Theoretical models of magnetic reconnection have been traditionally developed within the framework of magnetohydrodynamics (MHD). However, in low-density astrophysical plasmas like those found in the magnetopause and the magnetotail, kinetic effects such as the Hall current are expected to play a significant role. We present results from externally driven magnetic reconnection simulations, within the framework of incompressible Hall MHD in 2 1/2 dimensions. We evaluate the relevance of the Hall current in the reconnection process by performing a set of simulations with different values of the Hall parameter. We compute the corresponding reconnection rates as a function of time and explore the spatial structure of the fields in the surroundings of the diffusion region.