Question

ou have learned that earnings functions are one of the most investigated relationships in economics. These typically relate the logarithm of earnings to a series of explanatory variables such as education, work experience, gender, race, etc. (a) Why do you think that researchers have preferred a log-linear specification over a linear specification? (b) To establish age-earnings profiles, you regress ln(Earn) on Age, where Earn is weekly earnings in dollars, and Age is in years. Plotting the residuals of the regression against age for 1,744 individuals looks as shown in the figure: Do you sense a problem? (c) You decide, given your knowledge of age-earning profiles, to allow the regression line to differ for the below and above 40 years age category. Accordingly you create a binary variable, Dage, that takes the value one for age 39 and below, and is zero otherwise. Estimating the earnings equation results in the following output (using heteroskedasticity-robust standard errors): = 6.92 – 3.13 × Dage – 0.019 × Age + 0.085 × (Dage × Age), R2 = 0.20, SER = 0.721. (38.33) (0.22) (0.004) (0.005) Sketch both regression lines: one for the age category 39 years and under, and one for 40 and above. Does it make sense to have a negative sign on the Age coefficient? Predict the ln(earnings) for a 30 year old and a 50 year old. What is the percentage difference between these two? (d) The F-statistic for the hypothesis that both slopes and intercepts are the same is 124.43. Can you reject the null hypothesis? (e) What other functional forms should you consider?

Answer 1

a) Log-lin function for age earnings relationships is better because it gives the percentage change in earnings for a given change in age rather than an absolute change which is given by the linear function. It makes more sense because people with different levels of income cannot have the same change in their income as age increases but maybe the proportional change is more or less the same.

b)Figure not given

c) The above figure represents the plot of two regression lines one for the age group 39 years and below and another for 40 years and above. Generally, in the real world earnings increases with experience and it is observed that as age increases experience also increases, so it does not make sense for age coefficient to have a negative sign.

ln(earnings) for 30 years old = 6.92 - 3.13 X 1 - 0.019 X 30 + 0.085 X (1 X 30) = 5.77

ln(earnings) for 50 years old = 6.92 - 3.13 X 0 - 0.019 X 50 + 0.085 X (0  X 50) = 5.97

The difference between the two is 0.2%.

d) The hypothesis can be rejected as the calculated value f F statistic is very large and will have a correspondingly very small p - value which results in rejection of hypothesis.