A probabilistic interpretation of the constant gain learning algorithm

This paper proposes a novel interpretation of the constant gain learning algorithm through a probabilistic setting with Bayesian updating. The underlying process for the variable being estimated is not specified a priori through a parametric model, and only its probabilistic structure is defined. Such framework allows to understand the gain coefficient in the learning algorithm in terms of the probability of changes in the estimated variable. On the basis of this framework, I assess the range of values commonly used in the macroeconomic empirical literature in terms of the implied probabilities of changes in the estimated variables.