  Planned experiments are the gold standard in reliably comparing the causal
effect of switching from a baseline policy to a new policy. One critical
shortcoming of classical experimental methods, however, is that they typically
do not take into account the dynamic nature of response to policy changes. For
instance, in an experiment where we seek to understand the effects of a new ad
pricing policy on auction revenue, agents may adapt their bidding in response
to the experimental pricing changes. Thus, causal effects of the new pricing
policy after such adaptation period, the {\em long-term causal effects}, are
not captured by the classical methodology even though they clearly are more
indicative of the value of the new policy. Here, we formalize a framework to
define and estimate long-term causal effects of policy changes in multiagent
economies. Central to our approach is behavioral game theory, which we leverage
to formulate the ignorability assumptions that are necessary for causal
inference. Under such assumptions we estimate long-term causal effects through
a latent space approach, where a behavioral model of how agents act conditional
on their latent behaviors is combined with a temporal model of how behaviors
evolve over time.
