Matching the moments: a test of three representative agent models

Abstract

No arbitrage profit opportunities implies state-contingent shadow prices that value the state-contingent payoffs of any asset traded in perfect markets. The shadow price is an implicit stochastic discount factor. I decompose the implicit model free nominal discount factor into its observable conditional mean—the price of a default free discount bond—and an unobservable innovation. I infer the unconditional covariance matrix between innovations in the model free discount factor and returns. Dynamic behavioural economic models specify, or imply, a discount factor. The theoretical mean of the nominal model generated discount factor is the observable price of a default free discount bond. A necessary condition for any model to be consistent with securities market data is that the moments of the deviations of the model-generated discount factor from its theoretical conditional mean (call the deviations residuals) match the moments of innovations in the model free discount factor. This is an easy specification test for any model. I match the moments for three representative agent specifications—power utility, habit formation, and a consumption-leisure choice model. The moments from the more complicated specifications come closer to matching the model free moments, but none of the representative agent models generates a covariance (risk premium) large enough to match the model free covariance