What is Structural Causal Model?
Structural Causal Model (SCM) is a formal system of autonomous structural assignments that maps exogenous background variables and causal parents to endogenous variables, supporting explicit reasoning about observations, interventions, and counterfactuals.
Quick Facts
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How It Works
Autonomous assignments give arrows causal meaning
An equation such as Y=f_Y(A,U_Y) says that A and background factor U_Y generate Y through a mechanism that can remain stable when another mechanism is changed. The missing arrows and independence assumptions among exogenous variables matter as much as the displayed arrows. Pearl's causal inference overview develops structural equations, graphical criteria, interventions, and counterfactuals as one formal language.
Intervention replaces a mechanism instead of conditioning on an event
The intervention do(A=a) removes the ordinary assignment for A and replaces it with the constant a, leaving other structural assignments unchanged. This surgical operation generally differs from observing A=a, because observation preserves causes of A while intervention disconnects them. Identification asks whether an interventional distribution can be derived from the observed distribution under the model's assumptions.
Counterfactuals reuse inferred background conditions
A unit-level counterfactual follows abduction, action, and prediction: update beliefs about exogenous variables from observed evidence, replace the selected mechanism, then propagate the modified model. Results depend on functional form, exogenous dependence, measurement, and invariance assumptions that observational fit alone cannot certify. Compare implied independences and experiments where available, version assumptions, and report when multiple SCMs fit the same data but answer counterfactuals differently.
Key Characteristics
- Separates exogenous background factors from endogenous modeled variables
- Defines one autonomous structural assignment for each endogenous variable
- Induces a causal graph while retaining functional information beyond the graph
- Represents interventions by replacing selected structural assignments
- Supports counterfactual reasoning through abduction, action, and prediction
- Requires causal assumptions that observational fit cannot validate by itself
Common Use Cases
- Distinguishing an intervention from conditioning on an observed feature
- Simulating policy changes under an explicit data-generating mechanism
- Defining unit-level counterfactual questions for model auditing
- Deriving adjustment or identification claims from causal assumptions
- Documenting which mechanisms are assumed invariant across environments
Example
Loading code...Frequently Asked Questions
How is a Structural Causal Model different from a Causal DAG?
A Causal DAG records variables and directed structural assumptions. An SCM additionally specifies assignments and exogenous variables that generate values. The graph can support path-based identification, while the functions are needed for many quantitative intervention and unit-level counterfactual questions.
Why is observing A=a different from intervening with do(A=a)?
Conditioning on `A=a` retains the process and common causes that produced the observed value. `do(A=a)` replaces A's structural assignment and severs its incoming causal links. The two distributions agree only under conditions that eliminate the resulting selection or confounding differences.
Does fitting structural equations prove the SCM is causal?
No. Multiple causal structures and functions can fit the same observational distribution. Causal interpretation requires design knowledge, temporal ordering, invariance assumptions, experiments or other identifying evidence, plus tests of observable implications and sensitivity to uncertain structure.
What are endogenous and exogenous variables in an SCM?
Endogenous variables are determined by assignments inside the model using their causal parents. Exogenous variables represent background factors whose causes are outside the modeled system. Assumptions about dependence among exogenous variables determine whether latent common causes are present.
Is Structural Causal Model the same as Synthetic Control Method?
No. Both are abbreviated SCM in some literature. A Structural Causal Model defines causal mechanisms, interventions, and counterfactuals. Synthetic Control Method constructs a weighted comparison unit for a comparative-case design. The estimands, assumptions, and algorithms are different.