Endogenous Variables

The Problem of Endogeneity

One of the most commonly used statistical models is ordinary least squares regression (OLS). A variety of assumptions must hold for OLS to be the best unbiased estimator, including the independence of errors. In regression models, problems with endogeneity may arise when an independent variable is correlated with the error term of an endogenous variable. When observational data are used, as is the case with many studies in the social sciences, problems with endogeneity are more prevalent. In cases where randomized, controlled experiments are possible, such problems are often avoided.

Several sources influence problems with endogeneity: when the true value or score of a variable is not actually observed (measurement error), when a variable that affects the dependent variable is not included in the regression, and when recursivity exists between the dependent and independent variables (i.e., there is a feedback loop between the dependent and independent variables). Each of these sources may occur alone or in conjunction with other sources.

Figure 1 Variables B and C Are Endogenous

The solution to problems with endogeneity is often to use instrumental variables. Instrumental variables methods include two-stage least squares, limited information maximum likelihood, and jackknife instrumental variable estimators. Advantages of instrumental variables estimation include the transparency of procedures and the ability to test the appropriateness of instruments and the degree of endogeneity. Instrumental variables are beneficial only when they are strongly correlated with the endogenous variable and when they are exogenous to the model.

Endogenous Variables in Structural Equation Modeling

In structural equation modeling, including path analysis, factor analysis, and structural regression models, endogenous variables are said to be “downstream” of either exogenous variables or other endogenous variables. Thus, endogenous variables can be both cause and effect variables.

Consider the simple path model in Figure 1. Variable A is exogenous; it does not have any variables causally prior to it in the model. B is endogenous; it is affected by the exogenous variable A while affecting C. C is also an endogenous variable, directly affected by B and indirectly affected by A.

As error associated with the measurement of endogenous variables can bias standardized direct effects on endogenous variables, structural equation modeling uses multiple measures of latent constructs in order to address measurement error.

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