This paper develops and tests a non-linear utility-based econometric model of the temporal behavior of aggregate stock price movements, based on a constant relative risk aversion utility function and an observable information set consisting of aggregate consumption, aggregate dividends and past stock prices. The stochastic process derived from time-series analyses of consumption and dividends measured over annual intervals is used to derive and empirically test a closed-form solution for stock price movements. The endogenization of discount rate changes in the utility-based model is shown to be more consistent with aggregate stock price movements over a twenty year holdout period than constant discount rate models. The model is also used to estimate the representative investors relative risk aversion. The estimate of 4.22 is consistent with that used by Grossman and Shiller in their perfect foresight model and is significantly higher than the relative risk aversion of 1.0 implied by logarithmic utility.