Chapter 9 Identify
Causal effects
Everything up to here has been an answer to the question what goes with what. Chapter 5 compared groups, Chapter 6 fitted lines through clouds, Chapter 8 looked for structure behind the measurements. Each of them describes the data honestly, and none of them can tell you what would happen if you changed something.
That gap is not closed by a better estimator. A regression coefficient is a conditional mean, no more and no less, and whether it deserves to be read as the effect of rather than the difference between is settled outside the model — by where the data came from and by how the treatment was assigned. This chapter is about that question, which economists call identification.
There are only two ways to earn a causal claim. Run the experiment, and let a coin sever the link between the treatment and everything else about the people who receive it. Or find a situation in which something else already did the severing — a lottery, a policy date, an administrative threshold, a rule nobody designed with your research question in mind — and then argue the case. Section 9.1 is about both: the logic of randomisation, why economics rarely gets to use it, and the vocabulary of research design that the rest of the chapter takes for granted.
The four sections that follow are the standard catalogue of designs, ordered by how much they ask you to believe about what you cannot see. Section 9.2 builds comparability out of measured covariates. Section 9.3 builds it out of timing, Section 9.4 out of a threshold, and Section 9.5 out of a variable that moves the treatment and nothing else.
The four are built the same way on purpose, so that they can be read against one another. Each one states its assumption in a definition box and says plainly what could make it false. Each one then builds a small world by hand — a wage premium, a school programme, a funding threshold, a letter about a training voucher — with the true effect written into the data-generating process, runs the design on it, and opens the envelope at the end to see how close it came. Each one has a real data set beside the invented one, because a simulation can show that an estimator works when its assumption holds and can never show whether the assumption holds anywhere. And each one closes with the same admission in a different currency: the assumption cannot be tested, so here is a way of asking how large a violation would have to be before the answer changes.
Read across the four and a pattern appears that no single section makes visible. The designs are not four routes to one number. They deliver four different estimands, they fail in four different ways, and the failures are silent in all four. What separates them is not sophistication but how much of the argument the data can carry.