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What economic reasons might there be to expect age and fitness to affect earnings?

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1. You will find the data for this question in a file called wage.dta. The data are a sample of 300 male manual workers from the UK. We are interested in the regression of ln wage (wage) on education (educ):
lnwi =α+βedui+εi (1)
(a) Regress ln wage (wage) on education (educ). Interpret your results.
(b) Can you reject the hypothesis that an additional year of schooling increases wages by 1%?
(c) What is the R2 of the regression? Give the formula and explain what it is in words.
(d) Add years of experience (exp) to the regression. What happens to the estimated effect of educa- tion? Explain why this happens.

2. You have data from an extensive medical survey on health and economic status. A cross section of 500 men provides information on earnings w in £ per week, age in years a and an index of fitness f .
(a) You run the following regression of ln earnings on the fitness index:
ln w = 6.1 − 0.31 f + u R2 = 0.05 (2)
(3.7)
Here, and below, figures in parentheses are absolute t values and u is an error term. Calculate a
95% interval for the coefficient on the fitness index.
(b) You then add age to the regression with the following results:
lnw = 5.3+0.07a+ 0.12 f +u R^2 = 0.09 (3)
(4.8) (0.91)
Explain carefully why and how adding age to the regression can change the size and sign of the estimated fitness effect. Do the results indicate that age must be negatively or positively correlated with fitness in this sample?
(c) What economic reasons might there be to expect age and fitness to affect earnings? To what extent do you regard these results as supporting the contention that they do?

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