Endogenous Variable

Definition

An endogenous variable is a variable within a statistical or mathematical model whose value is determined by other variables in the same model. In typical use, an endogenous variable is the dependent variable whose changes correlate with—and may be caused by—other variables included in the system.

How it works

• Endogenous variables change as part of the functional relationships specified in a model.
• The correlation between variables can be positive or negative: a change in one variable predicts a change in the other, but not necessarily in the same direction.
• Identifying endogenous variables is central to causal modeling because they represent the outcomes the model seeks to explain.

Endogenous vs. Exogenous

• Exogenous variables are independent inputs to a model. They affect the model but are not affected by it.
• Endogenous variables are determined inside the model and respond to changes in other included variables.
• Determining which factors are exogenous versus endogenous matters for correct interpretation and estimation of causal effects.

Examples

• Price in a supply-and-demand model: price responds to both supply and demand and is endogenous within the market model.
• Baker’s output (number of cookies): determined by inputs such as ingredient quantities and labor time.
• Commute time and fuel consumption: longer commute times cause greater fuel consumption in a model that links the two.
• Personal income and consumption: higher income tends to increase consumer spending.
• Rainfall and crop growth: rainfall affects plant growth; in many agricultural models rainfall is treated as endogenous to crop outcomes (though sometimes it may be treated as exogenous if driven by external climate factors).
• Education and future earnings: education level is correlated with later income.

Note: Some relationships are effectively one-way (e.g., weather → tourism), where the dependent variable does not feed back to change the independent one.

Why it matters

Endogenous variables are central to understanding causation in econometrics and other modeling fields (e.g., agriculture, meteorology). Misidentifying endogenous and exogenous factors can lead to biased or incorrect conclusions about causal relationships. Analysts address endogeneity through study design, controlled experiments, or statistical techniques (for example, instrumental variable methods) to obtain valid causal estimates.

Key takeaways

• An endogenous variable is internal to the model and varies with other model variables.
• It is essentially the dependent variable whose changes the model aims to explain.
• Distinguishing endogenous from exogenous variables is critical for valid causal inference and reliable modeling results.