E-equilibria and adaptive expectations: Output and inflation in the LBS model

This paper examines issues of convergence, the variability of the dynamic paths and end value outcomes of output and inflation in the London Business School (LBS) macromodel where adaptive learning schemes are used to form expectations of future variables. First, we examine the sensitivity of the outcomes from an exogenous oil price shock to alternative formulations of the adaptive expectations scheme. The results suggest that convergence is not certain for ad hoc specifications of the expectations rule, but that where solutions do exist for a range of empirically estimated rules, the results show a sufficient degree of similarity, particularly for output, to suggest more than weak, possibly strong E-stability. Nonetheless, the dynamic paths for output and inflation differ significantly. We then focus on one simple expectations rule and test the variability of model outcomes when the associated hyperparameters differ. In some cases this leads to no convergence, but where a stable region is found the output and inflation results differ markedly, both for the dynamics and for the end values. Therefore the speed of learning as well as the expectations rule matters for the output and inflation paths.