wt+i and ?7t+i. E. Innovations in a Permanent Income Model.
9. Canonical Household Technologies 191
9.1. Introduction. 9.2. Definition of a Canonical Household Technol-
ogy. 9.3. Dynamic Demand Functions. 9.3.1. Wealth and the Multi-
plier ¡Iq . 9.3.2. Dynamic Demand System. 9.3.3. Gorman Aggregation
and Engel Curves. 9.3.4. Reopened Markets. 9.4. Computing Canon-
ical Representations. 9.4.1. Basic Idea. 9.4.2. An Auxiliary Problem
Induces a Canonical Representation. 9.5. An Operator Identity. 9.6.
X
Contents
Becker֊Murphy Model of Rational Addiction. A. Fourier Transforms.
9.A.I. Primer on z-Transforms. 9.A.2. Time Reversal and Parseval’s
Formula. 9.A.3. One-Sided Sequences. 9.A.4. Useful Properties. 9.A.5.
One-Sided Transforms. 9.A.6. Discounting. 9.A.7. Fourier Transforms.
9. A.8. Verifying Equivalent Valuations. 9.A.9. Equivalent Representa-
tions of Preferences. 9.A.10. First Term: Factorization Identity. 9.A.11.
Second Term. 9.A. 12. Third Term.
10. Examples
10.1. Partial Equilibrium. 10.2. The Setup. 10.3. Equilibrium Invest-
ment under Uncertainty. 10.4. A Housing Model. 10.4.1. Demand.
10.4.2. House Producers. 10.5. Cattle Cycles. 10.5.1. Mapping Cat-
tle Farms into Our Framework. 10.5.2. Preferences. 10.5.3. Technol-
ogy. 10.6. Models of Occupational Choice and Pay. 10.6.1. A One-
Occupation Model. 10.6.2. Skilled and Unskilled Workers. A. Decen-
tralizing the Household.
11. Permanent Income Models
11.1. Technology. 11.2. Two Implications. 11.3. Allocation Rules.
11.4. Deterministic Steady States. 11.5. Cointegration. 11.6. Con-
stant Marginal Utility of Income. 11.7. Consumption Externalities. A.
Exotic Tax Smoothing Models.
12. Gorman Heterogeneous Households
12.1. Introduction. 12.2. Gorman Aggregation (Static). 12.3. An Econ-
omy with Heterogeneous Consumers. 12.4. Allocations. 12.4.1. Con-
sumption Sharing Rules. 12.5. Risk Sharing. 12.6. Implementing the
Allocation Rule with Limited Markets. A. Computer Example.
13. Complete Markets Aggregation
13.1. Introduction. 13.2. Preferences and Household Technologies.
13.2.1. Production Technology. 13.3. A Pareto Problem. 13.4. Com-
petitive Equilibrium. 13.4.1. Households. 13.4.2. Firms of Types I and
II. 13.5. Computation of Equilibrium. 13.5.1. Candidate Equilibrium
Prices. 13.5.2. A Negishi Algorithm. 13.6. Complete Markets Aggrega-
tion. 13.6.1. Static Demand. 13.6.2. Frequency Domain Representation
of Preferences. 13.7. A Programming Problem for Complete Markets
Aggregation. 13.7.1. Factoring S*S. 13.8. Summary of Findings. 13.9.
217
233
253
269
Contents
XI
The Aggregate Preference Shock Process. 13.9.1. Interpretation of St
Component. 13.10. Initial Conditions.
14.1. Three Models of Seasonality. 14.2. A Periodic Economy. 14.3. As-
set Pricing. 14.4. Prediction Theory. 14.5. Term Structure of Interest
Rates. 14.6. Conditional Covariograms. 14.7. A Stacked and Skip-
Sampled System. 14.8. Covariances of the Stacked and Skip-Sampled
Process. 14.9. Tiao-Grupe Formula. 14.9.1. State-Space Realization of
Tiao-Grupe Formula. 14.10. Periodic Hall Model. 14.11. Periodic Inno-
vations Representations for a Periodic Model. A. Disguised Periodicity.
14. Periodic Models of Seasonality
291
A. MATLAB Programs
327
References
379
Subject Index
393
Author Index
397
MATLAB Index
399
A common set of mathematical tools un-
derlies dynamic optimization, dynamic es-
timation, and filtering. In Recursive Models
of Dynamic Linear Economies, Lars Peter
H ansen and Thomas Sargent use these
tools to create a class of econo metrically
tractable models of prices and quantities.
