The Econometric Analysis of Network Data

Description

The Econometric Analysis of Network Data serves as an entry point for advanced students, researchers, and data scientists seeking to perform effective analyses of networks, especially inference problems. It introduces the key results and ideas in an accessible, yet rigorous way. While a multi-contributor reference, the work is tightly focused and disciplined, providing latitude for varied specialties in one authorial voice. Contents Preface List of contributors 1 Introduction Paths, distance and diameter Measuring homophily Measuring agent centrality Degree centrality Refinements of degree centrality PageRank PageRank and the social multiplier Katz-Bonacich centrality Outdegree-based centrality measures References 2 Dyadic regression 2.1 Population and sampling framework Sampling assumption 2.2 Composite likelihood 2.3 Limit distribution Variance calculation Variance estimation Limit distribution 2.4 Empirical illustration Monte Carlo experiment 2.5 Further reading 2.A Derivations References 3 Strategic network formation 3.1 Basic ingredients of the environment 3.2 Relation to empirical games 3.3 Network formation 3.3.1 Iterative network formation 3.3.2 Non-iterative network formation 3.4 Concluding remarks References 4 Testing for externalities in network formation using simulation A strategic network formation game with transfers Test formulation Similarity of the test Choosing the test statistic Simulating undirected networks with fixed degree The algorithm Importance sampling Illustration using the Nyakatoke network References 5 Econometric analysis of bipartite networks 5.1 Introduction Scope of the paper and outline 5.2 Bipartite network models: the linear case 5.2.1 Bipartite networks Linear model Example 1: matched employer-employee data Example 2: buyer/seller network 5.2.2 Fixed effects: the AKM estimator Statistical properties 5.2.3 Random-effect approaches 5.2.3.1 Conditionally independent random effects 5.2.3.2 Random effects and network formation Illustration on simulated data 5.2.3.3 One-sided random effects Identification 5.3 Identification in nonlinear models 5.3.1 Motivation for nonlinearity 5.3.2 Identification in one-sided random effects 5.3.3 Identification in two-sided random effects 5.4 Estimation in nonlinear models 5.4.1 Fixed-effect and random-effect approaches 5.4.2 Discrete heterogeneity I: finite mixture methods 5.4.3 Discrete heterogeneity II: classification-based methods Two-step grouped fixed effects Co-clustering Illustration on simulated data (cont.) 5.5 Endogenous link formation and network dynamics 5.5.1 A static model of network formation 5.5.2 Network dynamics and externalities 5.6 Conclusion References 6 An empirical model for strategic network formation 6.1 Introduction 6.2 Set up 6.3 Exponential random graph and strategic network formation models 6.3.1 Exponential random graph models 6.3.2 Strategic network formation models 6.4 The model 6.4.1 Opportunities for establishing links 6.4.2 Link formation 6.4.3 Preferences 6.4.4 The likelihood function 6.5 Markov-chain-Monte-Carlo methods 6.5.1 Drawing from the posterior distribution of the parameters given the augmented data 6.5.2 Updating the sequence of opportunities 6.6 An application to high school friendships 6.6.1 Data 6.6.2 Estimation and inference 6.6.3 Goodness of fit 6.6.4 The effect of single-sex classrooms on network formation 6.7 Conclusion References 7 Econometric analysis of models with social interactions 7.1 Introduction 7.2 Identification of models of social interactions 7.2.1 The linear-in-means model 7.2.2 Non-linear models 7.2.3 Response functions 7.2.4 Treatment effects mediated through networks 7.2.4.1 Identification with random assignment of treatment 7.2.4.2 Identification without random assignment of treatment 7.2.5 Other approaches to identification 7.3 Specification of models of social interactions 7.3.1 Empirical individual treatment response 7.3.2 Empirical group treatment response 7.3.3 Recap 7.3.4 Immunization and infectious disease with social interaction 7.3.4.1 Models of the decision whether to get immunized 7.3.4.2 Models of health outcomes 7.4 Policy relevance of models of social interactions References 8 Many player asymptotics for large network formation problems 8.1 Introduction 8.2 Model 8.2.1 Data 8.2.2 Link preferences 8.2.3 Network statistics 8.2.4 Payoff specification 8.2.5 Solution concept 8.2.6 Tâtonnement and equilibrium selection 8.3 Many player asymptotics for economic models 8.3.1 Asymptotic sequence 8.3.2 Cross-sectional dependence 8.3.3 Asymptotic independence of ηij and Wi( D*) 8.3.4 Limiting approximations to model components 8.3.4.1 Approximations for discrete choice from large sets of alternatives 8.3.4.2 Inclusive values 8.3.4.3 Distribution of network variables 8.3.4.4 Fixed-point convergence 8.4 Limiting model 8.4.1 Link frequency distribution 8.4.2 Unique edge-level response 8.4.3 Equilibrium selection 8.4.4 Convergence results 8.5 Identification and estimation 8.5.1 Identification Identification of the reference distribution Identification of payoff functions 8.5.2 Maximum likelihood estimation 8.6 Conclusion 8.A Bounds for set-valued edge-level response 8.A.1 Set-valued edge-level response 8.A.2 Set estimation and bounds 8.B Convergence of link formation probabilities to logit References Index