It has now been a decade since the first of the variance-bounds papers was circulated in typescript. If initially less interest was displayed in this material than the authors had hoped and expected, the same is no longer true. This may be a good time to discuss a few of the many recent papers extending and criticizing the original results. The central idea underlying the variancebounds tests is very simple. Consider stock prices. The perfect foresight price of stock -that price which would prevail if future dividends xt+i were known-is

for successive values of the endogenous variables y,, with the x, treated as deterministic forcing variables. Here 0 is a parameter vector and the Et are random shocks. Lucas correctly observed that such a formulation is inconsistent with a view of agents as optimizers: except in special cases in which the future is irrelevant to present decisions, it makes no sense to think of agents as optimizing if they know that their budget constraints are liable to shift arbitrarily (i.e., in a way which is not characterized probabilistically) as government policy changes. Lucas was led to augment the foregoing equation by adding to the system a government policy function