They present examples from microeco-
nomics, macroeconomics, and asset pric-
ing. The models are cast in terms of a rep-
resentative consumer. While Hansen and
Sargent demonstrate the analytical bene-
fits acquired when an analysis with a rep-
resentative consumer is possible, they also
characterize the restrictiveness of assump-
tions under which a representative house-
hold justifies a purely aggregative analysis.
Based on the 2012 Gorman lectures, the
authors unite economic theory with a work-
able econometrics while going beyond and
beneath demand and supply curves for
dynamic economies. They construct and
apply competitive equilibria for a class of
linear-quadratic-Gaussian dynamic econ-
omies with complete markets. Their book
stresses heterogeneity, aggregation, and
how a common structure unites what super-
ficially appear to be diverse applications.
An appendix describes MATLAB® pro-
grams that apply to the book s calculations.
|
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| author | Hansen, Lars Peter 1952- Sargent, Thomas J. 1943- |
| author_GND | (DE-588)130587087 (DE-588)118751298 |
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| dewey-ones | 330 - Economics |
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| dewey-search | 330.01/511352 |
| dewey-sort | 3330.01 6511352 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:04:42Z |
| institution | BVB |
| isbn | 9780691042770 |
| language | English |
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| record_format | marc |
| series2 | The Gorman lectures in economics |
| spelling | Hansen, Lars Peter 1952- Verfasser (DE-588)130587087 aut Recursive models of dynamic linear economies Lars Hansen, Thomas J. Sargent Princeton Princeton University Press 2014 xv, 399 S. Diagramme txt rdacontent n rdamedia nc rdacarrier The Gorman lectures in economics Includes bibliographical references (p. 379-392) and index Makroökonomie (DE-588)4037174-8 gnd rswk-swf Lineares dynamisches System (DE-588)4167727-4 gnd rswk-swf Dynamische Optimierung (DE-588)4125677-3 gnd rswk-swf Mikroökonomie (DE-588)4039225-9 gnd rswk-swf Ökonometrisches Modell (DE-588)4043212-9 gnd rswk-swf Ökonometrisches Modell (DE-588)4043212-9 s Mikroökonomie (DE-588)4039225-9 s Makroökonomie (DE-588)4037174-8 s Lineares dynamisches System (DE-588)4167727-4 s Dynamische Optimierung (DE-588)4125677-3 s b DE-604 Sargent, Thomas J. 1943- Verfasser (DE-588)118751298 aut LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027204319&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027204319&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027204319&sequence=000006&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Hansen, Lars Peter 1952- Sargent, Thomas J. 1943- Recursive models of dynamic linear economies Makroökonomie (DE-588)4037174-8 gnd Lineares dynamisches System (DE-588)4167727-4 gnd Dynamische Optimierung (DE-588)4125677-3 gnd Mikroökonomie (DE-588)4039225-9 gnd Ökonometrisches Modell (DE-588)4043212-9 gnd |
| subject_GND | (DE-588)4037174-8 (DE-588)4167727-4 (DE-588)4125677-3 (DE-588)4039225-9 (DE-588)4043212-9 |
| title | Recursive models of dynamic linear economies |
| title_auth | Recursive models of dynamic linear economies |
| title_exact_search | Recursive models of dynamic linear economies |
| title_full | Recursive models of dynamic linear economies Lars Hansen, Thomas J. Sargent |
| title_fullStr | Recursive models of dynamic linear economies Lars Hansen, Thomas J. Sargent |
| title_full_unstemmed | Recursive models of dynamic linear economies Lars Hansen, Thomas J. Sargent |
| title_short | Recursive models of dynamic linear economies |
| title_sort | recursive models of dynamic linear economies |
| topic | Makroökonomie (DE-588)4037174-8 gnd Lineares dynamisches System (DE-588)4167727-4 gnd Dynamische Optimierung (DE-588)4125677-3 gnd Mikroökonomie (DE-588)4039225-9 gnd Ökonometrisches Modell (DE-588)4043212-9 gnd |
| topic_facet | Makroökonomie Lineares dynamisches System Dynamische Optimierung Mikroökonomie Ökonometrisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027204319&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027204319&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027204319&sequence=000006&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hansenlarspeter recursivemodelsofdynamiclineareconomies AT sargentthomasj recursivemodelsofdynamiclineareconomies |
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