Noah and Joseph Effects in Government Budgets : Analyzing Long-Term Memory

Abstract

This article examines the combined effects of what mathematician Benoit Mandelbrot has termed "Noah" and "Joseph" effects in U.S. national government budgeting. Noah effects, which reference the biblical great flood, are large changes or punctuations, far larger than could be expected given the Gaussian or Normal models that social scientists typically employ. Joseph effects refer to the seven fat and seven lean years that Joseph predicted to the Pharaoh. They are "near cycles" or "runs" in time series that look cyclical, but are not, because they do not occur on a regular, predictable basis. The Joseph effect is long-term memory in time series. Public expenditures in the United States from 1800 to 2004 shows clear Noah and Joseph effects. For the whole budget, these effects are strong prior to World War II (WWII) and weaker afterward. For individual programs, however, both effects are clearly detectable after WWII. Before WWII, budgeting was neither incremental nor well behaved because punctuations were even more severe and memory was not characterized by simple autoregressive properties. The obvious break that occurred after WWII could have signaled a regime shift in how policy was made in America, but even the more stable modern world is far more uncertain than the traditional incremental view.