# Recursive Models of Dynamic Linear Economies

Publication Year: 2013

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.

Based on the 2012 Gorman lectures, the authors 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 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.

Published by: Princeton University Press

Series: The Gorman Lectures in Economics

#### Cover

#### Title Page, Copyright

#### Preface

In 1992, Carolyn Sargent said, “You are writing the second edition of your book before you have published the first.” Her assertion was correct. We wrote 90 percent of this book between 1988 and 1994, but completed it only in 2012. Richard Blundell’s invitation to deliver the Gorman Lectures at University College...

#### Part I: Overview

#### 1. Theory and Econometrics

Economic theory identifies patterns that unite apparently diverse subjects. Consider
the following models:

1. Ryoo and Rosen’s (2004) partial equilibrium model of the market for engineers;

2. Rosen, Murphy, and Scheinkman’s (1994) model of cattle cycles;

3. Lucas’s (1978) model of asset prices;

4. Brock and Mirman’s (1972) and Hall’s (1978)

#### Part II: Tools

#### 2. Linear Stochastic Difference Equations

This chapter introduces the vector first-order linear stochastic difference equation.
^{1} We use it first to represent information flowing to economic agents, then
again to represent competitive equilibria. The vector first-order linear stochastic
difference equation is associated with a tidy theory of prediction and a host...

#### 3. Efficient Computations

This chapter describes fast algorithms for computing the value function and
optimal decision rule for the type of social planning problem to be described
in chapter 5.^{1} This same decision rule determines the competitive equilibrium
allocation to be described in chapter 7, while the optimal value function for the...

#### Part III: Components of Economies

#### 4. Economic Environments

This chapter describes an economic environment with five components: a sequence of information sets, laws of motion for taste and technology shocks, a technology for producing consumption goods, a technology for producing services from consumer durables and consumption purchases, and a preference...

#### 5. Optimal Resource Allocations

We eventually want to use our models to study aspects of competitive equilibria, including time series properties of various quantities, spot market prices, asset prices, and rates of return. The first welfare theorem asserts that competitive equilibrium allocations solve a particular resource allocation problem, which in...

#### 6. A Commodity Space

This chapter describes a concept of value that we shall later use to formulate a model in which the decisions of agents are reconciled in a competitive equilibrium. We describe a commodity space in which quantities and prices both will reside. The stochastic Lagrange multipliers of chapter 4 are closely related...

#### 7. Competitive Economies

This chapter describes a decentralized economy. We assign ownership and decision
making to three distinct economic entities, a household and two kinds
of firms. We define a *competitive equilibrium*. Two fundamental theorems of
welfare economics connect a competitive equilibrium to a planning problem...

#### Part IV: Representations and Properties

#### 8. Statistical Representations

This chapter shows how models restrict observed prices and quantities, and how
observations can be used to make inferences about parameters. Earlier chapters
have prepared a state-space representation that expresses states *xt* and observables
*yt* as linear functions of an initial state *x0* and histories of martingale...

#### 10. Examples

Some of the general equilibrium models in this book can be reinterpreted as partial
equilibrium models that employ the notion of a *representative firm*, and that
generalize the preference and technology specifications of Lucas and Prescott
(1971). The idea is that there is a large number of identical firms that produce...

#### 11. Permanent Income Models

This chapter describes a class of permanent income models of consumption. These models stress connections between consumption and income implied by present-value budget balance and generate interesting predictions about responses of components of consumption to shocks to consumers’ information...

#### 12. Gorman Heterogeneous Households

This chapter and the next describe methods for computing equilibria of economies with consumers who have heterogeneous preferences and endowments. In both chapters, we adopt simplifications that facilitate coping with heterogeneity. In the present chapter, we describe a class of heterogeneous consumer economies...

#### 13. Complete Markets Aggregation

Chapter 12 studied a setting in which households have heterogeneous endowments and preference shocks, but otherwise have identical preferences and household technologies, implying that all households share linear Engel curves with the same slopes. The property of identically sloped linear Engel curves delivers...

#### 14. Periodic Models of Seasonality

Until now, each of the matrices defining preferences, technologies, and information flows has been specified to be constant over time. In this chapter, we relax this assumption and let the matrices be strictly periodic functions of time. Our interest is to apply and extend an idea of Denise Osborn (1988) and Richard...

E-ISBN-13: 9781400848188

E-ISBN-10: 1400848180

Print-ISBN-13: 9780691042770

Print-ISBN-10: 0691042772

Page Count: 424

Publication Year: 2013

Edition: Course Book

Series Title: The Gorman Lectures in Economics

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