Question

In this section we will study the problem of gender-wage discrimination. It is often argued that women are paid less than equally qualified men to do the same job. This is also true in academia. The University of Calgary administrators are trying to determine the gender earnings gap in order to `compensate' women who are underpaid. In the empirical analyses that follow, the following variables are defined as:

Y - Log earnings

F - female indicator

Age - age of individual

Assoc - indicator for Associate Professor Rank

Full - indicator for Full Professor Rank

ϴ_f- faculty/college indicators (e.g., Social Science, Engineering, Business...)

ϴ_d- department indicators (e.g., economics, history...)

1. Consider the following:

E[Y_i|F_i = 1] - E[Y_i|F_i = 0]

Do you think that this identified the causal effect of being a woman on wage? Explain.

2. Consider the following regression equation:

Y_i = β₀ + αF_i + ε_i                                                                                                                       (1)

What variation in the data is being used to identify the male-female difference in earnings?

3. Consider the following augmented regression:

Y_i = β₀ + αF_i + βAge_i + ε_i                                                                                                          (2)

How does adding age to the regression change the source of variation used in identifying the male-

female wage differential?

If female professors are, on average, younger than male professors, how would you expect the estimate of α to change from equation (1)?

4. Consider the following augmented regression:

Y_i = β₀ + αF_i + βAge_i + γ₁Assoc_i + γ₁Full_i + ε_i                                                                                                                  (3)

Now what variation in the data is used to identify the male-female difference in earnings? How would the estimate of α change relative to equation (1) if females are over-represented in the assistant professor rank?

5. Consider the following augmented regression:

Y_i = β₀ + αF_i + βAge_i + γ₁Assoc_i + γ₁Full_i + ϴ_f + ε_i                                                                     (4)

Now what variation in the data is used to identify the male-female difference in earnings? How would the estimate of α change relative to question 2 if females are over-represented in the higher paying faculties/colleges? What is the difference between running this regression and running regression 3 separately for each faculty/college?

6. Discuss whether or not you would want to interact the department (or Assoc and Full) indicators with the female indicator. What other interactions might be important? What problems might you run into if you try to include too many interactions?

7. Suppose the regression in question e suggested that women were underpaid relative to men. Discuss a few things that might be “left out" of this regression that you would ideally want to control for.

Answer 1