Finding dynamic treatment effects under anticipation: The effects of spanking on behaviour

The dynamic treatment effect literature considers multiple treatments administered over time, with some treatments affected by interim outcomes. But the literature overlooks the possibility of individuals acting in anticipation of future treatments. This lack of anticipation aspect may not matter in the drug-response relationships which motivated the literature. But human beings (or animals with some intelligence) do not just respond to current and past treatments, but also 'reflect and anticipate' future treatments. For example, a punishment or reward is likely to prompt forward looking. Even if no personal punishment or reward is involved, people may take action in anticipation of a future government policy, which would be an important concern for policy makers. The paper explores how to find dynamic treatment effects allowing for forward looking or anticipation by extending available dynamic treatment effect approaches in the literature. Then the methods proposed are applied to the effects of spanking on a child's bad behaviour where a child may act better in anticipation of future spanking, which is analogous to the relationship between punishment and crime.