Initial Beliefs Uncertainty and Information Weighting in the Estimation of Models with Adaptive Learning

This paper evaluates how the way agents weight information when forming expectations can affect the econometric estimation of models with adaptive learning. One key new finding is that misspecification of the uncertainty about initial beliefs under constantgain least squares learning can generate a time-varying profile of weights given to past observations, distorting the estimation and behavioural interpretation of this mechanism in small samples of data. This result is derived under a new representation of the learning algorithm that penalizes the effects of misspecification of the learning initials. Simulations of a forward-looking Phillips curve model with learning indicate that (i) misspecification of initials uncertainty can lead to substantial biases to estimates of expectations relevance for inflation, and (ii) that these biases can spill over to estimates of inflation rates responsiveness to output gaps. An empirical application with U.S. data shows the relevance of these effects.