Harrodian Instability and Learning

It is a standard result in macroeconomic models populated by boundedly-rational agents that the stability of equilibria is left undetermined by the deep structural parameters, because it depends upon the nature of the prevailing beliefs. Apparently, a mean of avoiding this sort of indeterminacy is making belief formation endogenous, via methods and results borrowed from the learning literature. The paper attempts at clarifying the difficulties encountered by this line of argument when predictions of a variable are based on expectation functions defined on a space of realized values of the same variable and learning is based on gradient descent procedures. Since the analysis is carried out with reference to a simple macroeconomic model of Harrodian inspiration, the paper gives also some local results on the theme of Harrodian instabiliity.