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Spurious Regressions in Econometrics: Reconsideration

As every econometrician knows, in a regression with one regressor, the dependent and explanatory variables may be spuriously correlated if they may have been affected by some third variable, a common cause. In a highly regarded article, Granger and Newbold (1974) were not concerned with this type of spurious correlation but proposed an intuitively plausible method of finding evidence of spurious regressions, based on a t-ratio in a regression between two highly autocorrelated variables known to be independent of each other. The problem with this test is that, with insights gained from Pratt and Schlaifer (1984, 1988), in such a regression the included regressor is necessarily correlated with the error term made up of omitted regressors. As a consequence, the associated “t-ratio” does not have a t-distribution, rendering the t-test un-interpretable. Further, rather than collecting evidence for spurious correlation between two independent variables, a more urgent endeavor is to seek a methodology that removes spurious correlations from any regression between variables that may or may not be independent. This paper accomplishes this task by proposing a method that guarantees estimates free of any spuriousness, even when some co-determinants are unobserved.