The failure of orthogonality under nonstationarity: should we care about it? (Q544476)

Summary: We consider two well-known facts in econometrics: (i) the failure of the orthogonality assumption (i.e., no independence between the regressors and the error term), which implies biased and inconsistent least squares (LS) estimates and (ii) the consequences of using nonstationary variables, acknowledged since the seventies. LS might yield spurious estimates when the variables have a trend component, whether stochastic or deterministic. In this work, an optimistic corollary is provided: it is proven that the LS regression, employed in nonstationary and cointegrated variables where the orthogonality assumption is not satisfied, provides estimates that converge to their true values. Monte Carlo evidence suggests that this property is maintained in samples of a practical size.