C9.3 Use the data from JTRAIN.RAW for this exercise. (i) Consider the simple regression model log(scrap)
0  1grant  u, where scrap is the firm scrap rate and grant is a dummy variable indicating whether a firm received a job training grant. Can you think of some reasons why the unobserved factors in u might be correlated with grant? (ii) Estimate the simple regression model using the data for 1988. (You should have 54 observations.) Does receiving a job training grant significantly lower a firm’s scrap rate? (iii) Now, add as an explanatory variable log(scrap87). How does this change the estimated effect of grant? Interpret the coefficient on grant. Is it statistically significant at the 5% level against the one-sided alternative H1: grant 0? (iv) Test the null hypothesis that the parameter on log(scrap87) is one against the two-sided alternative. Report the p-value for the test.

(v) Repeat parts (iii) and (iv), using heteroskedasticity-robust standard errors, and briefly discuss any notable differences.