Semiparametric Dynamic Logit Model with Endogenous Networks

Abstract

Many choices persist over time and are made among friends. Teenagers who smoke tend to keep smoking, and they tend to have friends who smoke. Part of this persistence is habit, but part may come from characteristics researchers do not observe, such as a taste for risk, that shape both whether a student smokes and whom they befriend. Methods that treat friendships as given cannot separate the two when the characteristic changes over time. This paper shows how the friendship network itself can, in a dynamic logit model. Two people who form friendships in the same way are assumed to share the same unobserved influence on the outcome, the social influence function, so comparing them cancels it, even when that influence changes between waves, provided the change is shared by people who form friendships in the same way. No specific model of how friendships form is assumed. I propose an estimator built on this comparison and derive its large-sample behavior in two cases: exact matching, when the characteristic and the covariates take few distinct values, and approximate matching, with a jackknife correction for the bias it creates. In simulations, the estimator removes most of the bias left by peer-average controls and by the standard panel method that compares each person only with themselves over time, and its confidence intervals have coverage close to the correct level. An application to adolescent smoking in the Glasgow Teenage Friends and Lifestyle Study illustrates the method and the data it requires.