Winner of the New Statesman SPERI Prize in Political Economy 2016

Saturday 26 May 2012

Government debt and the burden on future generations

                In an earlier post, I looked at how we might think about the ‘cost’ of additional public debt, if that debt financed public investment, and our concern was intergenerational equity. Here I want to examine the question of how great the burden of extra debt is on future generations, if that debt financed not investment, but consumption spending or tax cuts that had only current period benefits.
                Our initial instinct would be that this burden is bound to be positive. The current generation gets the benefit of additional spending, or a tax cut, but future generations pay the cost in terms of finding the money to pay the interest on the debt. However, if the additional debt is never paid off, and remains a constant share of GDP, then there is a situation in which it is not a burden, which I discussed in that earlier post. Let the ‘growth corrected real interest rate’ be r-g.[1] Suppose r-g=0. In that case the interest on the outstanding debt each year could be entirely paid for by issuing new debt such that the total debt to GDP ratio remained unchanged. The debt is only a burden on the final generation, but there is no final generation.
                Normally r>g, so taxes do have to rise (or government spending has to fall) to pay part of the interest on the debt. Debt is a burden on that account. There is a trap that we can fall into here, which is the following. Suppose all the debt is owned domestically. What the government does is raise taxes to pay interest on the debt, so this is a transfer from tax payers to debt owners. The government is just taking with one hand and giving back with the other. If society is just paying itself, how can debt be a burden?
                It’s an easy mistake to make – I should know, because I made it in an earlier post, which Nick Rowe pointed out in a comment.  Incidentally, Nick has two excellent posts on these issues, here and here. The argument above is wrong because it can still involve a transfer between generations. This becomes very clear if we consider an unfunded pension scheme, which I will do in a later post. Someone who just gets interest on their wealth is clearly better off than someone who also has to pay tax increases to get that interest.
                If you are still not convinced, think of the following. Suppose the current generation gets a debt financed tax cut, but in a fit of conscience it decides to put it all into a trust fund to compensate future generations. (This is what happens under Ricardian Equivalence.) Suppose also that there is a final generation when all the extra debt is repaid, and it gets the complete trust fund. In real terms the size of the debt will cumulate up at the rate g, as each year a bit of new debt is issued to keep its total a constant proportion of GDP. However the trust fund cumulates with the real interest rate r. If r>g, the trust fund will exceed the amount of debt to be repaid, and so the final generation will be better off. As all this just involves intertemporal transfers, the final generation being better off must mean that the generations in between should have got some of the trust fund – they were losing out too.
                If there is a final generation (when the debt is paid off), then the answer to the question ‘is debt a burden’ is obvious. It is only if we think about never paying the debt off that we need to worry about the r>g condition. The argument I made in one of the earlier posts, and want to repeat now, is that there should normally be a final generation – the debt should be paid off eventually. This argument has nothing to do with intergenerational equity.
                Creating additional debt has two negative consequences aside from any intergenerational equity concerns. First, increasing taxes to pay the interest adds to the scale of tax distortions in the economy. Second, it seems likely that additional government debt will to some extent crowd out investment in productive capital, and this is a cost if, as also seems likely, we currently have less than the optimum amount of productive capital. (Economists will know that I am here assuming we do not have complete Ricardian Equivalence, and that the economy is not dynamically inefficient.) For both reasons, even if we ignored issues of equity, we should not be indifferent to the level of debt.
                So these arguments suggest we should aim to bring debt back to some target level. Those economists familiar with this area will know that there is one special, but frequently used, case where that is not true, and this paragraph is for them. As a consequence of Barro’s famous tax smoothing hypothesis, the short term costs of bringing debt back to some target can outweigh the long term benefits of doing so, if the real rate of interest is not greater than impatience (the rate of time preference). My own view is that this is a ‘knife edge’ result which really tells something different, which is that any adjustment towards a debt target should be very gradual. For more on this see another earlier post of mine.
                What the ideal level of debt should be is a complex question. But once we accept that in theory there is some ideal level of debt, this means that doing thought experiments where we forever depart from it are just that: thought experiments rather than practical policy. To put the same point more topically, if we accept that current levels of government debt are too high, we must have in mind some lower target for debt. If debt rises above this target, it should fall back towards it. In effect, that means there will be a final generation: any additional debt will eventually have to be repaid.
                So the burden of additional government debt for future generations involves the debt itself, and not just the growth corrected interest on that debt. However, the practical importance of this point for any particular generation is not great, because adjustment towards a debt target should be slow. Getting debt right is likely to be a cost for our children’s children as well as those generations currently alive.         

