Expected Returns and the Business Cycle: Heterogeneous Goods and Time-Varying Risk Aversion

This paper proposes a representative agent habit formation model where preferences are defined for both luxury goods and basic goods. The model matches the equity risk premium, risk-free rate, and volatilities. From the intratemporal first-order condition, one can substitute out basic good consumption and the habit level, yielding a stochastic discount factor driven by two observable risk factors: luxury good consumption, and the relative price of the two goods. I estimate these processes and find them to be heteroskedastic, implying time-variation in the conditional volatility of the stochastic discount factor. These dynamics occur both at the business cycle frequency and at a lower, "generational" frequency. The findings reveal that the time variation in aggregate stock market and Treasury bond risk premiums are consistent with the predictions of the model.