Okun’s Law implies the following relationship between the annual percentage chan

Question

Okun’s Law implies the following relationship between the annual percentage change in real GDP, pcrgdp, and the change in the annual unemployment rate, cunem: Pcrgdp= 3 -2 cunem. If the unemployment rate is stable, real GDP grows at 3% annually. For each percent- age 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 =" +#cunemt +% (i) Estimate the equation pcrgdpt =" +#cunemt +% and test the errors for AR(1) serial correlation, without assuming {cunemt : t=1, 2, ...} is strictly exogenous. What do you conclude? (ii) Do you get exactly 3 for the intercept and 2 for the slope? Did you expect to? (iii) Find the t statistic for testing H0: " = 2. Do you reject H0 against the two-sided alternative at any reasonable significance level? (iv) Find the F statistic and p-value for testing H0: " = 3, # = 2 against the alternative that H0 is false. Does the test reject at the 10% level? Overall, would you say the data reject or tend to support Okun’s Law? (v) Do series have unit root? Verify it using the available tests and explain. (vi) Test for trend. What do you conclude? (vii) Regress the squared residuals, û2 t , on cunemt (this is the Breusch-Pagan test for heteroskedasticity in the simple regression case). What do you conclude? (viii) Obtain the heteroskedasticity-robust standard error for the OLS estimate #. Is it substantially different from the usual OLS standard error? (ix) Obtain the Newey-West standard error for the OLS estimates in part (i), using a lag of 4. How do the Newey-West standard errors compare to the usual OLS standard errors? (x) Add lags 1 through 4 of cunem to the equation in part (i). Obtain the p-value for the joint F test for lags 1 through 4, and compare it with the p-value for the heteroskedasticity-robust test. How doe

Explanation / Answer

Answer)

(i) The estimated equation is
t pcrgdp = 3.344 1.891 t unem
(0.163) (0.182)
n = 46, R2 = .710

t unem ---> Lag(1)

Naturally, we do not get the exact estimates specified by the theory. Okun’s Law is expected to
hold, at best, on average. The estimates are not particularly far from their hypothesized values of
3 (intercept) and 2 (slope).
(ii) The t statistic for testing 0 1 H : = 2 is about .60, which gives a two-sided p-value of
about .55. This is very little evidence against H0; the null is not rejected at any reasonable significance level.
(iii) The t statistic for 0 0 H : = 3 is about 2.11, and the two-sided p-value is about .04. Therefore, the null is rejected at the 5% level, although it is not much stronger than that.
(iv) The joint test underlying Okun’s Law gives F = 2.41. With (2,44) df, we get, roughly, pvalue = .10. Therefore, Okun’s Law passes at the 5% level, but only just at the 10% level.

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