We consider an index model of dyadic link formation with a homophily effect index and a degree heterogeneity index. We provide nonparametric identification results in a single large network setting for the potentially nonparametric homophily effect function, the unobserved individual fixed effects and the unknown distribution of idiosyncratic pairwise shocks, up to normalization for each possible true value of the unknown parameters. Departing from the popular practice of restricting the norm of unknown parameters to be unity, we instead impose scale normalization on an arbitrary interquantile range, which proves particularly convenient for characterizing the identification relationships in our model, as quantiles provide direct linkages between the observable conditional probabilities and the unknown index values. We then use an inductive "in-fill " and " out-expansion" algorithm to establish our main identification results. We also provide a formal analysis of normalization that is without loss of generality in a precise sense, and discuss its implications concerning the interpretation of the results and counterfactual analyses of the model .
We consider an index model of dyadic link formation with a homophily effect index and a degree heterogeneity index. We provide nonparametric identification results in a single large network setting for the potentially nonparametric homophily effect function, the unobserved individual fixed effects and the unknown distribution of idiosyncratic pairwise shocks, up to normalization for each possible true value of the unknown parameters. We propose a novel form of scale normalization on an arbitrary interquantile range, which proves particularly convenient for characterizing the identification relationships in our model, as quantiles provide direct linkages between the observable conditional probabilities and the unknown index values. We then use an inductive "in-fill and out-expansion" algorithm to establish our main results, and consider extensions to more general settings that allow nonseparable dependence between homophily and degree heterogeneity .
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identification results. We also provide a formal analysis of normalization that is without loss of generality in a precise sense, and discuss its implications concerning the interpretation of the results and counterfactual analyses of the model
results, and consider extensions to more general settings that allow nonseparable dependence between homophily and degree heterogeneity