Strict exogeneity in the context of a fixed effects estimator is given by E(eit | αi; xi1... xit;... xiT) = 0.

Strict exogeneity as it applies to a fixed effects estimator refers to the assumption that the residual, eit, is not correlated with any of the explanatory variables, xi1...xiT. This means that the expectation of the residual given the explanatory variables, is equal to 0. In other words, the expected value of the residual is independent of the explanatory variables. This is necessary for the fixed effects estimator to be unbiased.