Problem Set 0: Review

1 Instructions

Due Upload your answer on Canvas before midnight on Tuesday, 28 January 2025.

Important You must submit your answers as an HTML or PDF file, built from an RMarkdown (.rmd) or Quarto (.qmd) file. Do not submit the .rmd or .qmd file. You will not receive credit for it.

If we ask you to create a figure or run a regression, then the figure or the regression results should be in the document that you submit (not just the code—we want the actual figure or regression output with coefficients, standard errors, etc.).

Integrity If you are suspected of cheating, then you will receive a zero—for the assignment and possibly for the course. We may report you to the dean. Cheating includes copying from your classmates, from the internet, and from previous assignments.

Objective This problem set has three goals: (1) review the central econometrics topics you covered in EC320; (2) refresh (or build) your R toolset; (3) start building your intuition about causality within econometrics/regression.

README! The data in this problem set come from the 2023 American Community Survey (ACS; downloaded from IPUMS USA). The ACS annually surveys approximately 3.5 million households. I’ve provided a random subset of 10,000 individuals—all of whom are at least 18 years old. The data are stored in a CSV file named data-acs.csv.

The table below describes each variable in the dataset.

Variable names and descriptions
Variable name	Variable description
`sex`	The individual’s sex (`Female` or `Male`). (`character`)
`age`	The individual’s age (`18` to `99`). (`integer`)
`race`	The individual’s race (6 broad categories). (`character`)
`hispanic`	Whether the individual is `Hispanic` or `Non-Hispanic`. (`character`)
`educ`	A rough estimate of the individual’s years of eduation (`1=` first grade; `17=` graduate school). (`integer`)
`empstat`	The individual’s employment status (`Employed`, `Unemployed`, `Not in labor force`). (`character`)
`hrs_wk`	The number of hours the individual works per week. (`integer`)
`income`	The individual’s income in dollars. (`integer`)
`deg_bachelors`	A binary indicator for whether the individual has a bachelor’s degree. (`integer`)
`deg_masters`	A binary indicator for whether the individual has a master’s degree. (`integer`)
`deg_profession`	A binary indicator for whether the individual has a professional degree (e.g., law or medicine). (`integer`)
`deg_phd`	A binary indicator for whether the individual has a doctorate. (`integer`)
`i_female`	A binary indicator for whether the individual’s sex is female. (`integer`)
`i_black`	A binary indicator for whether the individual is Black. (`integer`)
`i_white`	A binary indicator for whether the individual is White. (`integer`)
`i_hispanic`	A binary indicator for whether the individual is Hispanic. (`integer`)
`i_workforce`	A binary indicator for whether the individual is in the workforce (employed or unemployed). (`integer`)
`i_employed`	A binary indicator for whether the individual is employed. (`integer`)

2 Setup

[01] Load your R packages (and install any packages that are not already installed).

You will probably want tidyverse and here (among others).
Also: pacman and it’s p_load() function make package management easier—you just use p_load() to load packages, and R will install the packages if they’re not already installed. E.g., use p_load(tidverse, here) after you load the pacman package with library(pacman). Remember that you will have to install pacman (install.packages("pacman")) if you have not installed it already.

[02] Now load the data (stored in data-acs.csv).

As described above, I saved the data as a CSV, so you’ll want to use a function that can read CSV files.

Examples of functions that can read a CSV file:

read_csv() in the readr package, which is part of the tidyverse;
fread() in the data.table package;
read.csv(), which is available without loading any packages.

3 Get to know your data

[03] Use dim() or nrow() to confirm that you have 10,000 observations (rows) in your dataset.

[04] It’s good to know which variables are in the dataset and what type (class()) they are. How many categorical variables are in the dataset?

Hint: You have many options here; try glimpse() (in the tidyverse), summary(), or skim() (from the skimr package). Also: If you used read_csv() or fread() to load the data, then just typing the name of the dataset will display the first few rows and the class of each variable.

[05] How many observations are missing data on income?

Hints:

The function is.na() detects whether observations are missing.
You can filter your dataset to observations missing a variable using the filter() function, for example, my_data |> filter(is.na(my_variable)) would filter the dataset my_data to observations missing values for the variable my_variable.
You could also sum the results of is.na() to see how many of them are missing. is.na() returns TRUE or FALSE. TRUE is a 1, and FALSE is a 0.

[06] How many observations are missing data on education (educ)?

[07] If we regress income on educ, how many observations will be in that regression? Explain your answer.

4 Summarize income, education, and age

Time to make a few figures. Simple summaries and visualizations are fantastic ways to get to know the data and to try to figure out any potential issues/features. In this case, they will also provide insights into the distribution of income and education in the United States (in 2023).

