Abstract It has recently been proposed, within the framework of the linear shallow-water equations, that tropical Pacific decadal variability (PDV) can be accounted for by basin modes with eigenperiods of 10 to 20 yr, amplifying a midlatitude wind forcing with an essentially white spectrum. Here the authors use a different formalism of linear equatorial wave theory. The Green’s function is computed for the wind-forced response of a linear equatorial shallow-water ocean and use the earlier results of Cane and Moore to obtain a compact, closed form expression for the motion of the equatorial thermocline, which applies to all frequencies lower than seasonal. This expression is new and allows a systematic comparison of the effect of low- and high-latitude winds on the equatorial thermocline. At very low frequencies (decadal time scales), the planetary geostrophic solution used by Cessi and Louazel is recovered, as well as the equatorial wave solution of Liu, and a formal explanation for this convergence is given. Nonetheless, this more general solution leads one to a different interpretation of the results. In contrast to the aforementioned studies, the authors find that the equatorial thermocline is inherently more sensitive to local than to remote wind forcing and that planetary Rossby modes only weakly alter the spectral characteristics of the response. Tropical winds are able to generate a strong equatorial response with periods of 10 to 20 yr, while midlatitude winds can only do so for periods longer than about 50 yr. The results suggest that ocean basin modes are an unlikely explanation of decadal fluctuations in tropical Pacific sea surface temperature.