Causal Inference in Multilayered Networks Open Access

Abstract

Social and professional networks are critical to determining agents' choices in various contexts, ranging from innovation and trade to labor markets and educational achievement. The existence of network influences on decision-making processes can affect aggregate outcomes and the effects of policy intervention. Therefore, understanding whether network structures affect individuals' outcomes is relevant in social sciences such as economics, public health, sociology, and political science. However, empirically testing the existence of network effects with observational data becomes a challenge because of outstanding identification issues such as endogenous network formation. This dissertation provides novel methodologies to causally estimate network effects with observational data robust to network endogeneity issues. Differing from existing approaches, the methods I propose are semiparametric, do not require to specify a structural network formation model, and allow for the identification and estimation of heterogeneous network effects generated by different types of social/professional links.

The first chapter proposes a method to identify and estimate the linear model of peer effects parameters when a predetermined set of exogenous connections induce the observed interest network. The second chapter expands the results from the first chapter by allowing the possibility of multiple types of potentially endogenous networks to affect individual outcomes. I show that the identification of heterogeneous network effects is possible under the assumption that the dependence between individuals in the population vanishes with their distance in the network space. Finally, chapter three focuses directly on the process of determining the formation of network structures rather than their effect on outcomes. In particular, it provides a novel approach to identify and perform inference on the utility parameters of a network formation model with payoff externalities using observed network data. 

Table of Contents

1 Instrumental Network Estimation of Social Effects 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Peer Effects Model and Identification . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.5 Monte Carlo Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.6 Application to Publication Outcomes in Economics . . . . . . . . . . . . . . 25

1.6.1 Multiplex Network Data . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

1.8 Appendix: Proofs of Main Results . . . . . . . . . . . . . . . . . . . . . . . . 40

1.9 Appendix: Proofs of Auxiliary Results . . . . . . . . . . . . . . . . . . . . . 41

1.10 Appendix: Robustness and Additional Empirical Results . . . . . . . . . . . 47

2 Estimation of Multilayered Networks Effects with Observational Data 51

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.3 Multilayer Linear-in-Means (MLiM) Model . . . . . . . . . . . . . . . . . . . 60

2.3.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

2.4 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

2.4.1 Multilayer Measure of Distance . . . . . . . . . . . . . . . . . . . . . 66

2.4.2 Network Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

2.4.3 Example of a Network Formation Model . . . . . . . . . . . . . . . . 75

2.4.4 Identification Result . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

2.5 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

2.5.1 Covariance Matrix Estimation . . . . . . . . . . . . . . . . . . . . . . 95

2.6 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

2.7 Application to Publication Outcomes in Economics . . . . . . . . . . . . . . 99

2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

2.9 Appendix: Proofs of Main Results . . . . . . . . . . . . . . . . . . . . . . . . 106

2.10 Appendix: Proofs of Auxiliary Results . . . . . . . . . . . . . . . . . . . . . 109

2.11 Appendix: Multilayer Shortest Path Algorithms . . . . . . . . . . . . . . . . 121

2.12 Appendix: Additional Simulation and Estimation Results . . . . . . . . . . 123

3 Inference in Network Formation Models with Payoff Externalities 129

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

3.2 Network Formation Model and Identification . . . . . . . . . . . . . . . . . . 134

3.2.1 Network Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

3.2.2 Population Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 137

3.2.3 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

3.3 Bayesian Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

3.3.1 Simplified Version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

3.3.2 Full algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

3.3.3 Composite Likelihood Function . . . . . . . . . . . . . . . . . . . . . 158

3.4 Empirical Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

3.4.1 Network Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

3.4.2 Data on Individual Characteristics . . . . . . . . . . . . . . . . . . . 163

3.4.3 Subgraphs and Selection Probabilities . . . . . . . . . . . . . . . . . . 163

3.4.4 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

3.6 Appendix: Proofs of Main Results . . . . . . . . . . . . . . . . . . . . . . . 169

3.7 Appendix: Equilibrium in Directed Networks . . . . . . . . . . . . . . . . . 173 

About this Dissertation

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School	Laney Graduate School
Department	Economics
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Economics, General Economics, Theory Statistics
Keyword	Multidimensional Networks Data Network formation Peer Effects Bayesian Estimation Causal Inference Instrumental Variables
Committee Chair / Thesis Advisor	Kim P. Huynh, Bank of Canada David T. Jacho-Chavez, Emory University
Committee Members	Kyungmin (Teddy) Kim, Emory University Elena Pesavento, Emory University Christoph Breunig, Emory University

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