Abstract
This article characterises the dimension of indeterminacy of linear rational expectations (LRE) models and derives their full set of solutions. It extends the analysis of indeterminate equilibria in Lubik and Schorfheide (2003) where some equilibria are incorrectly classified as indeterminate even though they entail the same observable outcome.
Highlights
In this article, the uniqueness condition (equation (42) in Sims, 2001) is analysed in order to characterise the dimension of indeterminacy and to derive the full set of solutions of linear rational expectations (LRE) models
This article characterises the dimension of indeterminacy of linear rational expectations (LRE) models and derives their full set of solutions
The uniqueness condition (equation (42) in Sims, 2001) is analysed in order to characterise the dimension of indeterminacy and to derive the full set of solutions of LRE models
Summary
The uniqueness condition (equation (42) in Sims, 2001) is analysed in order to characterise the dimension of indeterminacy and to derive the full set of solutions of LRE models. An example of an LRE model with a unique solution but whose existence condition is satisfied by multiple candidates is presented This example is characterised as having indeterminate equilibria by Lubik and Schorfheide (2003). In order to analyse the existence and uniqueness of stable and causal solutions, we transform and partition system (1) into a ‘‘stable’’ and an ‘‘unstable’’ block of nS and nU rows respectively, where nS + nU = n To this end, we apply the so-called QZ-decomposition to ( 0, 1), i.e. the matrices 0 and 1 are decomposed as 0 = Q ′ Z ′, 1 = Q ′ Z ′, where QQ ′ = In = ZZ ′, and and are upper-triangular. The vectors wtS and wtU are of dimensions nS and nU , and QS and QU are of dimensions (nS × n) and (nU × n) respectively
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