In a very broad class of dynamic linear models, if agents possess knowledge of current endogenous variables in a least-squares learning process, determinacy of a rational expectations (RE) equilibrium is sufficient but not necessary for learnability of that equilibrium. Thus, since learnability is an attractive necessary condition for plausibility of any equilibrium, there may exist a single plausible RE solution even in cases of indeterminacy. This paper proposes and outlines a distinct criterion that plausible models should possess, termed "well formulated" (WF), which rules out infinite discontinuities in the implied impulse response functions. The paper explores the relationship between this WF property and learnability, under the information assumption mentioned above, and finds that they often agree but neither strictly implies the other. Extending the P-matrix requirement, implied for specified matrices by the WF property, to one that demands positive dominant-diagonal matrices would guarantee both WF and learnability, but a suitable rationale has not been found. Finally, under a second information assumption, which gives the agents only lagged information on endogenous variables during the learning process, the situation is less favorable in the sense that learnability can be guaranteed only under special assumptions.
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