When workers are doing badly you can always count on a large number of economists to come forward with ways to argue it really ain't so. For example, we have heard endless stories about how our price indices hugely overstate inflation — we're actually way better off than we think we are. Or, they point to the growth in non-wage benefits. One problem with that story is that non-wage benefits have been shrinking as a share of total compensation in recent years, not growing, but whatever.

One recent effort along these lines, which got mentioned in a NYT article, is the argument that aggregate wage growth is being depressed by the retirement of older, more highly paid workers. The argument is that individual workers are actually seeing a healthy pace of wage growth, but the change in composition leads to the aggregate growing more slowly.

While this argument has been given credence by many, it suffers from a simple logical flaw. It is not the change in the age composition of the work force that matters for the aggregate rate of change in wage growth, but the change in the change (the second derivative for calculus fans).

To see this point, imagine that everyone's wage rises at the rate of 3.0 percent annually and there is zero change in the age composition of the workforce. In this story, average wage growth would obviously be 3.0 percent. Now suppose that one percent of the workforce retires this year and is replaced by new entrants. Suppose that these retirees earned 50 percent more than the average and the new entrants earn 75 percent as much as the average.

The lower age for this one percent of the workforce would reduce the aggregate rate of wage growth from 3.0 percent to 2.74 percent. In this story, we could accurately say that changing demographics had slowed the pace of wage growth.

Now suppose that in the following year everyone's wage rose by 3.0 percent and again we saw one percent of the workforce retire to be replaced by new entrants who got half of their pay. In this story, the 99 percent of continuing workers see 3.0 percent wage growth. And, this year's new entrants should get 3.0 percent higher pay than last year's new entrants. This means that average wage growth should be 3.0 percent, in spite of the retirement of higher paid workers.

This is the problem of the age composition explanation for slow wage growth. While that may have been a useful explanation for slower wage growth when baby boomers were first hitting retirement age in large numbers, say 2010 to 2015, it can't make much sense in 2017. The oldest baby boomers are now age 71. The youngest are age 53. We have been at or near peak retirement rates for some time now. Any incremental increase in the rate of retirement in 2017 compared to 2016 would have to be extremely small, if it's positive at all.

In short, this story really can't hold water. There may well be some groups of workers who are doing well, while others are doing poorly, but the aggregate pace of wage growth should give us a pretty accurate measure of how workers are doing, and that's not good.



Luke's comment below was more careful in his arithmetic than I was. (I forgot that the average wage of the 99 workers who stay in the work force is not 99 percent of the total wage bill in year one if a worker earning 1.5 times the average just retired.) He is absolutely right, and if we do the arithmetic right then the retirement of the most highly paid workers can reduce the average rate of wage growth even if it continues at the same rate year after year. I should have been more careful and apologize for doing the exact opposite of what I try to do on this blog. I took something that was reporting correctly in the media and made it wrong.

Let me make two additional points on this issue. There is a countervailing factor, but it is not a simple arithmetic point. Most research shows that age-experience related wage growth tends to be weak as workers approach retirement. The idea is that workers get rewarded for gaining experience earlier in their career as they are gaining skills. After they have been in the workforce for 20–25 years, their additional experience no longer offers much of a premium since the additional skills gained from another year of work is not large. (This paper gives some of the evidence, as well as many references, on this point.)

This means that, other things equal, wage growth should slow when we get a large segment of the workforce in the heavily experienced segment of the workforce. This would have implied slower wage growth towards the end of the last decade as the oldest baby boomers were in their early sixties and most baby boomers were in their fifties.

That doesn't change the point that having the highest paid workers retiree should still slow the pace of wage growth, which I got wrong. But it means that as the percentage of workers in the heavily experienced cohorts declines due to retirement, the rate of wage growth should be accelerating for that reason. In a single year, this would not matter much, but over say a five to ten year period, if the share of the workforce in the heavily experienced cohorts falls by, say 5 percentage points, this could make a substantial difference in wage growth, other things equal.

The other point is that the age-experience story should be one that is based on productivity growth. In other words, the loss of the older worker due to retirement should be associated not only with slower wage growth, but also slower productivity growth. It should not be an explanation for a gap between productivity and wage growth. 

In the last three or four years, there has in fact not been a gap between productivity growth and average wage growth, as productivity growth has been extremely slow. However, there was a gap between productivity growth and wage growth (including non-wage compensation) in the years 2008–2011, as the labor market collapsed due to the recession. We might expect this gap to be largely reversed in a healthy labor market, meaning that wage growth would substantially outpace productivity growth. This has not happened thus far in the recovery.

None of this is an excuse for my sloppy arithmetic, but these are factors to be kept in mind as we assess wage growth going forward.