Okun's Law-for example, Mankiw (1994, Chapter 2)-implies the following relationship between the annual percentage change in real GDP, pcrgdp, and the change in the annual unemployment rate, (unem:
pcrgdp = 3 - 2 ( (unem.
If the unemployment rate is stable, real GDP grows at 3% annually. For each percentage point increase in the unemployment rate, real GDP grows by two percentage points less. (This should not be interpreted in any causal sense; it is more like a statistical description.)
To see if the data on the U.S. economy support Okun's Law, we specify a model that allows deviations via an error term, pcrgdp, = (0 + (1 (unemt + ut.
(i) Use the data in OKUN.RAW to estimate the equation. Do you get exactly 3 for the intercept and -2 for the slope? Did you expect to?
(ii) Find the t statistic for testing H0 : (0 = - 2. Do you reject H0 against the two-sided alternative at any reasonable significance level?
(iii) Find the / statistic for testing H0 : (0 = 3. Do you reject H0 at the 5% level against the two-sided alternative? Is it a "strong" rejection?
(iv) Find the F statistic and p-value for testing H0: (0 = 3, (1 = - 2 against the alternative that H0 is false. Overall, would you say the data reject or tend to support Okun's law?