Kotlarski's lemma for dyadic models
Grigory Franguridi, Hyungsik Roger Moon
TL;DR
The paper addresses the problem of identifying the distributions of latent components in a two-way dyadic model for bipartite networks, y_{i,ℓ} = c + α_i + η_ℓ + ε_{i,ℓ}. It extends Kotlarski's lemma (via the Evdokimov extension) to allow characteristic function zeros and applies it recursively to dyadic data to recover the distributions of the latent effects and errors. It provides two identification schemes for partially connected networks—one based on homogeneity of the error terms and another on homogeneity of the latent effects—and shows that a fully connected network achieves complete distributional identification without such homogeneity assumptions. The results enable distributional identification in dyadic models and lay groundwork for subsequent estimation procedures in this class of networks.
Abstract
We show how to identify the distributions of the latent components in the two-way dyadic model for bipartite networks $y_{i,\ell}= α_i+η_{\ell}+\varepsilon_{i,\ell}$. This is achieved by a repeated application of the extension of the classical lemma of Kotlarski (1967) in Evdokimov and White (2012). We provide two separate sets of assumptions under which all the latent distributions are identified. Both rely on some of the latent components being identically distributed.