This NYT article has been widely read and emailed. Ron Lieber argues yes, you should tell your children, but I’m not sure I can pull out the exact thread of his argument from the piece.
I say no you should not tell them. But you should tell them something about your monetary situation. If you are not so well off, you should tell your children that you are upwardly mobile, and will someday be more prosperous, through hard work. At the very least then they won’t be scared. If you are middle class, tell them a somewhat scaled-up version of the same. You don’t want to tell them anything they can use as a “club” against their possibly poorer friends, so leave creative ambiguity in your answer. If they boast about the family income, they will mostly end up embarrassing themselves, in addition to the negative externalities they might impose on others.
That said, you are marking out a range, so when they grow up and the time comes for them to learn the exact truth, they won’t feel you were tricking them or keeping family secrets. In the meantime you are a role model for upward mobility.
If you are well off or very well off, tell them “Yes, we are well off but the real metric of success is X,” depending on what you think they need to hear, within the bounds of realism of course. X might be how many friends you have, how happy your children are, how holy or pious or God-fearing you are, how many books you have read, or how much you have helped the world, among other candidates. Serve them up a weighted average of those Xxs over time, so as to a) avoid seeming like a monomaniac, and b) give them a sense that many values are important, and c) drive home that money is not at the top of the list, even if you think it is. They’ll have enough chances to learn to feel that way.
Remember, you’re trying to maximize some weighted average of covering your bases for future revelations, moral instruction, not scaring them with Piketty-like reasoning, stopping your kids from making fools of themselves with the information you give them, and stopping your children from making you look foolish or like a bad parent. You’re in essence the central bank here, and it’s creative ambiguity all the way.