Fundamental tax reform is examined in an overlapping-generations model in which heterogeneous agents face idiosyncratic wage shocks and longevity uncertainty. A progressive income tax is replaced with a flat consumption tax. If idiosyncratic wage shocks are insurable (i.e., no risk), this reform improves (interim) efficiency, a result consistent with the previous literature. But if, more realistically, wage shocks are uninsurable, this reform reduces efficiency, even though national wealth and output increase over the entire transition path. This efficiency loss, in large part, stems from reduced intragenerational risk sharing that was previously provided by the progressive tax system.