Computing population moments for heterogeneous agent models is a necessary step for their estimation and evaluation. Computation based on Monte Carlo methods is usually time- and resource-consuming because it involves simulating a large sample of agents and potentially tracking them over time. We argue in favor of an alternative method for computing both cross-sectional and longitudinal moments that exploits the endogenous Markov transition function that defines the stationary distribution of agents in the model. The method relies on following the distribution of populations of interest by iterating forward the Markov transition function rather than focusing on a simulated sample of agents. Approximations of this function are readily available from standard solution methods of dynamic programming problems. The method provides precise estimates of moments like top-wealth shares, auto-correlations, transition rates, age-profiles, or coefficients of population regressions at lower time- and resource-costs compared to Monte Carlo based methods.