Searching for the origins of dark matter
from Follow the Money

Searching for the origins of dark matter

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Budget, Debt, and Deficits


Hausmann and Sturzenegger, if nothing else, have spurred a lot of work with a catchy title and a bit of clever accounting. 

We now know that:

  • Dark matter stems more from low (reported) returns on foreign direct investment in the US than high (reported) returns on US investment abroad. 
  • US firms operating in Ireland are very, very profitable.  Pepsi makes Pepsi concentrate in Ireland for sale back to the US because of the superior productivity of Irish workers, not because of the superiority of Ireland’s tax code.  Pfizer manufactures in Ireland for the same reason.  Yeah, right.  But even with the Irish super-profits taxed at Ireland's low (10%) rate, the average return on US FDI is not all that great -- a bit over 7% in 2005, by my calculations.  Actually, I am not sure that Irish super-profits show up in the US data, only that Philip Lane and Frances Ruane found them in the Irish data.
  • Most of the difference between the Ok (reported) returns US firms get on their non-Irish FDI and the terrible (reported) returns foreign firms get on their investment in the US (4.15% in 2005, a good year) comes from the fact that US firms operating abroad seems to come from reinvested earnings.  US firms reinvest a reasonable share of their earnings, while foreign firms operating in the US do not.   Or at least are not reporting any reinvested earnings to the US statistical authorities.   Actual dividend payments by foreign firms operating in the US and US firms operating abroad are pretty similar.  See Daniel Gros.
  • Dark matter might be more properly called dark anti-matter, as Higgins, Klitgaard and Tille argue, since most dark matter stems from the fact that foreigners lending to the US have not gotten (on average) 5% back a year.

I want to try to move the ball forward in three ways –

  • First, I want to show the US hasn’t operated as a financial intermediary selling what Hausmann and Sturzenegger call insurance services to the world.  Hausmann and Sturzenegger think the US sells the world safe US debt, uses the proceeds to buy higher yielding foreign debt and pockets the difference.   It is a nice story, but not one that matches the data – as I will show.  I suspect that Hausmann and Sturzenegger overgeneralized based on US lending to Latin America – a very small share of total US lending.  In recent years, the US actually has been borrowing low and lending very low – not borrowing low and lending high.
  • Second, I want to try to quantify just how much “dark matter” stems from differences in the way reinvested earnings are reported in the data.  Reinvested earnings show up as income on US FDI abroad but not as a payments on foreign direct investment in the US. 
  • And third, I want to try to quantify how much of the growth in “dark matter” from 2002 through 2004 came from falling US interest rates, not superior US know-how.

This is a long, data intensive kind of post – really more of a draft paper.  Be forewarned.   On the other hand, some of the results are kind of cool, in a balance-of-payments geek kind of way. 

By my calculations, stripping out the difference in reinvested earnings and the effect of low US rates from the 2004 data reduces the amount of US dark matter from $3270b to around $300b.   Put a bit differently, if foreign firms reinvested in the US at the same rate as US firms (reinvested earnings accounted for 4.7% of the 7.1% return on US FDI abroad in 2004 and only 1.7% of the 3.9% return on foreign direct investment in the US; my calculation effecively upped reinvested earnings to 4.7% and the overall return on foreign investment in the US to 6.9%) and if the average interest rate on US debt had been 5% rather than 2.63%, the US would have had an income deficit of around $122b in 2004, not a surplus of around $36b.  And no one would be talking about dark matter.

Much, much more below the fold.   One note. I originally put this up on Friday, but the graphs then stopped loading over the weekend.  The graphs are pretty crucial to the story, so I took it down until we could fix the problems.  My apologies.

To quantify the dark matter that comes from various sources, I had to do a bit of digging, and then reorganize the data.

The breakdown between reinvested earnings and dividend payments comes from the BEA’s Survey of Current Business (including the back issues).  The BEA also provides a more detailed breakdown of US and foreign income payments in its report on the annual revisions to the balance of payments data. 

