Sunday, August 19, 2012

Does the federal debt “burden” our grandchildren?

Every politician claims that we must find a solution to the federal deficit, we must find a way to balance the federal budget, because failing to do that simply passes our debts on to our children and their children, that we are stealing from the future when we increase the federal debt. 

Is that really true?

As you may have guessed from my last post, my answer to that question is “it depends”.  (If you didn’t read my last post and you respond to this by saying “that’s typical, economists can never give a straight answer”, go back and read it now and stop whining.)

When I thought about writing on this topic I started by looking on the web for other comments, figuring I would find a few rants about it on political web sites that would provide some quotes I could use.  But I found a sizable discussion in the econoblogosphere, much of which seemed to me to miss the point---or at least to miss the point as I see it.  I’m hesitant to make too strong a denunciation of any participant in that discussion, because a lot of very impressive economists contributed to it, starting with Paul Krugman, here and here.  An economist named Nick Rowe in Canada was next with a response to Krugman, in which he claimed that Krugman “did not get the memo” telling us all to switch to the view that debt has to burden future generations.  I like Nick Rowe’s blog, I respect it and him enormously and read him often, but I didn’t get that memo either.  And his blog post surprised me.  Even when he says something I don’t completely agree with he generally says it with exceptional clarity and eloquence, but this post seemed confused and drifting to me.  But Simon Wren-Lewis at the Mainly Macro blog was eventually convinced by Nick Rowe’s argument.  And Steve Roth at Angry Bear discussed the Rowe argument without being completely convinced, but without overtly opposing it either, as far as I can tell.   (None of these blog posts are impenetrable or inaccessible to non-economists; any reasonably intelligent person can follow them.)

There was a lot of other discussion in the econoblogosphere as well, and substance in the comments in all of those posts, so if you are interested in this issue there’s plenty of good discussion.  If you are not interested in this issue, I have to assume that you won’t complain about the debt burden in the coming election or after.

Let me lay this out as I understand it, and if you’re not convince by my argument then you can read all those other blog posts to find one that suits you better.  I’m going to do things that look like I’m developing an economic model, and I guess I am.  But it’s such a simple model that I don’t really think it deserves the title.  Let’s call it an organized fiction with a purpose, or a parable,  or something.  But this is a complex topic, so I have to start very simple and then gradually relax simplifying assumptions to get to greater realism.  This step-by-step takes some space so this will be an even longer post than usual.  But if you’re distressed by our current debt it’s worth reading.  It may let you sleep better.  (Or not…it depends.) 

First lets look at two points in time (present and future), as Nick Rowe and many others did, and look at what happens if we borrow money in the present time and repay it completely in the future time by taxing the general population then.  Let’s start with a crazy assumption, just to build from the simple to the slightly less simple: let’s assume that there is no economic growth at all, positive or negative, so that the sheer quantity of stuff that is available for consumption or investment in the future time is the same as the sheer quantity of stuff available in the present.  Let’s also assume that there is no population growth.  See how easy economic modeling is?  Let’s also assume that there is really no good way to preserve stuff for that future time (it’s too far away).  In this model, the people alive now will consume whatever we produce now that is consumable, and the people who are alive in that distant future will consume whatever is produced then.  There is no way we can sneak into the future and steal the carrots from their garden, or buy the cars that are rolling off their assembly lines.   So what we do today, even if it’s running up a lot of debt, doesn’t (by our assumption of a constant quantity of production) have any effect on the sheer quantity of stuff they have to consume.  We have not harmed them materially as a generation by creating debt.   (Nick Rowe claimed in his post that he wasn’t using a time machine, but with the current assumptions, the absence of any growth or deterioration of productive capacity, how else can we take anything material from the future?  I know, this is insanely simplistic, but bear with me for a while.  It gets more realistic later.)

Even in this model, where we can’t change the amount that is available for consumption in the future, that doesn’t mean that current debt has no impact in the future.  As Nick Rowe pointed out, if we borrow money now from some sub-group of the present generation for distribution to some other sub-group (borrow from A to finance consumption by B), then we have created a debt to A in the present that we must (by our assumption) repay in the future.  In the future in our model we tax the general population to pay A back.  So A can consume more in the future, but all the rest of the population must consume a bit less to make that work. 

