Gender Wage Gap calculations

[Thea Fredriksen]

Hello,

I wish to perform an analysis of the gender wage gap, similar to the one attached. My question is what the text in "Notes" mean with regards to calculating the female/male log hourly ratios. I have in my own dataset, generated log wages for men and women, however, I am not quite sure how to generate a ratio. When I take logwages of women divided by log wages of men to get a ratio, the ratio is almost 1, which makes me think that this is not the correct way to do it. The "Notes" section says that they take the logwages of women minus the logwages of men, however, is this equal to the ratio then?

This is what I have done so far:

// Generating mean log wages for men and women//

bysort year sex: egen meanlnwage = mean(lnwage)
bysort year: egen meanlnwagef = mean(lnwage / (sex == 2))
bysort year: egen meanlnwagem = mean(lnwage / (sex == 1))

//Generating gender wage gap and displaying for each year//

gen gap = meanlnwagem-meanlnwagef
egen tag = tag(year)
tabdisp year if tag, c(meanlnwagem meanlnwagef gap)


The table below is what I want to achieve:

[Øyvind Snilsberg]

if you look up properties of logarithms you'll see that the log of a quotient is the difference of the logs
also for female/male ratio it should be meanlnwagef - meanlnwagem, not meanlnwagem - meanlnwagef

[Thea Fredriksen]

if you look up properties of logarithms you'll see that the log of a quotient is the difference of the logs
also for female/male ratio it should be meanlnwagef - meanlnwagem, not meanlnwagem - meanlnwagef

Thank you for clarifying. Am I correct to understand that you take meanlnwagef - meanlnwagem, and then take 1 minus that in order to get a number equal to that in the table, as meanlnwagef - meanlnwagem is 0.2 using my data. Would the ratio then be 80%?

[Øyvind Snilsberg]

maybe you'll find the following example useful,

* Example generated by -dataex-. To install: ssc install dataex
clear
input int year byte(sex wage)
1980 1 15
1980 1 16
1980 1 17
1980 1 18
1980 1 19
1980 2 11
1980 2 12
1980 2 13
1980 2 14
1980 2 15
1989 1 25
1989 1 26
1989 1 27
1989 1 28
1989 1 29
1989 2 21
1989 2 22
1989 2 23
1989 2 24
1989 2 25
end

collapse wage, by(year sex)

reshape wide wage, i(year) j(sex)

gen D = ln(wage2/wage1)

gen expD = exp(D)

[Thea Fredriksen]

maybe you'll find the following example useful,

* Example generated by -dataex-. To install: ssc install dataex
clear
input int year byte(sex wage)
1980 1 15
1980 1 16
1980 1 17
1980 1 18
1980 1 19
1980 2 11
1980 2 12
1980 2 13
1980 2 14
1980 2 15
1989 1 25
1989 1 26
1989 1 27
1989 1 28
1989 1 29
1989 2 21
1989 2 22
1989 2 23
1989 2 24
1989 2 25
end

collapse wage, by(year sex)

reshape wide wage, i(year) j(sex)

gen D = ln(wage2/wage1)

gen expD = exp(D)

Thank you, that was very helpful!

[Thea Fredriksen]

maybe you'll find the following example useful,

* Example generated by -dataex-. To install: ssc install dataex
clear
input int year byte(sex wage)
1980 1 15
1980 1 16
1980 1 17
1980 1 18
1980 1 19
1980 2 11
1980 2 12
1980 2 13
1980 2 14
1980 2 15
1989 1 25
1989 1 26
1989 1 27
1989 1 28
1989 1 29
1989 2 21
1989 2 22
1989 2 23
1989 2 24
1989 2 25
end

collapse wage, by(year sex)

reshape wide wage, i(year) j(sex)

gen D = ln(wage2/wage1)

gen expD = exp(D)

Is there anyway I can do this without losing all the other variables in my dataset?

[Øyvind Snilsberg]

absolutely,

bys year: egen wage1 = mean(wage) if sex==1
bys year (wage1): replace wage1 = wage1[1]

bys year: egen wage2 = mean(wage) if sex==2
bys year (wage2): replace wage2 = wage2[1]

gen D = ln(wage2/wage1)

gen expD = exp(D)