We investigate a non-linear representative consumer asset pricing model in a complete markets economy. The consumer is assumed to display time nonseparable preferences. The time nonseparability in preferences is due first to local substitution of consumption over time, and second to long-run habit persistence.We use a projection approach to solve this non-linear stochastic dynamic model with rational expectations. The projection method is implemented with a two state variables vector and the dividend variable is used as an exogenously given shock. We assume that the growth rate of dividend follows a first order Markov chain. The resolution of the dynamic problem is done in two steps. In the first step, we compute the approximations of marginal utility of consumption and intertemporal marginal rate of substitution in consumption (IMRS). Then, we calculate the approximations of equity price and risk-free asset price. We finally deduce the returns on the equity and the risk-free security implied by the dynamic.We carry out two complementary studies to see if this model could explain the U.S risk premia in the period 1965-1987. First, we test if the model's implications concerning the volatility of the IMRS are satisfied. We find that the IMRS implied by the model fits statistically the Hansen and Jagannathan bound. Secondly, we analyze the time-series properties of the simulated model. In particular, we have done a sensitivity analysis to find the parameter values that fit the first two observed moments. They are chosen in order to meet the positivity of the marginal utility of consumption. For a set of parameter values, we find that the model fits the sample average and volatility of the ris-free asset. However, the simulated mean of the equity return is 1% under the observed mean, and the model is not able to generate enough volatility for the equity return.
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