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Recursive Models of Dynamic Linear Economies$
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Lars Peter Hansen and Thomas J. Sargent

Print publication date: 2013

Print ISBN-13: 9780691042770

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691042770.001.0001

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Statistical Representations

Statistical Representations

(p.153) Chapter 8 Statistical Representations
Recursive Models of Dynamic Linear Economies

Lars Peter Hansen

Thomas J. Sargent

Princeton University Press

This chapter describes links between competitive equilibria and autoregressive representations. It shows how to obtain an autoregressive representation for observable variables that are error-ridden linear functions of state variables. In describing how to deduce an autoregressive representation from a competitive equilibrium and parameters of measurement error processes, it completes a key step that facilitates econometric estimation of free parameters. An autoregressive representation is naturally affiliated with a recursive representation of a likelihood function for the observable variables. More precisely, a vector autoregressive representation implements a convenient factorization of the joint density of a complete history of observables (i.e., the likelihood function) into a product of densities of time t observables conditioned on histories of those observables up to time t−1. The chapter also treats two other topics intimately related to econometric implementation: aggregation over time and the theory of approximation of one model by another.

Keywords:   competitive equilibria, autoregressive representations, aggregation, approximation, econometric estimation

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