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| In econometrics, '''exogeneity''' is an assumption about data used for statistical inference. | '''Exogeneity''' means that all predictors are independent of the outcome and the error term. |
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| == Meaning == | == Description == |
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| Exogeneity means that all treatment and control variables are independent of the outcome variable and the error term. So an assumption of exogeneity would be violated if... | Mathematically, exogeneity and [[Statistics/Homoskedasticity|homoskedasticity]] together can be expressed as: {{attachment:exo.svg}} The full set of variables is independently and normally distributed about 0. The [[Statistics/CovarianceMatrices|covariance matrix]] is fully specified as the [[LinearAlgebra/SpecialMatrices#Diagonal_Matrices|diagonal matrix]] of variances. The opposite condition is '''endogeneity'''. An assumption of exogeneity would be violated if... |
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| In a [[Econometrics/OrdinaryLeastSquares|mulivariate OLS regression]], the assumption of exogeneity can be expressed mathematically as: | It can also be useful to express exogeneity as a [[Statistics/ConditionalExpectations|conditional expectation]] like: |
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| {{attachment:exogeneity.svg}} | {{attachment:cond.svg}} |
Exogeneity
Exogeneity means that all predictors are independent of the outcome and the error term.
Contents
Description
Mathematically, exogeneity and homoskedasticity together can be expressed as:
The full set of variables is independently and normally distributed about 0. The covariance matrix is fully specified as the diagonal matrix of variances.
The opposite condition is endogeneity.
An assumption of exogeneity would be violated if...
- confounding variables were omitted
- in time series models, a lagged dependent variable can be correlated to the error term
if OLS is mistakenly used on a system of equations (i.e. simultaneous equation bias)
It can also be useful to express exogeneity as a conditional expectation like:
