The Failure of Orthogonality under Nonstationarity: Should We Care About It?

We consider two well-known facts in econometrics: (i) the failure of theorthogonality assumption (i.e., no independence between the regressorsand the error term), which implies biased and inconsistent Least Squares (LS)estimates and (ii) the consequences of using nonstationary variables, acknowledgedsince the seventies; LS might yield spurious estimates when thevariables do have a trend component, whether stochastic or deterministic. In this work, an optimistic corollary is provided: it is proven that the LSregression, employed in nonstationary and cointegrated variables where theorthogonality assumption is not satisfied, provides estimates that converge totheir true values. Monte Carlo evidence suggests that this property is maintainedin samples of a practical size