Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 6

This exercise also uses the data from VOLAT.RAW. Computer Exercise studies the long-run relationship between stock prices and industrial production. Here, you will study the question of Granger causality using the percentage changes.
(i) Estimate an AR(3) model for pcipt, the percentage change in industrial production (reported at an annualized rate). Show that the second and third lags are jointly significant at the 2.5% level.
(ii) Add one lag of pcspt to the equation estimated in part (i). Is the lag statistically significant What does this tell you about Granger causality between the growth in industrial production and the growth in stock prices
(iii) Redo part (ii) but obtain a heteroskedasticity-robust t statistic. Does the robust test change your conclusions from part (ii)
Exercise
Use the data in VOLAT.RAW for this exercise.
(i) Confirm that lsp500 = log(sp500) and lip = log(ip) appear to contain unit roots. Use Dickey-Fuller tests with four lagged changes and do the tests with and without a linear time trend.
(ii) Run a simple regression of lsp500 on lip. Comment on the sizes of the t statistic and R-squared.
(iii) Use the residuals from part (ii) to test whether lsp500 and lip are cointegrated. Use the standard Dickey-Fuller test and the ADF test with two lags. What do you conclude
(iv) Add a linear time trend to the regression from part (ii) and now test for cointegration using the same tests from part (iii).
(v) Does it appear that stock prices and real economic activity have a long-run equilibrium relationship