Homework 2

library(tidyverse)

Question 1

Here is code to import and clean the cps data.

D <- read.csv("../data/cps-econ-4261.csv") %>%
  filter(YEAR>=2014,YEAR<=2018) %>%
  mutate(EARNWEEK = na_if(EARNWEEK,9999.99),
         UHRSWORKT = na_if(na_if(na_if(UHRSWORKT,999),997),0),
         HOURWAGE = na_if(HOURWAGE,999.99)) %>%
  mutate(Wage = case_when(PAIDHOUR==1 ~ EARNWEEK/UHRSWORKT,PAIDHOUR==2 ~ HOURWAGE)) %>%
  mutate(kids = NCHILD>0,female = SEX==2) %>%
  filter(!is.na(Wage))

EDIT this code to also include only individuals who are younger than 40.

Question 2

Estimate the model:

\[\log(W_{n}) = \beta_{0} + \beta_{1}F_{n} \]

where \(W_{n}\) is the wage and \(F_{n}\) a dummy variable that is equal to one if the individual is female.

Question 3

Now calculate the difference between the sample mean of log wages for women and the sample mean for men. What do you notice? Explain why.

Question 4

Write down a linear model that allows for wage gaps to be different by the individual’s fertility status.

Question 5

Suppose that the null hypothesis is that wage gaps are the same for each fertility status. Write this null hypothesis in terms of the parameters of your model.

Question 6

Test the null hypothesis against a two-sided alternative. Make your test size 5%.

Question 7

Re-write the model to allow for: (1) A linear trend for all wages with age; (2) A linear trend for wage gaps with age; AND (3) A linear trend for the the difference in wage gaps by fertility status.

Use this model to test the null hypothesis that the difference in wage gaps by fertility status does not change with age. Use a two-sided alternative with size 10%.