The interaction between monetary incentives and non-monetary incentives is far from obvious. In some cases, they (imperfectly) complement each other: having one makes the other one more powerful. In other cases, they are (imperfect) substitute: having one makes the other one less powerful. As far as I know, there is currently no “general theory” of crowding in and crowding out. It means that we need to have a look at each specific instance of interactions between the two types of incentives.