Heterogeneous experience and constant-gain learning

Recent evidence suggests that agents may base their forecasts for macroeconomic variables mainly on their personal life experiences. We connect this behavior to the concept of constant-gain learning (CGL) in macroeconomics. Our approach incorporates both heterogeneity in the life cycle via the perpetual youth model and learning from experience (LfE) into a linear expectations model where agents are born and die with some probability every period. For LfE, agents employ a decreasing-gain learning (DGL) model using data only from their own lifetimes. While agents are using DGL individually, we show that in the aggregate, expectations follow an approach related to CGL, where the gain is now tied to the probabilities of birth and death. We provide a precise characterization of the relationship between CGL and our model of perpetual youth learning (PYL) and show that PYL can well approximate CGL while pinning down the gain parameter with demographic data. Calibrating the model to U.S. demographics leads to gain parameters similar to those found in the literature. Further, variation in birth and death rates across countries and time periods can help explain the empirical time-variation in gains. Finally, we show that our approach is robust to alternative ways of modeling individual agent learning.