Identification in Models for Matched Worker-Firm Data with Two-Sided Random Effects

This paper is concerned with models for matched worker-firm data in the presence of both worker and firm heterogeneity. We show that models with complementarity and sorting can be nonparametrically identified from short panel data while treating both worker and firm heterogeneity as discrete random effects. This paradigm is different from the framework of Bonhomme, Lamadon and Manresa (2019), where identification results are derived under the assumption that worker effects are random but firm heterogeneity is observed. The latter assumption requires the ability to consistently assign firms to latent clusters, which may be challenging; at a minimum, it demands minimal firm size to grow without bound. Our setup is compatible with many theoretical specifications and our approach is constructive. Our identification results appear to be the first of its kind in the context of matched panel data problems.