Instrumental Variables Methodology for Estimation of Peer Effects
Nicholas A. Christakis, Harvard University 
*A. James O'Malley, Harvard Medical School 
J. Niels Rosenquist, Massachusetts General Hospital 
Alan M. Zaslavsky, Harvard Medical School, Dept. of Health Care Policy 

Keywords: Genes, Instrumental variable, Longitudinal data, Peer effect, Social network, Two-stage least squares

We develop instrumental variables (IVs) methodology for estimation of peer effects given longitudinal social network data and genetic alleles as IVs. Because genes can affect phenotypes at any point during an individual’s life, we argue that a longitudinal model with lagged values of the phenotype is necessary for the IV assumptions to be plausible. We derive a general methodological approach that accommodates heterogeneity in peer effects across different types of relationships and modification of peer effects by covariates in the context of both network influence models (net effect of all peers) and dyadic influence models (total effect of a single peer). It is seen that the commonly-used two-stage least squares procedure takes an interesting form. For illustration of the methodology, we use data is from the Framingham Heart Study and consider the candidacy of genetic alleles that have been linked to obesity and smoking as IVs for peer effects of body mass index (BMI) and smoking respectively.