Friday, 30 December 2011

Is government debt a burden for future generations? or the paradox of the last generation.

Paul Krugman has a nice post which is entitled ‘Debt Is (Mostly) money we owe to ourselves’.  It is a point I have often used in the past to help students understand that macroeconomics is different from microeconomics. Government debt appears to be a ‘burden’ on taxpayers because the government must raise taxes to pay the interest on the debt. But if the debt is owned by the same taxpayers, the interest goes to them, so in income terms they are no worse off. However, I think the idea can be pushed too far. I do think it is reasonable to describe excess government debt as a burden for future generations.  
Before exploring this, we should note two factors that are very important but which we will ignore here. First, taxes will be raised in a way that distorts incentives, which has costs. Second, government debt can displace saving that go to produce capital, which reduces investment and the capital stock, which also reduces output. There is a lot more to say on both counts, maybe for another time. I ignore them here, because I want to focus on income flows at the aggregate level.
Consider this apparent paradox. Suppose some additional debt is generated by temporarily cutting taxes. Let us call those who receive this tax cut the tax cut generation. Suppose also that this debt is a ‘perpetuity’ – the debt is never repaid, but anyone holding it will receive interest forever. The debt is sold domestically. Those whose taxes are cut are clearly better off in income terms. But, as we noted above, future generations are not worse off in terms of simple income flows: in aggregate they pay higher taxes, but get the money back as interest on the debt they own. So we seem to have a free lunch: the tax cut generation gains, but no later generation loses. [This is a mistake - see the comment from Nick Rowe below, and my response. I say why and when this is a mistake is this later post. It does not affect my main point here.]
What is the source of this paradox? Well imagine the debt is no longer a perpetuity, but has to be repaid after a thousand years. To repay the debt, the government raises taxes. The generation paying taxes in a thousand years time loses out in a major way – their income decline matches the gain received by the tax cut generation. The paradox disappears. So the paradox arises if there is no last generation that has to repay the debt.
The same paradox arises with an unfunded social security scheme. This is where a government creates a pension scheme whereby pensions are paid using the contributions of those working. When the scheme is introduced, those who are just retiring are much better off: they get a pension ‘for free’. But those who pay into the pension scheme get their money back when they retire, so to the first approximation they are no worse off. (It is an approximation because we should worry about the return they get on this ‘forced saving’, but the important point here is that they get their contributions back.) Once again, we have a free lunch, but only because the pension scheme never comes to an end. If it did end, the last generation would pay contributions when working but receive no pension, so their loss would ‘match’ the gain of the retired when the scheme was introduced.
So it is possible that government debt need not be a burden on future generations, if it is never repaid. However, this is not a very realistic or sensible assumption. My own view is that it makes sense for governments to have a long run target for debt, and in that case any excess debt beyond this target will eventually have to be repaid. If that is the case, then additional debt incurred now is a burden on future generations, because they will in practice repay it (as the government slowly moves debt back towards its target).
Should this make those of us who advocate stimulus rather than austerity today think again? No – because the overall benefits still outweigh the costs. Would we really want to argue that expansionary fiscal policy should not have been used to avoid the Great Depression of the 1930s because it would mean we would be paying slightly higher taxes today? Of course not.   


  1. There are also these further complications to the simplicity of your model:

    1. The recipient of the tax reduction and the lender to the State are not the same person.

    2. They may not even belong to the same social group, or, increasingly relevant today, one ethnic group e.g. the Europeans, say, may get the tax reduction disproportionately, while the Africans, say, may buy the gilts more

    3. And then there are the external buyers of Government bonds. My retort to Krugman: increasingly, whether we are American, Irish or British, Debt is money we owe to foreign investors.

    4. Even without these complications, your own observation on the micro-effects (on incentives and so on) is very important. I accept, of course, that you had to abstract away from those for the purpose of the point you wished to make.


  2. I would say the paradox is resolved by noting that the money used to finance tax cuts has to come from the households who benefit from the tax cuts, so it's a wash. The households receive bonds but these are worthless because the interest earned is negated by the additional taxation the government levies to make the interest payments.

  3. Simon: Unless I've misunderstood you, this isn't quite right.

    Take a standard OLG model. If the debt is a perpetuity, then all cohorts paying taxes to pay the interest on the debt are worse off, both in terms of present value of lifetime consumption, and in terms of lifetime utility. The intuition is that the promise of interest is needed to compensate them for postponing their consumption stream until later in life, and yet that interest income is at the same time taxed away (in a lump sum tax) from the representative agent.

    However, if the interest rate is permanently less than the growth rate, then the debt can be rolled over forever without ever increasing taxes, and only then is there no burden on future generations. Samuelson 58.

    If you aggregate across generations in a particular time period you miss seeing the burden. You instead need to aggregate across time periods to look at the present value of lifetime consumption (or lifetime utility) for each cohort.

    I'm afraid Paul Krugman missed seeing this.

    I don't know if you saw my recent posts on this.

    1. Nick: You are right. In an effort to make my point that excess debt should be repaid, and therefore was a burden on future generations, I was too kind to the argument Krugman put forward. I wanted to avoid a discussion of how the return on debt compared to whatever other savings instrument would have been used, dynamic efficiency, Ricardian Equivalence and all that, because I thought it would distract from my basic point, but as a result what I wrote about the case where debt is not repaid was, as you put it, not quite right. (The annoying thing is that I know all this stuff, but perhaps as a result of following Brad's dictum about Paul, allowed myself to forget it.) However I don't think this alters the basic message of the post, which is that because of issues like tax distortions and crowding out, it is wrong to think that excess debt should persist forever, and so discussions of what happens if it does (and whether this is a burden or not) are of academic rather than policy interest.

  4. Simon: Yep. You knew this stuff. Brad and Paul are very very good. But the Doctrine of Pauline Infallibility has got to go. He screwed up here. Nobody's infallible. Stuff happens.

  5. The only way to 'repay' the debt is for the population to return their entire savings of govt bonds. This is either A) clearly impossible or B) can be done if the bonds are converted back to cash which, although still a govt liability, isn't classed as 'debt'. The recent QE purchase of £375 billion bonds illustrates this. Either way there will always be a perpetual and rising nominal figure for govt liabilities issued. What you are calling for is exactly the same as the bank in Monopoly to try and get its money back off the board. The game will be over. Additionally, are you familiar with the idea that net savings of bonds is functionally identical to taxation? Until spent, the fact that it's a number sitting in an account is irrelevant.

  6. Every business needs both a cash float and a stock inventory. Families save some cash inventory for the future. Some families save billions in cash inventory in perpetuity. Since the entire private banking sector nets to zero on the balance sheet, the only source of this long term inventory on the population's balance sheets MUST be liabilities that the government willingly offers the population as a savings mechanism (and one that the government actively promotes).


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