Context: Two social science researchers examined the impact of raising the minimum wage on employment in the fast-food industry. In 1992, the state of New Jersey (NJ) in the United States raised the minimum wage from $4.25 to $5.05 per hour. Did such an increase in the minimum wage reduce employment as economic theory predicts? As discussed above, answering this question requires inference about the NJ employment rate in the absence of such a raise in the minimum wage. Since this counterfactual outcome is not observable, we must somehow estimate it using observed data.
One possible strategy is to look at another state in which the minimum wage did not increase. For example, the researchers of this study chose the neighboring state, Pennsylvania (PA), on the grounds that NJ’s economy resembles that of Pennsylvania, and hence the fast-food restaurants in the two states are comparable. Under this cross-section comparison design, therefore, the fast-food restaurants in NJ serve as the treatment group receiving the treatment (i.e., the increase in the minimum wage), whereas those in PA represent the control group, which did not receive such a treatment. To collect pretreatment and outcome measures, the researchers surveyed the fast-food restaurants before and after the minimum wage increase. Specifically, they gathered information about the number of full-time employees, the number of part-time employees, and their hourly wages, for each restaurant.

The CSV file minwage.csv contains this data set.
Variable Description
chain: name of the fast-food restaurant chain
location: location of the restaurants (centralNJ, northNJ, PA, shoreNJ, southNJ)
wageBefore: wage before the minimum-wage increase
wageAfter: wage after the minimum-wage increase
fullBefore: number of full-time employees before the minimum-wage increase
fullAfter: number of full-time employees after the minimum-wage increase
partBefore: number of part-time employees before the minimum-wage increase
partAfter: number of part-time employees after the minimum-wage increase

Question: What is the difference in the proportion of full-time employees in NJ and PA? Please round to the nearest thousandth.
Answer: 0.048
Topics: Social science, Statistics, Probability

Question: We would like to reduce the confounding bias due to different fast-food chains and the location of restaurants. We only consider Burger King restaurants, and focus on the Burger King restaurants located in northern and southern NJ that are near PA, while excluding those in the Jersey shore and central New Jersey. What is the difference in the proportion of full-time Burger King employees in NJ (northern and southern only) and PA? Please round to the nearest thousandth.
Answer: 0.032
Topics: Social science, Statistics, Probability, Confounding bias

Question: Estimate the average treatment effect of raising the mininum wage on the proportion of full-time employees using difference-in-differences (DiD). Please round to the nearest thousandth. The answer is positive if raising the mininum wage increases the proportion of full-time employees.
Answer: -0.062
Topics: Social science, Statistics, Probability, Difference in differences