The loyalty program that looked good until you checked

Question

A retailer launches a loyalty program at Store A and uses Store B as a control. Monthly sales before and after, in thousands of dollars:

Store A (treated): 100 before, 110 after.
Store B (control): 120 before, 138 after.

Compute the difference-in-differences estimate, and interpret the sign.

Accepted Answer

Both stores rose, so the raw gain is deceptive. Store A's sales went up 10 (from 100 to 110), which on its own looks like a win for the loyalty program. But Store B, with no program, went up 18 (from 120 to 138) over the same month. A strong tailwind, a good season, regional growth, a marketing push, lifted both stores, and it lifted the control by more. Difference-in-differences. Subtract the control's change from the treated store's change: 	ext{DiD} = (110 - 100) - (138 - 120) = 10 - 18 = -8. The estimate is negative 8 thousand dollars. In words: relative to what the broader trend deliver…

The loyalty program that looked good until you checked

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