[1] If r is the nominal interest rate, g is the growth in nominal income. If r is a real interest rate, g is the real growth rate.


  1. What is the capital asset model you have in mind when you say that government debt crowds out private investment? In a depressed economy at least, it's reasonable to assume that term government debt is negative beta, in which case it would be "crowding in." What if governments borrow at the short rate? Is there risk premium in default-free t-bills?

    Also, I'm not familiar with the empirical evidence on r vs g for sovereign issuers. Do you have any references for the claim that r>g (I'm not doubting it).


  2. "Getting debt right is likely to be a cost for our children’s children as well as those generations currently alive."

    Yes, but, you know what? I have a two year old daughter, and there's little more that I'd like for her than a ten-fold increase in spending on basic scientific and medical research (not to mention, alternative energy, infrastructure, education...), even if it's funded with debt (paying close to zero real interest).

    The benefits to her – and my grandchildren – from those investments ridiculously dwarf the (near zero) interest on the debt to pay for them.

    If you really care about your children and grandchildren than you want the government to invest vastly more in high social return projects, not cut them; that just makes no sense.

    1. But my preference is to pay for these in the, at least not too far future, with tax increases, for a number of reasons, but one is that if we can bring our national debt down to zero (or a surplus), it will be a lot easier for us over the long run to get the support to properly respond to recessions.

    2. "...that just makes no sense." Of course it makes no sense. That's why the median voter loves it -- because he wouldn't know sense if it bit him in the ass.

      So it makes no sense -- but it wins elections. And we live in a world where two years is forever.

  3. "First, increasing taxes to pay the interest adds to the scale of tax distortions in the economy."

    Those distortions aren't always negative; they can be highly positive. There's the well known taxing of pollution externalities, but there's also preventing or diminishing plutocrats from bending government to their will, buying elections, etc. Raising taxes on the super rich can actually cause a virtuous circle. As I wrote in a post on this (maybe you saw it in Mark Thoma's links):

    It looks like such a virtuous circle may have occurred in the early part of the 20th century. The top marginal income tax rate went from 7% in 1915 to 77% just three years later! This was shortly followed by the New Deal, unprecedented levels of professionalism and efficiency in civil service, and respect for it, a golden era of high and evenly spread growth, the birth of the great middle class, widespread and easy college access, the highest level of college graduates in the world (after a generation of Republican dominance we're down to 11th), Medicare, and Medicaid.


  4. I'd like to see the arguments here separated into three separate strands:

    - Efficiency of implementation. If we say things like "adds to the scale of tax distortions" we're implicitly making an argument about how tax changes would be implemented, not really a core economic argument about the tax level. Certainly a valid focus of discussion, but distortions could increase or decrease independent of the total tax burden, and (as Serlin points out) could be positive. So let's separate that issue out, by assuming for this discussion that we adopt optimal policies.

    - Fiscal transfers. That is what this post is about (as far as I can tell). But without further argument it tells us nothing about what happens in the economy of real goods and services due to these transfers. More about this below.

    - Real goods and services. If we have effectively full employment, and effectively ideal allocation of capital, then I think all fiscal transfers only affect the distribution of goods and services, not total wealth. (Separating out policy lets us assume that if these are possible we achieve them.) In that case there can't be intergenerational transfers, there's no way (short of a time machine) for them to occur.