Now, if A is a different country, China for example, then we might actually harm the people who live in the borrowing country by creating an external debt: in that kind of future, people in China would consume more, and people here in the United States would have to consume less to pay for that.  We would work just as hard, but some of our product would leave the country as exports purchased with our debt repayment.  But as Krugman pointed out in his posts, for the most part the debt we owe externally is still a small part of our total debt; for the most part we still do owe most of the federal debt (and total debt) to people or institutions inside this country.   Krugman has some graphs looking at total debt (not just Treasury debt) as a percent of GDP, and net foreign debt.  But just looking at federal debt, it’s still true that we owe most of it to ourselves, in spite of all the alarm you hear about the Treasury’s debt to China.  Here’s a graph that I generated in Excel from the “Treasury Direct” bulletin using data for December 2011 showing who owns the federal debt:

There are a couple of things here that I want to emphasize.  See the dark blue slice of pie at the top, at the far north north-east?  That is the amount of Treasury debt that is owned by the Federal Reserve system.    This is what the Fed has bought on the open market to drive interest rates down.  It’s a significant chunk of the Treasury’s total debt, and it’s not a chunk we really owe to anyone identifiable within the country or outside the country: the Federal Reserve owns it.   That means, in a way, that either that we all own it or no one owns it, and if we as a country chose to do this we could simply vaporize that debt without harming anyone.  (I’m not suggesting that---the Fed can use those Treasury bonds when it thinks it needs to; they are a tool the Fed can use later.  But the point is that as they are now, they don’t provide any private person or institution the ability to demand future consumption.) The next chunk, the red chunk to the east, is the Treasury debt owned by the United States government in one trust fund or another.  The government quite literally owes that to itself, or more correctly one part of the government, the Treasury, owes it to other parts of the government.  That cluster of small slices to the south is a bunch of things like private or state pension plans, insurance companies, state and local governments, mutual funds, and so on. 

Still, there is that big, kind of dusty purple slice to the north-west labeled “foreign and international”.  China is part of that.   In the model I have so far, that means that in the future time period people or firms from China could demand some of the stuff we make here, and they could consume or invest the future product of our work. 

But of course my model is pretty simplistic, isn’t it?  No growth?  Really?  Ok, so let’s accept the possibility of growth at a fixed rate, but leave everything else as it was.  If we assume that our current borrowing has no impact on growth, then the outcome of our simple model still holds: nothing we do with our finances, by (very simplistic and unrealistic) assumption, can have any impact on the sheer quantity of stuff we produce in the future, so the only thing it impacts is the distribution of that stuff.  So the only way current borrowing can change the outcome is by having an impact the rate of growth, and on our ability to produce in the future. To make a model that enables current debt to burden or benefit future generations, we have to dispense with not just a no-growth assumption, but also with a fixed growth assumption.  We have to assume that current debt somehow impacts economic growth.

There are two competing visions on this, and you’ll hear both of them repeatedly over the next couple of months. 

First vision: if we borrow money to invest in things, like infrastructure improvements, that can create higher economic growth, then we actually make the people in the future as a whole better off!  Note that this does not require us to do any tiresome calculations about the rate of growth enabled by our investments, or the rate of interest we pay on the debt.  Those things, still in this simplistic model, will change the distribution of claims on the production in the future, but they won’t change the sheer quantity: if we are growing faster, we will have more stuff in the future, and all of it will be consumed then.  We can’t consume future product now by the act of borrowing, no matter what the interest rate is.

So why do we care about the interest rate we pay and the growth it enables?  Well, if we pay too high an interest rate then the people who lend us money now will have an excessive claim to product in the future, so that while our borrowing may change not how much we produce, it may change what we produce: we may produce more grand yachts and less corn, because that is what will be in demand then. 

