Sources of entropy in representative agent models of asset pricing

We use asset returns to characterize the properties of the pricing kernel, including its volatility (measured by entropy) and time-dependence. Then we explore similar properties of a number of popular representative agent models: long-run risk, time-varying volatility and risk, several versions of habits, and jumps (interpreted here as departures from conditional lognormality). Using common loglinear approximations, we show analytically how each of these models generates entropy and time-dependence and comment on their ability to reproduce some of the salient features of asset returns. We think the exercise clarifies the mechanisms behind these models and reveals their similarities and differences.