If annuities such as Social Security are not chosen freely, the consumption path typically cannot be determined independently of the path of annuities. This constraint reduces the value of the annuity from the point of view of the annuitant. I measure the value of the annuity by the marginal rate of substitution (MRS), the amount of bequeathable wealth that will substitute for a dollar of annuity wealth. In the analytical section of the paper, I show that the MRS increases as bequeathable wealth increases; in that sense the wealthy benefit more from Social Security than the poor. In the empirical section, I estimate the MRS for a sample of retired single elderly. The MRS varies considerably from individual to individual because of differences in the mix of bequeathable wealth and annuities. For the parameter values that best fit the data, a substantial fraction of the sample has more Social Security than it would like in that it would be willing to trade, at the margin, a claim to Social Security for an increase in bequeathable wealth.