The theory of full consumption insurance posits that households are insulated from all idiosyncratic shocks so that the ratio of the marginal utilities of consumption of any two households is constant over time. Consumption insurance therefore implies absence of consumption mobility between any two time periods. This implication requires knowledge of the evolution of the entire consumption distribution, not just its mean as in standard tests of complete markets. We test this unexplored prediction of the theory using a panel drawn from the Bank of Italy Survey of Household Income and Wealth. We design an appropriate non-parametric test and find substantial mobility of consumption even controlling for possible preference shifts and measurement error in consumption. The findings strongly reject the theory of full consumption insurance.