Historically, the Consumption Capital Asset Pricing Method (C-CAPM) has performed poorly in that estimated parameters are implausible, model restrictions are often rejected and inferences appear to be very sensitive to the choice of economic agents' preferences. In this study, we estimate and test the C-CAPM with Constant Relative Risk Aversion (CRRA) using time series data from Germany, South Africa, Britain and America during relatively short time periods with the latest available data sets. Hansen's GMM approach is applied to estimate the parameters arising from this model. In general, estimated parameters fall outside the bounds specified by Lund & Engsted (1996) and Cuthbertson & Nitzsche (2004), even though the models are not rejected by the J-test and are associated with relatively small minimum distances.