Network Regressions and Supervised Centrality Estimation - Supplemental Materials of Proof

41 Pages Posted: 3 Feb 2022

See all articles by Junhui Cai

Junhui Cai

University of Notre Dame - Mendoza College of Business

Dan Yang

The University of Hong Kong

Wu Zhu

School of Economics and Management, Tsinghua University

Haipeng Shen

The University of Hong Kong - Faculty of Business and Economics

Linda Zhao

University of Pennsylvania - Statistics Department

Date Written: November 15, 2021

Abstract

Networks are ubiquitous and play a crucial role in our lives. The position of an agent in the network, usually captured by the “centrality”, has implications for the agent’s behavior and serves as an important intermediary of network effects. Therefore, the centrality is often incorporated in regression models to elucidate the network effect on an outcome variable of interest. In empirical studies, researchers often adopt a two-stage procedure to estimate the centrality and to infer the network effect – they first estimate the centrality from the observed network and then employ the estimated centrality in the regression for estimation and inference. Despite its prevalent adoption, this naive two-stage procedure lacks theoretical backing and can fail in both estimation and inference. We therefore propose a unified framework that combines a network model and a network regression model, under which we prove the shortcomings of the two-stage in centrality estimation and the undesirable consequences in the network regression. We then propose a novel supervised network centrality estimation (Su- perCENT) methodology that simultaneously combines the information from the two models. SuperCENT dominates the two-stage procedure in the estimation of the centrality and the true underlying network universally. In addition, SuperCENT yields superior estimation of the network effect and provides valid and narrower confidence intervals than those from the two-stage. We apply our method to predict the currency risk premium based on the global trade network. We show that a trading strategy based on SuperCENT centrality estimates yields a return three times as high as the two-stage method, and the inference drawn by SuperCENT verifies an economic theory via a rigorous statistical testing while the two-stage procedure cannot.

Suggested Citation

Cai, Junhui and Yang, Dan and Zhu, Wu and Shen, Haipeng and Zhao, Linda, Network Regressions and Supervised Centrality Estimation - Supplemental Materials of Proof (November 15, 2021). Available at SSRN: https://ssrn.com/abstract=3963526 or http://dx.doi.org/10.2139/ssrn.3963526

Junhui Cai

University of Notre Dame - Mendoza College of Business

Mendoza college of business
University of Notre Dame
Notre Dame, IN 46556-5646
United States

Dan Yang

The University of Hong Kong ( email )

Pokfulam Road
Hong Kong
China

Wu Zhu (Contact Author)

School of Economics and Management, Tsinghua University ( email )

Beijing, PA 19104
China

Haipeng Shen

The University of Hong Kong - Faculty of Business and Economics ( email )

Hong Kong

Linda Zhao

University of Pennsylvania - Statistics Department ( email )

Wharton School
Philadelphia, PA 19104
United States

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