The Forward Method as a Solution Refinement in Rational Expectations Models

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Abstract
This paper generalizes the standard forward method of recursive substitution to a general class of linear Rational Expectations models with potentially multiple fundamental solutions. We propose a key property embedded in the forward solution -- the no-bubble condition -- as an economically sensible solution refinement in the class of fundamental solutions. In the literature, the no-bubble condition has been assumed to rule out non-fundamental bubble solutions. However, since the condition involves expectations of the future endogenous variables, it must be verified for every Rational Expectations equilibrium. We show that the forward solution is the only fundamental solution satisfying the no-bubble condition and that it is hard to justify economically fundamental solutions violating this condition. We provide several economic examples where the fundamental solutions obtained by other solution methods and refined by other solution selection criteria violate the no-bubble condition.