where "X", "y" and "e" denote column vectors of length "T". This equation is similar to the equation involving formula_55 in the introduction (this is the matrix version of that equation). When "X" and "e" are uncorrelated, under certain regularity conditions the second term has an expected value conditional on "X" of zero and converges to zero in the limit, so the estimator is unbiased and consistent. When "X" and the other unmeasured, causal variables collapsed into the "e" term are correlated, however, the OLS estimator is generally biased and inconsistent for "β". In this case, it is valid to use the estimates to predict values of "y" given values of "X", but the estimate does not recover the causal effect of "X" on "y".