Noisy Earnings Reports and the Equity Premium

In this paper we examine the impact of noisy earnings signals on the equity premium. The motivation for the model is that many agents make current investment decisions based upon IBIS reports that are later revised to actual earnings reports. Agents know that the earnings forecasts are less volatile than actual earnings but they do not know the direction of the revisions. We model this problem by adding a signal extraction component to the standard Lucas model framework to arrive at a general equilibrium model similar to those that Bomfim (2001) and Aruoba (2004) use to examine signal extraction problems in the context of economic announcements. In our model, agents make their investment decisions based upon a noisy signal about the current period dividend payment and then, after the security market clears, the agents learn the true dividend payment and make their current period consumption decisions. The security price is determined when the earnings forecast is announced but the agent must anticipate that the earnings report will be revised before the final consumption decision is made. This leads to a very complex pricing equation with three sources of risk: the current period earnings revision, next period's earnings forecast and the subsequent revision. We examine this model both computationally and analytically. First, we choose a dividend process and agent preferences consistent with the model analyzed by Burnside (1998) and extend his analytical results to our model. Next, we solve the same model computationally using projection methods on a continuous state space. This allows us to examine the accuracy of the computational solutions for various parameterizations. Finally, we extend the model to more general specifications that admit only computational solutions. We conclude with a discussion of how to extend the model, both analytically and computationally, to multiple assets with differing signal-to-noise ratios.