Simultaneous Equations Models with Limited Dependent Variables and Social Interactions

Zhou, Sutianjie

Graduate Thesis Or Dissertation

Simultaneous Equations Models with Limited Dependent Variables and Social Interactions Public Deposited

Analytics

Citations

Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/9z9031571

Abstract

My dissertation studies the behaviors of agents engaged in interconnected activities within a social network. This research comprehensively analyzes how agents' decisions across multiple activities are influenced by those of their peers. I characterize the Bayesian Nash Equilibrium of the underlying network game and provide a sufficient condition for the existence and uniqueness of the equilibrium. I also propose a computationally feasible estimation method to recover the structural parameters and investigate its finite sample performance through Monte Carlo simulations.

The first chapter, ''Simultaneous Equations with Censored Outcomes and Social Interactions,'' considers a simultaneous equations model where agents participate in multiple activities with censored outcomes. An agent's decision in an activity depends on not only their latent incentives in other activities but also their rational expectation of other agents' decisions in all related activities. The second chapter, ''Simultaneous Equations with Limited Dependent Variables and Social Interactions,'' further extends this model to allow the observed outcome in different activities to be continuous, censored, or binary. I provide a microfoundation of the econometric model and derive a sufficient condition for the existence and uniqueness of the equilibrium. I propose a two-stage estimation procedure for the model, where I estimate the reduced form parameter using the nested pseudo-likelihood method in the first stage and recover the structural parameters from the reduced form parameters in the second stage. I establish the asymptotic properties of the proposed estimator and conduct Monte Carlo simulations to study its finite sample performance.

The third chapter, ''A Simultaneous Equation Tobit Model with Social Interactions,'' considers a similar model to the first chapter. The key difference is that we assume an agent's decision in an activity depends on their actual decisions instead of latent incentives in other activities. This introduces an additional complication to the analysis as it becomes impossible to derive the reduced form of the structural model. Hence, instead of using the two-stage estimation procedure developed in the first two chapters, I propose a new estimator that directly estimates the structural parameters. I show in Monte Carlo simulations that the new estimator works well in finite samples.

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