The Social Security formula is worth following closely, because most descriptions of it are loose in three places.
First, the statute names no index. Section 415(i)(1)(D) defines the CPI increase percentage by reference to "the Consumer Price Index for that quarter (as prepared by the Department of Labor)," and the surrounding definitions do not specify a version. The Social Security Administration supplies the choice in its own annual determination, explaining that when automatic increases began in 1975 "only one CPI existed, namely the index now referred to as CPI for Urban Wage Earners and Clerical Workers (CPI-W)," and that "although the Bureau of Labor Statistics has since developed other CPIs, we follow precedent by continuing to use the CPI-W." So the widespread statement that the law requires CPI-W is wrong, and the argument for a different measure is not simply a question of amending the statute.
Second, the comparison is not year over year. Section 415(i)(1)(A) makes the base quarter the calendar quarter ending September 30, and section 415(i)(1)(B) makes a base quarter a "cost-of-living computation quarter" only where the applicable increase percentage is greater than zero. The increase is then measured from the most recent computation quarter. In a year that produces no increase the baseline does not move, so the next increase is measured across the whole gap rather than from the intervening year. That is why "this year against last year" is not a description of the formula, and it is what explains stretches in which no adjustment was paid.
Third, benefits never fall from this mechanism. Because a quarter only counts when the increase percentage exceeds zero, a period of falling prices produces no adjustment rather than a reduction.
A provision almost nobody knows about sits in the same subsection and is live law. Section 415(i)(1)(C)(ii) provides that for a year in which the OASDI fund ratio is less than 20.0 percent, the applicable increase percentage becomes the CPI increase percentage or the wage increase percentage, "whichever ... is the lower." So the measure itself switches once trust-fund reserves fall below that level, and in a year when wages grew more slowly than prices the adjustment would follow wages. On a page about inflation protection, a statutory stabilizer that changes the yardstick under stress is load-bearing.
The mechanics of the announcement are prescribed too. The rounding runs in two steps under 20 CFR 404.275: each quarterly average is rounded to the same number of decimal places as the published index figures, and the resulting percentage increase is then rounded to the nearest tenth of one percent. Section 415(i)(2)(D) requires the Commissioner to publish the determination in the Federal Register within 45 days after the close of the quarter, which is why the notice rather than any summary is the source of record. And section 415(i)(2)(B) makes the increase effective for months after November, meaning it applies to the December benefit, which is the payment received in January. Calling it "the January increase" describes the deposit rather than the statutory month.
Where the umbrella earns its name is the comparison across programs. Under 5 USC 8340 a CSRS annuity receives the full index increase. Under 5 USC 8462(b)(1) a FERS annuity receives, where the price index change does not exceed 3 percent, "the lesser of— (i) the percent change in the price index ... or (ii) 2 percent," and where the change exceeds 3 percent, "the excess of— (i) the percent change ... over (ii) 1 percent." Section 8462(b)(3) then states that a FERS annuity "shall not be subject to adjustment under section 8340," severing the two systems by design. So a retired federal employee under FERS and a Social Security recipient in the same household, in the same year, from the same movement in prices, receive different increases as a matter of statute.
The absence of a COLA is the umbrella's most consequential entry. Most private defined benefit pensions provide no adjustment at all, so a nominal monthly pension loses purchasing power every year it is paid, which is a large part of why a fixed pension and an inflation-adjusted benefit cannot be compared at face value. And a COLA is not a household inflation guarantee even where one exists, for a mechanical reason rather than a rhetorical one: CPI-W is built on the spending patterns of urban wage earners and clerical workers, which is not the basket of a retired household. Nor does an adjustment arrive alone. Medicare premiums are set on their own schedule, so the increase a household keeps can be smaller than the percentage that was announced.