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You Have Learned That Earnings Functions Are One of the Most

question 10

Essay

You 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? In addition to the interpretation of the slope coefficients, also think about the distribution of the error term.
(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: $You have learned that earnings functions are one of the most investigated relationships in economics. These typically relate the logarithm of earnings to a series of explanatory variables such as education, work experience, gender, race, etc. (a)Why do you think that researchers have preferred a log-linear specification over a linear specification? In addition to the interpretation of the slope coefficients, also think about the distribution of the error term. (b)To establish age-earnings profiles, you regress ln(Earn)on Age, where Earn is weekly earnings in dollars, and Age is in years. Plotting the residuals of the regression against age for 1,744 individuals looks as shown in the figure: Do you sense a problem? (c)You decide, given your knowledge of age-earning profiles, to allow the regression line to differ for the below and above 40 years age category. Accordingly you create a binary variable, Dage, that takes the value one for age 39 and below, and is zero otherwise. Estimating the earnings equation results in the following output (using heteroskedasticity-robust standard errors): \begin{array} { l } \widehat { \text { LnEarn } = } 6.92 - 3.13 \times \text { Dage } - 0.019 \times \text { Age } + 0.085 \times ( \text { Dage } \times \text { Age } ) , R 2 = 0.20 , \text { SER } = 0.721 . \\ \quad\quad\quad\quad( 38.33 ) ( 0.22 )\quad\quad\quad\quad(0.004)\quad\quad\quad\quad(0.005) \\ \end{array} Sketch both regression lines: one for the age category 39 years and under, and one for 40 and above. Does it make sense to have a negative sign on the Age coefficient? Predict the ln(earnings)for a 30 year old and a 50 year old. What is the percentage difference between these two? (d)The F-statistic for the hypothesis that both slopes and intercepts are the same is 124.43. Can you reject the null hypothesis? (e)What other functional forms should you consider?$ 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): $\begin{array} { l } \widehat { \text { LnEarn } = } 6.92 - 3.13 \times \text { Dage } - 0.019 \times \text { Age } + 0.085 \times ( \text { Dage } \times \text { Age } ) , R 2 = 0.20 , \text { SER } = 0.721 . \\\quad\quad\quad\quad( 38.33 ) ( 0.22 )\quad\quad\quad\quad(0.004)\quad\quad\quad\quad(0.005) \\\end{array}$
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?

Definitions:

Sales

The activities involved in selling products or services, including marketing, negotiation, and transaction processes.

Desired Profit

The amount of net income that a company aims to achieve within a specific period.

Contribution Margin Ratio

The contribution margin ratio is a financial metric that measures the proportion of revenue that exceeds total variable costs, indicating how much of each sale contributes to covering fixed costs.

Profit-Volume Ratio

A financial tool used to analyze the relationship between profit and sales volume, showing the impact of sales changes on profits.