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Limit Theorems for Network Dependent Random Variables

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  • Denis Kojevnikov
  • Vadim Marmer
  • Kyungchul Song

Abstract

This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly transformed variables. We provide a law of large numbers and central limit theorem for network dependent variables. We also provide a method of calculating standard errors robust to general forms of network dependence. For that purpose, we rely on a network heteroskedasticity and autocorrelation consistent (HAC) variance estimator, and show its consistency. The results rely on conditions characterized by tradeoffs between the rate of decay of dependence across a network and network's denseness. Our approach can accommodate data generated by network formation models, random fields on graphs, conditional dependency graphs, and large functional-causal systems of equations.

Suggested Citation

  • Denis Kojevnikov & Vadim Marmer & Kyungchul Song, 2019. "Limit Theorems for Network Dependent Random Variables," Papers 1903.01059, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:1903.01059
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    Cited by:

    1. Ruonan Xu, 2023. "Difference-in-Differences with Interference," Papers 2306.12003, arXiv.org, revised May 2024.
    2. Kojevnikov, Denis & Song, Kyungchul, 2023. "Econometric inference on a large bayesian game with heterogeneous beliefs," Other publications TiSEM aca0631e-4f8a-45c7-af3a-4, Tilburg University, School of Economics and Management.
    3. Clemens Possnig & Andreea Rotu{a}rescu & Kyungchul Song, 2022. "Estimating Dynamic Spillover Effects along Multiple Networks in a Linear Panel Model," Papers 2211.08995, arXiv.org.
    4. Denis Kojevnikov, 2021. "The Bootstrap for Network Dependent Processes," Papers 2101.12312, arXiv.org.
    5. Michael P. Leung, 2019. "Inference in Models of Discrete Choice with Social Interactions Using Network Data," Papers 1911.07106, arXiv.org.
    6. Kojevnikov, Denis & Song, Kyungchul, 2023. "Some impossibility results for inference with cluster dependence with large clusters," Other publications TiSEM 80b8e4ed-54bc-4a34-883f-f, Tilburg University, School of Economics and Management.
    7. Christis Katsouris, 2024. "Robust Estimation in Network Vector Autoregression with Nonstationary Regressors," Papers 2401.04050, arXiv.org.
    8. Tadao Hoshino & Takahide Yanagi, 2021. "Causal Inference with Noncompliance and Unknown Interference," Papers 2108.07455, arXiv.org, revised Oct 2023.
    9. Davide Viviano, 2020. "Experimental Design under Network Interference," Papers 2003.08421, arXiv.org, revised Jul 2022.
    10. Michael P. Leung, 2022. "Causal Inference Under Approximate Neighborhood Interference," Econometrica, Econometric Society, vol. 90(1), pages 267-293, January.
    11. Nathan Canen & Ko Sugiura, 2022. "Inference in Linear Dyadic Data Models with Network Spillovers," Papers 2203.03497, arXiv.org, revised Jun 2023.
    12. Kojevnikov, Denis & Song, Kyungchul, 2023. "Econometric inference on a large Bayesian game with heterogeneous beliefs," Journal of Econometrics, Elsevier, vol. 237(1).
    13. Kojevnikov, Denis & Song, Kyungchul, 2023. "Some impossibility results for inference with cluster dependence with large clusters," Journal of Econometrics, Elsevier, vol. 237(2).
    14. Christian Cox & Akanksha Negi & Digvijay Negi, 2022. "Risk-Sharing Tests with Network Transaction Costs," Monash Econometrics and Business Statistics Working Papers 5/22, Monash University, Department of Econometrics and Business Statistics.
    15. Michael P. Leung & Pantelis Loupos, 2022. "Graph Neural Networks for Causal Inference Under Network Confounding," Papers 2211.07823, arXiv.org, revised Mar 2024.
    16. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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