Expectations, Learning Gains, and Forecast Errors: Assessing Nonlinearities with a Functional Coefficient Approach

This paper investigates potential nonlinearities in the gain function, which, under adaptive learning, regulates the updating of agents' beliefs in response to recent forecast errors. I use data on professional survey forecasts to estimate nonparametric functional-coefficient regression models. The estimation results reveal nonlinearities in the relationships between expectations and forecast errors, which are indicative of nonlinear gain functions. Gains increase when forecast errors are historically large, and respond asymmetrically to past overpredictions and underpredictions. The findings suggest incorporating nonlinearities in the modeling of learning gains, instead of relying on the constant-gain assumption.