The theory of intertemporal choice predicts that the cross-sectional variance of the marginal utility of consumption is equal to its own lag plus a constant and a random component. Using general preference specifications and some assumptions about the nature of the random component, we provide an explicit test of this hypothesis. Our approach circumvents the necessity to identify a pure age profile of the cross-sectional variance of consumption and yields a well-specified statistical test. This test is applied to data from the United States, the United Kingdom, and Italy. The results are remarkably consistent with the restrictions implied by the theory of intertemporal consumption choices.