ECON 4309 · Quantitative Methods for Social Sciences · Reading companion

Causal Diagrams, in about 15 minutes

A plain-language guide to three short chapters of The Effect by Nick Huntington-Klein: Ch. 6 (Causal Diagrams), Ch. 7 (Drawing Causal Diagrams), and Ch. 8 (Causal Paths and Closing Back Doors). Read this first, play with the two simulators, and then use the reading guide at the end to decide which parts of the chapters to read closely.

Note: This is the printable version. The interactive version, with the simulators, is on the course website.

1. The big idea in 60 seconds

The book's working definition of a cause is worth memorizing: X causes Y if, when you step in and change X, the distribution of Y changes. The chapter's example: people wear shorts more on days they eat ice cream, but putting someone in shorts won't make them buy ice cream. Both are driven by something else (hot weather). Correlation without causation.

The three chapters build one recipe:

1. Draw the diagram (Ch. 6 and 7). Include everything important, leave out the rest, and own those choices as assumptions.
2. List every path from treatment to outcome and mark each as Good or Bad (Ch. 8).
3. Close every Bad path by controlling for something on it, without closing a Good path and without controlling for a collider (Ch. 8).

2. Words you need

We'll use Lecture 4's running example throughout: what is the effect of an extra year of education on earnings? In the lecture's diagram, a person's background, location, and year of birth affect both education and earnings, and education affects earnings partly through job connections.

3. Drawing a diagram (Ch. 7)

Chapter 7 walks through a study the author worked on: does taking an online course make community-college students more likely to drop out? The lecture follows the same steps for education and earnings:

1. List variables. Start with treatment and outcome. Then ask: what causes the treatment? What causes the outcome? What causes those? (For online classes: preferences, available time, work hours, internet access, past academics, demographics, and so on.)
2. Draw arrows. For each pair, ask whether one causes the other. If two things are related but neither causes the other, add a common cause like U1.
3. Simplify. The book's first draft is a hairball, so it trims it with four tests (each comes with a "probably," so think before you cut):
   • Unimportance: tiny effects can go (the chapter's example: quiet cafés nearby might nudge a few students toward online classes, but not many).
   • Redundancy: variables with exactly the same arrows in and out can be merged (Race and Gender become "Demographics"; the lecture groups socioeconomic status and demographics into "Background").
   • Mediators: a variable that only passes an effect along (A → B → C, nothing else touching B) can be replaced by A → C, unless the mechanism is what you're studying.
   • Irrelevance: a variable that sits on no path between treatment and outcome can go.
4. No cycles. If it looks like A causes B and B causes A, add time. The book's example is a fistfight: my punch now causes your punch next period, which causes my punch the period after. The lecture's version: Wealth_t−1 → Power_t → Wealth_t.

4. Simulator: open and close the paths

This is the lecture's education-and-earnings diagram, with two additions so you can see every kind of variable: Schooling laws (from the lecture's variable list) and Owns a home, which we added as a collider. Owning a home is plausibly caused by both education and earnings. Click a box to control for it. The list below the diagram updates to show which paths are open.

The book practices this on its own example: does drinking wine make you live longer? Its diagram has two front doors (Wine → Lifespan, and Wine → Drugs → Lifespan) and four back doors that run through Income and Health, which share an unobserved cause U1. Controlling for Income closes three of the back doors. Adding Health closes the fourth. Note that you never had to control for U1, which is lucky, because you can't.

5. Confounders, mediators, colliders

The lecture sorts the associations in a diagram into three types. The middle variable plays a different role in each, and the right move is different:

Why does controlling for a collider create a link? The book uses a sandwich. Suppose your boss sometimes buys lunch for the office, but always announces it after you've ordered. Buying a sandwich and being given one are unrelated. But if you know someone ate a sandwich, the two become linked: if they didn't buy one, they must have been given one. Knowing the collider makes its causes predict each other.

The lecture's version: survey workers at a tech company and you'll find that people with better programming skills have worse social skills. That's not because coding ruins your social life. The company hires people who are strong in at least one of the two, so among the hired, a person weak in one is probably strong in the other. Similarly, height seems unrelated to basketball skill among NBA players. The book adds a warning: choosing a sample is controlling. Study only college students and you have controlled for college attendance, whether you meant to or not.

6. Simulator: see the bias in data

The diagram tells you which paths are open. This simulator shows what an open path does to your numbers. All the data here are simulated, made up so we know the true answer. They are not from the book or the lecture.

7. Why controlling works

Every open path is a story for why treatment and outcome move together. The Ch. 6 police example has two Bad stories (last year's crime, and local "law and order" politics, each of which affects both police and crime) and Good ones (police reduce crime directly, and by making crime less likely to pay off). To get at the Good stories, you need to get rid of the variation that comes from the Bad ones.

A path carries association only if every variable on it is free to vary. The book's example: in a sample where nobody uses drugs, Wine → Drugs → Lifespan can't explain anything, because Drugs never changes. Controlling for a variable does the same thing statistically. The lecture describes it in two equivalent ways and lists the tools for doing it:

• Hold it constant: compare candidates as if they had the same quality.
• Remove what it predicts: strip out the part of money and the part of win margin that quality explains, then relate what's left (Simulator 2's "Quality removed" view).
• Ways to do it: add it to a regression (margin ~ money + quality), matching, stratifying, or inverse probability weighting. You'll meet these later in the course.

Colliders are the exception. A collider doesn't cause anything on its path, so it can't supply an alternative story. It is the thing being caused, which is why its path starts out closed. Controlling for it makes its causes related to each other, and that opens the path.

8. What has to be true (and how to check it)

9. What you actually estimate

Which paths count as Good depends on your research question, not on the diagram.

The book is explicit that either question can be valid. Just decide which one you're asking before you pick your controls. Controlling for a mediator by accident (the lecture calls it overcontrolling) quietly changes your question from "total" to "direct."

10. Doing it in R (with AI help)

In this class, AI writes most of the code. Your job is the design and the checking. The dagitty and ggdag packages (or the website dagitty.net) will find paths and adjustment sets for you, but only for the diagram you give them.

11. How to read the chapters

Together the three chapters run about 16,000 words, but they're among the most readable in the book, and Ch. 8 is the foundation for everything after it. Here's where to spend your time: