A comment on the previous post asks:
What is the source of the (small) beneficial effect that higher inflation has on the SS balance? Why does higher inflation help the SS balance?
Good question. There are actually two inflation series that are relevant, the CPI and the GDP price deflator. Quoting from Section V.B of the Trustees Report:
Future changes in the Consumer Price Index for Urban Wage Earners and Clerical Workers (hereafter denoted as CPI) will directly affect the OASDI program through the automatic cost-of-living benefit increases. Future changes in the GDP chain-type price index (hereafter, the GDP deflator) affect the nominal levels of the GDP, wages, self-employment income, average earnings, and the taxable payroll.
As to why there is a slight positive effect of inflation on the program's finances, Section VI.D5 of the Trustees Report later states:
The patterns described above result primarily from the time lag between the effects of the CPI changes on taxable payroll and on benefit payments. When assuming a greater rate of increase in the CPI (in combination with a constant real-wage differential), the effect on taxable payroll due to a greater rate of increase in average wages is experienced immediately, while the effect on benefits due to a larger COLA is experienced with a lag of about 1 year. Thus, the higher taxable payrolls have a stronger effect than the higher benefits, thereby resulting in lower cost rates. The effect of each 1.0-percentage-point increase in the rate of change assumed for the CPI is an increase in the long-range actuarial balance of about 0.21 percent of taxable payroll.
That seems like a pretty tenuous justification, and, not surprisingly, the effect is not large. More importantly, there is typically a "wedge" between the inflation in the CPI and the GDP price deflator (assumed to be 0.3 percentage point per year, see Table V.B1). Very roughly, the CPI is what we consume, and the GDP deflator is what we produce. The most important item that is weighted more in the former than the latter is oil, since we import so much of it. If we get unexpectedly higher inflation due to oil prices, that will likely worsen, not improve, Social Security's finances.