    Given these points, I think to get intergenerational effects of debt, above and beyond effects on distribution, there has to be some effect on efficiency of allocation (e.g. unemployment, mis-allocation of capital, mis-allocation of cash flows, maybe other things). Furthermore by our optimal policy assumption, these must be inevitable mis-allocations. Otherwise we are just seeing distributional effects over time.

    But this kind of effect is worse than a transfer, it is a deadweight loss. Welfare has not just been transferred, later generations have worse total welfare.

    So this is a serious possible effect, but it can't be supported by a purely fiscal argument, or even an argument that combines fiscal issues with claims about systematic policy inefficiency (as this one does). The argument needs to deal with the consequences of these for the real economy.

    If we want to deal with actually implementable policies, then we have to compare feasible policies involving more debt with equally feasible policies involving less debt -- not with optimal policies. So a concern that taxation to pay down debt would be distorting isn't relevant unless we have some reason to believe that it would be more distorting (in terms of net long term welfare) than taxation, or not creating public goods, or whatever we do to avoid taking on the debt. This is certainly debatable, and is being debated, with so far nothing close to a consensus.

  5. There are so many missing assumptions; I'm not sure where to start.

    1) Simon, implicitly, assumes zero inflation.
    2) Simon, implicitly, assumes full resource utilization.
    3) Simon, implicitly, also assumes perfectly equal income distribution.
    4) Almost all laws (sometimes the lack of regulation) creates winners and losers; sometimes more winners than losers; sometimes more losers than winners.
    5) Simon, implicitly, assumes the federal government has no printing press.

    So to look at the effect of debt, by itself, without discussing the above assumptions, is pure folly.

    1. EXACTLY... economists, funded by governments have been misrepresenting (i.e. bold-faced lying) for generations.... DEbt IS a burden... the repayment of it pulls public money out of spending for new projects / stimulus / services, and DOES NOT EVER trickle down to "Joe Commoner"... it goes out to the wealthy who had the good sense to save in the first place... they, in turn NEVER SPEND ON PUBLIC GOOD investments... they invest in "plant / equipment" that creates a ROI, which, in a very small way, contributes to employment / std of living / etc.

      Saying "it increases GDP" is the stupidest thing of all... when was the last time "GDP" paid your mortgage ???

      Debt is bad, saving is good. Governments buy votes with debt. Governments are inherently dishonest and self-interested...

  6. Simon: thanks for your kind words.

    "My own view is that this [Barro's tax-smoothing model] is a ‘knife edge’ result which really tells something different, which is that any adjustment towards a debt target should be very gradual."

    I like that; I think it's a good way of looking at it.

    Two random thoughts on the optimal target long run debt/GDP ratio:

    1. Start with Barro's tax-smoothing model, and introduce uncertainty (say, about the Present Value of future government spending), and assume that the marginal deadweight cost of tax revenue increases at an increasing rate (as it must eventually, if there's a top of the Laffer Curve out there somewhere). Jensen's inequality then implies tax rates that are expected to fall over time, which in turn implies the debt/GDP ratio is expected to fall over time. (It's like precautionary saving, only applied to the government). The optimal long run target debt/GDP ratio is then zero (or maybe even negative, if the government can earn a return r>g on its investments).

    2. Maybe r depends (positively) on the debt/GDP ratio. In which case the target debt/GDP ratio is that at which r=g. This assumption seems plausible to me. Government debt is in some ways "special" (not a perfect substitute for other forms of debt), and so there must be a demand to hold some government debt even when it pays very low rates of return.

    1. Nick. I think your random thoughts are sensible. I can see a lot of arguments why you might VERY GRADUALLY want to head towards very little or even negative government debt. (It has been done - see Australia and NZ.) However one argument that seems to go the other way is the 'shortage of safe assets' literature. Have you posted, or do you have, any random thoughts on this?

    2. We normally assume away political factors in economics, or just ignore them. But obviously they can be very important. I’d like to move toward zero debt, or net government savings, over the long run (once the economy has recovered), largely for political reasons. It might be a lot easier to sell and get enacted deficit spending in a recession if you start with net government savings, and you’ve established a track record of rebuilding those savings when the recession ends.

