Use the data from JTRAIN for this exercise.

(i) Consider the simple regression model log1scrap2 5 b0 1 b1grant 1 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 log1scrap87 2. 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: bgrant , 0?

(iv) Test the null hypothesis that the parameter on log1scrap87 2 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.