But we can go a bit farther if we relax another of our initial assumptions: the assumption that we repay the debt in the future time by taxing the public.  Let’s assume now that we roll over the initial debt in the future, but not the interest on that debt; that is, if we borrow $100 in the present time, then we borrow $100 (and only $100) in the future time to pay that principal back.  Under this assumption if we borrow now, and with the money we create a rate of growth greater than the interest rate we pay, then in the future everyone is better off.  Everyone!    Our grandchildren can pay off the interest on the loan, roll over the principal, and still have something left over to distribute among themselves.  And as a bonus, the $100 our grandchildren borrow to roll over the principal is a smaller fraction of their (larger) GDP than it is of ours---so that debt turns into a shrinking fraction of GDP as well.

Second vision: we borrow money now to finance consumption.   But where does that “extra” consumption come from?  Still in our simple model with the assumptions that remain, either the people who lend the money consume less in the present to provide consumption goods to the people we help to support with the money, or it comes out of some other kind of production.  Typically, the argument is that when the government borrows now, it “crowds out” investment, which creates economic growth.  So when we borrow now, and crowd out investment, then we are actually reducing the quantity of physical stuff that could otherwise have been created in the future: in this case, we truly would be consuming today by reducing consumption in the future, not by digging up future carrot patches, but by reducing the present investments needed to create those carrot patches in the first place. 

But this argument depends a great deal on one of the last simplifying assumptions we started with.  It depends on the assumption that the total quantity of stuff we can produce now is fixed.  In other words, it depends on the assumption that we can’t produce more than we are producing.  This amounts to an assumption that we are at full employment of everything, of labor and of factories and of land and of everything.  Does that sound like the situation we are in now?

We finally have eliminated enough of our starting assumptions that the model looks a lot more realistic.  In the future we will be able to produce more than we can now (GDP grows over time); we will roll over some part of our debts in the future; what we borrow now can, under some conditions, reduce what future generations can produce, and therefore how much they can consume, but under others conditions it can expand how much they can produce.  So I’m back to my start: can debt we create now burden our grandchildren?  It depends.  If we are at less than full employment, so that we can borrow money and use it to increase our current production, debt is ok, we will be materially better off in the present and will not materially burden the future.  If we borrow now and invest in projects that increase economic growth by more than the interest we pay, then debt is ok, and will not burden the future.  Both of those conditions hold at the moment: interest rates paid by the treasury are currently less than zero!  So if we invest in infrastructure that has any positive impact on economic growth at all, it’s a good investment.  And we are now well under full employment of our resources, so we can borrow and hire the unemployed (both unemployed people and unemployed industrial capacity) without crowding out other uses of those same resources.  (I’ll write post about crowding out in the financial sense---but that’s another topic for another day.

So as a general answer to the question “can current debt burden future generations”,  my answer is “it depends”.  But in the current situation, all the things it depends on are resolved, and the answer is no.   We have a lot of resource that are unemployed, and there are plenty of infrastructure tasks that would enhance our rate of economic growth in the future.  We can borrow to put people to work producing consumption goods, and we will be materially better off in the present with no harm to the future.  Or we can borrow to invest in infrastructure, be better off in the present and benefit the future.  Let’s borrow now: the cost is low, there’s a lot to do, and we can benefit the unemployed in the present, and benefit (benefit, not burden!) everyone in the future.

After we truly recover, so that employment and borrowing costs are both higher, those things will not be nearly as true.  So we should grab this chance while we have it.


  1. Stuart:

    I think you went wrong at this point: " We have not harmed them materially *as a generation* by creating debt."

    We need to distinguish between:

    1. Those people alive at a particular time.

    2. A generation ("cohort" might be a better word).

    It is true that (in your model) it is impossible to reduce the consumption at a future time of all the people alive at that time.

    But it is possible to reduce the lifetime consumption of a future *generation/cohort*.

    I had overlapping generations/births/deaths in my model. That feature is crucial. If everyone were born in the year zero, lived forever, and there were never any births after that, then it would be impossible (given our other assumptions of no capital etc) to impose a burden of "future generations*. Because everybody would belong to the same generation.

