Title: Arbitrary initial conditions and the dimension of indeterminacy in linear rational expectations models
Authors: Marco Maria Sorge - University of Salerno (Italy) [presenting]
Abstract: Indeterminate equilibrium rational expectations (RE) models are ubiquitous in both theoretical and applied work in dynamic macroeconomics. The issue of characterizing the exact dimension of indeterminacy - i.e. of deriving the full set of causal and stable solutions to linear RE models - has only recently been addressed in the context of general, multivariate settings. Existing results are complemented by identifying bounds on the observable dimension of indeterminacy of linear RE models in the presence of arbitrary initial conditions. In particular, it is established that, provided the underlying RE model admits a non-unique (causal, stable) solution, then (i) the exact dimension of indeterminacy is always lower than (or at most equal to) the degree of indeterminacy as previously identified, and (ii) the maximal dimension of indeterminacy cannot exceed the one associated with the model's counterpart featuring initial conditions which are set to lie onto the model's stable saddle path. Implications for the estimation of indeterminate equilibrium RE models are discussed.