We will continue the analysis of height and wages in Britain. We want to know if the relationship between height and wages in the United States also occurs among British men. Table 5.13 describes the data set heightwage_british_males_multivariate.dta, which contains data on males in Britain from Persico, Postlewaite, and Silverman (2004).

(a) Persico, Postlewaite, and Silverman (2004) argue that adolescent height is most relevant because it is height at these ages that affects the self-confidence to develop interpersonal skills at a young age. Estimate a model with wages at age 33 as the dependent variable and both height at age 33 and height at age 16 as independent variables. What happens to the coefficient on height at age 33? Explain what is going on here.

(b) Let's keep going. Add height at age 7 to the above model, and discuss the results. Be sure to note changes in sample size (and its possible effects), and discuss the implications of adding a variable with the statistical significance observed for the height at age 7 variable.

(c) Is there multicollinearity in the model from part (b)? If so, qualify the degree of multicollinearity, and indicate its consequences. Specify whether the multicollinearity will bias coefficients or have some other effect.

(d) Perhaps characteristics of parents affect height (some force kids to eat veggies, while others give them only french fries and Fanta). Add the two parental education variables to the model, and discuss the results. Include only height at age 16 (meaning we do not include the height at ages 33 and 7 for this question - although feel free to include them on your own; the results are interesting).

(e) 1Perhaps kids had their food stolen by greedy siblings. Add the number of siblings to the model, and discuss the results.

(f) We have included a variable, Ht16Noisy, which is the height measured at age 16 with some random error included. In other words, it does not equal the actual measured height at age 16 but is a "noisy" measure of height at age 16. Estimate the model using the variable Ht16Noisy instead of height16, and discuss any changes in coefficient on the height variable. Relate the changes to theoretical expectations about measurement error discussed in the chapter.

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Variable name TABLE 5.13 Variables for Height and Wages Data in Britain Description gwage33 Hourly wages (in British pounds) at age 33 height33 Height (in inches) measured at age 33 height16 Height (in inches) measured at age 16 height07 Height (in inches) measured at age 7 momed siblings Education of mother, measured in years Number of siblings Ht16Noisy Height (in inches) measured at age 16 with measurement error added in