A General Framework for the Variance Bounds Inequality

Abstract

Suppose now that agents have sufficient information to forecast dividends perfectly up to period m (and so assume m ≥ t, ∀t = 1,..., T) and let us define p _mt * in the following way:

$$ p_{mt}^{*}=\sum\limits_{\tau =t+1}^{m}{\frac{{{d}_{\tau }}}{{{(1+r)}^{\tau -t}}}}+\frac{{{p}_{m}}}{{{(1+r)}^{m-t}}}$$

(6.1)

Notice that Shiller’s ex post perfect foresight price is a limiting case (for m = ∞) of (6.1). Also, the approximation usually used of the ex post rational price to implement operational tests of the variance bounds inequality, is obtained by setting in (6.1) m = T. As a straightforward consequence of Proposition 5.1, we have the following corollary:

Chapter based on a joint research with Margaret Bray (see Bray and Marseguerra, 1996).