This paper proposes a very tractable approach to modeling changes in regime. The parameters of an autoregression are viewed as the outcome of a discrete-state Markov process. For example, the mean growth rate of a nonstationary series may be subject to occasional, discrete shifts. The econometrician is presumed not to observe these shifts directly, but instead must draw probabilistic inference about whether and when they may have occurred based on the observed behavior of the series. The paper presents an algorithm for drawing such probabilistic inference in the form of a nonlinear iterative filter. The filter also permits estimation of population parameters by the method of maximum likelihood and provides the foundation for forecasting future values of the series. An empirical application of this technique to postwar U.S. real GNP 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% permanent drop in the level of GNP.

University (f/' Virgiiwa All but one of the U.S. recessions since World War II have been preceded, typically with a lag of around three-fourths of a year, by a dramatic increase in the price of crude petroleum. This does not mean that oil shocks caused these recessions. Evidence is presented, however, that even over the period 1948-72 this correlation is statistically significant and nonspurlious, supporting the proposition that oil shocks were a contributing factor in at least some of the U.S. recessions prior to 1972. By extension, energy price increases may account for much of post-OPEC macroeconomic performance. This paper is drawn from chap. 2 of my Ph.D. dissertation at the University of California, Berkeley. Earlier versions of this paper were presented at the NBER/NSF Time Series (Conference in San Diego, March 13, 198 1, and at the NBER conferencee on Inflation and Business FluctUations, April 30-May 1, 1982, (Cambridge, Massachusetts. In addition to the helpful sLuggestions of' my adviser, James Pierce, I ami indebted to the many indiVidLuals whose comments and criticisms have helped sharpen the focus of this inquiry, including Allen Berger,

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