What Is a Causal Effect When Firms Interact? Counterfactuals and Interdependence

TL;DR

This paper develops a framework for understanding causal effects in interconnected economic systems, emphasizing the importance of counterfactual assumptions and showing that standard estimators may not identify true causal effects.

Contribution

It introduces a formal causal framework for interdependent firms, clarifies the role of counterfactual assumptions, and distinguishes different causal regimes in networked environments.

Findings

Causal effects are not uniquely defined under interdependence.

Learning the network alone is insufficient for causal inference.

Different counterfactual regimes lead to distinct causal interpretations.

Abstract

Many empirical studies estimate causal effects in environments where economic units interact through spatial or network connections. In such settings, outcomes are jointly determined, and treatment induced shocks propagate across economically connected units. A growing literature highlights identification challenges in these models and questions the causal interpretation of estimated spillovers. This paper argues that the problem is more fundamental. Under interdependence, causal effects are not uniquely defined objects even when the interaction structure is correctly specified or consistently learned, and even under ideal identifying conditions. We develop a causal framework for firm-level economies in which interaction structures are unobserved but can be learned from predetermined characteristics. We show that learning the network, while necessary to model interdependence, is not sufficient for causal interpretation. Instead, causal conclusions hinge on explicit counterfactual assumptions governing how outcomes adjust following a treatment change. We formalize three economically meaningful counterfactual regimes partial equilibrium, local interaction, and network, consistent equilibrium, and show that standard spatial autoregressive estimates map into distinct causal effects depending on the counterfactual adopted. We derive identification conditions for each regime and demonstrate that equilibrium causal effects require substantially stronger assumptions than direct or local effects. A Monte Carlo simulation illustrates that equilibrium and partial-equilibrium effects differ mechanically even before estimation, and that network feedback can amplify bias when identifying assumptions fail. Taken together, our results clarify what existing spatial and network estimators can and cannot identify and provide practical guidance for empirical research in interdependent economic environments