In aggregation theory, index numbers are judged relative to their ability to track the exact aggregator functions nested within the economy's structure. We compare two statistical index numbers—the Divisia monetary aggregate and the simple-sum monetary aggregate—with the exact rational expectations monetary aggregate, using actual data. Because we are not using simulated data, we estimate the parameters of the Euler equations, and thereby of the nested monetary aggregator function, using the generalized method of moments. We explore the tracking errors of the two index numbers relative to the estimated exact aggregate. We investigate the circumstances under which risk aversion increases tracking error. We also use polyspectral methods to test for the existence of remaining nonlinear structure in the residual tracking errors.