In this article, we discuss generalized method of moments estimation of the covariance structure of longitudinal data on earnings, and we introduce and illustrate a Stata program that facilitates the implementation of the generalized method of moments approach in this context. The program, gmmcovearn, estimates a variety of models that encompass those most commonly used by labor economists. These include models where the permanent component of earnings follows a random growth or random walk process and where the transitory component can follow either an AR(1) or an ARMA(1,1) process. In addition, time-factor loadings and cohort-factor loadings may be incorporated in the transitory and permanent components.