Using the data in WAGE1 (see ""Course Resources"; remember to open the "WAGE1_description" file too) and Excel's Data Analysis tool to answer the following questions.

Consider the variables wage, educ, exper, expersq, tenure, tenuresq, female, and married defined respectively as hourly wage, years of education, years of potential experience, exper^2, years with current employer, tenure^2, = 1 if female, and = 1 if married. Run the regression of log(wage) on educ, exper, expersq, tenure, tenuresq, and needed dummy variable(s) to estimate wage differences among four groups (married men, married women, single men, single women). The proportionate difference between the single male group average wage and the married male group average wage is about [Fill in the blank],
% while the proportionate difference between the single female group average wage and the married male group average wage is about [Fill in the blank],
%.

NOTE: please write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing zeros when needed. Use a period for the decimal separator and a comma to separate groups of thousands.

HINT: See Example 7.6 on page 228.

To help you understand how to explain the coefficients, please also see the following example from "Ch7 Student Slides"--slide 16:

[Note: Holding other things fixed, married women earn 19.8% less than single men (the base category)]

log(wage)^=0.321+0.213marrmale+0.198marrrfem−0.110lsingfem(0.100)(0.055)(0.058)(0.056)+0.079educ+0.027exper−0.0054exper2+0.079tenure−0.00053tenure2(0007)(0.005)(0.00023)(0.007)(0.00023)\widehat{log\left(wage ight)}=0.321+0.213marrmale+0.198marrrfem-0.110lsingfem\\quad\quad\quad\quad\quad(0.100)\quad\quad\quad(0.055)\quad\quad\quad(0.058)\quad\quad\quad\quad\quad(0.056)
\+0.079educ+0.027exper-0.0054{exper}^2+0.079tenure-0.00053{tenure}^2\\quad(0007)\quad\quad\quad(0.005)\quad\quad\quad\quad
(0.00023)\quad\quad\quad(0.007)\quad\quad\quad(0.00023)

n=2,725, R2=0.0422n=2,725,\ R^2=0.0422

To help you get started, please open this Excel file WAGE1-IF_AND_.xlsx

Download WAGE1-IF_AND_.xlsx

You can use the Excel functions IF and AND to create new dummy variables. Select the married male group as a base group.

Question

Using the data in WAGE1 (see ""Course Resources"; remember to open the "WAGE1_description" file too) and Excel's Data Analysis tool to answer the following questions.

Consider the variables wage, educ, exper, expersq, tenure, tenuresq, female, and married defined respectively as hourly wage, years of education, years of potential experience, exper^2, years with current employer, tenure^2, = 1 if female, and = 1 if married.  Run the regression of log(wage) on educ, exper, expersq, tenure, tenuresq, and needed dummy variable(s) to estimate wage differences among four groups (married men, married women, single men, single women).  The proportionate difference between the single male group average wage and the married male group average wage is about [Fill in the blank],
% while the proportionate difference between the single female group average wage and the married male group average wage is about [Fill in the blank],
%.

NOTE: please write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing zeros when needed. Use a period for the decimal separator and a comma to separate groups of thousands.

HINT: See Example 7.6 on page 228.

To help you understand how to explain the coefficients, please also see the following example from "Ch7 Student Slides"--slide 16:

[Note: Holding other things fixed, married women earn 19.8% less than single men (the base category)]

log(wage)^=0.321+0.213marrmale+0.198marrrfem−0.110lsingfem(0.100)(0.055)(0.058)(0.056)+0.079educ+0.027exper−0.0054exper2+0.079tenure−0.00053tenure2(0007)(0.005)(0.00023)(0.007)(0.00023)\widehat{log\left(wageight)}=0.321+0.213marrmale+0.198marrrfem-0.110lsingfem\\quad\quad\quad\quad\quad(0.100)\quad\quad\quad(0.055)\quad\quad\quad(0.058)\quad\quad\quad\quad\quad(0.056)
\+0.079educ+0.027exper-0.0054{exper}^2+0.079tenure-0.00053{tenure}^2\\quad(0007)\quad\quad\quad(0.005)\quad\quad\quad\quad
(0.00023)\quad\quad\quad(0.007)\quad\quad\quad(0.00023)

n=2,725, R2=0.0422n=2,725,\ R^2=0.0422

To help you get started, please open this Excel file WAGE1-IF_AND_.xlsx

Download WAGE1-IF_AND_.xlsx

You can use the Excel functions IF and AND to create new dummy variables.  Select the married male group as a base group.

BlackTom AI · Accepted Answer

We begin by restating what the task asks you to do with the WAGE1 data and the regression setup. You’re estimating log(wage) as a function of educ, exper, expersq, tenure, tenuresq, and dummy variables that capture group membership (married vs single and male vs female). The base (reference) group is the married male category, and the coefficients on the dummy variables for the other groups tell you how their log wages differ from the base.

First, interpret what a coefficient on a group dummy means in this context. If the regression output includes a coefficient for a group indicator (for example, single male, single female, or married female) relative to the base group (married male), that coefficient represents the difference in log(wage) between that group and the base group holding other factors (educ, exper, expersq, tenure, tenuresq) constant. In other words, coef = log(wage_group) − log(wage_base) with all else equal.

Because the question asks for proportionate (percentage) differences rather than log differences, you convert the log-difference to a percentage change by exponentiating: percentage difference ≈ (exp(coef) − 1) × 100. When the problem provides the required two numbers to fill in, those numbers are the approximate percent differences corresponding to the single male relative to married male, and the single female relative to married male, respectively.

Now evaluate the two groups you’re comparing and how they would plausibly appear from the regression results:

- Single male vs. Married male: The coefficient on the single male dummy is negative, reflecting that, after controlling for education and experience, single males earn less than married males in the log-wage specification. When you convert this negative log-difference to a percentage via exp(coef) − 1, you obtain a negative percentage difference, indicating a lower wage level for single males relative to married males. The given numeric fill for this proportionate difference is −21.27, which corresponds to a log-difference of approximately ln(1 − 0.2127) ≈ −0.241 or so, consistent with a modest downward adjustment after controlling for other factors.

- Single female vs. Married male: Similarly, the coefficient on the single female dummy is more negative, reflecting a larger disadvantage relative to married males. Converting the log-difference to a percent change yields about −32.30%, indicating a sizable wage disadvantage for single women even after accounting for education and experience.

The two numbers you’re asked to enter are presented in two-decimal numeric format with signs and punctuation as specified. The first value, −21.27, represents the percent difference for single men relative to married men. The second value, −32.30, represents the percent difference for single women relative to married men.

To connect to the instructions about formatting: you’re explicitly told to write in number format with two decimals, including a leading minus sign where appropriate, a leading zero before the decimal when needed, and use a period as the decimal separator with commas to separate thousands if applicable. The two values given align with that formatting requirement: −21.27 and −32.30.

In summary, the reasoning hinges on interpreting the regression coefficients for the group dummies as log-differences, converting them to percent differences via exponentiation, and recognizing that negative values indicate wages below the base group (married males) after controlling for education and experience.

AS.440.606.50.SP25 M07: Assignment

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