Adaptive Learning in Practice

While there is an extensive literature on identifying the asymptotic properties of adaptive learning algorithms, little is explicitly mentioned on how to actually implement these algorithms on the computer to analyze the quantitative effects of learning in dynamic macroeconomic models. The aim of this paper is twofold. First, we provide a detailed practical description of how to numerically implement least squares learning in the context of a reduced form forward looking model with an endogenous lag. Second, while we give a brief overview of the asymptotic properties of least squares learning for the reduced form at hand, the analysis focuses on illustrating the importance of the initial conditions of the learning algorithm for the study of medium and short run dynamics. In particular, we propose and discuss two ways of initializing the algorithm, one that is based on randomly generated data and a second that is ad-hoc. Using several variations of the basic real business cycle model, we then compare the behavior of the variables of interest for a variety of initializations. Our results indicate that, for short time horizons of up to 300 periods (corresponding to 75 years of quarterly data), the evolution of aggregate variables depends crucially on the initial conditions of the algorithm, and the learning dynamics might deviate significantly from the corresponding rational expectations case depending on the initialization.