All birds can lay eggs with out a man around. The bodies job is to reproduce, even if there is no rooster around, the body still does what it knows it's supposed to do, make the egg.
If you think about it people lay eggs with out being fertile. We women bleed every month to release the egg that was not fertile. But since we are mammals and not birds we do it a little differently. And our eggs are very very tiny. I know it's gross to think about.
Parrots do not usually lay eggs unless they are mating. I don't know why but I had some parrots that would not lay even with a mate. Parrots are one of the few animals that must make an emotional bond before mating and maybe this is necessary for ovulation.
That's interesting. Do parrots mate for life? I wonder how this applies to monogamous species that mate for life and lose their mate. Do the females stop ovulating if they lose their male partner? Anyone know?