      Likewise, politically there can be big benefit with highly progressive taxation in greatly decreasing the ability of the rich to bend government to their will, and I think we’ve seen this historically. See my comment above for more.

  7. I find this reasoning bewildering. Whatever the size of the debt obligation for the hypothetical last generation, any debts that are paid at that time will be paid by people alive at that time to people alive at that time.

    And no matter how large interest payments are for any intervening generations, any payments that are made at any will be made by people alive at the time of the interest payment to people alive at the time of the interest payment.

    So unless these redistributional payments produce harmful distortions, I don't see how any conclusions can be drawn about burdens. This has nothing to do with whether or not Ricardian equivalence holds.

  8. Dan,

    If one generation consumes more than it produces and there is a final generation, then some generation will consume less than it produces. Period.


  9. Anonymous, I take it that by "generation" in this context you do not mean something like the totality of individuals alive at some particular time, but instead an age cohort, so that more that one generation is alive at any given time. Then in that case, sure, tax obligations or debt obligations that are binding at any given time could result in an intergenerational redistribution. Or they could result in a redistribution from the poor to the rich; or from one ethnic group to another. All kinds of of bad distributional outcomes could occur; on the other hand all kinds of good distributional outcomes could occur.

    But anyway, does the whole question then of a generational debt burden come down to the fiction of a last generation? Obviously, for any civilized human society, in which the work product of the working age population supports both the elderly and the very young, one final generation of supporters might end up with the short end of the stick if they are indeed the last generation. But is this really something we should worry about?

  10. Bear of little brain that I am, I don’t understand how real resources produced in 2030 can be consumed in 2012. A building erected in 2030 cannot be used in 2012. And to take a current consumption item rather than a capital item, I don’t see how electricity generated in 2030 can be consumed in 2012.

    1. I have the same problem.

    2. Here's an example I gave in the comments on Nick's post of how it can matter if you debt finance in ripping off one generation:

      Two person country: 20 year old Junior and 70 year old Grandpa. Junior loans the government $100K. The government gives the $100K to Grandpa as an old age pension.

      30 years later Grandpa's gone and he got a free pension that he never paid for. At the same time, in year t=30, Junior gets taxed $100K plus interest to pay off the government bond he holds. Well this is out one pocket, in the other. But then, the government says we're done deficit financing pensions. We now want to pay as we go now. So Junior, we're going to raise your taxes enough so that you give us the present value of your future $100K pension.

      So, Grandpa got a free pension, and poor Junior paid for two, but only got one.

      This shows that what Nick talked about could happen in theory.

      As far as this, if there's a last generation, let's think about this. Our sun will be going strong for billions of years. Now, assuming we don't destroy the planet, or die out from war, have you thought about what technology will be like in even a million years?? Robots building robots, the matrix? In that case, I don't think we'll have to shed a tear for a generation billions of years in the future (and while we're at it, they're not sure whether the universe will contract in another big bang).

      There's certainly, however, a reason to be concerned about my daughter's generation and my grandchildren's generation.

  11. Dan: yes, "cohort" is perhaps a better word than "generation".

    If r>g, and unless the proceeds are invested to benefit future cohorts, an increase in the national debt will place a burden on some future cohort(s) to benefit the current cohort. Yes, this is something we should be worried about, since it is a decision *we* take which will have harmful consequences on future cohorts. (If some future cohort decides to stop having kids, so there is noone to look after them in their old age, that might be something for us to worry about, but it is their decision, not ours, and we (presumably) can't do anything about it anyway.)

    Ralph: there is no "time travel" of resources involved, but it is exactly as if there is time travel. I gave an example in the first post Simon links to above.

  12. Nick, I've always struggled to understand the bond sales in your apple story. But am I correct in thinking that the burden-generating aspect of the story all depends on the fact that the initial debt and subsequent rolled over debts are all used to finance increased consumption by the then-living older generation at the expense of the then-living younger generations?

