In the finance and accounting literature, the use of a common divisor in the dependent and independent variables of ordinary least-squares regressions is commonplace. What goes less recognized, however, is that their use induces spurious correlation between the regression variables and invalidates standard testing procedures. This paper analyses the common divisor problem by outlining analytical results concerning the expected R2 and providing a simulation procedure that generates test statistics from which critical values can be drawn. To illustrate the procedure, we re-investigate payout yield return predictability findings that have appeared in the literature and show that the results are spurious.
Powell, J., Shi, J., Smith, T., & Whaley, R. (2009). Common divisors, payout persistence, and return predictability. International Review of Finance, 9(4), 335-357. https://doi.org/10.1111/j.1468-2443.2009.01095.x