We will continue the analysis of height and wages in Britain. We'll use the data set heightwage_british_all_ multivariate.dta, which includes men and women and the variables listed in Table 7.4.

(a) Estimate a model explaining wages at age 33 as a function of female, height at age 16, mother's education, father's education, and number of siblings. Use standardized coefficients from Section 5.5 to assess whether height or siblings has a larger effect on wages.

(b) Use bivariate OLS to implement a difference of means test across males and females. Do this twice: once with female as the dummy variable and the second time with male as the dummy variable (the male variable needs to be generated). Interpret the coefficient on the gender variable in each model, and compare results across models.

(c) Now do the same test, but with \(\log\) of wages at age 33 as the dependent variable. Use female as the dummy variable. Interpret the coefficient on the female dummy variable.

(d) How much does height explain salary differences across genders? Estimate a difference of means test across genders, using logged wages as the dependent variable and controlling for height at age 33 and at age 16. Explain the results.

(e) Does the effect of height vary across genders? Use logged wages at age 33 as the dependent variable, and control for height at age 16 and the number of siblings. Explain the estimated effect of height at age 16 for men and for women using an interaction with the female variable. Use an \(\mathrm{F}\) test to assess whether height affects wages for women.

Data From Section 5.5:

We frequently want to compare coefficients. That is, we want to say whether X₁ or X₂ has a bigger effect on Y. If the variables are on the same scale, this task is pretty easy. For example, in the height and wages model, both adolescent and adult height are measured in inches, so we can naturally compare the estimated effects of an inch of adult height versus an inch of adolescent height.

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TABLE 7.4 Variables for Height and Wages Data in Britain Variable name gwage33 height33 Description Hourly wages (in British pounds) at age 33 Height (in inches) measured at age 33 Height (in inches) measured at age 16 Education of mother, measured in years Education of father, measured in years height 16 momed daded siblings female LogWage33 Log of hourly wages at age 33 Number of siblings Female indicator variable (1 for women, 0 for men)