We develop a finite-sample valid inference procedure for strategic network formation models in which linking decisions depend on endogenous network statistics (say, the number of common friends). Only a single network is required to be observed, and we restrict neither its density, nor the dependence structure induced by strategic interaction, nor the equilibrium selection mechanism. We exploit a bounding-by-c technique to construct a set of sandwich inequalities that are valid realization by realization, with the middle term involving only the i.i.d. pairwise error. We then average the sandwich inequalities over cells of exogenous covariates, and obtain identifying restrictions under a nonstandard pathwise limit formulation. For inference, we construct test statistics whose finite-sample uncertainty can be controlled by statistics of the exogenous covariates and errors alone, whose conditional distributions are exactly simulable in both semiparametric and parametric settings. Our proposed inference procedure is also computationally tractable, with no need to solve, simulate, or enumerate equilibrium network structures. In simulations, our procedure easily scales to networks of size 10,000, and yields confidence sets that certifies the sign of the strategic coefficient. In two empirical applications (with network size about 300~9500), we find statistical evidence for positive link interdependence at 95% confidence level.
We develop a novel method of inference for network-dependent high-dimensional random vectors. Dependence is characterized via a functional dependence measure based on graph distance, allowing the approximation theory to capture the interaction between the decay of dependence and the growth of network neighborhoods. We establish Gaussian approximation results for the maximum norm under finite-moment and sub-Weibull conditions, providing explicit conditions under which the dimension may increase with the network size. We also propose a high-dimensional network HAC covariance estimator and establish its convergence properties, yielding a feasible procedure for simultaneous inference. Simulation studies demonstrate favorable finite-sample performance of the proposed method. We apply the procedure to study how spillover effects vary with an index of network homophily by constructing confidence bands for the conditional spillover-effect function. The application reveals heterogeneity and local significance that would be obscured by conventional low-dimensional inference.
Estimating causal effects under network interference typically assumes that the network used for training and the network used for deployment coincide. In practice, an intervention is run on one population while the question of interest concerns a different population, and the two generally differ in topology, node-covariate composition, and spillover pathways. Transporting a causal effect across networks is therefore a data-fusion problem that no existing algorithm solves. We employ a selection diagram, extended to the network setting so that covariate shift and structural network shift enter as separate selectors, and derive from it a transport formula for the direct, spillover, and total effects in the deployment population. Each formula makes explicit which interventional mechanism is assumed invariant and which observational distribution must be reweighted. We then turn the formulas into TranCE (Transported Causal Effects), a doubly-robust algorithm combining an interventional outcome model, a domain density-ratio correction, and cross-fitted inference. Extensive experiments on two semi-synthetic benchmarks derived from real-world social networks and on a fully real weather-insurance field experiment, where the transported effects are checked against held-out randomized estimates, confirm the effectiveness of our approach. Our findings have the potential to improve intervention strategies in networked systems, particularly in social networks and public health.
Xiaojing Du, Jiuyong Li, Lin Liu et al.· 0 citations
Economic policies rarely affect only their direct targets. To study these spillovers, researchers summarize who else was treated with a simple exposure measure, such as the share of treated neighbors within a radius. But for many settings, economic theory provides little guidance on choosing the functional form (e.g., ring) of that measure or its parameters (e.g., radius). We show that the data can inform both choices. Correctly specified exposure measures imply orthogonality conditions that can be used for both estimation and testing. We establish consistency and asymptotic normality of the resulting estimator under spatial and network dependence in a design-based framework, with all randomness arising from treatment assignment. We then characterize the efficient moment conditions. Applied to two large-scale anti-poverty programs, the framework supports some prior radius estimates but rejects others. In the latter case, the revised radius yields substantively different policy-effect estimates.
This work forms a correction-aware network model that tracks susceptible, exposed, infectious, and corrected agents and derive its early-invasion condition for heterogeneous communication networks, and couple this propagation model to an analytic majority-vote benchmark in which a clean-task reliability target imposes a minimum connectivity requirement.
Analysis of experimental data becomes challenging when the underlying population is connected by a network. Exposure mapping is a common tool in the literature for defining and estimating spillover effects. These mappings reduce the dimensionality of the estimand, thereby facilitating identifiability. It is assumed that this mapping is correctly specified, leaving the choice of the exposure mapping to the analyst. This makes estimators of the spillover effect, such as the Horvitz-Thompson estimator, vulnerable to bias from model misspecification. Although these estimators have been shown to be robust to certain forms of controlled misspecification, there has been relatively little methodological progress in empirically investigating appropriate exposure mappings. In this paper, we propose a novel design-based model specification framework for causal inference. Building on this, we develop a randomization-testing procedure to assess the correct specification of an exposure-mapping model in the presence of network interference. We provide theoretical guarantees for the asymptotic validity of the proposed testing procedure. We establish the favorable power properties of our method through an extensive simulation study and illustrate it in a field experiment investigating the effect of anti-conflict norms among adolescents.
Experimental design under network interference is challenging because outcomes may depend on the treatment assignments of neighboring units. Existing approaches account for network structure but are typically assessed on small or simplified networks, limiting their applicability to complex real-world settings. We propose a network-aware treatment allocation framework that jointly accounts for allocation balance and network topology via an optimality criterion based on the Fisher information matrix. To address the resulting combinatorial optimization problem, we develop an efficient local search algorithm that scales to large networks. We further study the causal properties of the resulting designs by examining the estimation of total, direct, and indirect treatment effects in the presence of interference. Simulation studies across a range of random graph models, including Erd\H{o}s--R\'enyi, geometric random graphs, preferential attachment, and stochastic block models, illustrate how network topology influences optimal treatment allocations. Applications to college housing and ego-Facebook networks demonstrate the practical advantages of topology-aware experimental designs.