Exogenous variable

As explained in Causal Inference for Data Science

An exogenous variable is a variable whose variation is determined outside the modeled causal system and is not explained by its included predictors.

An exogenous variable represents variation determined outside the causal system being modeled. It collects unknown or unobserved factors that affect variables of interest and marks the model’s boundary with the rest of the world. section 7.1.3

In a causal model, Z, X, and Y are endogenous when their values depend on other modeled variables. The additional factors UZ, UX, and UY affecting them are represented as exogenous variables. section 7.1.3

The distinction supports modular causal reasoning:

• Represent each modeled variable with a function of its parents and its exogenous influences, such as X := fX(Z, UX). section 7.1.3
• Treat an unobserved factor as an exogenous component even when it is not stored because it is unavailable or judged unnecessary. section 7.1.3
• Use assumptions about exogenous terms when estimating effects; DML, for example, assumes E[U|D,C] = 0 and E[V|C] = 0. section 8.1.2

Price and sales

Suppose D is a product’s price and O is its sales. Unobserved influences on sales appear as U, while unobserved influences on price appear as V. The model separates these exogenous influences from the effect β of price on sales. section 8.1.2

Figure 7.7 Typical three-node DAG with confounding. Z is a confounder for X and Y.

Use the three-node causal graph to inspect how modeled variables and external influences fit around a confounding structure involving Z, X, and Y. section 7.1.3

How Causal Inference for Data Science covers it

How deep it goes

Defines exogenous inputs, embeds them in structural functions, and applies conditional-mean assumptions without identifying their exact laws.

Examples

Uses UZ, UX, UY, and the price–sales variables D and O to illustrate external influences in causal equations.

What it assumes

Assumes familiarity with causal variables and functions, while introducing the endogenous–exogenous distinction through a three-variable model.

What you can do after

Evaluate/understand causal models by separating modeled relationships from unobserved variation and stating assumptions about that variation.

How it connects

Connects exogenous variables to endogenous variables, causal models, structural functions, confounding, causal graphs, and Double Machine Learning.

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Also explained in

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  Causal AIAn exogenous cause is a causal input whose variation originates outside the endogenous system represented by a structural causal model.

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Related concepts

• structural causal modelpart of · A structural causal model represents causal relationships among variables through equations that determine each variable from other variables and exogenous factors.
• canonical distributionconfigured by · A canonical distribution is a standard mathematically characterized probability distribution used as a primitive for probabilistic models.
• parallel world graphused by · A parallel world graph is a graph representation that places variables from multiple counterfactual worlds together without necessarily permitting the same separation relations as a counterfactual graph.
• abductionused by · Abduction is the inference step that uses observed facts to infer the latent circumstances or exogenous values that could have produced them.

This explainer was generated by Manning's knowledge graph from the text of Causal Inference for Data Science. The section links point to the parts of the book it draws on.