Typical neoclassical life-cycle models predict that Social Security has a large and negative effect on private savings. We review this theoretical literature by constructing a model where individuals face uninsurable longevity risk and differ by wage earnings, while Social Security provides benefits as a life annuity with higher replacement rates for the poor. We use the model to generate numerical examples that confirm the standard result. Using several benefit and tax changes from the 1970s and 1980s as natural experiments, we investigate the empirical relationship between Social Security and private savings and find little to support the strong predictions from the theoretical model. We explore possible reasons for the divergence between theoretical predictions and empirical findings.