Arbitrary initial conditions and the dimension of indeterminacy in linear rational expectations models

Sorge, Marco M.

doi:10.1007/s10203-019-00269-4

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Parametrizing the Set Of Solutions1

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“…It follows that the dimension of the solution space is the dimension of the innovation space of the exogenous proceess multiplied by the winding number of det(M (z)). Funovits (2017Funovits ( , 2020) counts this dimension by different methods (see also Sorge (2019)).…”

Section: Parametrizing the Set Of Solutionsmentioning

confidence: 99%

The Linear Systems Approach to Linear Rational Expectations Models

Al-Sadoon

2017

Econom. Theory

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This paper considers linear rational expectations models from the linear systems point of view. Using a generalization of the Wiener-Hopf factorization, the linear systems approach is able to furnish very simple conditions for existence and uniqueness of both particular and generic linear rational expectations models. To illustrate the applicability of this approach, the paper characterizes the structure of stationary and cointegrated solutions, including a generalization of Granger’s representation theorem.

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Section: Parametrizing the Set Of Solutionsmentioning

confidence: 99%

The Linear Systems Approach to Linear Rational Expectations Models

Al-Sadoon

2017

Econom. Theory

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Politics, Financial Regulation and Housing Bubbles

Sorge

2023

J Real Estate Finan Econ

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The Spectral Approach to Linear Rational Expectations Models

Al-Sadoon

2024

Econom. Theory

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This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to be a finite-dimensional affine space in the frequency domain. It is demonstrated that solutions can be discontinuous with respect to the parameters of the models in the context of nonuniqueness, invalidating mainstream frequentist and Bayesian methods. The ill-posedness of the problem motivates regularized solutions with theoretically guaranteed uniqueness, continuity, and even differentiability properties.

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Arbitrary initial conditions and the dimension of indeterminacy in linear rational expectations models

Cited by 3 publications

References 15 publications

The Linear Systems Approach to Linear Rational Expectations Models

The Linear Systems Approach to Linear Rational Expectations Models

Politics, Financial Regulation and Housing Bubbles

The Spectral Approach to Linear Rational Expectations Models

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