MATCHING THE MOMENTS - A TEST OF 3 REPRESENTATIVE AGENT MODELS

No arbitrage profit opportunities implies state-contingent shadow pric es that value the state-contingent payoffs of any asset traded in perf ect markets. The shadow price is an implicit stochastic discount facto r. I decompose the implicit model free nominal discount factor into it s observable conditional mean-the price of a default free discount bon d-and an unobservable innovation. I infer the unconditional covariance matrix between innovations in the model free discount factor and retu rns. Dynamic behaviour nl economic models specify, or imply, a discoun t factor. The theoretical mean of the nominal model generated discount factor is the observable price of a default free discount bond. A nec essary condition for any model to be consistent with securities market data is that the moments of the deviations of the model-generated dis count factor from its theoretical conditional mean (call the deviation s residuals) match the moments of innovations in the model free discou nt factor. This is an easy specification test for any model. I match t he moments for three representative agent specifications-power utility , habit formation, and a consumption-leisure choice model. The moments from the more complicated specifications come closes to matching the model free moments, but none of the representative agent models genera tes a covariance (risk premium) large enough to match the model free c ovariance.