When talking about the national debt, people tend to use absolute metrics like the size of the outstanding federal debt ($19 trillion total, $14 trillion held by the public) or ratios like the ratio the outstanding debt to GDP.  Instead of trying to fathom the raw numbers, it is a good idea to scale by GDP which is a measure of the value of annual output or income.  For the 2016 fiscal year, the federal deficit is estimated to be about $540 billion or 3% of GDP, and the outstanding federal debt held by the public at the end of the year will be about $14 trillion, or 80% of GDP.  Many people describe disaster scenarios should the ratio of the debt to GDP rise substantially above 100% of GDP.

It is interesting to me that the amount of outstanding debt (a “stock”) relative to a measure of annual income (a “flow”) is viewed as a key metric.  This is comparing two unlike things.  People don’t make this mistake when considering the debt burden of a company or a household.  Typically, in the private sector one looks at the ratio of interest expense to income (aka, DTI or “debt to income”) or the ratio of the stock of debt to wealth (aka, “leverage”).  The former ratio is a ratio of “flows” and the latter ratio is a ratio of “stocks.”  The ratio of the stock of debt outstanding to GDP is a strange mix of stock and flow.

Let’s apply the traditional private sector ratios to public debt.  The ratio of interest payments on the debt to GDP is akin to the private sector DTI.  In 2016, this ratio was $250 billion/$14 trillion =1.8%.  This is pretty low.  By comparison, a conservatively underwritten mortgage loan allows DTI of at least up to 28%.  Similarly, AAA rated corporations have ratios of interest expense to profit (the inverse of the “times earned interest ratio”) of as much as 10-15%.

In order to estimate GDP “leverage” we need a measure of country wealth.  One possibility is to look at the Household Balance Sheet in the Federal Reserve’s Flow of Funds report. The latest reading of Household Net Worth (March 2016) is $87 trillion.  This yields a “leverage” value of $14 trillion/$87 trillion=16%, lower than most non-financial companies and massively lower than most financial institutions.

Of course, Household Net Worth may not be the best measure of country wealth.   The proper measure would value the aggregate stock of capital, labor and technology and then subtract from this current debt and the present value of future government liabilities, like Social Security and Medicare.

Another way to think about the problem is to view annual consumption spending as akin to a dividend income on an equity security.  That is, the economy is an asset that currently enables annual consumption of about $12.5 trillion.   To value this “asset” we can use the Gordon Model which assumes a steady growth rate of dividends (consumption).  The formula for the Gordon Model is very simple:  Value = C₁/(k-g) where C₁ is consumption next year, g is the annual real rate of growth of GDP (currently running around 1.5%) and k is the discount rate.  The discount rate is the risk-free rate plus an appropriate risk premium.   The equity risk premium is commonly believed to be approximately 4% today.  Consumption is a lot less volatile than the stock market, so a reasonable consumption risk premium would be much lower than 4%, let’s say 1%.  And so we simply add 1% to the real rate of interest on government bonds, currently about 1.5%, to arrive at our discount rate of 2.5%.

Thus, we get an “asset value” of $12.5 trillion/(.025-.015)=$1,250 trillion.  National wealth would be this asset value minus liabilities, including current debt plus the present value of future liabilities.  Continuing with this line of thinking, perhaps we can reasonably estimate the present value of future liabilities using the same technique.  Social welfare spending is running today about 8% of GDP, but is projected to grow to 10% of GDP or greater.  Assuming 10% of GDP and applying the Gordon model with the same growth and discount rates, we get total liabilities of about $200 trillion and “wealth” of $1,050 trillion.

Based on these estimates of liabilities and wealth, GDP leverage is still pretty small, about 19% ($200 trillion divided by $1,050 trillion).

The main point here is that the value of GDP is really big, and really sensitive to the assumed growth rate.  By comparison, the current level of outstanding debt is not so big.

This suggests a thought experiment.  Suppose we envision a massive infrastructure spending project wherein we fix the roads and bridges, improve the ports, connect everyone, and establish a fund to research anti-cancer drugs.  Or, take some other combination of projects.   Suppose that with the investment of say, $10 trillion, that we could increase the rate of economic growth by .1%.  Would it be worth it?  Well, let’s apply the net present value rule which says that a project is worthwhile if the present value of benefits exceeds the present value of costs.  On the cost side we have the present value of cost = $10T.  On the other side we have the increase in the value of GDP which will be an 11% gain (the multiplier on Consumption increases from 100 (1/.01) to 111 (1/.009)) for an increase in value of $139 trillion.  This is a no brainer.

Of course one problem with this experiment is that we divert a huge amount of resources from the private sector to the public sector.  It is widely believed in some circles that, while basic public expenditures are necessary, in general public sector spending is less efficient than private sector spending, so the desired increase in the rate of economic growth very likely would not materialize.  Still, the thought experiment suggests the enormous benefit of even modest improvements in the rate of economic growth.  How could we accomplish this?  Well, we might start with fixing the tax code and streamlining economic regulation.