Home > Economics > Nick Rowe’s utterly brilliant argument that public debt can be a burden to future people

Nick Rowe’s utterly brilliant argument that public debt can be a burden to future people

I didn’t properly understand Nick Rowe’s overlapping generations apple economy model the first time I read it. Like many people, I used to think it was an identity that debt can never be a burden to future people, considered as a whole. At any point in time bonds are held by people alive, and people who pay taxes are alive, so how can bonds and taxes be a ‘burden’ to the set of people alive at a particular point in time? Isn’t the burden of a taxpayer to pay bondholders automatically offset by a benefit accrued to the bondholder? Here’s why that identity is wrong (I almost exactly copy Nick’s model, but with less econ-speak).

Assume any person alive produces 100 apples a year. In year 1, Annie is the only person alive. The government* says ‘100 free apples for Annie’! This is financed by the government borrowing Annie’s apples, promising to give her 110 next year (10% interest). Annie produces and consumes 100 apples.

At the beginning of year 2, Annie gives berth to Bessie, and there’s been a 10% increase in apple productivity to 110 apples. Annie and Bessie each produce 110 apples. Annie’s bond matures and needs to be paid back. The government finances the 110 apples it owes to Annie by issuing a bond bought by Bessie. In year 2, Annie eats 220 apples, Bessie none. At the end of year 2, Annie dies of old age.

In year 3, Colin is born to Bessie, and apple productivity increase by 10% to 121 apples each. Bessie’s bond matures, but since Colin is a man and can’t give birth to anyone, and Bessie will die at the end of the year, there’s no market for a bond as there’s no prospect for it being paid back. Therefore, the government taxes Colin and takes his 121 apples and gives them to Bessie. Colin gets no apples, and Bessie gets 242. Bessie dies at the end of the year.

In year 4, apple productivity increases by 10%. Colin produces and consumes 133.1 apples and dies at the end of the year.

Had Annie the government not issued any bonds, Annie would have eaten 210 apples rather than 320. Bessie would have eaten 231 instead of 242, and Colin would have gotten 254.1 apples rather than 133.1. The debt accomplishes a transfer of consumption from Colin to Annie even though they weren’t alive at the same time, and even though (in any given year) the output was exactly the same and was consumed only by people alive at that time.

Wow, I got chills just writing that.

The lesson is: overlapping generations screw up a seemingly compelling identity statement. I can now fully understand why Bob Murphy was so astounded to change his mind on this. In fact, my mind is so thoroughly blown right now that I’m left seriously wondering which other models I use have some kind similar deficiency that I haven’t yet noticed.


*Assume for the sake of argument the ‘government’ is a deus ex machina

Categories: Economics
  1. David Franklin
    January 6, 2012 at 11:37 pm

    Richard – I’m no economist so sorry for my lack of background and/or understanding! What’s the identity you’re referring to that says bonds and taxes equalling out means no burden to any generation, and why does the relatively well-known concept of a pyramid scheme not disprove it instantly? Colin being a man, or debt being unserviceable in the long-term, seems to me to be exactly the same as being stuck on the bottom of the pyramid, and the transfer of consumption from the bottom to the top is something that people have fallen for / been warned against since the dawn of time.

    • January 6, 2012 at 11:42 pm

      So, the argument is that all payments are made between live people. If you then assume no difference in output in any given period, it seems intuitive that no one is ‘burdened’ by the payments. Output is the same, and not transferred between periods. Therefore, there is no burden between periods (‘past’ and ‘future’ people). But people (including myself) basically overlooked the fact that people inhabit multiple overlapping periods. This example brings out that fact.

  2. December 31, 2014 at 6:20 pm

    The government also pays back debt, not just by borrowing, but by printing money through open market operations. This article debunks the Krugman “we owe it to ourselves” argument: http://www.thecommentator.com/article/2144/debt_we_don_t_owe_it_to_ourselves

  3. December 31, 2014 at 6:30 pm

    One of the striking features about people who advocate higher government debt is that they rarely envision themselves being among those paying it back. Thus, when people say increased government debt is OK because “We owe it to ourselves”, what they actually mean is that increased government debt is OK because “Someone else owes it to ourselves.” Collective identities like “we” and “ourselves” obscure the issue. When it comes to government debt, the real question is, “Which individuals owe it to which other individuals?” http://www.thecommentator.com/article/2144/debt_we_don_t_owe_it_to_ourselves

  1. January 7, 2012 at 8:47 am
  2. January 22, 2012 at 5:22 pm
  3. April 12, 2012 at 10:35 am

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