Interventions in an economic mechanism have an effect on its performance. For example, raising the reserve price of an auction has an effect on its revenue. The effect from the intervention is causal if the observed effect is better than the counterfactual, i.e., the effect that would be observed under no intervention. As mechanisms are dynamical systems of interacting agents, their response to an intervention fluctuates until the system reaches a new equilibrium. Effects measured in the new equilibrium, the long-term causal effects, are more representative of the value of interventions. However, the statistical estimation of long-term causal effects is difficult because it has to rely, for practical reasons, on data observed before the new equilibrium is reached.
In this paper, we develop a methodology for estimating long-term causal effects of interventions in mechanisms, using the potential outcomes model of causal inference (Neyman 1923; Rubin, 1974). Our proposed methodology relies on a data augmentation strategy, where agents are assumed to adopt, at each timepoint, a behavior that is latent. A game-theoretic model defines the distribution of the actions an agent takes, conditional on the adopted behavior. A time-series model defines the temporal evolution of aggregate agent behaviors, and smooths out the estimates of individual agent behaviors. The two models are combined and are fit using short-term data from observed agent actions. The fitted model parameters are then used to predict the long-term agent actions and, thus, estimate the long-term causal effect of interest. We illustrate our methodology on a dataset from behavioral game theory, and discuss open problems to stimulate future research.
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