Not really - or rather, I'm not quite sure what would consitute "evidence" for moral questions.

To take a simpler example, most people would agree that it's the right thing to jump into a river to save a drowning toddler, even if there's a slight risk to your own life (the current is strong) and it's certain to damage your clothes and smartphone. Yet I don't see what would consitute "evidence" that it's the right thing to do.

(edit) But if you're asking about reasons for believing it's the right thing, I'd say that the future world would likely be a better place if wealthy, educated and responsible people have more kids.