Initial Beliefs Uncertainty

Abstract This paper evaluates how initial beliefs uncertainty can affect data weighting and the estimation of models with adaptive learning. One key finding is that misspecification of initial beliefs uncertainty, particularly with the common approach of artificially inflating initials uncertainty to accelerate convergence of estimates, generates time-varying profiles of weights given to past observations in what should otherwise follow a fixed profile of decaying weights. The effect of this misspecification, denoted as diffuse initials, is shown to distort the estimation and interpretation of learning in finite samples. Simulations of a forward-looking Phillips curve model indicate that (i) diffuse initials lead to downward biased estimates of expectations relevance in the determination of actual inflation, and (ii) these biases spill over to estimates of inflation responsiveness to output gaps. An empirical application with U.S. data shows the relevance of these effects for the determination of expectational stability over decadal subsamples of data. The use of diffuse initials is also found to lead to downward biased estimates of learning gains, both estimated from an aggregate representative model and estimated to match individual expectations from survey expectations data.