1. Consider the following wage equation that has been estimated from a random sample of 35-65 year old older male workers:
lnwi =3.825+0.152age-0.0014age2+0.103edui+εi (1) (12.10) (3.18) (2.05) (5.08)
where lnw is log wage, age is age measured in years divided by 10, edu is a dummy variable indicating if the individual has higher education qualifications. The numbers in parentheses are absolute t-ratios.
Hypothesis Testing
(a) Test the hypothesis that the returns to higher education estimated in the regression are above 10%. (Bear in mind the numbers in parentheses are absolute values of t-ratios!)
(b) Test the hypothesis that the returns to age is linear. Show that wages are predicted to peek around age 54.
Omitted variable bias
Next, you are interested in the effect of training courses on wages. You start with regressing log-wages on the number of weeks individual i has been in training in the last 3 years.
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Dependent variable:
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Log wages
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(1)
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(2)
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(3)
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Coeff t
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Coeff t
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Coeff t
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Constant
# Weeks of training Education
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3.825 0.0015
(12.10) (5.11)
-
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3.242 0.102
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(12.86) (5.31)
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3.582 0.0009 0.082
(12.04) (3.99) (6.61)
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Sampel size R-squared
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2536 0.314
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2536 0.281
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2536 0.29
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Note: Number in parentheses are absolute t-values
(c) Interpret the coefficient on the number of weeks of training courses. How much are wages predicted to increase if a worker spent 6 months in training course over the past 3 years?
1(d) You are worried that the estimate for the number of weeks in training on wages may be biased due to omitted variables, most importantly education. How does omitting education from regression (1) affect the estimate on weeks in training if education and weeks in training are positively correlated? What if education and training are negatively correlated? Which scenario do you consider more likely?
- (e) By comparing specifications (1) and (3), and (2) and (3), deduce the nature of the correlation between training and education in this sample. Explain.