As promised, today we're doing something more interesting with the Federal Reserve's data for the level of private debt that has accumulated over time in the United States than just calculating its amount, it year over year rate of growth (or velocity) and also the rate of change in its year over year growth rate (or acceleration).

Starting with our results for the acceleration for private debt, we first calculated its trailing twelve month average to smooth out the volatility in our results to better capture its general trends during the period from January 1955 through June 2015.

We next extracted the U.S. Bureau of Economic Analysis' data on the quarterly growth rate of real (inflation-adjusted) Gross Domestic Product (GDP) spanning the same period, using linear interpolation to estimate the real growth rate in the months in between the months ending each calendar quarter, and then calculating the trailing twelve month average of the real GDP growth rate to smooth out the volatility in the results and to better capture the general trends in real GDP growth rates over time.

We then graphed both the acceleration of private debt (dotted blue line) and its trailing twelve month average (solid blue line) in the chart below, in which we've also indicated the periods for when the real growth rate of U.S. GDP was falling (shown as the light red vertical bands). For added measure, we've also indicated the periods in which the National Bureau of Economic Research has determined the U.S. economy was in recession (darker red vertical bands).

What we observe in the chart above is a really remarkable correlation. When the general rate of acceleration of private debt in the U.S. is falling, very much more often than not, such periods either precede or coincide with the periods in which the real rate of growth of the U.S. economy was also falling.

We next calculated some very basic statistics related to that basic correlation. In the 726 months from January 1955 through June 2015, we counted a total of 395 in which the trailing twelve month rate of growth of GDP in the U.S. was falling and a total 366 in which the trailing twelve month average rate of acceleration was falling.

There were 245 months in which both the trailing twelve month averages of both the acceleration of private debt and the growth rate of real GDP in the U.S. were both falling. That works out to be a correlation of nearly 65% for periods in which the trailing twelve month average of private debt acceleration declined, or 62% if we look just at the periods in which the trailing twelve month average of the real GDP growth rate declined.

That works out to be very close to the results that Michael Biggs, Thomas Mayer and Andreas Pick found in their 2010 paper, in which they worked out the correlation between changes in the acceleration of debt and the level of employment in the U.S, which Steve Keen summarized that year (emphasis ours):

They first showed the cor­re­la­tion between what they called “the credit impulse”—the rate of change of the rate of change of debt, divided by GDP—and both GDP and employ­ment (for those who have access to research from Deutsche Secu­ri­ties, they have a sim­pler expla­na­tion of their analy­sis in Global Macro Issues for Decem­ber 17 2009: “The myth of the credit-less recovery”).

The chart below shows my con­fir­ma­tion of the rela­tion­ship with the data on the annual change in unem­ploy­ment in the USA and the annual rate of accel­er­a­tion of pri­vate debt since 1955. The cor­re­la­tion is –0.67: a stag­ger­ing cor­re­la­tion of a first and a sec­ond order vari­able over such a period, and across both booms and busts.

We noted above that the change in the rate of acceleration of private debt often either leads or coincides with changes in the real GDP growth rate, which is something that we can directly observe in the acceleration of private debt in the U.S. turning downward before as as the real GDP growth rate in the U.S. falls, and also as it turns upward either before or as the real GDP growth rate in the U.S. rises, which is very clearly evident during the periods in which the U.S. economy was in recession.

It occurred to us that the simple correlation between a declining rate of acceleration for private debt and a falling rate of real GDP growth isn't necessarily capturing the full dynamic between the two. So we went the extra mile and calculated the correlation for when the trailing twelve month average of private debt acceleration was either falling or negative and the periods in which the real growth rate of U.S. GDP was falling.

For the period from January 1955 through June 2015, we found that nearly 88% of periods in which the trailing twelve month average of private debt acceleration declined or was negative occurred when the U.S.' real GDP growth rate was falling, and if we look just at the periods in which the trailing twelve month average of the real GDP growth rate declined, we find that nearly 84% of those periods are ones in which the acceleration of private debt was either falling or negative.

Speaking of which, in looking at the period since June 2013, we see that the acceleration of private debt in the U.S. has been falling and, through June 2015, the most recent month for which we have data, has become negative. We expect that the U.S. Federal Reserve will update its data for the U.S.' private debt through September 2015 sometime in mid-December 2015.

Update 14 December 2015: Added the words "growth rate" in boldface type to the second to last paragraph above for clarification.

References

Political Calculations. The Position, Velocity and Acceleration of Private Debt. [Online Article]. 5 November 2015.

Biggs, Michael and Mayer, Thomas and Pick, Andreas, Credit and Economic Recovery: Demystifying Phoenix Miracles (March 15, 2010). Available at SSRN: http://ssrn.com/abstract=1595980 or http://dx.doi.org/10.2139/ssrn.1595980.

Keen, Steve. Deleveraging, Deceleration and the Double Dip. Steve Keen's Debtwatch. [Online article]. 10 October 2010. Accessed 28 October 2015.

Data Sources

U.S. Federal Reserve. Data Download Program. Z.1 Statistical Release (Total Liabilities for All Sectors, Rest of the World, State and Local Governments Excluding Employee Retirement Funds, Federal Government). 1951Q4 - 2015Q2. [Online Database]. 18 September 2015. Accessed 28 October 2015.

U.S. Bureau of Economic Analysis. National Income and Product Accounts. Table 1.1.1. Percent Change from Preceding Period in Real Gross Domestic Product. 1947Q1 through 2015Q3 (first estimate). [Online Database]. Accessed 28 October 2015.

National Bureau of Economic Research. U.S. Business Cycle Expansions and Contractions. [PDF Document]. Accessed 28 October 2015.