The least controversial has been the adoption of the REH as one of several possible expectations
formation hypotheses in an otherwise conventional macroeconometric model
containing expectational variables. In this context the REH, by imposing the appropriate
cross-equation parametric restrictions, ensures that ‘expectations’ and ‘forecasts’ generated
by the model are consistent. In this approach the REH is regarded as a convenient
and effective method of imposing cross-equation parametric restrictions on time series
econometric models, and is best viewed as the ‘model-consistent’ expectations hypothesis.
There is now a sizeable literature on solution, identification, and estimation of linear
RE models. The canonical form of RE models with forward and backward components
is given by
yt = Ayt−1 + BE (yt+1 |Ft )