Endogenous Variable

An Endogenous Variable is a variable whose value is determined by the changes of other variables in the system.

• Context:
  • It can be expressed as [math]\displaystyle{ y=f(x,z)+ u }[/math] where [math]\displaystyle{ y }[/math] is the endogenous variable, u is a fixed value and a exogenous variable, [math]\displaystyle{ f(x,y) }[/math] is function of independent variables [math]\displaystyle{ x }[/math] and [math]\displaystyle{ z }[/math] representing a composition of the other variables in the system. Note that, [math]\displaystyle{ x }[/math] and [math]\displaystyle{ z }[/math] are purely exogenous variables only if there is no reverse causation between [math]\displaystyle{ y }[/math] and [math]\displaystyle{ x }[/math] and/or [math]\displaystyle{ z }[/math].
  • It can also be defined a variable which determined "within" the model while exogenous variables are determined "outside" the model.
• Example(s):
  • Investment and Demand for Money are endogenous variables in the IS-LM Model as these variables are influenced by level of Income and Interest Rate.
  • The Quantity(Q) is an endogenous variable in the supply and demand model, where the quantity demanded is determined by a function of exogenous variables (a and b) and price (P), Q= a - bP. Price can also be considered an endogenous variable in this model by reverse causation if the price is determined by the inverse function P=(Q-a)/b.
  • …
• Counter-Example(s)
  • Dependent Variable.
  • Exogenous Variable.
• See: Endogeneity, Endogenous Process, Econometrics, Linear Regression, Economic Multiplier.

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References

2016

• (Business Dictionary, 2016) ⇒ http://www.businessdictionary.com/definition/endogenous-variable.html
  • QUOTE: Dependent variable generated within a model and, therefore, a variable whose value is changed (determined) by one of the functional relationships in that model. For example, consumption expenditure and income is considered endogenous to a model of income determination

• (Statistics How To, 2016) ⇒ http://www.statisticshowto.com/endogenous-variable/
  • QUOTE: Endogenous variables are used in econometrics and sometimes in linear regression. They are similar to (but not exactly the same as) dependent variables. Endogenous variables have values that are determined by other variables in the system (these “other” variables are called exogenous variables. According to Daniel Little, University of Michigan-Dearborn, an endogenous variable is defined in the following way: A variable [math]\displaystyle{ x_j }[/math] 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).

• (Investopedia, 2016) ⇒ http://www.investopedia.com/terms/e/endogenous-variable.asp
  • QUOTE: An endogenous variable is a classification of a variable generated by a statistical model that is explained by the relationships between functions within the model. For example, the equilibrium price of a good in a supply and demand model is endogenous because it is set by a producer in response to consumer demand. It is the opposite of an exogenous variable.

• (Weisstein, Eric W., 2016) ⇒ "Endogenous Variable." From MathWorld -- A Wolfram Web Resource. http://mathworld.wolfram.com/EndogenousVariable.html
  • An endogenous variable is an economic variable that is related to other economic variables and determines their equilibrium levels.

• (UnderstandingSociety gateway, 2016) ⇒ http://www-personal.umd.umich.edu/~delittle/Encyclopedia%20entries/Endogenous%20variable.htm
  • QUOTE: 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 (x1, x2, … , xk) (y = M(X)). A variable xj 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 xj 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.

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