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| The full set of variables is independently and normally distributed about 0. The covariance matrix is fully expressed as the [[LinearAlgebra/SpecialMatrices#Diagonal_Matrices|diagonal matrix]] of each term's variance. | 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. |
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:
