Long-term causal effects in multiagent economies

The effect of a treatment in a multiagent economy, e.g., a price increase, is {\em causal} if the treated economy would be different, e.g., in terms of revenue, relative to the {\em control} economy. Causal effects measured in an equilibrium of the economy, the {\em long-term causal effects}, are more representative of the value of such treatments. However, the statistical estimation of long-term causal effects is difficult because it has to rely, for practical reasons, on experimental data where agents are randomly assigned to the treated or the control economy, and their actions are observed before an equilibrium is reached. We propose a methodology to define and estimate long-term causal effects, which relies on a model of agent behaviors that plays a two-fold role. First, it predicts how agents would behave under different assignments, and, second, it predicts how agents would behave in equilibrium. These two prediction tasks enable the estimation of long-term causal effects under suitable assumptions, which we state explicitly.