Parameter estimation of affine term structure models by means of the generalized method of moments is investigated. Exact moments of the affine latent process as well as of the yields are obtained by using results derived for polynomial processes. Then the generalized method of moments, combined with multi-start random search and Quasi-Bayesian methods, is used to get reliable parameter estimates and to perform inference. After a simulation study, the estimation procedure is applied to empirical interest rate data.