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Exogenous Variables
Exogenous originated from the Greek words exo (meaning “outside”) and gen (meaning “born”), and describes something generated from outside a system. It is the opposite of endogenous, which describes something generated from within the system. Exogenous variables, therefore, are variables that are not caused by any other variables in a model of interest; in other words, their value is not determined in the system being studied.
The concept of exogeneity is used in many fields, such as biology (an exogenous factor is a factor derived or developed from outside the body); geography (an exogenous process takes place outside the surface of the earth, such as weathering, erosion, and sedimentation); and economics (exogenous change is a change coming from outside the economics model, such as changes in customers’ tastes or income for a supply-and-demand model). Exogeneity has both statistical and causal interpretations in social sciences. The following discussion focuses on the causal interpretation of exogeneity.
Exogenous Variables in a System
Although exogenous variables are not caused by any other variables in a model of interest, they may cause the change of other variables in the model. In the specification of a model, exogenous variables are usually labeled with Xs and endogenous variables are usually labeled with Ys. Exogenous variables are the “input” of the model, predetermined or “given” to the model. They are also called predictors or independent variables.
The following is an example from educational research. Family income is an exogenous variable to the causal system consisting of preschool attendance and student performance in elementary school. Because family income is determined by neither a student's preschool attendance nor elementary school performance, family income is an exogenous variable to the system being studied. On the other hand, students’ family income may determine both preschool attendance and elementary school performance. High-income families are more likely than low-income families to enroll their children in preschools. High-income families also tend to provide more resources and support for their children to perform well in elementary school; for example, high-income parents may purchase more learning materials and spend more spare time helping their children with homework assignments than low-income parents.
Whether a variable is exogenous is relative. An exogenous variable in System A may not be an exogenous variable in System B. For example, family income is an exogenous variable in the system consisting of preschool attendance and elementary school performance. However, family income is not an exogenous variable in the system consisting of parental education level and parental occupation because parental education level and occupation probably influence family income. Therefore, once parental education level and parental occupation are added to the system consisting of family income, family income will become an endogenous variable.
Exogenous Variables in Path Analysis
Exogenous and endogenous variables are frequently used in structural equation modeling, especially in path analysis in which a path diagram can be used to portray the hypothesized causal and correlational relationships among all the variables. By convention, a hypothesized causal path is indicated by a single-headed arrow, starting with a cause and pointing to an effect. Because exogenous variables do not receive causal inputs from other variables in the system, no single-headed arrow points to exogenous variables. Figure 1 illustrates a hypothetical path diagram.
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