3. Over the past 35 years, an increasing number of mothers have gone back to wor

Question

3.         Over the past 35 years, an increasing number of mothers have gone back to work relatively quickly after giving birth. Consider a labor market where a worker’s wage is a function of his or her years of education past the compulsory level (E), work experience (X), and years of tenure with their current employer (T). Suppose the relationships between wages, education, experience, and tenure for males (M) and females (F) can be represented by the equations

WM = 3 + 0.5E + 0.4X + 0.2T

and

WF = 3 + 0.4E + 0.3X + 0.3T.

On average, E = 4, X =20, and T = 8 for men, while for women the averages are E = 4, X = 14, and T = 4.

A) Find the average wage of men and women. What is the ratio of female to male wages? What is the gap between women and men’s wages in percentage terms?

B) What wage would women earn if they had the same pre-market characteristics as men on average? What would be the ratio of women’s to men’s wages?

C) Express the amount of current wage discrimination in percentage terms.

Suppose in the analysis that years of tenure are either unmeasurable or unobservable to the researcher. As a result, the analysis produces the following wage equations.

WM = 4.6 + 0.5E + 0.4X

and

WF = 4.2 + 0.4E + 0.3X.

D) Find the average wage of men and women. What is the ratio of female to male wages? What is the gap between women and men’s wages in percentage terms?

E) What wage would women earn if they had the same pre-market characteristics as men on average? What would be the ratio of women’s to men’s wages?

F) Express the amount of current wage discrimination in percentage terms.

G) Does this (failing to include tenure in the model) overstate or understate the effects of gender discrimination?

Explanation / Answer

Solution: We arer given that:

WM = 3 + 0.5E + 0.4X + 0.2T

WF = 3 + 0.4E + 0.3X + 0.3T

And, the averages are E = 4, X =20, and T = 8 for men, while E = 4, X = 14, and T = 4 for women.

A) So, WM = 3 + 0.5*4 + 0.4*20 + 0.2*8 = 3+2+8+1.6 = 14.6

WF = 3 + 0.4*4 + 0.3*14 + 0.3*4 = 3+1.6+4.2+1.2 = 10

Ratio of female to male wages = WF/WM = 10/14.6 = 0.685 (approx)

Gap in percentage terms = (WM - WF)*100/WM = (14.6 - 10)*100/14.6 = 31.5% (approx).

B) Now, suppose the averages (pre-,arket characterstics) are E = 4, X =20, and T = 8 for women too. (same as men)

Then WF = 3 + 0.4*4 + 0.3*20 + 0.3*8 = 3+1.6+6+2.4 = 13

Then Ratio of WF to WM = 13/14.6 = 0.89 (approx)

C) Wage discrimination is calculated as keeping all pre-market conditions constant (or same) for both groups. We see from part B) then even after keeping the pre-market characterstics constant, women earn (100 - 0.89*100 =) 11% less than men. So, in percentage terms, amount of wage discrimination = 11%

D) With averages: E = 4, X =20 for men, and E = 4, X = 14 for women, now

WM = 4.6 + 0.5E + 0.4X = 4.6 + 0.5*4 + 0.4*20 = 14.6

WF = 4.2 + 0.4E + 0.3X = 4.2 + 0.4*4 + 0.3*14 = 10

Again, the wages obtained are same as part A), so, Ratio of female to male wages = 0.685, and wage gap (in percentage terms) = 31.5%

E) Again, if pre-market characterstics for women are same as that of men, i.e, E =4, and X = 20,

WF = 4.2 + 0.4*4 + 0.3*20 = 11.8

Ratio of women to men wage = 11.8/14.6 = 0.81 (approx)

F) Amount of current discrimination in percentage terms = (14.6 - 11.8)*100/14.6 = 0.19 (or also = 100 - 0.81*100).

So, now women earn 19% less than men.

G) Clearly, with inclusion of tenure, wage discrimination was of 11%, while on failing to include it results in wage discrimination of 19%. So, this failure overstates the effects of gender discrimination.

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