Empirical analyses of the effects of public and private pensions on household saving impose strong assumptions in order to obtain a tractable empirical model: fixed retirement and pension claiming ages, no borrowing constraint, little or no uncertainty, and no institutional restrictions on pension claiming. I specify a richer version of the life cycle model that relaxes these assumptions. I calibrate, solve, and simulate the model and use the results to study three issues: (1) How much household wealth is crowded out by pensions? (2) Can linear regression analysis accurately estimate the magnitude of crowdout when the assumptions used in the empirical analysis are invalid? (3) How valuable are pensions to households? Simulation results indicate that private pensions in the US crowd out less than $0.15 of household saving per dollar of pension wealth. Crowdout by Social Security is larger at $0.33, but far smaller than the one-for-one offset predicted by a stylized version of the life cycle model. Regression estimates of crowdout using the simulated data are systematically larger than simulated crowdout, indicating that empirical estimates of crowdout are quite sensitive to the assumptions required in order to use the regression approach. The welfare analysis implies that, conditional on Social Security, DB pensions are worth less than their expected present discounted value to households, while DC pensions are worth more than their dollar value. In the absence of a private pension, Social Security is worth 50% more to households than its expected dollar value.