This paper models occasional, discrete shifts in the growth rate of a nonstationary series. Algorithms for inferring these unobserved shifts are presented, a byproduct of which permits estimation of parameters by maximum likelihood. An empirical application of this technique suggests that the periodic shift from a positive growth rate to a negative growth rate is a recurrent feature of the U.S. business cycle, and indeed could be used as an objective criterion for defining and measuring economic recessions. The estimated parameter values suggest that a typical economic recession is associated with a 3 percent permanent drop in the level of GNP.

A lifetime utility model, in which the date of death is uncertain and in which bequests give utility, is analyzed and estimated. The parameter estimates imply that most bequests are accidental, the result of mortality risk, and that the shape of the desired consumption path is sensitive to variations in mortality rates. On average, the elderly in the sample dissave, which is consistent with a life-cycle model in which utility does not depend on bequests.

The authors model an oligopoly facing uncertain demand where each firm chooses as its strategy a "supply function" relating its quantity to its price. A supply function adapts better to an uncertain environment than either a fixed price or a fixed quantity; it could be committed to through the choice of organizational structure and employee decision rules. The authors give conditions for existence and for uniqueness of a Nash equilibrium in supply functions under uncertainty. They compare the equilibrium with the Cournot and Bertrand equilibria as they vary the demand and cost curves, the number of firms, and the form of uncertainty.