Table 5.10 describes variables from heightwage.dta we will use in this problem.

(a) Estimate two OLS regression models: one in which adult wages is regressed on adult height for all respondents, and another in which adult wages is regressed on adult height and adolescent height for all respondents. Discuss differences across the two models. Explain why the coefficient on adult height changed.

(b) Assess the multicollinearity of the two height variables using (i) a plot, (ii) the VIF command, and (iii) an auxiliary regression. Run the plot once without a jitter subcommand and once with it, and choose the more informative of the two plots.

Table 5.10:

(c) Notice that IQ is omitted from the model. Is this a problem? Why or why not?

(d) Notice that eye color is omitted from the model. Is this a problem? Why or why not?

(e) You're the boss! Use the data in this file to estimate a model that you think sheds light on an interesting relationship. The specification decisions include whether to limit the sample and what variables to include. Report only a single additional specification. Describe in no more than two paragraphs why this is an interesting way to assess the data.

TABLE 5.10 Variables for Height and Wages Data in the United States Variablename wage96 height85 height81 athlets clubnum siblings age male Description Hourly wages (in dollars) in 1996 Adult height: height (in inches) measured in 1985 Adolescent height: height (in inches) measured in 1981 Participation in high school athletics (1=yes, 0-no) Number of club memberships in high school, excluding athletics and academic/vocational clubs Number of siblings Age in 1996 Male (1 yes, 0 = no)