Use the data in MINWAGE.RAW for this exercise, focusing on sector 232.
(i) Estimate the equation
gwage232t = (0 + (1 ygmwaget + (2 gcpi i+ ut,
and test the errors for AR( 1) serial correlation. Does it matter whether you assume gmwage and gcpi are strictly exogenous? What do you conclude overall?
(ii) Obtain the Newey-West standard error for the OLS estimates in part (i), using a lag of 12. How do the Newey-West standard errors compare to the usual OLS standard errors?
(iii) Now obtain the heteroskedasticity-robust standard errors for OLS, and compare them with the usual standard errors and the Newey-West standard errors. Does it appear that serial correlation or heteroskedasticity is more of a problem in this application?
(iv) Use the Breusch-Pagan test in the original equation to verify that the errors exhibit strong heteroskedasticity.
(v) Add lags 1 through 12 of gmwage to the equation in part (i). Obtain the p-value for the joint F test for lags 1 through 12, and compare it with the p-value for the heteroskedasticity-robust test. How does adjusting for heteroskedasticity affect the significance of the lags?
(vi) Obtain the p-value for the joint significance test in part (v) using the Newey-West approach. What do you conclude now?
(vii) If you leave out the lags of gmwage, is the estimate of the long-run propsensity much different?