Matching the moments: a test of three representative agent models

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 ...