C11.11 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, Δunem:
pcrgdp = 3 - 2 Δunem.
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, pcrgdpt = β0 + β1Δunemt + 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: β1 = −2. Do you reject H0 against the two-sided alternative at any reasonable significance level?
(iii) Find the t statistic for testing H0: β0 = 3. Do you reject H0 at the 5% level against he two-sided alternative? Is it a “strong” rejection?
(iv) Find the F statistic and p-value for testing H0: β0 β = 3, β1 = −2 against the alternative that H0 is false. Overall, would you say the data reject or tend to support
Okun’s law?
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