Consistently estimating graph statistics using Aggregated Relational Data

Aggregated Relational Data, known as ARD, capture information about a social network by asking a respondent questions of the form "How many people with characteristic X do you know?" rather than asking about connections between each pair of individuals directly. Despite widespread use and a growing literature on ARD methodology, there is still no systematic understanding of when and why ARD should accurately recover features of the unobserved network. This paper provides such a characterization. First, we show that ARD provide sufficient information to consistently estimate the parameters of a common generative model for graphs. Then, we characterize conditions under which ARD should recover individual and graph level statistics from the unobserved graph.