The Parallel Trends Assumption

By the end of this lesson, you should be able to: state parallel trends precisely, read an event study, run a pre-trend test, and know how much a passing result is actually worth.

The one thing DiD needs

Lesson 10 recovered a price effect by subtracting what the control countries did. That works only if the treated country would have moved by the same amount as the controls, had nothing happened.

$E[Y_{1t}^{(0)} - Y_{1,t-1}^{(0)}] = E[Y_{0t} - Y_{0,t-1}]$

The superscript $(0)$ is the untreated potential outcome for the treated unit: what Portugal would have done without the price rise. That quantity does not exist in your data and never will. Parallel trends is a claim about a world you cannot observe.

So it can't be tested. What can be tested is a consequence of it, and the gap between those two things is this whole lesson.

Two panels, same shape, different verdicts

The second one is wrong by more than the effect it's trying to measure. Nothing about the two datasets looks different: same countries, same panel length, same 2×2 arithmetic.

The difference is that CI-02's treated country was already pulling away from the others before the change, for reasons unrelated to it.