Kotlarski's lemma for dyadic models

TL;DR

This paper extends Kotlarski's lemma to identify latent component distributions in dyadic bipartite network models, providing conditions for full identification based on distributional assumptions.

Contribution

It introduces a novel application of Kotlarski's lemma to dyadic models, enabling the identification of latent distributions under new assumptions.

Findings

Identification of latent distributions achieved under specific assumptions.

Extension of Kotlarski's lemma to dyadic network models.

Conditions for full distributional identification in bipartite networks.

Abstract

We show how to identify the distributions of the latent components in the two-way dyadic model for bipartite networks $y_{i,\ell}= \alpha_i+\eta_{\ell}+\varepsilon_{i,\ell}$. 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.