The relationship between oil price shocks and U.S. macroeconomic fluctuations advocated by Hamilton (1983) broke down in the 1980s amidst a new regime of highly volatile oil price movements. Several authors have argued that asymmetric and nonlinear transformations of oil prices restore that relationship and thus that the economy responds asymmetrically and nonlinearly to oil price shocks. In this paper, I show that this is only part of the story: the two leading such transformations do not in fact Granger cause output or unemployment in the post-1980 period without further refinements, and they derive much of their apparent success from data in the 1950s. If output is expressed in year-over-year changes, which are smoother than the usual quarterly changes, and the equations exclude variables like interest rates and inflation, then asymmetric and nonlinear oil prices predict output but not unemployment, while the real level of oil prices predicts unemployment but not output. I interpret this evidence as supportive of significant oil price effects on the macroeconomy which a) are at relatively low frequencies, b) are indirect, through variables like interest rates and inflation, c) can induce departures from Okun's law, and d) changed qualitatively around 1980.