A previous paper, McKenzie and Hagfors (1996 J. Plasma Phys. 55(3), 539–585) henceforth referred to as P1, discussed the excitation of parametric instability in a homogeneous plasma pumped by an external electrostatic field. The discussion was carried out in the fluid approximation, and growth rates and resonance frequencies for several different modes were calculated, some of which had previously been overlooked because of inconsistent cut-off of certain series expansions. In this brief note we show that the fluid treatment gives growth rates and resonance frequencies that agree well with the kinetic treatment.