Complementarities in Sparse Two-Sided Interaction Models

Abstract

This paper studies complementarities in two-sided interaction models when only a sparse subset of potential matches is realized. I introduce the Tukey model, adding one complementarity parameter to two-way fixed effects. Variation within a four-cycle in the observed matching network identifies this parameter, while connectedness permits identification of agent productivities. I propose a cycle-based estimator that avoids estimating latent productivities. The estimator is consistent and asymptotically normal under sparse-network asymptotics, yielding a formal test of no complementarities. An application to World Bank manager-country assignments finds negative complementarities, suggesting that more capable managers are especially valuable in more complex environments.