Abstract
We develop a tractable exactly solved present-value model to study the dynamics of stock returns, dividend growth rates, and the price-dividend ratio. We show that standard predictive regressions of returns and dividend growth rates on the lagged price-dividend ratio suffer from a problem that is akin to an errors-in-variables problem. By using non-linear filtering techniques to estimate the structural parameters of our present-value model, we can mitigate this errors-in-variables problem. We then use this framework to decompose the price-dividend ratio and excess stock returns, and study the influence of approximation errors that would arise if we were to log-linearize the model. Our model induces heteroscedasticity in returns, even though the latent processes for expected returns and expected dividend growth rates are homoscedastic.
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