Statistics How To

Exogeneity: Definition

Regression Analysis >

Exogeneity is a standard assumption made in regression analysis, and when used in reference to a regression equation tells us that the independent variables X are not dependent on the dependent variable (Y). This does not mean there is no connection; since Y is dependent, it will still depend on the independent variable(s) X and on the error term.

When used to refer to a variable, it means that that particular variable is independent (not affected by) other variables in the system. An exogenous variable is able to influence the system without being influenced by it.

Types of Exogeneity

There are two main forms of exogeneity, depending on the level of independence shown by the variable.

  1. Strictly exogenous means the error term is unrelated to any instance of the variable X; past, present, and future. X is completely unaffected by Y.
  2. Sequentially exogenous means in which the error term is unrelated to past instances of the variable X. A sequentially exogenous variable is also known as a predetermined variable. X is not affected by past instances of Y; but future instances of X may be affected by current or future instances of Y.

If an equation or variable is neither strictly exogenous nor sequentially exogenous, it is called endogenous.

Example of Strict Exogeneity

Suppose you were modeling how the weather affected the probability of softball practice in a small town in the Midwest. The weather is your independent variable, and it affects the probability of softball practice, your dependent variable. The causal relationship is strictly one way; the probability of softball practice is unable to affect the weather in any way. So weather is an strictly exogenous variable.

References

  1. Brooks, Chris. Introductory Econometrics for Finance. Retrieved from https://books.google.com/books?isbn=052169468X on July 8, 2018
  2. Engle, Robert F., et al. “Exogeneity.” Econometrica, vol. 51, no. 2, 1983, pp. 277–304. JSTOR. Retrieved from www.jstor.org/stable/1911990 on July 8, 2018.
  3. Fingleton, Bernard. Endogeneity, Exogeneity and instrumental variables. Retrieved from http://www.cantab.net/users/bf100/pdf/iv_slides_fingleton.pdf on July 8, 2018
  4. Finkel, Steven. Analysis of Panel Data : Dynamic Panel Models and SEM-Econometric Model Integration. University of Gothenburg, 17 June 2015.
    https://gul.gu.se/public/pp/public_file_archive/archive.html?publishedItemId=30026152&courseId=70156&fileId=30025891l
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Exogeneity: Definition was last modified: August 2nd, 2018 by Stephanie