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The Local Approach to Causal Inference under Network Interference

Eric Auerbach, Hongchang Guo, Max Tabord-Meehan

TL;DR

This paper develops a flexible nonparametric framework for causal inference when outcomes are affected by network interference, by encoding local network structure as rooted networks and treating the rooted-network as the effective treatment. It introduces a k-nearest-neighbors estimator for policy effects, proves finite-sample MSE bounds and asymptotic normality, and provides a permutation-based test for policy irrelevance within a multiple-networks setting. The empirical illustration on social favor exchange demonstrates how network structure—captured via local configurations—influences outcomes beyond simple exposure maps. Collectively, the approach generalizes exposure mapping, reduces misspecification risk, and offers practical tools for estimating and testing policy effects across sparse networks. The work advances causal inference in networks by combining a rigorous local topology with robust nonparametric estimation and hypothesis testing.

Abstract

We propose a new nonparametric modeling framework for causal inference when outcomes depend on how agents are linked in a social or economic network. Such network interference describes a large literature on treatment spillovers, social interactions, social learning, information diffusion, disease and financial contagion, social capital formation, and more. Our approach works by first characterizing how an agent is linked in the network using the configuration of other agents and connections nearby as measured by path distance. The impact of a policy or treatment assignment is then learned by pooling outcome data across similarly configured agents. We demonstrate the approach by deriving finite-sample bounds on the mean-squared error of a k-nearest-neighbor estimator for the average treatment response as well as proposing an asymptotically valid test for the hypothesis of policy irrelevance.

The Local Approach to Causal Inference under Network Interference

TL;DR

This paper develops a flexible nonparametric framework for causal inference when outcomes are affected by network interference, by encoding local network structure as rooted networks and treating the rooted-network as the effective treatment. It introduces a k-nearest-neighbors estimator for policy effects, proves finite-sample MSE bounds and asymptotic normality, and provides a permutation-based test for policy irrelevance within a multiple-networks setting. The empirical illustration on social favor exchange demonstrates how network structure—captured via local configurations—influences outcomes beyond simple exposure maps. Collectively, the approach generalizes exposure mapping, reduces misspecification risk, and offers practical tools for estimating and testing policy effects across sparse networks. The work advances causal inference in networks by combining a rigorous local topology with robust nonparametric estimation and hypothesis testing.

Abstract

We propose a new nonparametric modeling framework for causal inference when outcomes depend on how agents are linked in a social or economic network. Such network interference describes a large literature on treatment spillovers, social interactions, social learning, information diffusion, disease and financial contagion, social capital formation, and more. Our approach works by first characterizing how an agent is linked in the network using the configuration of other agents and connections nearby as measured by path distance. The impact of a policy or treatment assignment is then learned by pooling outcome data across similarly configured agents. We demonstrate the approach by deriving finite-sample bounds on the mean-squared error of a k-nearest-neighbor estimator for the average treatment response as well as proposing an asymptotically valid test for the hypothesis of policy irrelevance.

Paper Structure

This paper contains 34 sections, 13 theorems, 86 equations, 11 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Local configurations
  3. Informal description
  4. Formal definition
  5. Terminology and notation
  6. Rooted networks
  7. Econometric model
  8. Main specification
  9. Examples
  10. Parameters of interest
  11. Applications to causal inference
  12. Multiple-networks setting
  13. Estimating Policy Effects
  14. Estimator
  15. Bound on estimation error
  16. ...and 19 more sections

Key Result

Theorem 4.1

Under Assumptions ass:sampling, ass:no_ties, ass:m_smooth, and ass:var, where $\varphi_g(x) = \phi_g \circ \psi_g^{\dagger}(x)$, $\psi_g^{\dagger}:[0,1] \rightarrow \mathbb{R}_{+}$ refers to the upper generalized inverse and $U_{(k,C)}$ is distributed $Beta(k,C-k+1)$.

Figures (11)

  • Figure 1: Illustration of local configurations.
  • Figure 2: These three networks constitute the "cutlery ensemble." We use them to describe three different ways that agents can monitor each other in a social network. The first network on the left is the "knife" network rooted at agent $\alpha$. The second network in the middle is the "fork" network rooted at agent $\beta$. The third network on the right is the "spoon" network rooted at the agent $\gamma$.
  • Figure 3: Eight rooted networks truncated at radius $2,$ labeled $g_1$ to $g_8$.
  • Figure 4: Four rooted networks truncated at radius $2,$ labeled $g_3$, $g_4$, $g_9$, and $g_{0}$.
  • Figure 5: Estimated $\psi_g(\cdot)$ for $g_1$ to $g_8$ under different network formation models
  • ...and 6 more figures

Theorems & Definitions (33)

  • Example 3.1
  • Example 3.2
  • Example 3.3
  • Example 4.1
  • Example 4.2
  • Theorem 4.1
  • Corollary 4.1
  • Theorem 4.2
  • Corollary 4.2
  • Theorem 4.3
  • ...and 23 more