In this paper, we consider a dynamic economy in which the agents in the economy are privately informed about their skills, which evolve stochastically over time in an arbitrary fashion. We consider an asset pricing equilibrium in which equilibrium quantities are constrained Pareto optimal. Under the assumption that agents have constant relative risk aversion, we derive a novel asset pricing kernel for financial asset returns. The kernel equals the reciprocal of the gross growth of the γth moment of the consumption distribution, where – is the coefficient of relative risk aversion. We use data from the consumer expenditure survey (CEX) and show that the new stochastic discount factor performs better than existing stochastic discount factors at rationalizing the equity premium. However, its ability to simultaneously explain the equity premium and the expected return to the Treasury bill is about the same as existing discount factors.