Applied Class #1 - R Refresher

Introduction

This applied class will give you an opportunity to practice your R skills. For background material on R programming see my crash course [solutions] along with my introduction to dplyr [solutions], and my introduction to ggplot[solutions].

Part 1 - Discrimination in the Labor Market

In this question you’ll partially replicate a well-known paper on racial bias in the labor market: “Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination” by Marianne Bertrand and Sendhil Mullainathan. The paper, which I’ll refer to as BM for short, appears in Volume 94, Issue #4 of the American Economic Review. You will need to consult this paper to complete this problem.

For convenience, I’ve posted a copy of the dataset from this paper on my website at https://ditraglia.com/data/lakisha_aer.csv. Each row of the dataset corresponds to a single fictitious job applicant. After loading the tidyverse library, you can read the data into a tibble called bm using the read_csv() function as follows:

library(tidyverse)
bm <- read_csv('https://ditraglia.com/data/lakisha_aer.csv')

You may want to consult the introduction and conclusion of BM, along with parts A-D of Section II of their paper as you work through the following exercises.

  1. Carry out the following steps:
    1. Display the tibble bm. How many rows and columns does it have?
    2. Display only the columns sex, race and firstname of bm. What information do these columns contain? How are sex and race encoded?
    3. Add two new columns to bm: female should take the value TRUE if sex is female, and black should take value TRUE if race is black.
  2. Randomized controlled trials are all about balance: when the treatment is randomly assigned, the characteristics of the treatment and control groups will be the same on average. To answer the following parts you’ll need a few additional pieces of information. First, the variable computerskills takes on the value 1 if a given resume says that the applicant has computer skills. Second, the variables education and yearsexp indicate level of education and years experience, while ofjobs indicates the number of previous jobs listed on the resume.
    1. Is sex balanced across race? Use dplyr to answer this question. Hint: what happens if you apply the function sum to a vector of TRUE and FALSE values?
    2. Are computer skills balanced across race? Hint: the summary statistic you’ll want to use is the proportion of individuals in each group with computer skills. If you have a vector of ones and zeros, there is a very easy way to compute this.
    3. Are education and ofjobs balanced across race?
    4. Compute the mean and standard deviation of yearsexp by race. Comment on your findings.
    5. Why do we care if sex, education, ofjobs, computerskills, and yearsexp are balanced across race?
    6. Is computerskills balanced across sex? What about education? What’s going on here? Is it a problem? Hint: re-read section II C of the paper.
  3. The outcome of interest in bm is call which takes on the value 1 if the corresponding resume elicts an email or telephone callback for an interview. Check your answers to the following against Table 1 of the paper:
    1. Calculate the average callback rate for all resumes in bm.
    2. Calculate the average callback rates separately for resumes with “white-sounding” and “black-sounding” names. What do your results suggest?
    3. Repeat part 2, but calculate the average rates for each combination of race and sex. What do your results suggest?
  4. Read the help files for the dplyr function pull() and the base R function t.test(). Then test the null hypothesis that there is no difference in callback rates across black and white-sounding names against the two-sided alternative. Comment on your results.

Part 2 - Making Change

Do you remember physical money? In olden times I used to collect small change in a jar and periodically sort through it so I could do my laundry. I always seemed to have too many of the coins I didn’t need, and to few of the ones I did need! This problem is about making change; it’s also about making functions. To answer it you’ll need two pieces of outside information. First: US coinage consists of pennies ($0.01), nickels ($0.05), dimes ($0.10), quarters ($0.25), and dollar coins ($1.00). Second: UK coinage consists of pence, 2p coins, 5p coins, 10p coins, 20p coins, 50p coins, 1 pound coins, and 2 pound coins.

You’ll also need to use the R operators %/% and %%. These represent integer division and modulo. For example 16 divided by 3 equals 5 with a remainder of 1 so 16 %/% 3 returns 5 while 16 %% 3 returns 1. Before beginning this exercise, experiment with %/% and %% to make sure you understand how they work. If necessary, search the internet to find out more about them or read the R help file “Arithmetic Operators.”

For technical reasons that I won’t delve into here, the simplest reliable way of representing monetary values in a computer is by using whole numbers rather than decimals. Rather than representing fourteen pounds and thirty-two pence as 14.32, for example, we’d store this value as 1432. In short, we store the number of pence (or cents) as an integer. Please follow this convention throughout.

  1. The following code block outlines a simple algorithm for making change. The customer is owed a certain number of cents, an integer between 1 and 99, and your task is to calculate how many quarters, dimes, nickels, and pennies to remove from the cash register. The rule is to always give as many high denomination coins as you can before moving on to lower denomination coins. If the customer is owed $0.75, for example, you remove three quarters rather than seven dimes and a nickel. Fill in the gaps in the code, run it, and display the resulting vector change. Check the result by hand to make sure your logic is correct.
cents <- 73
quarters <- cents %/% 25
cents <- cents %% 25

dimes <- ______ # Delete the underscores & fill in the gap!
cents <- ______ # ditto! 

nickels <- ______ # ditto!
cents <- ______ # ditto! 

change <- c('quarters' = quarters,
            'dimes' = dimes,
            'nickels' = nickels,
            'pennies' = cents)

  1. You’ve written some handy code! But now suppose you wanted to reuse it to make change for a different amount, say $0.37 or $0.19. Copying-and-pasting your existing code is tedious and error prone. Instead of doing this, write a function called make_change_US(). It should take a single input argument cents, a integer between 1 and 99, and return a vector called change listing the number of quarters, dimes, nickels, and pennies formatted as above. Run your function to make change for $0.37 and $0.19 and check the results against your hand calculations.

  2. The function make_change_US() has some limitations. Suppose we wanted to make change for UK currency rather than US currency. This would require us to write a completely new function despite the underlying logic of the problem being identical. There’s a better way forward. Write a new function called make_change() that it takes two input arguments. The first argument is cents. As before, this is a integer between 1 and 99. The second argument is new: currency is a named vector that stores the denominations between 1 and 99 cents along with their labels. For example we would set currency equal to c('quarter' = 25, 'dime' = 10, 'nickel' = 5, 'penny' = 1) for US currency and c('50p' = 50, '20p' = 20, '10p' = 10, '5p' = 5, '2p' = 2, '1p' = 1) for UK currency. As above, make_change() should return a named vector called change indicating how many of each coin to give as change, but now this vector should take its names from currency. The logic is the same as above, but the implementation is a bit trickier. While there are various ways to solve this, the simplest is probably to use a for loop. Test make_change() by making change for 78 cents/pence in US/UK currency. Compare your results to make_change_US(78) to double-check.