[Paper Review] Identification and Inference of Network Formation Games with Misclassified Links

Luis E. Candelaria, Takuya Ura|arXiv (Cornell University)|Apr 26, 2018

Game Theory and ApplicationsDecision Sciences18 references4 citations

TL;DR

This paper develops a robust identification and inference method for network formation games under link misclassification, using moment conditions to characterize the identified set of preference parameters for homophily and network externalities. The approach enables asymptotically valid inference in large networks despite misclassified links, validated through an empirical application to a rural Indian lending network.

ABSTRACT

This paper considers a network formation model when links are potentially misclassified. We focus on a game-theoretical model of strategic network formation with incomplete information, in which the linking decisions depend on agents' exogenous attributes and endogenous network characteristics. In the presence of link misclassification, we derive moment conditions that characterize the identified set for the preference parameters associated with homophily and network externalities. Based on the moment equality conditions, we provide an inference method that is asymptotically valid when a single network of many agents is observed. Finally, we apply our misclassification-robust method to study the preference parameters of a lending network in rural villages in southern India.

Motivation & Objective

• To address the lack of methods for identifying and inferring structural parameters in strategic network formation models when links are misclassified.
• To model link misclassification as conditionally random, affecting both the outcome (link formation) and the belief system used in equilibrium.
• To derive moment conditions that characterize the identified set of preference parameters under misclassification, ensuring robustness to measurement error.
• To develop an asymptotically valid inference procedure for a single large network, controlling for size even when parameters are partially identified.
• To apply the method to a real-world lending network in southern India, assessing the impact of misclassification on estimated preferences.

Proposed method

• Derives moment equality conditions linking observed link probabilities to unobserved beliefs and structural parameters, enabling identification under misclassification.
• Uses a latent index model where the true link formation decision depends on observed attributes, network statistics, and unobserved shocks.
• Characterizes the relationship between observed (misclassified) links and the underlying belief system via Lemma 2, enabling reduction to a single-agent decision model.
• Imposes a conditional misclassification model (Assumption 3) where misclassification probabilities depend on link status but are conditionally random.
• Proposes a computationally feasible confidence interval procedure that controls size under partial identification, using a profiled empirical likelihood approach.
• Generalizes the model to allow for covariate-dependent misclassification in Appendix B, increasing practical applicability.

Experimental results

Research questions

• RQ1 How does link misclassification affect the identification of preference parameters in strategic network formation models?
• RQ2 What moment conditions can be used to characterize the identified set of structural parameters when links are misclassified?
• RQ3 Can valid inference be conducted asymptotically when only a single large network is observed under misclassification?
• RQ4 How do false positives and false negatives in link data affect estimated preferences for reciprocity, homophily, and network externalities?
• RQ5 To what extent do standard inference methods break down under link misclassification, and how can they be corrected?

Key findings

• Even with significant misclassification (e.g., up to 90% false positives), the method correctly identifies that reciprocation, gender homophily, and kinship are the primary drivers of lending decisions in the rural Indian network.
• The 95% confidence interval for the reciprocation parameter remains within [0.500, 1.676] even under 90% false positive misclassification, indicating robustness.
• The length of the confidence interval for the 'same family' parameter increases by a factor of 20.987 under 90% false positives, reflecting higher uncertainty for this parameter.
• The confidence interval for 'supported trust' widens from 97.32 to 110.258 under 90% misclassification, showing increased imprecision but still capturing the true parameter range.
• The method maintains valid coverage even under partial identification, with the confidence interval size increasing systematically with misclassification rates.
• Empirical results confirm that homophily on gender and kinship, along with reciprocity, remain the most important determinants of lending behavior, even when link data is noisy.