Recent work on linked employer--employee data has shown, among other results, that person effects and firm heterogeneity in wages explain about half of the inter-industry wage differentials each. One puzzling feature of this decomposition is the pattern of correlations: intra-industry correlation between firm and worker effects is negative, while it is positive on the inter-industry level. As no ready theory can explain this, we investigate a tractable parametric model of unobserved heterogeneity among workers and firms and in an ongoing project estimate it on aggregate moments.