An empirical model of dyadic link formation in a network with unobserved heterogeneity

I study a dyadic linking model in which agents form directed links that exhibit homophily and reciprocity. A fixed effect approach accounts for unobserved sources of degree heterogeneity. I consider inference with respect to homophily preferences and a reciprocity parameter, as well as a test of model specification. The specification test compares observed transitivity to the transitivity predicted by the dyadic linking model. My test statistics are robust to the incidental parameter problem (Neyman and Scott 1948). This is accomplished by using analytical formulas that approximate the effect of the incidental parameter on the bias and the variance of the test statistics. The approximation is justified under dense large network asymptotics. In an application to favor networks in Indian villages, the model specification test detects that the dyadic linking model underestimates the true transitivity of the network.