Extant theoretical work on long-term care (LTC) and its insurance has neglected an important fact: Benefits of LTC insurance as well as the amount of public subsidization of LTC can differ between severe and mild dependency. The objective of this paper is to revisit the study of optimal purchase of LTC insurance and its crowding out by public subsidies dissociating coverage for the risk of dependency in nursing home and of dependency at home. This study examines three prevalent models of LTC insurance indemnities commonly encountered in various LTC insurance markets. It also studies the presence of potential intergenerational moral hazard and shows how it drives the crowding out or crowding in of LTC insurance by public subsidization according to the insurance models and risk aversion behaviours.