Econometrics of Networks
Friday, Jan. 3, 2020 2:30 PM - 4:30 PM (PDT)
- Chair: Arthur Lewbel, Boston College
Measurement Errors in Large Nonlinear Panels and Networks
AbstractWe consider estimation of general nonlinear semiparametric panel data models with fixed effects. Estimation of such models implicitly relies on the “within” variation of covariates, which aggravates the Errors-In-Variables (EIV) bias problem. First, we derive the formulas for the bias of m-estimators in large panel data. We show that the bias of common parameters includes both the direct effect of EIV and the EIV bias of the incidental parameters (fixed effects). Then, we propose an estimator that removes the EIV bias in nonlinear models using panel instrumental variables. We show how lagged values of covariates can serve as such instruments in panel data. The estimator does not involve any nonparametric estimation, and can accommodate serially correlated and/or multivariate measurement errors. We establish the asymptotic properties of the estimator. Combined with a jackknife procedure, the estimator is asymptotically normal and unbiased. The properties of the estimator are illustrated in a Monte Carlo simulation. In addition, the estimation approach can be adapted for estimation of large network data models with measurement errors. In particular, we show how the network structure provides instruments needed to eliminate the EIV bias.
Inference in Models of Discrete Choice with Social Interactions Using Network Data
AbstractWe study econometric models of discrete choice with social interactions mediated by a network. Since network data commonly consists of observations on a single large network, we consider an asymptotic approximation that sends the size of the network to infinity. We prove a central limit theorem for network moments relevant for inference in discrete games of complete information on networks and dynamic models where social interactions enter through lagged dependent variables.
Limit Theorems for Network Dependent Random Variables
AbstractThis paper considers a general form of network dependence where dependence between two sets of random variables becomes weaker as their distance in a network gets longer. We show that such network dependence cannot be embedded as a random field on a lattice in a Euclidean space with a fixed dimension when the maximum clique increases in size as the network grows. This paper applies Doukhan and Louhichi (1999) weak dependence notion to network dependence by measuring dependence strength by the covariance between nonlinearly transformed random variables. While this approach covers examples such as strong mixing random fields on a graph and conditional dependency graphs, it is most useful when dependence arises through a large functional-causal system of equations. The main results of our paper include the law of large numbers, and the central limit theorem. We also propose a heteroskedasticity-autocorrelation consistent variance estimator and prove its consistency under regularity conditions. The finite sample performance of this latter estimator is investigated through a Monte Carlo simulation study.
Identification and Estimation of Large Network Games with Private Link Information
AbstractWe study the identification and estimation of large network games where each individual holds private information about its links and payoffs. Extending Galeotti, Goyal, Jackson, Vega-Redondo and Yariv (2010), we build a tractable empirical model of network games where the individuals are heterogenous with private link and payoff information, and characterize its unique, symmetric pure strategy Bayesian Nash equilibrium. We then show that the parameters in individual payoffs are identified under "large market" asymptotics, whereby the number of individuals increases to infinity in a fixed and small number of networks. We also propose a consistent two-step m-estimator for individual payoffs. Our method is distribution-free in that it does not require parametrization of the distribution of shocks in individual payoffs. Monte Carlo simulation show that our estimator has good performance in moderate-sized samples.
Social Networks with Misclassified or Unobserved Links
AbstractWe study the identification and estimation of social network models when network links are either misclassified or unobserved. We first derive conditions under which some misclassification of links does not interfere with the consistency or asymptotic properties of standard instrumental variable estimators of social effects. Second, we construct a consistent estimator of social effects in a model where network links are not observed at all. Our method does not require repeated observations of individual network members. We apply our estimator to data from Tennessee's Student/Teacher Achievement Ratio (STAR) Project. Without observing the latent network in each classroom, we identify and estimate peer and contextual effects on students' performance in mathematics. We find that peer effects tend to be larger in bigger classes, and that increasing peer effects would significantly improve students' average test scores.
- C2 - Single Equation Models; Single Variables
- C3 - Multiple or Simultaneous Equation Models; Multiple Variables