Use the data in OKUN.RAW to answer this question; see also Computer Exercise.(i) Estimate...

Use the data in OKUN.RAW to answer this question; see also Computer Exercise.

(i) Estimate the equation pcrgdpt = β0 + β1 Δunemt + ut and test the errors for AR(1) serial correlation, without assuming { Δunemt: t = 1, 2, ...} is strictly exogenous. What do you conclude?

(ii) Regress the squared residuals, û2t, on Aunemt (this is the Breusch-Pagan test for heteroskedasticity in the simple regression case). What do you conclude?

(iii) Obtain the heteroskedasticity-robust standard error for the OLS estimate . Is it substantially different from the usual OLS standard error?

Exercise 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?