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May 15, 2005

What Is "Progressive Price Indexing"?

Guest post: hilzoy

I have been messing around with a long post on Social Security, and in the course of writing it I realized that I did not fully understand what 'price indexing' was, in the context of Social Security. The general concept of price indexing was easy enough: something that is currently indexed to wages would, under price indexing, be indexed to prices instead. Since prices tend to rise more slowly than wages, this would lead benefits to grow more slowly (or: be cut, depending on which you prefer) over time. But what, exactly, were people proposing to price-index? I had somehow picked up the (correct) idea that the mysterious indexed entity was not benefits themselves: these are adjusted each year according to the Consumer Price Index, which is to say: they are price-indexed. Price-indexing, I knew, had something to do with the initial calculation of benefits, and thus with the mysterious arcana of Social Security benefit calculations that I have thus far tried very hard to avoid having to figure out. But I realized, as I wrote my Social Security post, that I couldn't avoid this any longer. If I was to be a Truly Responsible Bloggerâ„¢, I had to figure it out. Having done so, I thought I might as well try to explain it as clearly as possible, since it's not what you might think.

Warning: it's wonky.

Here is how your Social Security benefits are calculated, assuming you retire at 65 and are not disabled:

  • First, the Social Security Administration selects the 35 years in which you earned the most. The amount you earned in any of those years before you turned 60 is adjusted by the amount that wages rose between that year and the year you turned 60. (Earnings in years after you turned 60 are not adjusted.) These adjusted annual earnings are then averaged, and divided by 12 to yield your "average indexed monthly earnings" (AIME).

  • Next, a formula is applied to your AIME. Each month, Social Security will provide you with 90% of the first $627 of your average indexed monthly earnings; 32% of your earnings between $627 and $3779, and 15% of any covered earnings above that point.

  • The dollar amounts just mentioned ($627, $3779) are called "bend points": the points at which additional monthly income stops being replaced at one rate and begins to be replaced at a lower rate. (Imagine a graph plotting Social Security benefits for each dollar of monthly income. These are the points at which the line on this graph would bend.) The 'bend points' are adjusted each year by the increase in average wages. So if wages were to rise 3% this year, then next year's bend points would be 3% higher.

  • Once your benefits have been calculated, they are adjusted each year to take account of inflation (that is: they are price-indexed.)

I spelled this out so that you can see that there are a number of adjustments taking place:

  • Your earnings are adjusted for to take account of increases in wages in calculating your average indexed monthly earnings.

  • The 'bend points' that determine how much of your monthly earnings are replaced at 90%, how much at 32%, and how much at 15% are adjusted to take account of wage growth.

  • And your benefits, once they have been calculated, are adjusted to take account of increases in prices.

Clear? I hope so. That's as clear as I can make it.

Now: presumably, the switch from wage-indexing to price-indexing cannot involve a change to the way your benefits, once calculated, are adjusted to keep up with the cost of living, since this adjustment is already price-indexed. It must involve either (a) the calculation of your average indexed monthly earnings, or (b) the calculation of the bend points. And there is a big difference between these two, which turns on the question: when does this indexing begin?

When your average indexed monthly earnings are calculated, you begin with your actual earnings in your 35 best years. Suppose the first of these years occurs after price-indexing takes effect: your actual wages will reflect any growth in wages that has occurred between the onset of price indexing and that year. So any divergence between using wage- and price-indexing in calculating your average indexed monthly earnings would concern the difference between the rates of growth of wages and prices during your working life. Moreover, the difference between wage and price indexing will be greatest in that first year; thereafter, it will shrink. And assuming that the relationship between wages and prices holds steady, each generation will lose about as much as those who came before.

This is not true if price-indexing is used to calculate 'bend points'. These are indexed to a particular year (currently, 1979), and absent any changes in Social Security's rules, they will go on being indexed to that year indefinitely. Thus, the calculation of the first bend point today is as follows: $180 (the first bend point in 1979) times $34,064.95 (the average wage in 2003) divided by $9,779.44 (the average wage in 1979) equals $627.00. If we do not change Social Security, we will continue to calculate the bend points relative to 1979 as long as our country survives.