[08] Calculate the mean and median of the variables income, educ, age.

Hint: You can also use the mean() and median() functions directly. You can use the summarise_all() function to calculate the mean and median of all variables in a dataset—and select() allows you to select specific variables.

Example: Calculating the mean and standard deviation of hrs_wk:

# Calculate the mean and standard deviation of 'hrs_wk'
acs_df |>
  select(hrs_wk) |>
  summarise_all(list(mean = mean, stnd_dev = sd), na.rm = TRUE)

[09] In [08], You should have found that the mean of income is much larger than the median. What does this result suggest about the distribution of income in the dataset?

[10] Create a histogram of income to visualize the distribution of income in the dataset.

Important: Make sure to label your axes and title your plot.

Hints: You have a few options for creating histograms:

ggplot2 includes the geom_histogram() function;
hist() is a base R function that can create histograms.

Note that both functions allow you to select the number of bins in the histogram. ggplot2 uses either the bins or the binwidth arguments; hist() uses the breaks argument.

[11] In a couple (2–3) sentences, explain whether the histogram in [10] supports recent concerns/discussions about income inequality in the United States.

[12] One may be concerned that our sense of income is a bit distorted because we (1) have individuals who are out of the workforce and/or (2) have individuals outside of their “prime working years”. Repeat the histogram in [10] for individuals who are (1) in the workforce (i_workforce == 1) and between the ages of 25 and 64 (age >= 25 & age <= 64).

Hint: You can use the filter() function to select observations that meet certain criteria, e.g., filter(my_data, i_female == 1) would filter the dataset my_data to the observations for whom i_female is equal to the value 1.

Important: Again, don’t forget to label your plot’s axes. A title would be good too.

[13] Did changes the sample in [12] change the distribution of income? Briefly explain your answer.

5 Analyze the returns to education

Throughout the class we’ve been talking about the returns to education… let’s run a few regressions to actually investigate these returns.

[14] Let’s start with a simple linear regression of the relationship between income and education. In other words: regress income on educ (with an intercept).

Note: Use the full dataset unless otherwise specified.

Generate a summary of the regression (estimated intercept, coefficient, and standard errors). You have a few options here:

use the tidy() function from the broom package on the output of the lm() function;
use the summary() function on the output of lm();
use feols() (from the fixest package) to estimate your regression (and possibly use etable() to display the results);
use the modelsummary() function from the modelsummary package.

[15] Interpret the intercept and coefficient from the regression in [14].

[16] Based upon the regression in [14], what is the estimated income for someone with 12 years of education (i.e., a high school diploma)?

[17] Compare your estimate in [16] to the mean income for individuals with 12 years of education. Do the linear-regression-based estimates get close to the mean? Should they? Explain your answer.

Hint: Remember your friend filter() from earlier in problem [12].

[18] Earlier we examined how the distribution of income changes when we restrict the sample to individuals in the workforce. Explain how omitting these variables (i_workforce and age) from the regression in [14] might bias the estimated returns to education.

[19] Now add workforce participation (i_workforce) and age (age) to the regression from [14]. Provide a summary (e.g., table) of the regression results.

[20] Do the results in [19] suggest that our simple linear regression (in [14]) had an issue with omitted variable bias? Explain.

[21] One more regression: Add the binary indicator for whether the individual has a bachelor’s degree (deg_bachelors) to the regression in [19]. Provide a summary of the regression results.

[22] Why do you think the returns to education changed so much when we included the binary indicator for a bachelor’s degree in the regression?

6 Shifting gears: Who graduates?

The previous results suggest that maybe there’s something special about having a bachelor’s degree. Let’s explore this a bit more.

[21] First off, what share of the sample has a bachelor’s degree?

[22] Now regress the indicator for whether the individual has a bachelor’s degree (deg_bachelors) on age (age), the indicator for whether the individual is female (i_female), and the interaction between age and female.

Provide a summary of the regression results.

Hint: To take the interaction between two variables, you can use the : operator in the regression formula. For example, lm(y ~ x1 + x2 + x1:x2) would include the interaction between x1 and x2.

[23] Interpret the intercept and each of the coefficients from the regression in [22].

Hint: Remember that a regression with a binary dependent variable can be interpreted as modeling the probability that the dependent variable is equal to one.

[24] Based on the regression in [23], what is the probability that a 25-year-old female has a bachelor’s degree? What about a 25-year-old male?

7 Wrap up

[25] What are your main takeaways/insights about income and education from this problem set and its data? Explain your answer using figures/regressions from above and any additional analyses you think are relevant.