Some exact and inexact linear rational expectation models in vector autoregressive models

•Compare exact and inexact linear rational expectation models.•Characterize the difference.•Discuss possible elimination to avoid constrained optimization for maximizing likelihood.

In this paper we consider maximum likelihood estimation in some exact and inexact linear rational expectation (LRE) models. The implications of the two models on the coefficients of the vector autoregressive (VAR) model are spelled out. The inexact version is more complicated and possible simplification of the resulting constrained optimization problem is discussed.