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Daniel Little, University of Michigan-Dearborn

Endogenous variable: A factor in a causal model or causal system whose value is determined by the states of other variables in the system; contrasted with an exogenous variable. Related but non-equivalent distinctions are those between dependent and independent variables and between explanandum and explanans. A factor can be classified as endogenous or exogenous only relative to a specification of a model representing the causal relationships producing the outcome y among a set of causal factors X (x_1, x₂, …, x_k) (y = M(X)). A variable x_j is said to be endogenous within the causal model M if its value is determined or influenced by one or more of the independent variables X (excluding itself). A purely endogenous variable is a factor that is entirely determined by the states of other variables in the system. (If a factor is purely endogenous, then in theory we could replace the occurrence of this factor with the functional form representing the composition of x_j as a function of X.) In real causal systems, however, there can be a range of endogeneity. Some factors are causally influenced by factors within the system but also by factors not included in the model. So a given factor may be partially endogenous and partially exogenous—partially but not wholly determined by the values of other variables in the model.

Consider a simple causal system—farming. The outcome we are interested in explaining (the dependent variable or the explanandum) is crop output. Many factors (independent variables, explanans) influence crop output: labor, farmer skill, availability of seed varieties, availability of credit, climate, weather, soil quality and type, irrigation, pests, temperature, pesticides and fertilizers, animal practices, and availability of traction. These variables are all causally relevant to crop yield, in a specifiable sense: if we alter the levels of these variables over a series of tests, the level of crop yield will vary as well (up or down). These factors have real causal influence on crop yield, and it is a reasonable scientific problem to attempt to assess the nature and weight of the various factors. We can also notice, however, that there are causal relations among some but not all of these factors. For example, the level of pest infestation is influenced by rainfall and fertilizer (positively) and pesticide, labor, and skill (negatively). So pest infestation is partially endogenous within this system—and partially exogenous, in that it is also influenced by factors that are external to this system (average temperature, presence of pest vectors, decline of predators, etc.).

The concept of endogeneity is particularly relevant in the context of time series analysis of causal processes. It is common for some factors within a causal system to be dependent for their value in period n on the values of other factors in the causal system in period n-1. Suppose that the level of pest infestation is independent of all other factors within a given period, but is influenced by the level of rainfall and fertilizer in the preceding period. In this instance it would be correct to say that infestation is exogenous within the period, but endogenous over time.

Hendry, D.F. 1995. Dynamic Econometrics. Oxford: Oxford University Press.

Pearl, Judea. 2000. Causality: Models, Reasoning, and Inference. Cambridge: Cambridge University Press.

Encyclopedia of Social Science Research Methods, edited by Michael Lewis-Beck (University of Iowa), Alan Bryman (Loughborough University), and Tim Futing Liao. Sage Publications.

Exogenous variable (see also endogenous variable): A factor in a causal model or causal system whose value is independent from the states of other variables in the system; a factor whose value is determined by factors or variables outside the causal system under study. For example, rainfall is exogenous to the causal system constituting the process of farming and crop output. There are causal factors that determine the level of rainfall—so rainfall is endogenous to a weather model—but these factors are not themselves part of the causal model we use to explain the level of crop output. As with endogenous variables, the status of the variable is relative to the specification of a particular model and causal relations among the independent variables. An exogenous variable is by definition one whose value is wholly causally independent from other variables in the system. So the category of “exogenous” variable is contrasted to those of “purely endogenous” and “partially endogenous” variables. A variable can be made endogenous by incorporating additional factors and causal relations into the model. There are causal and statistical interpretations of exogeneity. The causal interpretation is primary, and defines exogeneity in terms of the factor’s causal independence from the other variables included in the model. The statistical or econometric concept emphasizes non-correlation between the exogenous variable and the other independent variables included in the model. If x_j is exogenous to a matrix of independent variables X (excluding x_j), then if we perform a regression of x_j against X (excluding x_j), we should expect coefficients of 0 for each variable in X (excluding x_j). Normal regression models assume that all the independent variables are exogenous.

Engle, R. F., D. F. Hendry, and J. F. Richard. 1983. Exogeneity. Econometrica 51:277-304.

Pearl, Judea. 2000. Causality: models, reasoning, and inference. Cambridge: Cambridge University Press.

Woodward, James. 1995. Causation and Explanation in Econometrics. In On the Reliability of Economic Models: Essays in the Philosophy of Economics, edited by D. Little. Bostn: Kluwer Academic Publishers.

Encyclopedia of Social Science Research Methods, edited by Michael Lewis-Beck (University of Iowa), Alan Bryman (Loughborough University), and Tim Futing Liao. Sage Publications.

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