That data allowed me to take dividend payments on portfolio debt out of the “other” category and get data showing the total amount of interest the US paid on its debt, and the amount of interest the US received on the money it lent to the world.  Once I had the relevant income stream, it was pretty easy to calculate an average interest rate on US borrowing, and on US lending  -- and to compare the two.

I also reorganized the data presented in the net international investment position in order to better highlight the potential sources of dark matter.   That is to sat that I matched the income streams from different assets against each other to see if they generated any dark matter – that is excess returns that helped keep the US income balance positive despite the United States formal debt.

The US had about $10 trillion in foreign assets -- $3.3 trillion of FDI, $2.5 trillion of portfolio equity and $4.2 trillion in loans to foreigners.   The US had around $12.5 trillion in foreign liabilities: $2.7b trillion in foreign direct investment in the US, $1.9b trillion in portfolio equity – i.e. foreign purchases of US stocks, a bit over $0.3 trillion (330 billion) in foreign holdings of US currency and $7.6 trillion in old fashioned interest bearing foreign debt.  The assets generated $376.5b in income, the liabilities required making $340.3b in payments.

I tried to match US assets with comparable liabilities when possible.  For example, I matched the $2.7b in foreign FDI in the US against $2.7b in US FDI abroad.  Foreigners investing in the US got $105.1b from their investment, while the US got $190.5b from a comparable amount of its direct investment abroad.   Had those income flows been equal, they wouldn’t have generated any dark matter.  But since the US got $85.3b more than it paid, in Hausmann and Sturzenegger’s terminology, the swap of US direct investment abroad for foreign direct investment  in the US generated $1.7 trillion in dark matter.

$80.7b of the $85.3 difference in income came from the difference in reinvested earnings, only $4.6b came from the difference in actual dividend payments.  That different in US and foreign returns on FDI stems almost entirely from the gap in “reinvested earnings” – as the next graph shows.


Since US direct investment abroad exceeds foreign direct investment in the US, the US also in some sense borrowed (issued debt) to invest abroad.  That too generated some excess returns, and thus some dark matter.

I also matched the dividend payments on US holdings of foreign stocks against the dividends on foreign holdings of us stocks, and then noted that since US holdings exceed foreign holdings, the US also borrowed to buy foreign stock.

And I matched some US lending to foreigners against foreign lending to the US.  This is what Hausmann and Sturzenegger call insurance – or it would be, except for the fact that in 2004, the US paid more to borrow from abroad (2.63%) than it got lending abroad (2.10%) so the US lost money in this transaction.  Almost $22b by my calculations.  That subtracted from the total “dark matter”

But a certain fraction of US debt is just debt – it cannot be matched against any external asset.  That is what it means to be a net debtor.  But even external debt can generate dark matter in the world of Hausmann and Sturzenegger.  Since Hausmann and Sturzenegger expect all debts to pay 5%, if you happen to be able to borrow for less, you can book the difference as an income gain, and a dark asset.  In 2004, this was a significant source of imaginary (dark) assets …. The US paid $52.5b less than it should have, creating over a trillion dollars in “dark” assets.

Finally, the US reaps a windfall gain from the fact that foreigners are willing to hold US currency, and effectively provide the US with an interest free loan.  Every dollar bill held abroad generate a dollar of dark matter.  This isn’t controversial.  Willem Buiter thinks it is the only real source of dark matter around.

All this is, as they say, just accounting. But the results are sort of interesting.  The following chart shows the sources of the dark matter than Hausmann and Sturzenegger inferred by looking at the US income balance.


Three things jumped out at me.

First, most dark matter comes from the difference in reported reinvested earnings.  The wine colored (mauve?) bar is by far the biggest.  Daniel Gros gets the Oscar.

Second, falling interest rates were a big reason why the amount of dark matter rose from 2000 to 2003.  The gap between what the US should pay and what it actually had to pay kept getting better.  That shows up in the orange-pink bar. 

Third, it turns out that the US got substantially less on its lending than what it paid to borrow – so insurance services generated a dark liability, not a dark asset.  Look at the dark purple bar at the bottom.

