Econometrics of network models

Paula, Áureo de

doi:10.1920/wp.cem.2016.0616

Cited by 19 publications

(15 citation statements)

References 46 publications

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“…This review complements other available overviews within econometrics by Graham (2015), Chandrasekhar (2015), de Paula (2017) and Graham (forthcoming). In particular, it follows closely (but expands upon) previous surveys in de Paula (2017) and corresponding material in Graham and de Paula (2020).…”

Section: Introductionsupporting

confidence: 81%

Econometric Models of Network Formation

Paula

2020

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This article provides a selective review on the recent literature on econometric models of network formation. The survey starts with a brief exposition on basic concepts and tools for the statistical description of networks. I then offer a review of dyadic models, focussing on statistical models on pairs of nodes and describe several developments of interest to the econometrics literature. The article also presents a discussion of nondyadic models where link formation might be influenced by the presence or absence of additional links, which themselves are subject to similar influences. This is related to the statistical literature on conditionally specified models and the econometrics of game theoretical models. I close with a (non-exhaustive) discussion of potential areas for further development.

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Section: Introductionsupporting

confidence: 81%

Econometric Models of Network Formation

Paula

2020

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“…Secondly, it would be interesting to extend our approach to situations where players endogenously form pairs or groups in an unobserved manner to the researcher. Our approach might be extended to such situations, in combination with recent developments on network formation models (see de Paula, 2017). Thirdly, it may be beneficial to develop treatment evaluation techniques under treatment decision games of incomplete information.…”

Section: Resultsmentioning

confidence: 99%

Treatment Eﬀect Models with Strategic Interaction in Treatment Decisions

Hoshino

Yanagi

2018

SSRN Journal

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We develop identification and estimation methods for treatment effect models with strategic interaction in the treatment decisions. We consider models where one's treatment choice and outcome can be endogenously affected by others' treatment choices. We formulate the interaction of the treatment decisions as a two-player complete information game with potential multiple equilibria. For this model, using a latent index framework and the assumption of a stochastic equilibrium selection rule, we prove that the marginal treatment effect from one's own treatment and that from his/her partner's can be separately point-identified with potential over-identifiability. Based on our constructive identification results, we propose a two-step semiparametric procedure for estimating the marginal treatment effects using series approximation. The proposed estimator is shown to be uniformly consistent and asymptotically normal. As an empirical illustration, we investigate the impacts of risky behaviors on adolescents' academic performance.1 To the best of our knowledge, few studies address treatment evaluation in the presence of strategic interaction, where the treatment decisions are explicitly modeled as games. One important exception is Balat and Han (2018), who mainly investigate the partial identification of average treatment effects (ATE). Thus, our main parameters of interest (MTE) are different from theirs (ATE). In addition, the key identification assumptions in Balat and Han (2018) are shape restrictions on the conditional mean outcome functions, while we mainly rely on a stochastic equilibrium selection rule, as stated below.2 As another related work, Mogstad et al. (2019) introduce partial monotonicity to deal with issues due to multiple instruments. However, partial monotonicity is not designed for settings with multivalued or multidimensional treatments such as our situation.

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“…As discussed by de Paula et al (2017b), the identification condition is closely linked to the sparsity of the network. We say that a network is sparse if it is not dense, where dense means that the number of links is O(m).…”

Section: Sparsitymentioning

confidence: 99%

“…The assumption thatχ ij,ik (θ ) = 0 whenever max{d(i, j ), d(i, k)} >d implies that the individuals cannot receive positive payoffs from an infinite number of links, and it ensures that h ij (W m,−ij , θ) < ∞. 8 Note that this is weaker than assuming that individuals only have a finite number of links, as for instance in de Paula et al (2017a). Indeed, at this point, individuals can have an infinite number of links; however, only a finite number of those links can affect the payoff of any particular link.…”

Section: Introductionmentioning

confidence: 99%

“…As the data requirement is large, the computational burden is also important.Accordingly, many recent approaches only require the observation of a single network, at one point in time; see, e.g. Graham (2017) Leung (2014Leung ( , 2015 and de Paula et al (2017a). In particular, a significant part of that literature focuses on ERGMs, which we formally define in the next section.…”

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confidence: 99%

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My friend far, far away: a random field approach to exponential random graph models

Boucher

Mourifié

2017

The Econometrics Journal

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We explore the asymptotic properties of strategic models of network formation in very large populations. Specifically, we focus on (undirected) exponential random graph models. We want to recover a set of parameters from the individuals' utility functions using the observation of a single, but large, social network. We show that, under some conditions, a simple logit-based estimator is coherent, consistent and asymptotically normally distributed under a weak version of homophily. The approach is compelling as the computing time is minimal and the estimator can be easily implemented using pre-programmed estimators available in most statistical packages. We provide an application of our method using the Add Health database.Exponential random graph models S15 formed, the estimated influence of peers is likely to be biased. 2 An understanding of how the networks are formed could allow us to control for this endogeneity, and it might suggest policy instruments that would help to influence network formation processes.In this paper, we use the network formation model of Mele (2017), for which the joint distribution is an exponential random graph model (ERGM). The estimation of ERGMs is typically challenging because of the intractable denominator of the joint distribution. We use random field theory to provide a simple pseudo maximum likelihood estimator (MLE), as in Besag (1975) and Strauss and Ikeda (1990), based on the product of the conditional distributions. To our knowledge, this paper is the first to apply random field theory to empirical models of network formation. The approach is promising and has been recently employed by Leung (2014) in a similar context. Our approach only requires the observation of a single, potentially very large, network.Our model allows for a large set of admissible preferences, which are characterized by intuitive conditions. Specifically, we show that our estimator is consistent and asymptotically normally distributed, provided that individuals' preferences exhibit a weak version of homophily. Homophily is one of the most robust empirical characteristics of social networks. It formalizes the observation that similar individuals are more likely to interact with each other. As homophily is featured in both theoretical -see, e.g. Boucher (2015), Bramoullé et al. (2012) and Currarini et al. (2009, 2010) -and empirical -see, e.g. Mele (2017) and Christakis et al. ( 2010) models of network formation, our methodology is applicable to many existing models of network formation. We apply this new methodology to the formation of friendship networks by US teenagers.A fundamental challenge in estimating a network formation process is the highly dependent nature of most socio-economic relationships. Consider a friendship: the probability that Alice and Bob are friends depends on their individual characteristics. However, it can also depend on Bob's friendship with Charlotte (who perhaps does not like Alice). The probability that Alice and Bob are friends might then depend on Charlotte's individual c...

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Econometrics of network models

Cited by 19 publications

References 46 publications

Econometric Models of Network Formation

Econometric Models of Network Formation

Treatment Eﬀect Models with Strategic Interaction in Treatment Decisions

My friend far, far away: a random field approach to exponential random graph models

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