And this means that changing the sort of indexing used to calculate the bend points is a much, much bigger deal, in the long run, than changing the means of indexing used to calculate your average indexed monthly earnings. If price-indexing is used to calculate your average indexed monthly earnings, then you will be affected only by the divergence between the rates of growth in wages and prices over your working life. But if price-indexing is used to calculate the bend points, then the bend points will continue to decline, as a share of wages, as long as Social Security exists. Moreover, this decline will compound itself, like interest rates. Whereas, if price-indexing were introduced into the calculation of people's average indexed monthly earnings, each generation would lose about as much as the last as long as the relation between wage growth and price growth held steady, using price indexing to calculate the bend points means that every generation will have a smaller share of its income replaced than those that preceded it, until the end of time (or Social Security, whichever comes first.)

The version of price indexing that President Bush seems to be considering is a version of the second: adjusting the 'bend points' in accordance with the growth in prices, not wages. Specifically, he seems to be considering "progressive price indexing", a sort of hybrid between wage and price indexing. According to the Pozen plan (warning: long wonky pdf) on which the President's vague gestures in the general direction of a plan are supposedly based, people who make around $20,000 a year would have their benefits calculated as they do now. The cap on maximum earnings replaced by Social Security, by contrast, would be price-indexed. And the bend points in between would be calculated using a combination of the two approaches.

This means that while people making below $20,000 a year would receive the same benefits under the President's approach that they would receive if Social Security remained unchanged, people making more would receive significant cuts. The more time goes by, the deeper those cuts become. Eventually, the difference between the benefits given to those making below $20,000 and those making more would approach zero. (The Center for Budget and Policy Priorities estimates that benefits would be essentially flat for anyone making $20,000/year or more by 2100.)

All of this, of course, doesn't take into account the effects of personal accounts; but that's a topic for another day. All I really wanted to do with this post was to make it clear what 'price indexing' is, on the assumption that if I, a reasonably well-informed person, didn't get it, I might not be alone.

[Cross-posted at Obsidian Wings]


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Why? Why are you USians doing this? Why?

Am I to understand that in the USA, if you worked shit jobs at minimum wage all your life, your pension would be a pittance? are to understand.

Elegant elucidation and upholding the notion that writers trained as philosophers are among our most compelling species.

couple of questions: The price of WHAT? And, how did the choice of 1979 come about? It was a time of "stagflation" (which, I assume, means that wages were flat in a stagnating economy, while prices rose- the "inflation" factor- because of the OPEC oil, um, revaluation).
.."But if price-indexing is used to calculate the bend points, then the bend points will continue to decline, as a share of wages, as long as Social Security exists.." Sorry- I don't understand. Do you mean that there will be no more fixed reference point, no "1979" anymore? Or that one's wages no longer figure into the calculation? I don't want to read Pozen... sigh... ^..^

"The price of WHAT?" -- the Consumer Price Index, generally.

Why 1979? That was when changes to SS enacted in 1977 took effect.

There will be a fixed reference point. (What it is will presumably depend on when SS reform passes, if it does.) Starting in that year, the following will happen (according to the Pozen plan, which this aspect of the President's plan seems to be based on): income below a given point will yield benefits as before. (That point is currently about $20,000; it will be wage-indexed going forward.) The SS administration will then figure out the following question: by what percentage would the benefits on income between that point ($20,000) and the maximum income replaced by SS (currently about $90,000) have to be reduced in order that someone making the full $90,000 (or more) would pay the same amount that s/he would pay if price-indexing were in effect, pegged to that initial year? Then all benefits on income above the point that's now at $20,000 would be reduced by that percentage. That means that for anyone making $90,000 or more, it will be as if price-indexing were in effect (pegged to some new reference point -- the President, I think, suggests 2012.) People making between $20,000 and $90,000will get less than under wage indexing, but more than under price indexing. People making below $20,000 will get the same benefits as under wage indexing.

OK: Here's the point. To figure out what someone would get under price indexing, you adjust the bend points for price growth (=growth in the Consumer Price Index) relative to your index year. So, for instance, if that year is 2012, and the bend point is set at $1000 (for ease of calculation), and during the first year after that, wages grow by 4% and prices grow by 3%, then in 2013 the bend points under wage indexing will be 1040, and under price indexing they will be 1030. Suppose the same growth in wages and prices happens the next year as well: then the bend points would be (1.04 * 1.04 * 1000 = 1081.6) under wage indexing, and (1.03 * 1.03 * 1000 = 1060.9) under price indexing. The point is: this process goes on forever, or at least until the end of SS. And each year that wages grow faster than prices, the gap grows. And whereas if you're indexing a person's wages using price growth rather than wage growth, the process whereby the difference between the two compounds over time only has your working life to play with, if you're indexing the bend points, this process, with its associated compounding, goes on ad infinitum.

