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Evaluating Policy Effects under Network Interference without Network Information: A Transfer Learning Approach

Tadao Hoshino

TL;DR

The paper tackles evaluating policy effects when network spillovers matter but the target network is unobserved. It transfers ATTE from a source with a known network and guards against misspecification by bounding the target ATTE within a $(\delta,q)$-Wasserstein ball around a baseline degree distribution, using a tractable LP characterization. Estimation rests on a varying-coefficient kernel model to recover $m(g,x)$, with inference via a functional delta method and a dependent wild bootstrap; an empirical demonstration with Cai et al. (2015) shows informative bounds even with unobserved networks. The approach offers a practical, robust way to quantify policy effects under network interference in large-scale settings where full network data are infeasible, while highlighting limitations and avenues for future refinement.

Abstract

This paper develops a sensitivity analysis framework that transfers the average total treatment effect (ATTE) from source data with a fully observed network to target data whose network is completely unknown. The ATTE represents the average social impact of a policy that assigns the treatment to every individual in the dataset. We postulate a covariate-shift type assumption that both source and target datasets share the same conditional mean outcome. However, because the target network is unobserved, this assumption alone is not sufficient to pin down the ATTE for the target data. To address this issue, we consider a sensitivity analysis based on the uncertainty of the target network's degree distribution, where the extent of uncertainty is measured by the Wasserstein distance from a given reference degree distribution. We then construct bounds on the target ATTE using a linear programming-based estimator. The limiting distribution of the bound estimator is derived via the functional delta method, and we develop a wild bootstrap approach to approximate the distribution. As an empirical illustration, we revisit the social network experiment on farmers' weather insurance adoption in China by Cai et al. (2015).

Evaluating Policy Effects under Network Interference without Network Information: A Transfer Learning Approach

TL;DR

The paper tackles evaluating policy effects when network spillovers matter but the target network is unobserved. It transfers ATTE from a source with a known network and guards against misspecification by bounding the target ATTE within a -Wasserstein ball around a baseline degree distribution, using a tractable LP characterization. Estimation rests on a varying-coefficient kernel model to recover , with inference via a functional delta method and a dependent wild bootstrap; an empirical demonstration with Cai et al. (2015) shows informative bounds even with unobserved networks. The approach offers a practical, robust way to quantify policy effects under network interference in large-scale settings where full network data are infeasible, while highlighting limitations and avenues for future refinement.

Abstract

This paper develops a sensitivity analysis framework that transfers the average total treatment effect (ATTE) from source data with a fully observed network to target data whose network is completely unknown. The ATTE represents the average social impact of a policy that assigns the treatment to every individual in the dataset. We postulate a covariate-shift type assumption that both source and target datasets share the same conditional mean outcome. However, because the target network is unobserved, this assumption alone is not sufficient to pin down the ATTE for the target data. To address this issue, we consider a sensitivity analysis based on the uncertainty of the target network's degree distribution, where the extent of uncertainty is measured by the Wasserstein distance from a given reference degree distribution. We then construct bounds on the target ATTE using a linear programming-based estimator. The limiting distribution of the bound estimator is derived via the functional delta method, and we develop a wild bootstrap approach to approximate the distribution. As an empirical illustration, we revisit the social network experiment on farmers' weather insurance adoption in China by Cai et al. (2015).
Paper Structure (17 sections, 4 theorems, 83 equations, 4 figures, 2 tables, 2 algorithms)

This paper contains 17 sections, 4 theorems, 83 equations, 4 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Paper organization
  3. Problem Setup
  4. The Linear Programming Problem
  5. A linear-programming characterization of ATTE
  6. Examples of degree distributions
  7. Estimation and Asymptotic Properties
  8. Estimation
  9. Asymptotic properties
  10. Monte Carlo Simulation
  11. An Empirical Illustration
  12. Conclusion
  13. Technical Appendix
  14. Derivation of the dual problem (\ref{['eq:dual']})
  15. The dual problem of Example \ref{['exp:simple']}
  16. ...and 2 more sections

Key Result

Proposition 3.1

Suppose that $m(v,x)$ is bounded uniformly in $(v,x) \in \mathcal{G} \times \mathcal{X}$. Then, for any $q \in [1, \infty)$ and $\delta > 0$,

Figures (4)

  • Figure 3.1: Upper and lower bounds of $\kappa^\mathcal{J}$
  • Figure 3.2: Real data examples of degree distribution
  • Figure 6.1: Conditional degree distributions
  • Figure 6.2: Estimated coefficient functions

Theorems & Definitions (9)

  • Remark 2.1: Separating the direct and spillover effects
  • Definition 3.1: $q$-Wasserstein distance
  • Example 3.1
  • Remark 3.1: Non-uniqueness of the solution
  • Remark 3.2: Interpretation of $\delta$
  • Proposition 3.1: Dual problem
  • Proposition 4.1: Asymptotic normality of $\widehat{\beta}$ and $\widehat{m}$
  • Theorem 4.1: Asymptotic distribution of $\widehat{\overline{\kappa}}_{\delta, q}$
  • Theorem 4.2: Validity of the wild bootstrap