We (i) formalize long-run neutrality (LRN) and long-run superneutrality (LRSN) in the context of a bivariate ARIMA model, (ii) show how the restrictions implied by LRN and LRSN depend on the orders of integration of the variables, (iii) apply our analysis to previous work, showing how that work is related to LRN and LRSN, and (iv) provide some new evidence on LRN and LRSN.