Recursive Models of Dynamic Linear Economies 1st Edition by Lars Peter Hansen, Thomas Sargent 9781400848188 1400848180

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ISBN 10: 1400848180
ISBN 13: 9781400848188 
Author:  Lars Peter Hansen, Thomas J. Sargent

A guide to the economic modeling of household preferences, from two leaders in the field A common set of mathematical tools underlies dynamic optimization, dynamic estimation, and filtering. In Recursive Models of Dynamic Linear Economies, Lars Peter Hansen and Thomas Sargent use these tools to create a class of econometrically tractable models of prices and quantities. They present examples from microeconomics, macroeconomics, and asset pricing. The models are cast in terms of a representative consumer. While Hansen and Sargent demonstrate the analytical benefits acquired when an analysis with a representative consumer is possible, they also characterize the restrictiveness of assumptions under which a representative household justifies a purely aggregative analysis. Hansen and Sargent unite economic theory with a workable 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 economies with complete markets. Their book, based on the 2012 Gorman lectures, stresses heterogeneity, aggregation, and how a common structure unites what superficially appear to be diverse applications. An appendix describes MATLAB programs that apply to the book’s calculations.

Recursive Models of Dynamic Linear Economies 1st Table of contents:

Part I: Overview

1. Theory and Econometrics

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

2.1. Introduction

2.2. Notation and Basic Assumptions

2.3. Prediction Theory

2.4. Transforming Variables to Uncouple Dynamics

2.4.1. Deterministic Seasonals

2.4.2. Indeterministic Seasonals

2.4.3. Univariate Autoregressive Processes

2.4.4. Vector Autoregressions

2.4.5. Polynomial Time Trends

2.4.6. Martingales with Drift

2.4.7. Covariance 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 Coefficients

2.5. Concluding Remarks

3. Efficient Computations

3.1. Introduction

3.2. The Optimal Linear Regulator Problem

3.3. Transformations to Eliminate Discounting and Cross-Products

3.4. Stability Conditions

3.5. Invariant Subspace Methods

3.5.1. Px as Lagrange 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

3.10. Linear Exponential Quadratic Gaussian Control

3.10.1. Doubling Algorithm for a Risk-Sensitive Problem

Appendices

A. Concepts of Linear Control Theory

B. Symplectic Matrices

C. Alternative Forms of the Riccati Equation

Part III: Components of Economies

4. Economic Environments

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

5.1. Planning Problem

5.2. Lagrange Multipliers

5.3. Dynamic Programming

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 Adjustment Costs

5.9. Altered Growth Condition

5.10. A Jones-Manuelli (1990) Economy

5.11. Durable Consumption Goods

5.12. Summary

Appendices

A. Synthesizing a Linear Regulator

B. A Brock-Mirman (1972) or Hall (1978) Model

5.B.1. Uncertainty

5.B.2. Optimal Stationary States

6. A Commodity Space

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 Information

6.6. Lagrange Multipliers

6.7. Summary

Appendices

A. Mathematical Details

Part IV: Representations and Properties

8. Statistical Representations

8.1. The Kalman Filter

8.2. Innovations Representation

8.3. Convergence

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

Appendices

A. Initialization of Kalman Filter

B. Zeros of Characteristic Polynomial

C. Serially Correlated Measurement Errors

D. Innovations in yt+1 as Functions of wt+1 and ηt+1

E. Innovations in a Permanent Income Model

Part V: Additional Topics

14. Periodic Models of Seasonality

14.1. Three Models of Seasonality

14.2. A Periodic Economy

14.3. Asset 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 Innovations Representations for a Periodic Model

Appendices

A. Disguised Periodicity

A. MATLAB Programs

References

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