Prominent among contemporary ethics is the debate as to whether identity matters for moral judgments. We face decisions daily that may impact who gets to live (e.g. surgery) or to die (e.g., abortion, euthanasia), and such decisions may not only influence the targeted person but also i) other people within a population; and even ii) the identity of those who come to exist in the future. A prominent example of this non-identity problem is linked to environmental decisions, where less sustainable behaviour in the present may influence the amount and identity of people who get to live in the future. Despite the great deal of research on egalitarianism in behavioural economics, little to no research has been done regarding the non-identity problem. However, such problems are a fruitful new experimental paradigm as behaviour in it has the potential to be against what would be predicted by most, if not all, models of other-regarding preferences. In this paper we introduce an experimental game that captures the qualitative features of the non-identity problem for the first time, and we analyse behaviour and moral judgments in the game. By comparing the distribution of choices and predicted choices by a set of moral rules, we are able to document whether simple moral rules are able, on average, to causally drive a behaviour that is a limitation of canonical models of other-regarding preferences.