Trend, Forecast and Actual: Decomposing the Differences

Second post in a series. Post one is here.

The previous post argued that if we want to know how much of the slowdown in US growth is a result of the Great Recession, a reasonable starting point is to look at revisions to estimates of potential GDP since the recession. As it turns out, while CBO forecasts prior to the recession did predict slower growth than the long-run trend, the predicted slowdown was only about a quarter what we’ve actually seen. That suggests that most of the output shortfall relative to trend is due to the collapse in demand following the financial crisis, rather than to slower growth in the economy’s productive capacity.

The next natural step is to separate slower growth into various components and see how they behave individually. There are various ways to do this, but perhaps the most straightforward is the identity:

output = productivity * employment  = productivity * laborforce * (1 – unemployment)

The big advantage of this is that we are working with fairly directly observable aggregates. Another advantage, important for present purposes, is that the CBO gives the relevant components for its estimates of potential output. Productivity here means labor productivity — output per worker. As applied to potential, unemployment means the non-accelerating inflation rate of unemployment, or NAIRU — the unemployment rate supposed to be consistent with stable inflation, which is targeted by the central bank.

So, here are the CBO’s forecasts of the three components over the past 10 years. The format is the same as the figure for output in the previous post: The horizontal axis is the year being forecasted, and the different lines represent forecasts made in various years — the blue-green ones before the start of the recession, the orange-red ones after it. (The forecasts are published in January, so the 2009 one is the first to incorporate data from the recession.) The heavy black lines show the actual historical behavior of the variable.cbo productivitycbo laborforce

In the following graph, the forceast lines are for the NAIRU, the black line is for the actual unemployment rate.

cbo nairu

We see some interesting things here. With respect to productivity, there are modest downward adjustments in 2007 and 2008 but the big adjustment come later, especially in 2009 and 2014. And the later adjustments are not just to the level of productivity but to the trend.  Not only is there no convergence between actual productivity and pre-recession forecasts, the gap has continued to get wider over time. For laborforce, by contrast, the biggest adjustments come before the recession, especially in 2003, when the trend is revised downward. The post-recession revisions are smaller. The actual trajectory of the laborforce does show a definite reversion toward the immediate pre-recession forecasts. Finally, the estimated NAIRU was adjusted upward during the recession and back down since then with no systematic movement one way or the other. So the fairly stable gap between post-recession output and the pre-recession trend is a bit misleading. It combines two opposite developments, a widening productivity gap and a narrowing laborforce gap.

These results are summarized in the following table. The first column shows the difference between actual 2016 output and what you would predict by projecting forward the 1990-2006 trend. [1] The second column shows the deviation from trend that was already predicted in the CBO’s 2006 forecasts for 2016. The third column shows the revisions made since 2006.

Actual vs Trend Predicted vs Trend Post-Recession Revision
Output -14.1 -4.2 -10.4
Productivity -5.4 5.1 -8.7
Laborforce -9.2 -8.9 -1.8
Unemployment -0.3 -0.4 0.1

What do we see here? Again, if we look at the shortfall of GDP relative to the pre-2006 trend, about 30 percent was predicted by the CBO. But the picture is quite different for employment and productivity taken separately. The deceleration in laborforce growth (which is about one-third slower population growth, two-thirds declining laborforce participation) was almost entirely predicted by the CBO. But in 2006 the CBO was also predicting above-trend productivity growth, which would have largely offset slower growth of the laborforce. The downward revisions over the past decade have mainly been to productivity — 9 percent, versus only a 2 percent downward revision to potential laborforce. Unemployment does not play an important role in either case — both actual unemployment and the estimated NAIRU are very close to their 2006 values. (This is different from Europe, where higher NAIRUs explain a large part of the change in potential output.)

Now this is a bit of a puzzle. I mentioned in the previous post a couple articles on hysteresis; I also very much like this piece by Laurence Ball. But all of them discuss hysteresis primarily in terms of the laborforce — the long-term unemployed giving up on job search and so on. That doesn’t mesh well with the fact that the downward revisions in potential output reflect mainly slower productivity growth rather than slower laborforce growth.

One natural way to interpret this is that (as Claudia Sahm suggests on twitter) the downward revisions in potential output since 2007 simply reflect a correction to earlier overestimates to productivity growth, which perhaps gave too much weight to a one-time acceleration in the 1990s. I ‘ll return in a later post to why I don’t accept this. For now, let’s just say that we take seriously the Summers-Ball view that downward revisions to potential output since the recession are a measure of hysteresis. Then we have to broaden our understanding of what hysteresis means. We can’t think of it as mainly a labor-market phenomenon.

In the next post, I’ll discuss a couple remaining points on the CBO forecasts. Then, a post arguing that the simultaneous deceleration of employment, productivity and prices looks more like an extended business-cycle downturn than a decline in the economy’s productive capacity. Then we’ll look at demographics and laborforce participation. And then back to the question of productivity, which I’d like to link to Joan Robinson’s concept of disguised unemployment.


[1] I use the years 1990 and 2006 because those are two years where actual output is very close to the CBO estimate of potential.

The Non-Accelerating What Now Rate of Inflation

The NAIRU is back. Here’s Justin Wolfers in the Times the other day:

My colleague Neil Irwin wrote about this slow wage growth as if it were bad news. I feel much more optimistic. … It is only when nominal wage growth exceeds the sum of inflation (about 2 percent) and productivity growth (about 1.5 percent) that the Fed needs to be concerned…

Read that last sentence again. What is it that would be accelerating here?

The change in the wage share is equal to the increase in average nominal wages, less inflation and the increase in labor productivity. This is just accounting. So Wolfer’s condition, that wage growth not exceed the sum of inflation and labor productivity growth is, precisely, the condition that the wage share not rise. If we take him literally — and I don’t see why we shouldn’t — then the Fed should be less concerned to raise rates when inflation is higher. Which makes no sense if the goal is to control inflation. But perfect sense if the real concern is to prevent a rise in the wage share.