Tuesday, October 24, 2017

Wage growth

Sandy Black:
Nice discussion of why, since the 1970s, hourly inflation-adjusted wages of the typical worker have grown only 0.2% per year.
The linked article does "discuss" stagnant wages, but doesn't really say why. Their description of what makes wages grow is in fact just a series of mathematical definitions written as prose:
For wages to grow on a sustained basis, workers’ productivity must rise, meaning they must steadily produce more per hour, often with the help of new technology or capital. Further, workers must receive a consistent share of those productivity gains, rather than seeing their share decline. Finally, for the typical worker to see a raise, it is important that workers’ gains are spread across the income distribution.
The first part is a description of the Solow growth model with constant returns to scale, and a fixed exponent. The last bit is just tautological: a typical worker sees gains if and only if those gains are shared across the income distribution. They might as well have said that for a typical worker to see a raise, it is important that the typical worker sees a raise.

But then  the article just whiffs on any substantive explanation, telling us what "decline is plausibly due to" an that "[a]ssigning relative responsibility to the policies and economic forces that underlie rising inequality or declining labor share is a challenge." It talks about "productivity" and "dynamism", which are more quantifying the issues we are seeing than explaining them. While it is generally useful to quantify things, one must avoid creating measures of phlogiston or attributing causality to quantities you defined [2].

Anyway, I looked at hourly wages a couple months ago with the dynamic equilibrium model and found that the dynamic equilibrium growth rate was about 2.3% — therefore with 2% inflation, the real growth rate would be about 0.3%:

In this picture, wages going forward will continue to be "stagnant" because that is their normal state. The high wages of the past were closely linked with the demographic transition.

But this got me interested in the different possible ways to frame the data. Because we don't really have much equilibrium data (most of the post-war period is dominated by a major demographic shift), there's a bit of ambiguity. In particular, I decided to look at wages per employed person. I will deflate using the GDP deflator later (following this post, except with NGDP exchanged for W/L), but first look at these two possible dynamic information equilibria:

These show the data with a given dynamic equilibrium growth rate subtracted. One sees two transitions: women entering the workforce and baby boomers leaving it after the Great Recession (growth rate = 3.6%). The other sees just the single demographic transition (growth rate = 2.0%). These result in two different equilibria when deflated with the GDP deflator — dynamic equilibrium growth rates of 2.2% and 0.6%, respectively:

We can see that the 2.2% dynamic equilibrium is a better model:

The two models give us two different views of the future. In one, wages are at their equilibrium and will only grow slowly at about 0.6%/y in the future (unless e.g. another demographic shock hits). In the other (IMHO, better) model, wages growth will increase in the near future from about 1%/y to 2.2%/y. However both models point to the ending of the demographic transition (and the "Phillips curve era") in the 90s as a key component of why today is different from the 1970s, therefore (along with the other model above) we can take that conclusion to be more robust.

As for future wage growth? There isn't enough data to paint a definitive picture. Maybe wage growth will have to rely on asset bubbles (the first model at the top of this post)? Maybe wage growth will continue to stagnate? Maybe wage growth will happen after we leave this period of Baby Boomer retirements?

My own intuition says a combination of 1 (because they do in both the hourly wage and W/L models [1]) and 3 (because it is the better overall model of W/L).


Here's a zoom-in on the W/L model for tracking forecast performance:



[1] In fact, you can see the asset bubbles affecting W/L on the lower edge of the graph shown above and again here — there are two bumps associated with the dot-com and housing bubbles:

[2] Added in update: I wanted to expound on this a bit more. The issue is that when you define things, you have a tendency to look for things that show an effect creating a kind of selection bias. "Dynamism" becomes important because you look at falling wages and look for other measures that are falling, and lump them under a new concept you call "dynamism". This is similar to an issue I pointed out some time ago that I'll call " = 0.7 disease". If you were to design an index you wanted to call "dynamism" that combined various measures together, you might end up including or leaving out things that correlate with some observable (here: wages) depending on whether or not you thought they improved the correlation. Nearly all economic variables are correlated with the business cycle or are exponentially growing quantities so you usually start with some high , and this process seems to stop before your R² gets too low. I seem to see a lot of graphs of indices out there with correlations on the order of 0.8 (resulting in an  of about 0.6-0.7):

The issue with defining factors like productivity or dynamism is similar to the " = 0.7 disease": since you defined it, it's probably going to have a strong correlation with whatever it is you're trying to explain.


