Increases in oil prices have been blamed for several recessions in developed countries. To quantify the effect of oil prices on real economic activity, researchers have done regressions like those discussed in this chapter. Let GDPt denote the value of quarterly gross domestic product in the United States and let Yt = l00ln(GDPt/GDPt-1) be the quarterly percentage change in GDP. James Hamilton, an econometrician and macroeconomist, has suggested that oil prices adversely affect that economy only when they jump above their values in the recent past. Specifically, let Ot equal the greater of zero or the percentage point difference between oil prices at date t and their maximum value during the past year. A distributed lag regression relating Yt and Ot, estimated over 1955:1-2000:1V, is

a. Suppose that oil prices jump 25% above their previous peak value and stay at this new higher level (so that Ot = 25 and Ot+1 = Ot+2 = ... = 0). What is the predicted effect on output growth for each quarter over the next 2 years?
b. Construct a 95% confidence interval for your answers in (a).
c. What is the predicted cumulative change in GDP growth over eight quarters?
d. The HAC F-statistic testing whether the coefficients on Ot and its lags are zero is 3.49. Are the coefficients significantly different from zero?

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Y, = 1.0-0.0550,-0.0260-1-0.0310,-2-0.1090,-3-0.1 280.4 (0.1) (0.054) 0057 (0.048 0.042) (0.053) +0.0080,-s+0.0250,-6-0.0190-7+0.0670- r-8 (0.025) (0.0480.039) 0.042)