Tuesday 14 April 2015

A Comparison of the Long Term Effects of Private Sector vs Public Sector Debt

An improvement on the last post

Following a suggestion from Professor Steve Keen, I have made an update to my last post, to include in my regression the second derivative of the debt - the change of change of debt. The effect of this has been a great improvement in robustness. The reason is that, although an increase in the level of debt typically increases GDP growth for that year, there is also the problem of the direction of causality. In a year where the economy is doing badly, the poor performance of the economy will force an increase in the debt. Vice versa, when an economy is doing well, monetary policy may slow down the increase in debt. For this reason the change of change of debt helps to better isolate how increase in debt causes increase in GDP.

The other important change is that I am including government debt in the regression. Because change in government debt is almost always a response to market conditions, it is impossible to use this method to get a multiplier for the positive impact of government debt. I will leave this to people who understand it better than me. However, I can get an estimate for the negative effect of increased levels of government debt. 

This enables a comparison. For X amount of growth one can either use Y amount of private debt (using the multiplier, Mpriv, calculated below) or Z amount of government debt (using the multiplier, Mgov, provided by more knowledgeable economists) - a comparison of the long term costs, the coefficient of which I will call LTC, is possible by comparing Y*LTCpriv to Z*LTCgov.

The new test

For the new test, I have regressed four variables against the growth rate. These are a) level of private sector debt, b) change in private sector debt, c) level of government debt, d) change of change of total (government and private) debt. Variable d is used as a bellwether for the general economic condition and thus helps to improve the robustness of results.

First, I will show a scatterplot of the regression results - showing how just using debt levels can give a very good estimate for GDP growth - the results are 61% correlated to actual GDP growth. 

On an aggregate level, this prediction works pretty well. Below is a graph of actual average GDP growth vs a prediction made solely using the four debt variables:

As can be seen, this makes a pretty good prediction considering nothing is known about the economy other than debt levels (I think that the tick up at the end is related to austerity artificially affecting the second derivative).

The results from this are as follows.

Multiplier on Private Sector Debt:
Mpriv = 10.6%

Long Term Cost of Private Sector Debt:
LTCpriv = -1.5%

Long Term Cost of Government Debt:
LTCgov = -0.9%

And if anyone is interested, the change in change in debt coefficient (the economic condition proxy) was -8.9%.

What does this mean?

Supposing the economy is in a rut and, as a policy maker, you are given two choices to buy growth - either lower interest rates to increase private debt, or increase fiscal spending which increases public debt (in fact QE and helicopter drops are also possible but these are, to differing degrees, more frowned upon for now so I will ignore these here). You are trying to buy 2% economic growth above where it currently is.

The economy is not doing too well so let's assume a multiplier of 50% on government spending - ie. if the government spends $1m, $0.5m will be added to GDP.

To buy this growth one can either A) increase private sector debt by 2%/10.6% = 18.9%

Or one can B) increase government spending by 2%/50% = 4%

Now, the long term cost in terms of drag, DR, on future GDP per year is:

Case A: DRpriv= 18.9%*-1.5% = -0.28% per year

Case B: DRgov= 4%*-0.9% = -0.036% per year

Remember that this is for every year going forwards.

Conclusion: The cost of using private sector debt is almost an order of magnitude higher.

Given the two choices, public sector debt is always preferable. Of course other alternatives which reduce debt to GDP (possibly by inflation) but increase demand are even better. Helicopter drops and monetising of debt are the two that spring to mind.

As an explanation for 'Secular Stagnation'

I believe that the situation that we are currently in can largely be explained as a consequence of debt.

Below is the graph of expected GDP based just on debt levels and annual change in debt levels (not the second derivative, as this is cheating - it has some knowledge of GDP):

If this is the case, we can expect low growth until the debt overhang is reduced.

Below are individual graphs for the UK and the US. Both are severely hampered by the private sector debt overhang.

Due to a comment below, and the fact that a reader of this post may not have read the original post, I wanted to make a brief note on the mechanism for this effect. I believe that high debt overhang affects future economic growth in two main ways:

1) Because interest is being paid by the debtors to creditors. The marginal propensity to spend of the debtors is typically higher than that of the creditors (the creditors may in fact be foreign). Therefore demand in the economy is reduced. 

2) Because debt causes financial instability. Typically one gets an economically destructive boom and bust cycle as well as a misallocation of resources due to housing bubbles, financial bubbles etc.

I also wanted to comment on the probable reason why public sector debt is so much cheaper to the economy. The interest rate on government debt is lower than that on private debt. Hence the interest drag on the economy is lower.


  1. Excellent post. My only questions is how does this differ from a Balance Sheet Recession?

  2. Thanks! I suppose, if the definition of a balance sheet recession is that it is the paying down of debt that causes the recession, then the difference is that this is a drag on growth whether or not people are reducing their debt.

    The drag is caused by the payment of interest from those with a high propensity to spend to those with a low propensity to spend, and also because of the financial instability.

  3. "Drag caused by the payment of interest." You just hit the nail on the head sir.
    Great post!!

  4. Linear regression isn't applicable here. Clearly, the data isn't homoskedastic and the errors seem to be correlated (pull up a plot of the residuals if you don't believe me). I'm pretty sure this data is fat-tailed.

    1. Thanks for the comment Suvy.

      The data is slightly fat tailed (3.4 degrees of freedom on a t-location scale distribution) but I wouldn't say that it is enough to make linear regression inapplicable.

      However, I have run a robust fit and it comes up with the following coefficients:

      Mpriv = 10.1%
      LTCpriv = -1.56%
      LTCgov = -0.74%

      All are within the standard error of the least squares regression.

      But actually makes things look slightly worse for private sector debt relative to public sector debt!


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