Differential Mortality and Progressivity of Social Security

This paper is motivated by two facts: 1) There is a significant difference in mortality across income groups. 2) This difference in mortality is getting larger. I study the extent in which progressively of social security is affected by differences in mortality across income groups and how changes in mortality differential affect the progressively of the social security and its budget. I use a life cycle overlapping generation model in which individuals are different in their lifetime earning profiles and higher earning individuals have lower mortality. I first calibrate the relation between earning and mortality using 1983-1997 data (reported in Cristia (Journal of Health Economics, 2009)) and compare current US system with a system in which there is a separate budget for each earning/mortality group (therefore by design there is no redistribution across earning/mortality groups). I find that these two systems have very similar replacement ratios, expect for the lowest 2% of earning distribution. To find the value of redistribution in current US social security system I calculate welfare differences between the resulting allocations. I find that the welfare gains from progressivity in current social security system are not monotone in lifetime earnings. Individuals in bottom two percent of earning distribution gain the most from it (up to 2.83% of their consumption) while those in second decile lose the most (up to 1% of their consumption). However, ex post gains and losses completely offset each other. There is no ex ante welfare gain. Using more recent earning and mortality relationship (1998-2003), I find that increase in the mortality differential will increase the cost of the social security by about 5%. Adjusting the benefit to maintain the cost will make the system even more regressive.