An equilibrium model of child maltreatment

We propose a dynamic equilibrium model of human capital development of a child that can explain why a parent-child relationship might lead to child maltreatment. Assuming that a parent cannot observe a child's human capital accumulation or effort, and that the child's time preference develops endogenously, an unstable path of the parent's beliefs regarding the child can persist in equilibrium when the parent faces a high degree of uncertainty in inferring the child's human capital. The parent with an initial high estimate of the human capital then tends to underestimate the child's effort, which results in persistently punitive - abusive - interactions.