We study the effects of permanent and temporary income shocks on precautionary saving and investment in a "store-or-sow" model of growth. High volatility of permanent shocks results in high precautionary saving in the safe asset and low investment, or a "volatility trap." Namely, big savers invest relatively little. In contrast, low volatility of permanent shocks leads to low precautionary saving and high or low investment, depending on the volatility of temporary shocks. Empirical evidence shows a nonlinear relationship between investment and saving and that investment is a hump-shaped function of the volatility of permanent shocks, as predicted by the model.