Wednesday, January 30, 2013

Does Modigliani-Miller apply to countries?

If it does, the capital structure of the US is just fine.  Current GDP is 15.8 trillion.  Let's apply a  real discount rate of 4 percent (which is probably high, given that the yield on 10-years TIP is negative), and assume a real long-term growth of 2 percent (which is likely low).  This means the country is worth about $316 trillion (this figure includes human capital as well as asset values).

Total debt outstanding in the US, public and private, is $55 trillion.  So we are about 17 percent debt funded, which means we are about 83 percent equity funded.  This should be OK.  What I am missing here?

(note: it was Matthew Yglesias' Slate piece today that got me thinking along these lines).



Leigh Caldwell said...

Nice idea, though is GDP properly considered analogous to profit, or is it in fact more like revenue?

I realise this is why you specify human capital - so the wage component of GDP is presumably meant to represent a return on that capital. But humans have operating costs too - perhaps it would be more appropriate to count disposable income as the "return" on human capital, rather than total wages?

As always, applying models designed for price-taking entities in a competitive market to mostly closed nation states is risky - lots of micro theory is of limited use for macro.

Your deeper point holds, of course: on any measure, the asset value of the US far exceeds its debt load. One could quibble that the supposed long-term costs of Medicare and Social Security under current policy should count as debt, but those policies are certain to be modified.

Anonymous said...

I like this analysis. I think you are missing the off balance sheet debt (pensions, healthcare etc.)

Don Coffin said...

This really isn't a comment on this post. I recently (on Brad DeLong's blog) ran across the course outline for a stat clas being taught by Cosmo Shalizi; here's the first assignment:, which is titled "What's That Got to
Do with the Price of Condos in California?" Here's the data set for it:, What do you think of the assignment? (Asking because the topic of the assignment is interesting...)

Don Coffin

Marry Jones said...

I do not even have to take a closer look at all those numbers provided; no calculation is required to see that we are closer than never to a very serious problem. The country is most likely going to default on its existing loans once it hit the debt ceiling in a few months. We can suppose that we could have get another loan (I am saying this as if it is as easy as if an average person with a job can get fast payday loans online or what so ever). But how about paying interest rate on the loans already and who is going to loan us one more time? I would certainly not approve a loan for a country the US has become.

willie green said...

What is most interesting is that even if asset figure is much lower. If we assume taking human capital out of balance sheet still leads to a value of at least 125 trillion the country still has net equity of 70 trillion. This means the country is more than solvent.

Unknown said...

There seems to be some confusions.
1) MM can be applied to only a sole accounting unit. In your case, there are lots of accounting units. Because somebody's debt is another's asset, it needs consolidation.
2) GDP is not only the aggregate of product, but that of expenditure.
All the people cannot reduce his debt by saving at once.
3) MM assumes the insider(share holder) and the outsider(debt holder). But in your case, there exist only insiders.

GL said...

So I assume 4% is the WACC, which should be used to capitalize unlevered cash flows, or free cash flow to the firm. However, GDP is not free cash flow to the firm, and it’s not really revenue either, so I think the formula is flawed. I don’t know how to calculate FCF to the firm for the entire nation, so I am not going to try.
I think it’s a much easier to determine US government’s capital structure though (but still no perfect way, at least not that I know of) by capitalizing US government’s net income by its cost of equity. I am not sure what the cost of equity is, but I know net income is negative, that means our market capitalization is really zero. Even if we can figure out the FCF to the firm for the US government (which I don’t know how to get), I am sure our enterprise value is a lot less than 316 trillion (US gross tax receipt is around $5 trillion, let’s say 20% margin (based on my experience, a 20% margin is very generous), then we’re looking at $25 trillion EV, less debt of $17, then we’re looking at 68% debt, 32% equity. This is a very simple back of the envelope calculation, so don’t take it too seriously.