Causal inference · Lesson 1 of 3

The counterfactual, and the problem at the centre

Every causal claim needs a substitute for what would otherwise have happened. Name it and defend it.

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A causal claim is a claim about a counterfactual: this happened, and had the cause been absent, something else would have. "The training improved her performance" means her performance is better than it would have been without the training.

The fundamental problem is that you can never observe both. She either took the training or she did not. The counterfactual version of her does not exist, so every causal claim rests on a substitute for it — and choosing and defending that substitute is the entire discipline.

The substitutes available: another person or group who did not receive it; the same unit at an earlier time; a statistical model of what would have been expected. Each is a claim that the substitute is *comparable in every relevant way except the cause*.

That claim is called the identification strategy, and it is what a good causal paper argues for at length. Notice that it is an argument, not a computation — the statistics come after and cannot rescue a bad comparison.

So when you read a causal claim, the question is not "what test did they run?" but "what is standing in for the counterfactual here, and is it plausible?"

See it happen

People who completed an optional leadership course were promoted more often over the next two years.

The read that arrives on its own

The course works — promotion rates are higher among those who took it.

The same situation, with this idea

You ask what the counterfactual is. The comparison is people who did not take an *optional* course. Those who opt in are likelier to be ambitious, better supported, already noticed. The substitute is not comparable in every relevant way except the course, so the difference includes whatever made them volunteer. The number is real; the causal claim needs a better comparison.

After this, you can

ask what is standing in for the counterfactual before looking at any test.

The takeaway

Every causal claim needs a substitute for what would otherwise have happened. Name it and defend it.

Easy to take the wrong way

That observational data can never support causal claims. It can — through designs that make the comparison credible, which is what the rest of this module is.

Try this

For a causal claim you rely on, write the counterfactual in one sentence and name what stood in for it.