Fixed-Population Causal Inference for Models of Equilibrium

TL;DR

This paper develops a framework for causal inference in network models with endogenous outcomes, defining estimands that are identifiable from a single experiment under minimal assumptions, and analyzing their properties.

Contribution

It introduces a novel fixed-population, design-based approach for causal inference in complex network interference models, including equilibrium settings.

Findings

Unbiased and consistent IPW estimators for causal parameters.

Identification of LATE-type averages in equilibrium models.

Structural assumptions allow parameter recovery with causal interpretation.

Abstract

In contrast to problems of interference in (exogenous) treatments, models of interference in unit-specific (endogenous) outcomes do not usually produce a reduced-form representation where outcomes depend on other units' treatment status only at a short network distance, or only through a known exposure mapping. This remains true if the structural mechanism depends on outcomes of peers only at a short network distance, or through a known exposure mapping. In this paper, we first define causal estimands that are identified and estimable from a single experiment on the network under minimal assumptions on the structure of interference, and which represent average partial causal responses which generally vary with other global features of the realized assignment. Under a fixed-population, design-based approach, we show unbiasedness and consistency for inverse-probability weighting (IPW) estimators for those causal parameters from a randomized experiment on a single network. We also analyze more closely the case of marginal interventions in a model of equilibrium with smooth response functions where we can recover LATE-type weighted averages of derivatives of those response functions. Under additional structural assumptions, these ``agnostic" causal estimands can be combined to recover model parameters, but also retain their less restrictive causal interpretation.