Empirical models for dyadic interactions between n agents often feature agent-specific parameters. Fixed-effect estimators of such models generally have bias of order n−1, which is nonnegligible relative to their standard error. Therefore, confidence sets based on the asymptotic distribution have incorrect coverage. This paper looks at models with multiplicative unobservables and fixed effects. We derive moment conditions that are free of fixed effects and use them to set up estimators that are n-consistent, asymptotically normally distributed, and asymptotically unbiased. We provide Monte Carlo evidence for a range of models. We estimate a gravity equation as an empirical illustration.