In: Statistics and Probability
Suppose a manufacturing firm has two factories (Factory 1 and Factory 2), and a single production process (Process A) that is used in both factories. A new process (Process B) is developed that potentially reduces production costs. To test whether Process B is less costly than Process A, an experiment is designed where:
Note that resources (i.e. materials, workers, equipment) are not reassigned across factories.
Let Yi be the cost of producing product i, let Xi be 1 if Process B is used to produce i and 0 if Process A is used, and let Wi be 1 if product i is produced in Factory 1 and 0 if it is produced in Factory 2.
In a regression of Yi on X, it is advisable to:
a. |
Exclude Wi as products are randomly assigned and including Wi would increase standard errors. |
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b. |
Exclude Wi as it is uncorrelated with Xi |
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c. |
Include Wi as E(ui | Xi) ≠ 0, but E(Xi | Wi) = 0 |
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d. |
Include Wi as E(ui | Xi) ≠ 0, but E(ui | Xi, Wi) = E(ui | Wi) |