Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 19

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, ?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, pcrgdpt = ?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: ?1 = ?2. Do you reject H0 against the two-sided alternative at any reasonable significance level?

(iii) Find the t statistic for testing H0: ?0 = 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: ?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?

Step 1 of 4

Consider is the annual percentage change in real GDP andis the change in annual unemployment rate. Okun’s law is given by:

Estimating the equation,

The result is as follows:

It is evident that, exactly 3 for intercept and -2 for the slope is not obtained for the equation. It was not expected to obtain exactly 3 for intercept and -2 for the slope for the equation as the data for and is updated every year as the result, the coefficients are likely to change as the data update under evolving economic situation.