by Daniel on October 1, 2003

This should be classified as “playing with numbers” rather than serious economic analysis, but I found it interesting at least. Basically, following on from Chris’s demographics post earlier in the week, I thought I’d follow up an idea I’ve had for a while and carry out some “financially adjusted demographics”. The idea is quite simple; there’s two ways in which you can add to a country’s effective labour power:

1. Increase the population
2. Acquire overseas assets, effectively giving you a claim on the population of other countries.

It’s always struck me that demographic analyses (particularly those carried out by people looking at pensions issues) tend to fixate on the first and ignore the second. Turns out that it doesn’t make a huge difference to the numbers, but it does make a difference.

Basically, my modus operandi was this; in any given year, the current account balance is (by accounting identity) equal to the net amount of financial claims acquired on the outside world. If you have a surplus, you’re piling up claims. If you have a deficit, other people are piling up claims on you. Easy enough.

I then made a monstrous but superficially attractive simplifying assumption; if you take the GDP per capita and the life expectancy of a country, then you can calculate the capitalised present value of the GDP produced by an average person over his or her life for that country. This allows you to convert the dollar amounts of assets and liabilities into rough population terms. So the idea is, say, that if the capitalised value of the GDP produced by an Elbonian is $1,000,000 over his life then in principle, whenever Elbonia has a net external debt of $1,000,000, then that’s equivalent to having one Elbonian spending his life working for foreigners. I got the idea from the people who calculate “Tax Freedom Day”.

I’ve set out the calculation for the G5 below. You’ll note that for each of the economies, I’ve assumed that the long term growth rate is equal to the discount rate used for capitalising the GDP. This is because I can’t think of any other relationship between the two that makes sense, but I guess if you really wanted to, you could email me and I’ll send you the spreadsheet so you can put your own numbers in. Note that the data comes from the CIA factbook, and the current account figure given is a fairly simplistic net exports measure, but it ought to be ballpark. If a thing’s not worth doing, it’s not worth doing properly, that’s what I say.


The USA still comes out far and away the best. Still, it’s a sobering thought that more than a twentieth of the population growth is required to finance the current account, and this is mainly because of the very high GDP per capita; if you took the US down to the G5 average, it would be more like one in ten. The UK looks really bad; our growth rate isn’t that good to begin with, and even a quite small deficit makes a material difference. Germany manages to rescue what would be an absolutely horrendous population growth rate with a substantial surplus, ending up merely worrying.

The bottom three rows do the same sort of calculation, but as their base they use the international investment position rather than the current a/c balance. The IIP is basically the stock equivalent of the balance of payments; it’s a measure of domestic ownership of foreign assets net of domestic ownership of foreign assets. And the results (because we’re of necessity dealing with bigger numbers) are a bit more interesting. The USA jumps out the page as the only net debtor, to the tune of a cool two trillion dollars. And this is the equivalent of over 800,000 US productive lives. It’s a John Birch Society nightmare; if the United Nations had demanded that nearly a million Americans be forced to work for other countries for their whole lives, there would I imagine be a bit of an outcry, but the last ten years’ trade deficit has accomplished the economic equivalent. Japan has got 600,000 foreigners already under harness to work at financing their pension timebomb and is recruiting more at a rate of 180,000 a year. And the British Empire (in the sense of foreign lives controlled by the UK economy) has dwindled to a measly 6,706 souls. That wouldn’t even fill a football stadium.

(By the way, for God’s sake don’t show this to your economics professors. I must reiterate that it’s as spurious as hell, although no more spurious than a lot of things you see in the newspapers).



dsquared 10.01.03 at 9:01 pm

I sincerely hope that this looks as good on your screen as it does on mine. I realise the table is a bit wide, but the alternative was to leave out Japan.


msw 10.01.03 at 9:23 pm

The CIA world factbooks gives its GDP numbers in PPP, but its debt numbers are in actual dollars. I think you need the same units for the above chart to work.



anon 10.01.03 at 10:23 pm

Uh Britain comes out worst, US second.
The other guys are all in negative figures, which means that they arent wasting any pop growth on their foreign debt.


Damien Smith 10.02.03 at 12:23 am

Is this in discrete or continuous time? Ramsey or OLG?

