Magnetospheric convection can be seen as a form of interchange motions, but unlike in an ideal MHD system, is subject to the ionospheric boundary condition. For general time-dependent interchanges, the Hall current in the ionosphere generates a field-aligned current independent of any background gradients. The effect of the Hall conductivity on time-dependent convection is isolated through a simple box model where pressure gradient and field line curvature are suppressed. Mathematical analysis suggests that the Hall conductivity can destabilize interchange modes with long longitudinal wavelength. The finding comes at the expense of a high degree of geometrical idealization. More realistic computations are needed to test the theory. ¿ American Geophysical Union 1996