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| = Exogeneity = '''Exogeneity''' means that all predictors are independent of the outcome and the error term. <<TableOfContents>> ---- == Description == 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... * 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 [[Statistics/ConditionalExpectations|conditional expectation]] like: {{attachment:cond.svg}} ---- CategoryRicottone |
