Is Real GDP at Potential?
I will present a way to determine potential real GDP using a regression of past data. First take the official CBO potential and subtract it from real GDP.
When the red line is above zero (0), real GDP is over potential. Normally the red line rises above potential before a recession. So it looks as though we are from a recession at the moment.
Now I will do a regression with this line against 3 variables.
- Capacity Utilization (TCU)
- Unemployment rate (UNRATE)
- Labor share index, non-farm business (LSI)
Generally in the regression, capacity utilization and unemployment will represent real GDP. Labor share will represent changes in potential.
But I will select parts of the line above for the regression. Yes, I am cherry-picking because I do not trust the CBO potential of the 1990’s. The CBO had a terrible time ascertaining potential in the 90’s with new technologies and such. The CBO is still having a terrible time as they constantly adjust potential.
The time periods for the regression are
- 1967 to 2nd quarter 1990
- 1st quarter 2004 to 2nd quarter 2007
I take out the 1990’s and the data since the crisis because there are more doubts about their validity.
Here is the report of the regression.
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | 0.950 | |||||
| R Square | 0.903 | |||||
| Adjusted R Square | 0.900 | |||||
| Standard Error | 50.45 | |||||
| Observations | 108 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 3 | 2452450 | 817483.4 | 321.21 | 1.99E-52 | |
| Residual | 104 | 264682.6 | 2545.02 | |||
| Total | 107 | 2717133 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | -829.32 | 237.82 | -3.49 | 0.000717 | -1300.93 | -357.70 |
| TCU | 23.37 | 2.20 | 10.63 | 2.62E-18 | 19.01 | 27.72 |
| LSI | -8.12 | 2.25 | -3.61 | 0.00048 | -12.59 | -3.66 |
| UNRATE | -41.84 | 5.14 | -8.14 | 8.93E-13 | -52.03 | -31.65 |
The adjusted R square is 90%. The P-values are low.
What does this regression look like plotted against the official line above?
The new plot (green line) is a way to assess real GDP in relation to potential. The line tracks well with official numbers before 1990 and before the crisis.
But how does the regression fill in the time periods left out of the regression? It shows that real GDP was over potential in the 1990’s in a moderate way as compared to the steep rise to a very high spike seen in official data. The line implies that in the 90’s, real GDP went over potential about to the same extent as before the 1980 and 1991 recessions. (Maybe the Fed did not have to raise the Fed rate as much as they did near the turn of the century.)
The regression implies that real GDP was sitting at potential for a few years before the crisis.
These differences from the official line (red) are somewhat reasonable.
Yet, now the regression is implying that real GDP reached potential during 2014. This may also be reasonable because one might expect unemployment to drop quicker than expected when real GDP reaches potential.
Note: One might assume that labor share is fairly constant and that the real driving forces behind the regression are capacity utilization and unemployment. However, labor share itself was changing in response to these cycles of real GDP around potential.
When labor share drops, the regression says that potential drops. And when labor share rises, the regression says that potential is rising. When labor share drops, real GDP seems to move faster toward potential, because according to the regression potential is dropping toward real GDP.
- Is real GDP at potential?
- Will real GDP rise much more?
- or Will the utilization of labor and capital stabilize now if real GDP is at potential?
- Will the decline in capacity utilization during March stick around?
- Even if labor share was to rise now, would real GDP still seem to stabilize around potential according to the regression? So that a rise in labor share is matched by changes in the utilization of labor and capital to keep real GDP near potential?
Time will tell…
Does the past foretell the future? I never thought so. Things change, old rules don’t have a good track record.
An R square of 90 is pretty impressive. How did you get to that number?
In the chart it says 23.36 * cap ex, blah, blah. Why two decimal places? Did you sit there and change the number down to 0.01 to get to R90?
You take data, all from pre 2007 and then make conclusions about something in 2015. As you’ve reported a gazillion times, EVERYTHING changed from 2008 on.
In 2015 there are 21 central banks that are pursuing unprecedented monetary policies. There are trillions of government bonds that have a negative yield. G-10 short term interest rates have never been lower than today.
Very different world today. Don’t rely on 20 year old tea leaves.
What does your model say if labor share goes back to its peak or to its 1995 levels? As an advocate of calculus for everyone, I believe more models need to look at rates of change. I suspect that labor share depends on GDP growth, possibly also on the difference between GDP and potential GDP.
I don’t see your result as inconsistent with wage increases coming when we get closer to potential GDP leading to increases in potential GDP. Which makes the model less valuable for prediction.
The ’90s still shows a period of “unprecedented” stability and somehow the ability to really kick the can down the road in terms of the plug getting pulled on the party.
I wonder if that is really true, or if there is some other factor that is hard limiting the calculation there in one direction or the other.
It does track nicely with what we believe to be the case about the period from 1980 though, this last recession being more or less as bad as the one in the 80’s, the gradual recovery (in fact the slope is nicely paired against the other recoveries post 1990).
That it fits what we expect in this case makes me worried that the formula is somehow informed by expectations.
Arne,
If labor share rises back to 1995 levels, the intuition is that real GDP will level out at potential. When you see real GDP level out in the 1990’s and before the crisis, capacity utilization stopped rising during those periods. Unemployment can still come down because there is profit potential in more labor hours, but there is no more profit potential in expanding capital usage.
Yet I have little expectations that labor share is going to rise much before the next recession. The labor share index may reach between 99 and 100. But that would mean the top end of business cycle has come and that the Fed is terribly behind the curve.
J Goodwin,
I look at that spike of real GDP over potential in the late 90’s, and I think, What was the CBO thinking? Did they really think that real GDP could be that far above potential?
There were many economists saying the CBO data was wrong. … me too.
There was a lot of stability during the 90’s as you say. I feel that monetary policy reached the sweet spot perfectly. Then the Fed seemed to think that real GDP was far above potential and raised rates.
On another note, it is interesting how the line of my regression is a lot smoother than the official line.
And you are right, the model above is not for predicting, but for seeing where we were and where we are. But it does not predict how labor share will change, nor how productivity will change, nor how real GDP will change.
Edward,
if you want to make your argument convincing – you need to superimpose a third graph, core inflation (perhaps a derivative of it – for instance moving average rate of change).
Reason,
I actually checked rate of change of headline and core inflation on the graphs above before I posted. I was going to add it, but then I cut that portion out of the post not to make it too long.