The

exogeneity assumption is a restriction on the joint distribution of the error term and the regressors:

E(U|X) = 0

Differently put, for any values x_{1}, ..., x_{K} we have:

E(U| X_{1} = x_{1}, ..., X_{K} = x_{K}) = 0.

The expected error for any value of the regressors is zero.

By the law of expected iterations, the exogeneity assumption implies:

- E(U|X
_{k}) = 0, for any k∈[1,k] - E(U) = 0

This then implies: cov(U,X_{k}) = 0.

Under the exogeneity assumption, we have:

E(Y| X_{1} = x_{1}, ..., X_{K} = x_{K}) = b_{0} + b_{1}X_{1} + ... + b_{K}X_{K}.

We can then study the causal effects of the X variables on the outcome without observing the error term U.