    But suppose your story started this way: instead of apples, the government borrows construction supplies and raw materials from the whole population used to manufacture schools and educational equipment for its youngest members. And it does this in every generation, with the current crop of bond-holders in each generation paid off with a share of the work product of the well-educated workers of that generation. Then if there is a "last generation" in the sense r>g and that in some generation the debt cannot be rolled-over, isn't the result exactly the opposite? The first generation of lenders in this case loaned some of its resources to the young, but died before receiving the payback, while the last generation of bond-holders receives a payback, but never has to convey some of its own resources to the young.

  13. The assumption that r is 'normally' greater than g depdends entirely on whether we are talking about a government that has a central bank of its own, free to operate in the public interest, or not.

    The assumption holds in cases where a CB is entirely absent (e.g., in the case of US states), or run as a branch of a larger CB system (e.g., national CBs in the Eurozone, in relation to the ECB), or otherwise pledged to convert the currency it manages into something else on demand and at a fixed rate of exchange. It also holds where (for whatever reasons) the treasury has incurred obligations denominated in some unit of account besdides that controlled by its own CB.

    Where none of these conditions hold, however, the assumption that r is 'normally' greater than g (and the related assumption that the stock of public debt will be equivalent to the cumulative total of deficit spending) is, at best, an observation about the political choices of those who run the CB. It certainly does not represent an economic law in action.

  14. Hi Nick,

    I am currently a 2nd year economics major and i am a bit confused by the article. I think i have failed to understand the passage where you explained about the older generation saving up in the trust fund, and that the paragraph explains why government debt is a burden to future generations. I thought that it is a burden when Ricardian Equivalence does not hold? and how it is not about intergenerational equity?

    Also, how would the notion that it is a burden be applied to the current situation in Greece or the Euro-zone as a whole?


  15. i meant Simon. sorry!

    1. This passage was just meant to show that intermediate generations, as well as the final generation, are disadvantaged by debt if r>g. So, if Ricardian agents wanted to compensate future generations, they would have to compensate all future generations, and not just the generation that pays back the debt.

  16. hello,

    how would you explain the situation where the government borrows money in exchange for bonds to foreigners. how would this effect the future generation?

  17. Dan: "But am I correct in thinking..."

    Basically yes. The way I think about it is like this: the debt creates a burden on future generations, but the investment in schools creates a benefit for future generations, and if the schools are "profitable", those benefits exceed the costs/burden. Future cohorts would be better off on net; but would gain even more if we paid for the schools by raising taxes than by issuing debt.

  18. Simon,

    Since Nick isn't biting, I'll have a go at it...

    I've never understood the "safe assets shortage" argument. I don't see how the
    availability of risk-free assets can increase risk taking capacity. What *does* make
    sense to me is the possibility of a shortage of *negative* beta (not zero beta)
    assets, which serve to reduce the total risk of investment portfolios. Since, in a
    demand deficient economy, inflation shocks tend to drive stocks and bonds strongly
    in opposite directions, government bonds become an especially good hedge for stocks,
    and perhaps even negative beta to the whole market (including bonds). This is the
    "crowding in" effect I was suggesting above.

    I don't, however, find that explanation totally satisfactory. What you might wish
    for, is a demonstration that it is marginal additional investment in public goods
    funded by additional government bonds (rather than the bonds themselves) which are
    the *real* benefit to market portfolio in an inter-temporal general equilibrium.

    There. Random thoughts. Probably a lot more random that you were hoping for.


  19. " In real terms the size of the debt will cumulate up at the rate g, as each year a bit of new debt is issued to keep its total a constant proportion of GDP. However the trust fund cumulates with the real interest rate r."

    I'm not sure why you say the debt will cumulate at the rate g, but I assume it's because you're assuming the government levies taxes to pay off the difference r-g. In that case, isn't it natural to assume each generation dips into the trust fund to pay these taxes? And if so, wouldn't the trust fund grow at the the g, the same as the government debt? So, the final generation would have just enough to pay off the debt.

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