  1. Perhaps the framing is the issue, but it seems like you suggest that the demographic tradition caused wage growth. I would equivalently say that high labor demand caused both a high wage growth, and a demographic 'pull'.

    Maybe we other mean that the equilibrium state at the time matched to higher wage growth, which also induced growth otherwise.

    If we take pop growth as causal, there is literally no way to shift the growth path without mass immigration.

    But another option is that the root is in either demand growth or productivity growth, and those do have answers (I think you have looked at productivity before). That seems a more interesting (or less depressing) direction.


    1. It is plausible, but unfortunately this gets the causality wrong in the models above. Demographic shift in labor force precedes the demographic shift in NGDP growth, inflation, housing prices, etc:


      The demographic shift in labor force participation precedes nearly every other shock (starting in the 1960s, centered in 1975 -- the rest are centered in 1977 through 1980, and are narrower therefore starting later):


      It looks like women entered the workforce and that caused a shock to demand.

      Of course "stagnation forever because it's all about population growth" is a bit depressing from an economics standpoint. It isn't called the dismal science for nothing. Additionally, we shouldn't choose the subject of study using optimism or pessimism as a guide. I literally had no idea that something optimistic I learned about the unemployment rate (it seems to always gradually fall) would lead to this kind of pessimistic demographic determinism (they're actually the same underlying dynamic information equilibrium models).

    2. Actually something I found out about real GDP in an earlier post could actually mean the end of the demographic shift means the end of recessions (older recessions being caused by "industrialization" -- i.e. men entering the workforce -- and agricultural cycles). In the future there might not be any recessions unless they are caused by asset bubbles (the modern equivalent of agricultural cycles) bursting.

      That is total speculation at this point.

    3. Well, if AI is hyperefficient then this model does imply an absolutely massive wage growth as a consequence of AI.

      Alternately, I suppose, demand is caused by lack of time. If that is the model, then we would see demand correlate to hours worked.

      In the end, I still believe that we ought to try for predictive physical models as opposed to curve fits. Even wrong ones (just be honest about the likelihood and explanatory power).

    4. I will just say that curve fitting is usually the first step in science when data comes before theory. A good example is Planck's blackbody radiation law.

      I talk about this at length here:


      Also, the information equilibrium models are predictive (I in fact show a prediction above), so I'm not sure what you mean by "predictive" that is a quality we ought to aim for that somehow isn't exhibited by the information equilibrium approach.

  2. Interesting as always Jason. Since you are now positing that we have reached thermoeconomic equilibrium (maybe) with a stable workforce, I wonder if you have given any thought to Michal Kalecki's work on the endogenous origin of the business cycle. He states that is caused by fluctuations in business investment which are inherent in the profit recovery cycle. I had been meaning to bug you about what you thought about this, and now since you have apparently vanquished the business cycle, this might be a nice time to ask your opinion: Kalecki and the business cycle

    1. Ha! I haven't really "vanquished" the business cycle -- I just thought it was a really odd possible interpretation of the data.

      About Kalecki, I am not sure. I am under the impression that the business cycle itself is more of a social phenomenon which is why it is random. Then again, the interest rate predictor of recessions is something like Kalecki in the sense that the interest rate represents the price of investment. As investment opportunities become scarce, the interest rate rises -- and if it is above equilibrium (i.e. too much investment) for too long, there is an eventual crash. But I haven't gone into too much detail about that specific interpretation yet and it's probably something I should think about since lots of people like Kalecki and might find that argument in favor of information equilibrium convincing.


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