Nah. You already said it’s spurious. I could nitpick, but I’m not gonna.


Atrios 10.02.03 at 1:59 am

This smacks of the reasons for Hitler’s territorial ambitions. Though, for him it was land to feed the aryan people. Obviously, the resident populations were, uh, expendable.


Tom T. 10.02.03 at 2:03 am

Maybe I’m mistaken, but it seems to me that your analysis confuses principal and interest. Grossly simplifying, the current account measures the principal amount of debt that Elbonia owes to foreign lenders, right? The work done by Elbonians for the benefit of foreigners, however, should be measured as the amount needed to pay interest on that debt. The principal amount cancels out because it’s on both sides of the equation; i.e., the reason some other country has a claim on Elbonia is because the other country first gave Elbonia that amount of money to use.

An example: Suppose the Bank of Elbonia has a cash-flow problem on Sep. 30, so it borrows $1 million abroad on an overnight loan from the Bank of Frobozzia. That’s the last day of the fiscal quarter, so that $1 million shows up on Elbonia’s current account. On October 1, the Bank of Elbonia repays the $1 million to the Bank of Frobozzia, plus $100 interest. Is the amount of work that Elbonian workers did “under harness” to Frobozz the $1 million or the $100? I think it’s the latter, but I think your analysis assumes it’s the former.

Apologies if I’m missing something. In any event, even if I’m right, this doesn’t change your ultimate conclusion, just its magnitude.


Andrew Boucher 10.02.03 at 5:13 am

Does the analysis include counterparty risk? Suppose foreigners buy a lot of American MBSs and then Fannie and Freddie go belly up and they don’t get their money back. Then Americans have kept the suitcases and the toys, and the foreigners have nothing but worthless paper.


dsquared 10.02.03 at 6:40 am

Tom: I see what you mean, but I’m implicitly assuming that the current a/c deficit has been spent on consumption and so the principal amount isn’t available for a quick repayment like that. In the case of the US, I think that’s a reasonable first approximation.

Note also that your example is partial. The £1m loan would show up on the capital account, not the current a/c and would presumably have to have a counterpart in the current a/c. The question of what that current a/c item was an whether it could also be reversed as easily as the financial flow is key to making the example work.

Damien: Fool that I am, I actually spent five minutes wondering whether it was worth the trouble to do the compounding continuously.

msw: Yeh, but they’re dollar PPP estimates. The point of PPP is to get a more realistic estimate of the size of the local economy in $, so I think I’d defend this.


Mike D. 10.02.03 at 7:12 am

Doesn’t the crux of the problem for Germany and other countries facing long term population decline lie in the shrinking labor force, rather than the population as a whole? It seems that rather than “net new citizens” you want “net new workers”, balancing workers entering the labor force with retirees. I think the picture would look very different, and much worse for every country on the list. Check the World Population Data Sheet from the Population Reference Bureau at for the simplest global summary of population data by country. We’ve never seen age structures so weighted to the elderly population in any modern human society. I’m not sure how it will work.


dsquared 10.02.03 at 11:51 am

Potentially a good point, although you’d then have to capitalise the average wage rather than GDP per capita, I think.


Sniffy McNickles 10.02.03 at 3:46 pm

I think your assumptions are falling for the lump of labour fallacy.

If my labour has a net future value of $1M, what are the underlying assumptions for that number? Are you assuming I’m doing a rational minimax of my hourly input against value of my efforts for a given task?

(As an example, I currently work about 25 billable hours a week on software development and about 25 nonbillable hours a week on paperwork and lead development for the company I own. This is my own estimate of the best choice for me. It could be that I could double my price, work 12.5 billable hours a week, and cut some of that paperwork. Then, of course, I could use the 15 or so hours to flip burgers, thereby marginally increasing my income. Decide for yourself whether or not the fact that I don’t is a market failure.)

I realize you’re talking macroeconomics, but even there overall changes to the nature of an economy fall to the lump of labour. India is making a concerted effort to increase the value of a unit of labour, as is China. I fully expect to see massive changes in the work habits of both of those countries over the next 15 years as a result, if they can continue course. I don’t believe any estimate of the future value of a citizen unit can be used for any meaningful purpose.

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