library(tidyverse)
wages <- Sleuth2::ex1029Case Study 2
Data Problem 10.29 in The Statistical Sleuth, 2nd Edition
Setup
The data for this case study come from a sample of 25,631 male respondents to the March 1988 U.S. Current Population Survey (CPS).1 The CPS is a labor force survey that has been administered monthly by the U.S. Census Bureau since the 1940s. It provides current estimates of the economic status and activities of the American populace, including information on weekly wages the previous year (measured here in 1992 dollars), years of education, years of experience, race (represented here through a single indicator of whether the respondent was Black), proximity to a metropolitan area (represented here through a single indicator of whether the respondent worked in a standard metropolitan statistical area, i.e., in or near a city), and region of the country (categorized as Northeast [NE], Midwest [MW], South [S], and West [W]).
A defining and enduring feature of racial inequality in the American labor force is the pay gap between Black and white workers. In this case study, you will analyze the data to determine whether and to what extent Black males were paid less than non-Black males in the same region and with the same levels of education and experience.
Task
The U.S. Census Bureau suspects that the extent to which Black workers were paid differently than non-Black workers depends on the region of the country. In order to investigate the evidence for this theory, fit a model that allows the effect of race to vary across geographic regions, while also adjusting for years of education and experience. Then, use this model to compute estimates for the pay gap between Black and white workers in each region of the country and conduct an appropriate hypothesis test to determine whether the differences in these pay gaps are statistically significant. Finally, choose an appropriate multiple regression model (informed by your previous hypothesis test) to answer the question: were Black males paid less than non-Black males in the same region and with the same levels of education and experience?
Tip
Suggestion: when building your regression model, refrain from looking at interactive effects, except for the one implied by the U.S. Census Bureau’s suspicion.
Note
Please follow the general instructions and guidelines for case studies and incorporate any comments and feedback that you received on the first assignment. Remember that your goal is to answer the bolded task, not to provide the reader with a full history of your analysis. As such, details such as checks of the regression conditions, decisions to transform the explanatory or response variables, and other pieces of information should be included in the appendix at the end of the report.
To access the dataset for this case study, you will need to run the following lines in R:
References
Bierens, Herman J, and Donna K Ginther. 2001. “Integrated Conditional Moment Testing of Quantile Regression Models.” Empirical Economics 26 (1): 307–24. https://doi.org/10.1007/s001810000059.