Reductions in Social Security benefits are extremely unpopular across the political spectrum. The program enjoys enormous support among both Democrats and Republicans and people are far more likely to say that benefits should be raised than cut. For this reason, the public should be paying attention to a little noticed provision in the tax bill passed by the House today and which also appears in the bills under consideration in the Senate.

In both cases, the basis for indexing tax brackets would be shifted from Consumer Price Index (CPI) to the Chained Consumer Price Index (CCPI). The difference is that the CCPI takes account of when people change their consumption patterns in response to changes in relative prices.

The classic example is that beef rises in price and chicken falls, we would expect people to consume less beef and more chicken. The CPI assumes that people don't change their consumption patterns while the CCPI adjusts its basket to assign less importance to beef and greater importance to chicken.

For this reason, the CCPI shows a somewhat lower rate of inflation than the CPI. Typically the gap is 0.2–0.3 percentage points. This matters in the tax bill because the cutoff for the tax brackets is adjusted each year by the CPI. If the CCPI is used rather than CPI, then the cutoffs would rise less rapidly.

For example, if the cutoff for the 25 percent bracket is $40,000 for a single individual and the CPI showed 2.0 percent inflation, then it would rise to $40,800 for the next year. This means a single person would face a tax rate of 25 percent on income above $40,800. If the CCPI showed an inflation rate of 1.7 percent, then the cutoff would rise to $40,680. This means a single person would face a tax rate of 25 percent on income above $40,680.

In a single year, this difference will not mean much, but after 10 years, the difference in the indexes would be between 2.0–3.0 percent and it would grow more through time. This will add a fair bit to many people's tax bills.

All of this matters for Social Security because after people retire the benefits are indexed to the CPI. There were efforts in the Obama years to change the indexation to the CCPI, but these were beaten back. If the tax brackets are already indexed to the CCPI, then the pressure to switch indexes for Social Security will be considerably stronger. That would mean a cut in benefits for some who has been retired for ten years of between 2.0–3.0 percent, after twenty years 4.0–6.0 percent, and after thirty years 6.0–9.0 percent. This is real money.

There is an argument that we should use a different index for the elderly. After all they consume more housing and health care than the rest of the population, items that tend to rise more in price than the overall CPI. They also are likely to be less prone to switch their consumption patterns in responses to changes in price than the rest of the population.

However, if Congress is in a budget cutting mood, they are unlikely to be interested in such fine distinctions. Switching Social Security benefits to the same index as is used for tax brackets is likely to be seized as a quick out that can save lots of money — at the expense of retirees' Social Security benefits.

So, folks who care about Social Security benefits should be very worried about this seemingly minor point in the Republican tax bills. It could make a big difference in future years for people who depend on these benefits.