Triple Differences and Placebo Tests

The one idea: Difference-in-differences nets out one confounding trend using one comparison group. When you suspect a second trend is contaminating that comparison — something else hit your treated market at the same time — a second comparison dimension can net that out too. And whatever design you land on, you can stress-test its credibility by checking that it correctly finds nothing where nothing should be.

⚠️ The trap: "Our DiD estimate is statistically significant, so parallel trends must have held." That feels right and it's wrong. A significant DiD coefficient is fully consistent with a violated parallel-trends assumption — the significance test checks whether the estimate differs from zero given sampling noise, not whether the design's core assumption is true. Placebo tests probe the assumption; the coefficient's own p-value never does.

Difference-in-differences solved one problem: a launched market drifts on its own, so before/after and cross-section comparisons both lie, and subtracting the control market's change fixes it — provided the only thing distinguishing treated from control, trend-wise, is the treatment. That proviso is parallel trends, and the DiD lesson was honest that it's untestable by definition. This lesson gives you two more tools for the situations where you doubt it anyway: a design that removes a second confound, and a family of checks that stress-test any quasi-experimental design's credibility, DiD included.

When one comparison group isn't enough

DiD assumes the control market's trend is what the treated market would have done absent treatment. That assumption breaks cleanly when something else — not the treatment — hits the treated market at the same time. A concurrent brand campaign, a local news…