Very good post but wrong on one specific and important point.

The price indexing recommended by the President's Commission, the later Graham proposal, and the more recent Pozen arrangement, would all leave the indexing of the AIME and the bend points the same as under current law, but would reduce the PIA factors (the 90%, 32% and 15%) which under current law are fixed, by the ratio of the change in prices to the change in wages. The intermediate assumptions of the 2005 Trustees Report project that prices will grow by 2.8 percent per year, and wages by 3.9 percent.

The reduction in the PIA and in the factors would then be the ratio of 2.8/3.9 or 1.028/1.039, which equals 0.989. The PIA factors (90, 32, 15) would then get reduced by thihs 0.989 factor if the ratio of prices to wages holds constant.

But ultimately, yes, the replacement rate from benefits would drop considerably, eventually reaching zero in the very very long run.

I might add that reducing the PIA factors is a larger reduction over time than just price indexing the bend points.

In addition, the long term effect of price indexing just the bend points is that eventually, as the wage indexing of the AIME continues, and the growth of the bend point amounts slows, eventually everyone's AIME would exceed the 15% bracket, causing everyone's benefit to be in effect, a flat 15% of their lifetime earnings, regardless of earnings level. That is, price indexing only the bend points would eventually eliminate the system's progressive benefit structure.

Indexing the PIA factors by the price/wage ratio maintains the progressivity, but results in much larger reductions over time.

Bulworth: Thanks. You're right. But: this applies only to income between the new 'bend point', which will be wage-indexed in future, and the cap on replaceable income, right? (For those of you who are following at home, these are the points that are now around $20,000 and $90,000, respectively.) And also, as I understand it, this income will (under the Pozen plan) be multiplied not by the ration of the change in prices to the change in wages, but by whatever factor would be required to make top earners pay the same as they would under price indexing. (I'm taking this from p.2 of the SSA report on the Pozen plan.)

Thanks, hilzoy... It's clearer, now. It will be interesting to see what effects a devalued currency and an upward spiral to energy costs have on the "price index" side of these calculations. (I wonder how much of an effect executive salaries have had on "average wages" in the last decade.) Is there some way to separate the rise in prices due to relative scarcity of, or pressure upon, a resource (& other "real" cost increases) vs. increases caused by "inflation"?
Many regions of the country (including parts of mine- the Great Northwet) are counting on retiring baby boomers to provide some economic input that will, hopefully , replace what is disappearing in the resource-extraction sectors. It's conceivable that a growing number might decide to go abroad, in order to make their money go farther (eg the many Polish-Americans who moved from the greater Chicago area back to greater Warsaw, even before the USSR dismantlement). But I digress... thanks, again. ^..^


Basically the Pozen proposal would create a new bend point (about $1520 in today's terms), and a new PIA factor so that the PIA factors would be

if aime < first bend point then PIA = first bend point * 0.90; LOWEST EARNER

if first bend point < aime <= new second bend point then PIA = (first bend point * 0.90) + ((AIME - first bend point) * 0.32);

if new second bend point < aime <= old second bend point then PIA = (first bend point * 0.90) + ((new second bend point - first bend point) * 0.32)) + (aime - new second bend point)* (0.32*reduction factor);

and if aime < new second bend point then PIA = first bend point * 0.90 + (new second bend point * 0.32) + ((old second bend point - new second bend point)*(0.32*reduction factor)) + ((aime - old second bend point)*(0.15*reduction factor))

Those with AIME amounts at or below this new second bend point would have benefits wage indexed because the 90% and 32% would stay the same and would be the only factors that could be applied to this person's AIME.

For those with AIME amounts above the new second bend point, their benefits would be partially wage indexed and partially price indexed.

The amount of their AIME below the new second bend point amount would be wage indexed and any AIME amount above that amount would be price indexed because either the third now reduced PIA factor would apply to some portion of their AIME and as their AIME gets closer to the maximum amount (the 90,000/12 under current law), more of their AIME would fall under both the newly reduced 32% factor and the old and now reduced 15% factor.

As an illustration, by 2075 the new third PIA factor would have declined from 0.32 to 0.0403 while the original 0.15 factor would decline to 0.0189.

My inner beaucrat (Glenn Springstead) is coauthoring a paper on price indexing at the National Tax Conference meetings at the end of this week. Unfortunately, the paper doesn't have much on Pozen but does go into some wonkery about the other various types of price indexing and the various parts of the formula and who would get affected.

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