# Exogenous and endogenous variables

In an economic model, an **exogenous variable** is one whose value is determined outside the model and is imposed on the model, and an **exogenous change** is a change in an exogenous variable.[1]^{:p. 8}[2]^{:p. 202}[3]^{:p. 8}

In contrast, an **endogenous variable** is a variable whose value is determined by the model. An **endogenous change** is a change in an endogenous variable in response to an exogenous change that is imposed upon the model.[1]^{:p. 8}[3]^{:p. 8}

In econometrics, an exogenous variable is assumed to be fixed in repeated sampling, which means it is a nonstochastic variable. An implication of this assumption is that the error term in the econometric model is independent of the exogenous variable.[4]

## Examples

In the simple supply and demand model, a change in consumer tastes is unexplained by the model and imposes an exogenous change in demand that leads to a change in the endogenous equilibrium price and the endogenous equilibrium quantity transacted. Here the exogenous variable is a parameter conveying consumer tastes. Similarly, a change in the consumer's income is exogenously given, outside the model, and appears in the model as an exogenous change in demand.[1]^{:p. 10}

In the LM model of interest rate determination,[1]^{:pp. 261–7} the supply of and demand for money determine the interest rate contingent on the level of the money supply, so the money supply is an exogenous variable and the interest rate is an endogenous variable.

In a model of firm behavior with competitive input markets, the prices of inputs are exogenously given, and the amounts of the inputs to use are endogenous.[2]^{:p. 202}

## Sub-models and models

An economic variable can be exogenous in some models and endogenous in others. In particular this can happen when one model also serves as a component of a broader model. For example, the IS model of only the goods market[1]^{:pp. 250–260} derives the market-clearing (and thus endogenous) level of output depending on the exogenously imposed level of interest rates, since interest rates affect the physical investment component of the demand for goods. In contrast, the LM model of only the money market takes income (which identically equals output) as exogenously given and affecting money demand; here equilibrium of money supply and money demand endogenously determines the interest rate. But when the IS model and the LM model are combined to give the IS-LM model,[1]^{:pp. 268–9} both the interest rate and output are endogenously determined.

## References

- Mankiw, N. Gregory.
*Macroeconomics*, third edition, 1997. - Varian, Hal R.,
*Microeconomic Analysis*, third edition, 1992. - Chiang, Alpha C.
*Fundamental Methods of Mathematical Economics*, third edition, 1984. - Wooldridge, Jeffrey M. (2009).
*Introductory Econometrics: A Modern Approach*(Fourth ed.). Mason: South-Western. p. 49. ISBN 978-0-324-66054-8.