Micro data studies of household saving often find a significant group in the population with virtually no wealth, raising concerns about heterogeneity in motives for saving. In particular, this heterogeneity has been interpreted as evidence against the life cycle model of saving. This paper argues that a life cycle model can replicate observed patterns in household wealth accumulation after accounting explicitly for precautionary saving and asset-based, means-tested social insurance. We demonstrate theoretically that social insurance programs with means tests based on assets discourage saving by households with low expected lifetime income. In addition, we evaluate the model using a dynamic programming model with four state variables. Assuming common preference parameters across lifetime income groups, we are able to replicate the empirical pattern that low-income households are more likely than high-income households to hold virtually no wealth. Low wealth accumulation can be explained as a utility-maximizing response to asset-based, means-tested welfare programs.