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.

What Do Changing Estimates of Potential Output Tell Us?

I want to revisit the question we were debating last spring, about the space for additional expansionary policy in the US. How far is the economy from potential, in whatever relevant sense? This post will be the first in a series, and there will be a paper sometime in the fall.


One way to approach the question is to ask another one: How much of the shortfall in output relative to the pre-2008 trend is the result of the recession, as opposed to “structural” factors that would have led to slower growth in any case? The two questions are somewhat independent: Even if demographic factors, let’s say, were tending to reduce laborforce growth, there’s no reason in principle that couldn’t be overcome by stronger demand. On the other hand, even if we reject the idea that the recession itself resulted from a decline in productive capacity, it’s possible that a persistent demand shortfall could over time damage capacity in a way that can’t subsequently be repaired by restoring demand. Still, an output shortfall that is due to the collapse in spending in 2008-2009 is more likely to be reversed by increased spending, than one that is due to other causes.

Laurence Ball, DeLong and Summers, and Fatas and Summers, among others, try to answer the question of how much the decline in output is due to the recession, by comparing pre-recession estimates of potential output with more recent ones. A change in potential output attributable to changes in current output is often referred to as “hysteresis.” Changing forecasts are a reasonable measure of hysteresis: If predictable that structural factors like the changing age mix of the population were going to lead to slower growth, then it should in fact have been predicted; so systematic deviations from the forecasts must reflect something else. Now, if you are committed to the view that demand effects are strictly short-run, then a persistent deviation from trend necessarily reflects supply-side developments of some kind. But as long as we have no strong priors either way, the evolution of estimated potential over time should be informative about how much of the output shortfall is the result of the recession and how much is due to other causes.

The three papers do different versions of this exercise and all find that (1) the bulk of the slowdown in growth since 2008 is due to the recession, or at least was not predicted prior to it; and (2) there is no tendency for output to return to potential, rather, changes in current output are fully passed through to later estimates of potential. Here’s a simple version. The figure shows the CBO’s 10-year forecasts of potential GDP from 2002 through this year, along with historical GDP. (All are in 2009 dollars.)

potentialGDPThe horizontal axis shows the year the estimate is for. The different lines show estimates made in different years. So the purple line at the top is the ten-year forecast of potential output published in January 2002, while the pink line at the bottom is the ten-year forecast published in January of this year. What do we see?

First, there has been a systematic reduction in estimates of potential. While there are some upward adjustment in the early years, more recently all the adjustments have been downward. The estimates of 2015, for example, first made in 2005, has been reduced every year since then. Same goes for 2016 and all future years. These are not random errors. And they are not small: the estimate of 2016 potential GDP made by the CBO in 2016 was more than 10 percent greater than the estimate this year.

Second, there is no tendency for output to return to earlier estimates of potential. While the official output gap has gotten much smaller since 2009, this is entirely a result of the downward adjustment of potential; there has been no closing of the gap between output and potential estimated in 2009 or earlier years.

On the other hand, these revisions can’t be all due to the recession, since the CBO significantly reduced its forecasts of potential output growth over 2005-2007. The largest revision comes in 2009, after the first year of recession. (Again, these are January forecasts.) But there had already been significant downward adjustments at that point. (Especially, as we’ll see in the net post, in predicted laborforce growth.) Still, most of the deviation from trend reflects post-recession adjustments in potential.

It breaks down like this. Current GDP is 12 percent below what you would have predicted based on long-run growth rates up to 2008. The CBO puts the current output gap at around 2 percent. This reflects the fact that the CBO currently considers full employment to be 4.8 percent unemployment, slightly below the current level. The remainder of the 12-point gap represents a slowdown in potential output growth. How much of that was predicted in 2005? Less than none – at that time, the CBO’s forecast for 2015 output was 1.5 percent above the long run trend. By January 2008 — the last pre-recession forecast — the CBO had revised its 2015 forecast down by about 4 percent, to 3 percent below trend. In 2009, after the first year of the recession, it revised it down another 3 points, to 6 percent below trend. And over the past seven years it’s been revised down seven more times for a total of 5 points, to reach the current estimate of potential of around 10 percent below trend. So about a quarter of the 12 point gap between current GDP and its long-run trend was predicted before the recession.

Now the fact that the slowdown was not predicted before the recession, doesn’t prove that it is due to the recession. It does, I think, allow us to reject things like “aging of the baby boomers” as the main explanation for the shortfall: Something that easily predictable, would have been predicted. (And as we’ll see in a later post, demographic changes cannot in fact explain the slowdown in output growth— the effect of aging on labor force participation, while real, is too small to explain the actual decline, and it’s offset by a comparable but less-discussed shift in the other direction — the declining share of households with young children.) It is, however, possible that some new development (a “shock” in the jargon, but I don’t like this term) just happened to reduce the economy’s productive capacity at the same time it was recovering from the recession.

In their 2012 article, DeLong and Summers argue that the absence of wage and price growth is strong evidence against this latter explanation:

It is possible that these revisions reflect not … hysteresis but merely the recognition that previous forecasts of potential output were too high. However, an elementary signal extraction point rebuts this interpretation. … one should not reduce one’s estimate of potential output if lower-than-previously-expected levels of production are associated with lower-than-previously-expected levels of inflation. … Typically, the bad news that leads to a marking down of potential output is not news that output is lower than, but rather news that output and inflation together are above, their anticipated co-movement line. Such news is not in evidence.

Over the past four years inflation has only fallen further, so the point presumably still holds.

So if we take the unpredicted decline in potential as a measure of the effects of the recession, we’re left with something like this: Of the gap between actual US GDP and its pre-2008 trend, 75 percent is due to the continuing effects of the recession, 25 percent to other factors. That seems like a reasonable place to start.