Inference in Models of Discrete Choice with Social Interactions Using Network Data

Leung, Michael P.

doi:10.2139/ssrn.3446926

Cited by 5 publications

(11 citation statements)

References 53 publications

(97 reference statements)

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“…Since

R_{n}

has the form of a network HAC, we expect that it typically converges to the population variance of the unit‐level exposure effects, although this requires additional weak dependence conditions on the distributions of

Y_{i} false(bold-italicd false)

and A . Some such conditions are given in Theorem 4.2 of Leung (2019).…”

Section: Variance Estimationmentioning

confidence: 99%

Causal Inference Under Approximate Neighborhood Interference

Leung

2022

ECTA

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This paper studies causal inference in randomized experiments under network interference. Commonly used models of interference posit that treatments assigned to alters beyond a certain network distance from the ego have no effect on the ego's response. However, this assumption is violated in common models of social interactions. We propose a substantially weaker model of “approximate neighborhood interference” (ANI) under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, effect on the ego's response. We formally verify that ANI holds for well‐known models of social interactions. Under ANI, restrictions on the network topology, and asymptotics under which the network size increases, we prove that standard inverse‐probability weighting estimators consistently estimate useful exposure effects and are approximately normal. For inference, we consider a network HAC variance estimator. Under a finite population model, we show that the estimator is biased but that the bias can be interpreted as the variance of unit‐level exposure effects. This generalizes Neyman's well‐known result on conservative variance estimation to settings with interference.

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“…Since

R_{n}

Y_{i} false(bold-italicd false)

and A . Some such conditions are given in Theorem 4.2 of Leung (2019).…”

Section: Variance Estimationmentioning

confidence: 99%

Causal Inference Under Approximate Neighborhood Interference

Leung

2022

ECTA

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“…A further strand of literature to which we refer to is inference under interference. References include Aronow et al (2017), Forastiere et al (2016, Manski (2013), Leung (2019), Vazquez-Bare (2017), Li et al (2019), Athey et al (2018), Ogburn et al (2017), Goldsmith-Pinkham and Imbens (2013), Sävje et al (2017) among others. All these references discuss valid inferential procedure for treatment effects under interference, but they do not provide insights for variance-optimal designs.…”

Section: Related Literaturementioning

confidence: 99%

“…In this paper, instead, we consider the case where units are arbitrarily connected and locally dependent. Leung (2019) and Chin (2018) discusses the problem of inference under local interference while assuming independence of treatment assignments. On the other hand, in this paper, we show that the optimal randomization scheme naturally induces dependence on treatment assignments, which makes their result not applicable in the context under consideration.…”

Section: Related Literaturementioning

confidence: 99%

“…Under anonymous interactions and one-degree interference, potential outcomes are functions of their treatment assignment, the number of treated neighbors, the number of neighbors, and possibly unobservable characteristics. We assume that the marginal distribution of the unobservables does not depend on the network structure, similarly, for instance, to Leung (2019), whereas their joint distribution is allowed to depend on the network, allowing, for instance, for local dependence across units.…”

Section: Introductionmentioning

confidence: 99%

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Experimental Design under Network Interference

Viviano¹

2020

Preprint

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This paper discusses the problem of the design of experiments under network interference. We allow for a possibly fully connected network and a general class of estimands, which encompasses average treatment and average spillover effects, as well as estimands obtained from interactions of the two. We discuss a near-optimal design mechanism, where the experimenter optimizes over participants and treatment assignments to minimize the variance of the estimators of interest, using a first-wave experiment for estimation of the variance. We guarantee valid asymptotic inference on causal effects using either parametric or non-parametric estimators under the proposed experimental design, allowing for local dependence of potential outcomes, arbitrary dependence of the treatment assignment indicators, and spillovers across units. We showcase asymptotic optimality and finite-sample upper bounds on the regret of the proposed design mechanism. Simulations illustrate the advantage of the method over state-of-art methodologies.

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“…The key condition for our result is a restriction on the strength of strategic interactions. Leung (2019) used this condition to prove a CLT for graphical games. An analogous condition is used by Leung and Moon (2019) to obtain a CLT for network formation games.…”

Section: Graphical Gamesmentioning

confidence: 99%

Equilibrium computation in discrete network games

Leung

2020

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Counterfactual policy evaluation often requires computation of game‐theoretic equilibria. We provide new algorithms for computing pure‐strategy Nash equilibria of games on networks with finite action spaces. The algorithms exploit the fact that many agents may be endowed with types such that a particular action is a dominant strategy. These agents can be used to partition the network into smaller subgames whose equilibrium sets may be more feasible to compute. We provide bounds on the complexity of our algorithms for models obeying certain restrictions on the strength of strategic interactions. These restrictions are analogous to the assumption in the widely used linear‐in‐means model of social interactions that the magnitude of the endogenous peer effect is bounded below one. For these models, our algorithms have complexity O p ( n c ), where the randomness is with respect to the data‐generating process, n is the number of agents, and c depends on the strength of strategic interactions. We also provide algorithms for computing pairwise stable and directed Nash stable networks in network formation games.

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Inference in Models of Discrete Choice with Social Interactions Using Network Data

Cited by 5 publications

References 53 publications

Causal Inference Under Approximate Neighborhood Interference

Causal Inference Under Approximate Neighborhood Interference

Experimental Design under Network Interference

Equilibrium computation in discrete network games

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