Causal Inference cheatsheet
CausalInference
Cheatsheet
A single-page reference for causal inference methods and the load-bearing assumption behind each one, following Facure’s Causal Inference for the Brave and True.
I keep forgetting which method assumes what, so I put together a single page I can scan before reaching for a technique. It follows the terminology in Matheus Facure’s Causal Inference for the Brave and True, which is the resource I keep coming back to.
It is not exhaustive, and it is not a substitute for reading the book. It is the thing I glance at to remember what “regression discontinuity” actually buys me before I commit to it.
Core concepts
| Concept | What it means | Example |
|---|---|---|
| Causal Inference | Determining the cause-and-effect relationship between variables. | The impact of a new drug on patient recovery. |
| Treatment / Intervention | The variable or action being studied for its effect on an outcome. | A new teaching method. |
| Outcome | The variable that is influenced by the treatment. | Student test scores. |
| Confounder | A variable that influences both the treatment and the outcome, biasing the estimated effect. | Age in a study linking exercise to heart health. |
| Randomized Controlled Trial (RCT) | Units are randomly assigned to treatment or control to ensure comparability. See the chapter. | Randomly assigning patients to a drug or a placebo. |
| Observational Study | You observe the effect of treatments without controlling assignment. | Smoking and lung cancer, studied from existing data. |
| Counterfactual | What would have happened to the same units under a different treatment. | The unemployment rate had the stimulus not passed. |
| Selection Bias | Bias from studying subjects who are not representative of the population. | Only healthy volunteers enroll, inflating the drug’s apparent effect. |
| Instrumental Variables (IV) | A variable that affects treatment but only touches the outcome through it. | Distance to the nearest college as an instrument for education. |
| Difference-in-Differences (DiD) | Compare outcome changes over time between a treatment and a control group. | A new law’s effect, comparing regions before and after. |
| Regression Discontinuity (RD) | Use a cutoff to assign treatment, compare units just above and below it. | A scholarship’s effect, comparing students around the eligibility line. |
| Propensity Score Matching | Match treated and untreated units with similar probability of being treated. | Matching patients on demographics and clinical history before comparing. |
| Synthetic Control | Build a weighted blend of control units to stand in for the treated one. See the chapter. | A policy’s effect in one country vs a synthetic of several others. |
| Mediation Analysis | How an intermediate variable carries the effect from cause to outcome. | Stress reduction mediating exercise and mental health. |
| Natural Experiment | A real-world event that mimics random assignment. | A natural disaster’s effect on economic outcomes. |
| Heterogeneous Treatment Effects | How the effect varies across subgroups. | Whether a job-training program helps differently by age or education. |
| Panel Data and Fixed Effects | Repeated observations on the same units to absorb time-invariant confounders. | Education policy, tracked across years of student data. |
| Synthetic DiD (SDID) | Combines synthetic control and DiD. | A law’s effect, treated region vs synthetic control over time. |
The assumptions that actually bite
Most causal estimates fall apart not in the math but in one of these three. They are usually untestable, which is exactly why they are worth writing down.
| Assumption | What it means | Where it breaks |
|---|---|---|
| Ignorability / Exchangeability | Conditional on observed covariates, treatment is as good as random. | An unmeasured confounder you never recorded. |
| SUTVA | No interference between units, one version of treatment. | One person’s vaccination affecting another’s outcome. |
| Common Support / Overlap | Treatment and control overlap in covariate space. | A region where only treated units exist, forcing extrapolation. |
Picking a method: the one thing that matters for each
When I reach for one of these, the question is never “what does it do” but “what does it need to be true.” Here is the load-bearing assumption behind each, the thing that, if violated, quietly makes the estimate wrong.
| Method | Use it when | The assumption it lives or dies on |
|---|---|---|
| RCT | You can assign treatment yourself. | Randomization actually happened (no broken blinding, no attrition). |
| IV | Treatment is confounded but you have a clean instrument. | The instrument touches the outcome only through treatment. One alternate path kills it. |
| DiD | You have before/after data for a treated and a control group. | Parallel trends: the two groups would have moved together absent treatment. |
| RD | Treatment flips at a sharp threshold. | Units can’t precisely manipulate which side of the cutoff they land on. |
| Propensity Score Matching | Selection is on observables you measured. | You actually observed the confounders. It can’t fix unobserved ones. |
| Synthetic Control | One treated unit, many candidate controls, long pre-period. | The synthetic blend tracks the treated unit well before treatment. |
| Mediation | You want the pathway, not just the total effect. | No unmeasured confounding of the mediator-outcome link (the part people forget). |
| Panel / Fixed Effects | Repeated measures, confounders that don’t change over time. | The confounders really are time-invariant. |
| SDID | DiD’s parallel-trends looks shaky and you have a panel. | A weaker, reweighted version of parallel trends still holds. |
Things I’ve learned to check before trusting a result
- Plot the overlap. If treated and control don’t share covariate space, the model is extrapolating and nobody told you.
- Stress the key assumption, not the data. More features won’t save a design whose identification is broken.
- Run a sensitivity analysis. “How big would an unobserved confounder have to be to flip this?” is often more honest than the point estimate.
- Be suspicious of a clean answer from messy observational data. It usually means an assumption is doing more work than you realize.
More causal inference notes: