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.

pot 6

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.

  1. Capacity Utilization (TCU)
  2. Unemployment rate (UNRATE)
  3. 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

  1. 1967 to 2nd quarter 1990
  2. 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.

Regression Statistics
Multiple R 0.950
R Square 0.903
Adjusted R Square 0.900
Standard Error 50.45
Observations 108
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?

pot 7

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.

pot 8

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…