Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 8

Use the data in TRAFFIC2.RAW for this exercise. These monthly data, on traffic accidents in California over the years 1981 to 1989, were used in Computer Exercise
(i) Using the standard Dickey-Fuller regression, test whether ltotacct has a unit root. Can you reject a unit root at the 2.5% level
(ii) Now, add two lagged changes to the test from part (i) and compute the augmented Dickey-Fuller test. What do you conclude
(iii) Add a linear time trend to the ADF regression from part (ii). Now what happens
(iv) Given the findings from parts (i) through (iii), what would you say is the best characterization of Itotacct: an process or an I(0) process about a linear time trend
(v) Test the percentage of fatalities, prcfat,, for a unit root, using two lags in an ADF regression. In this case, does it matter whether you include a linear time trend
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