2024 – 7 In Example 4 7 we used data on nonunionized manufacturing firms to estimate the relationship

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) 1b3log(employ) 1 u.

Using the 43 observations available for 1987, the estimated equation is

log(scrap) 5  11.74  2  .042  hrsemp 2  .951  log(sales) 1  .992  log(employ)

(4.57)     (.019)                   (.370)                       (.360)

n 5 43, R2 5 .310.

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) 5  11.74  2  .042  hrsemp 2  .951  log(sales/employ) 1  .041  log(employ)

(4.57)     (.019)                   (.370)                                    (.205)

n 5 43, R2 5 .310.

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.