Question

I have a question which involves the use of stata

what regression would I have to run to answer this question?

I have

• WEEKPAY – Gross weekly pay in the respondent’s main job
• GENDER – The respondent’s reported gender
• MON – The month the respondent started her current job
• YEAR– The year the respondent started her current job

What is the average size of the gender pay gap after the implementation (2018) of the regulation? Run a regression to estimate this. Think carefully about how the variables in your dataset might need to be transformed in order to interpret the estimated coefficients in a reasonable way. Justify your choice of model.

GRSSWK	Gender	Mon	Year
430	male	January	2018
420	male	January	2017
390	female	April	2017
390	male	June	2018
450	female	August	2017
400	female	December	2017
550	male	March	2017
500	male	March	2018
420	male	June	2018

Answer 1

Here we have to fit a proper regression model in the given data to answer the average size of the gender pay gap after the implimentation(2018) of regulation. Note that, here the first two columns and the last column are the variables. First column that is, column represents "gross weekly pay in the respondent's main job" , secoend column that is "gender of respondent" and the last column that is column represents "the year the respondent started his/her current job". Here 'year' and 'gender' are the covariates and 'GRSSWK' is the response variable. Note that, year is either 2018 or 2017 and gender is also of two category male or female. So this is a problem of ANOVA (analysis of variance) with covariates. So we fit simple linear regression model with two covariates x1 and x2 which are nothing but the indicator variables representing 'year' and 'gender' respectively.

For year 2018 x1 is '1' and '0' for 2017.

For male x2 is '1' and '0' for female.

Our model is

y=a + bx1 + cx2 + e

where y represents "GRSSWK", a,b,c are constants and 'a' is the intercept term and b & c are the regression coefficients. 'e' is the error term with mean 0 and constant variance.

The estimate of 'a' will give the average size of the gender pay gap after the implimentation(2018) of reulation.

We can use R to run the regression algorithm. R code is given below :

weekpay=c(430,420,390,390,450,440,550,500,420) ##...response y
year=c(1,0,0,1,0,0,0,1,1) ##....indicator vector of year (x1)
gender=c(1,1,0,1,0,0,1,1,1) ##....indicator vector of gender (x2)
year=as.factor(year) ##...factorising year
gender=as.factor(gender) ##...factorising gender
lm(weekpay~year+gender) ##... fitting regression model

Output of R :

Call:
lm(formula = weekpay ~ year + gender)

Coefficients:
(Intercept) year1 gender1
426.67 -50.00 58.33

Hence the average gener pay gap after the implimentation (2018) of regulation is 426.67 that is approximately 427.