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 example more closely and use all available firms.
(i) The population model estimated in Example 4.7 can be written as
log(scrap) = (0 + (1 hrsemp + (2log(sales) + (3log(employ) + u.
Using the 43 observations available for 1987, the estimated equation is

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) = (0 + (1 Pxhrsemp + (2 log(sales/employ) + (3log(employ) + u,
where (3 = (2 + (3. [Recall that log(x2/x3) = log(x2) - log(x3).] Interpret the hypothesis H0: (3 = 0.
(iii) When the equation from part (ii) is estimated, we obtain

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.

log(scrap)= 11.74-042 (4.57) 019) hrsemp_ .951 (.370) log(sales) + .992 log(employ) (.360) n 43, R 310. log(scrap)= 11.74 - .042 hrsemp- 951 log(sales/employ) + 041 log(employ) (.370) (4.57) (.019) .205) n43, R 310.