A Markov Model of Dynamic Network Formation: A Production Network Perspective

This paper develops a tractable model of dynamic network formation with heterogeneous forward-looking agents. The model bridges the gap between recent Macroeconomic models with exogenous production networks and static econometric models of networks formation games. I model network formation as a sequence of Bayesian incomplete information games in which the dynamic state dependencies of agents' strategies are Markov. This feature of aggregate state dependence allows me to investigate the role of network externality through a global interaction channel. I characterize the Bayesian Markov Perfect symmetric equilibrium by a set of fixed-point equations in conditional choice probabilities. I motivate this approach by developing a second-stage general equilibrium model of production networks in an open economy. This second stage model provides the payoff structure for the network formation and relevant Markov sufficient statistics. I propose a simple two-step maximum likelihood estimator and develop its asymptotic properties for a single large network. I apply this model to US input-output data. In counterfactual experiments, I find that network externality is quantitatively important for endogenous network formation. Furthermore, negative network externality provides an alternative explanation for network persistence. In an extension, I show how endogenous entry and exit of nodes be can jointly be formulated with endogenous network formation.