Problem: Let's suppose Cathy's Coffee Corner is planning to introduce a simple loyalty program: buy 10 cups of coffee, get 1 free. Let's suppose Alice is a customer who signed up for the loyalty program in October. In September, Alice was buying 2 cups of coffee per week. After joining the program, Alice was recorded as buying 4 cups of coffee per week. Another customer, Bob, did not join the loyalty program. He was buying 2 cups of coffee per week in September and was buying 3 cups of coffee per week in October.
Q1. Use the difference-in-differences approach to come up with an estimate of the effect of the loyalty program on Alice (assuming that Bob is a suitable control customer for Alice)
Q2. Based on your estimate in question 4, is the loyalty program worth the cost of giving a free cup every 10 purchases for Alice? Justify your answer.