We use molecular dynamics simulations with the monatomic water (mW) model to investigate the phase diagram, metastability, and growth of guest-free water clathrates of structure sI and sII. At 1 atm pressure, the simulated guest-free water clathrates are metastable with respect to ice and stable with respect to the liquid up to their melting temperatures, 245 +/- 2 and 252 +/- 2 K for sI and sII, respectively. We characterize the growth of the sI and sII water crystals from supercooled water and find that the clathrates are unable to nucleate ice, the stable crystal, We computed the phase relations of ice, guest-free sII clathrate, and liquid water from - 1500 to 500 atm. The resulting phase diagram indicates that empty sII may be the stable phase of water at pressures lower than approximately -4300 atm and temperatures lower than 275 K. The simulations show that, even in the region of stability of the empty clathrates, supercooled liquid water crystallizes to ice. This suggests that the barrier for nucleation of ice is lower than that for clathrates. We find no evidence for the existence of the characteristic polyhedral clathrate cages in supercooled extended water. Our results show that clathrates do not need the presence of a guest molecule to grow, but they need the guest to nucleate from liquid water. We conclude that nucleation of empty clathrates from supercooled liquid water would be extremely challenging if not impossible to attain in experiments. We propose two strategies to produce empty water clathrates in laboratory experiments at low positive pressures.