Testing Intertemporal Rational Expectations Model with State Uncertainty: An Application to the Permanent Income Hypothesis

In this paper we take a different modeling approach based on the component driven (CD) model developed in Kuan, Huang, and Tsay~(2003) to test the permanent income hypothesis (PIH), an example of intertemporal choice models. A key feature of this approach is that it explicitly allows for state uncertainty. By assuming that the labor income follows a CD process, we show that the agent's perception on the likelihoods of income innovations being permanent and transitory plays a crucial role in determining the optimal forecasts on the change of consumption. In particular, the effect of a current innovation is a weighted average of two distinct effects (resulted from permanent and transitory innovations), with the weights being the perceived likelihoods of respective states. Also, past innovations may affect consumption when there is a revision on the perceived likelihoods of previous states. If there is no state uncertainty, our result reduces to that of an existing model. Our empirical study shows that, while the CD model can characterize the U.S. consumption data well, the estimation results do not agree with the predictions of the PIH