It is easy to see why in the following chart, which compares the interest rate the US paid on its debts, the interest rate the US receives on its lending and the interest rate on the two year treasury. 


It turns out that the interest rate the US gets on its lending followed the two year Treasury rate more closely than the rate the US paid on its debts.    Why?   Simple, most US external loans are very short-term, and denominated in dollars. 

Incidentally, my preliminary calculations suggest that the gap between what the US paid and what it got shrunk substantially in 2005 – which is one reason why the income balance didn’t deteriorate by more.   Sort of interesting.    Interest rates on US lending fell faster when interest rates fell and now are rising faster as interest rates rise.    Again, the most likely reason is that US financial firms make lots of short-term cross border loans (they finance all sorts of “entities” in the Caribbean – otherwise known as hedge funds)  …

Just to have some fun, I also did a graph showing how much dark matter would disappear if foreign direct investment in the US reinvested as much as US direct investment abroad, or alternatively, US firms reported as few reinvested earnings as foreign firms operating in the US.


I also calculated the amount of dark matter that the US would have if it had paid a constant 5% on its debt.  I kept the difference in returns between US borrowing and US lending – all I did has take out the impact of low rates.   Specifically, I eliminated the dark matter that comes when the US borrows for less than 5%, and I reduced the dark matter than comes from borrowing to finance direct investment abroad.  Rather than paying 3.4% and getting 7%, in my thought experiment, the US paid 5% and still got 7%.  


Bingo, no more dark matter.  Or at least not much more dark matter than can be explained by the unquestioned gains from issuing a currency that lots of folks around the world hold without demanding any interest …

There still is a bit of variability in the reduced stock of dark matter that is left.  It went up a lot in 2002, for example, and again in 2005 … 

Why?  Look at the following graph, which I kept on the same scale as the previous bar chart showing the sources of dark matter.  It turns out that foreigners investing in the US had a terrible year in 2002 (the recession), creating a big gap between the dividends foreign firms in the US paid to their head office and the dividends US firms received on their foreign operations.    And then in 2005 the spread between what the US pays on its debt and what it gets on its lending shrank.  It 2004, the US paid 2.63% and got 2.10%, in 2005, I estimate that the US paid 3.39% and got 3.3% …  reducing a drain on the US income balance, and thus cutting into the scale of a “dark” liability.


Apart from making a few assumptions to fill in the 2005 data, I didn’t do anything other than move numbers around – everything sums up.   Just as Hausmann and Sturzenegger came up with a different way of presenting the income balance, I put together a slightly different way of presenting the same data that Hausmann and Sturzenegger use to calculate dark matter.  

Playing with the numbers though helps us understand where dark matter comes from – what part is most likely the product of bad data collection (the difference in reinvested earnings), what part comes from the fall in US rates (a big chunk) and what part reflects differences in return on US assets and US liabilities.   And in turns out that if you get rid of the difference in reporting of reinvested earnings and the impact of low US dollar rates, the US isn’t the shrewd capitalist our friends in Latin America imagine.   

Kind of interesting. 

And if you are interested in the Wily E. Coyote moment, by my calculations, increasing the interest rate the US pays on its debt and its liabilities to 5% on its end 2005 stock would increase total US interest payments by about $40b.  That is a bit less than I expected, since the interest rate on US loans to the world rises by more than the interest rate on the debt the US owes to the world.   But given that most US lending is short-term and interbank, it probably should carry a lower rate than US debt, which includes more longer-term claims and things like corporate debt and mortgage backed securities.  If the US ends up paying 5.2% on its debt and only got 5% on its loans, the increase in interest payments on existing US debt would be more like $75b.     Add on the $50b in interest the US will need to pay on the $1 trillion of new debt the US needs to take on every year to finance its current account deficit and US net interest payments could increase by say $140-175b over the next two years, depending on how quickly the average interest rate on US debt rises.  

In other words, net interest payments could double over the next two years, rising from an estimated $144b in 2005 to a bit under $300b in 2007 …

More on:

United States

Budget, Debt, and Deficits