Glossary
Causal inference
What is Causal Inference?
Causal inference is the set of methods used to determine whether a relationship between variables is causal (A causes B) rather than merely correlational (A and B occur together). It is the foundation of evidence-based practice in behavioral science.
How it works
Randomized comparisons
A randomized controlled trial helps estimate a causal effect by assigning participants to treatment and control groups by chance. Random assignment reduces systematic differences between the groups; problems such as missing outcomes can still complicate the comparison.
Nonrandomized methods
When randomization is impossible, quasi-experimental methods (difference-in-differences, regression discontinuity, instrumental variables) and observational adjustment methods such as propensity score matching require assumptions about confounding.
Causal assumptions and confounding
Directed acyclic graphs represent causal assumptions; drawing one does not itself estimate an effect. The fundamental challenge is confounding: other variables that influence both the treatment and the outcome.
Causal inference example: exercise and earnings
A company sees that employees who use the gym earn higher salaries and concludes that exercise causes higher earnings. One possible explanation is confounding by job level: senior employees might have both higher salaries and more flexible schedules. That possible explanation is enough to show why the association alone does not prove that exercise causes higher pay. It does not settle whether exercise has any effect on earnings.
Why it matters
Causal inference makes the question, comparison, and assumptions explicit. Hernán and Robins’s book, Causal Inference: What If explains why a causal claim needs more than an observed association: it needs a defensible comparison and explicit assumptions.
The comparison you want and the comparison you have
In the gym-and-earnings example, the causal question is what would happen to the same eligible employees' later earnings under a defined exercise program compared with no such program. We cannot observe both outcomes for the same person over the same period. Hernán and Robins call these potential outcomes. Causal inference needs a defensible way to learn about the missing comparison.
Suppose a survey records job level, gym use and salary. Comparing gym users with nonusers within job levels would address that measured difference. It would not automatically address differences in prior health, work hours or other causes of both participation and earnings. Measuring gym use before next year's salary would establish temporal order, but temporal order alone would not remove those explanations.
Randomly offering an exercise program creates a different comparison: the effect of the offer. Some invited employees will not exercise; some employees in the comparison group will exercise anyway. Comparing people according to assignment preserves the original randomized contrast. Comparing only those who actually exercise reintroduces self-selection. Estimating the effect of participation requires additional assumptions and analysis.
What nonrandomized designs must justify
- Difference-in-differences: compare changes in a treated group with changes in a comparison group. The crucial question is whether their untreated trends would have followed the required parallel pattern. Similar earlier trends are useful evidence, not proof of that unobserved future.
- Regression discontinuity: use a treatment threshold, such as an eligibility score. A causal interpretation near the cutoff needs continuity assumptions and attention to whether people can manipulate their position around it. The result need not describe people far from that cutoff.
- Instrumental variables: use a variable that changes exposure, with assumptions that it affects the outcome only through that exposure and does not share unmeasured causes with the outcome. A variable being correlated with treatment is not enough.
- Adjustment and matching: compare people with similar measured causes of exposure and outcome. Credibility depends on what was measured and the causal structure, not the sophistication of the matching software.
For the design assumptions, see J-PAL's comparison of evaluation methods and the World Bank's regression-discontinuity reference. These methods answer different versions of “what if?” They are not interchangeable certificates of causality. State the treatment, population, outcome and time window first; then say which assumption makes the observed comparison informative. The methods-selection guide starts with that decision.