7 In Example 4.7, we used data on nonunionized manufacturing firms to estimate the relationship between the scrap rate and other firm characteristics. We now look at this ex- ample more closely and use all available firms.
(i) The population model estimated in Example 4.7 can be written as log(scrap) 5 b0 1 b1hrsemp 1 b2log(sales) 1 b3log(employ) 1 u.
Using the 43 observations available for 1987, the estimated equation is
log(scrap XXXXXXXXXX hrsemp 2 .951 log(sales XXXXXXXXXXlog(employ)
XXXXXXXXXX) (.360)
n 5 43, R XXXXXXXXXX.
Compare this equation to that estimated using only the 29 nonunionized firms in the sample.
(ii) Show that the population model can also be written as
log(scrap) 5 b0 1 b1hrsemp 1 b2log(sales/employ) 1 u3log(employ) 1 u,
where u3 5 b2 1 b3. [Hint: Recall that log(x2/x3) 5 log(x2) 2 log(x3).] Interpret the hypothesis H0: u3 5 0.
(iii) When the equation from part (ii) is estimated, we obtain
log(scrap XXXXXXXXXX hrsemp 2 .951 log(sales/employ XXXXXXXXXXlog(employ)
XXXXXXXXXX) (.205)
n 5 43, R XXXXXXXXXX.
Controlling for worker training and for the sales-to-employee ratio, do bigger firms have larger statistically significant scrap rates?
(iv) Test the hypothesis that a 1% increase in sales/employ is associated with a 1% drop in the scrap rate.