  2. Simplest example: everybody lives 2 periods: in the first period they are young; and in the second they are old. Forget about interest rates. All the other assumptions the same as in your model.

    Suppose the government tells: the young in cohort B to give 1 apple each to the old in cohort A; the young in cohort C to give 1 apple each to the old in cohort B; and all cohorts from D onward to just eat their own apples, without giving any to anybody.

    Cohort A gets to eat 1 extra apple each (when old). They are better off.

    Cohort B eats 1 less apple when young but 1 more apple when old. They have the same lifetime consumption as before. (They may be better or worse of in lifetime utility, it depends).

    Cohort C eats 1 less apple when young. They are worse off.

    Cohort D just eats its own apples. No change.

    Debt is just the same as the above example, except you collect a paper receipt (called "a bond") when you give an apple to someone.

    1. Awesome.

      I just had an excellent dinner of wood-fired pizza and a glass---ok, a couple of glasses---of Morgadio 2010 Albarino, a very pleasant modestly priced white wine from Catalonia, and I returned, at an appropriately nocturnal hour, to check into my nocturnal blog. And I found that Nick Rowe had responded to my post! Life is pretty good.

      Seriously, I’m glad you’re here. Thank you for responding, and for braving the vast darkness of the interweb to visit me. I feel as though I should offer some refreshment, but I’m not sure how to do that electronically.

      On the comments: you’re completely right that “generation” is the wrong word, unless we are talking about very long time periods that are very far apart indeed. What I was looking at is a comparison of two---what shall I call them?---accounting periods? Something like that. Not exactly comparative statics, because that compares two instants, or two equilibria, and we are talking about the whole messy business of production and consumption. Nothing can be produced or consumed in an instant. So I guess I’m comparing two years, or two decades. I was asking: does the debt we added during the year 2010 have a negative impact on whoever will be around producing and consuming during the year 2040? Or, will the debt we add in the decade from 2010 and 2019 burden the consumption and production that will happen in the decade from 2060 to 2069? It doesn’t matter whether the people in the second period are the same people as those in the first, so “generation” or even “cohort” doesn’t quite describe it. Maybe “period population”? I don’t know. I’m open for suggestions.

      Your response did remove some of my confusion about your model: I was stuck in this comparative-accounting-period frame of mind, but you were not talking about that. You were talking about process. Overlapping cohorts, with each cohort forming a link in a chain. Your first link benefits from the creation of a new borrowing process---and your last link pays for it. Not by stealing apples from the future, but simply by being part of group A (the lenders or repayers) when they are young, and not having any group B to belong to when they are old.

      My only real complaint about this is the existence of a last link. It’s certainly possible to end the cycle of borrowing; that’s up to the cohorts that happen to be up and walking around at the time. Group C in your example lends an apple when they are young, and never demands repayment when they are old. Why not? Well, maybe they decided the whole chain needs to stop, and it’s worth it to them to sacrifice an apple in their old age to make it stop. In this country, for example, we can choose to end Medicare as we know it. But we don’t have to: that’s a choice. And similarly, the last link in the chain you described can choose to pay the cost and end the cycle of borrowing, or they can choose to continue it. But one of the characteristics of human history that we hope continues for a long time is that cohorts keep coming. There isn’t a last one---or we hope there isn’t.

      And I love this line: "They may be better or worse of in lifetime utility, it depends." does depend. The usual hypothesis is that they are better off over their lifetime, because they get the apple when they are old, unable to work, and likely to be hungry, but they give up an apple when they are young and vigorous and prosperous. But it does depend absolutely on whether the older cohort has other means of getting apples, and whether the young are actually prosperous relative to the old, and no doubt on many things I haven't thought of.

  3. Stuart: your response is refreshment enough!

    For cohort B, we would *normally* say they are better off, or at least not worse off, as long as they don't pay higher taxes to service the debt. That's because each member of generation B *voluntarily* buys a bond when young and sells it when old. And they wouldn't do that if it didn't make them better off.

    For cohort C, is really does depend, as you say. Three big things it is likely to depend on:

    1. If the government borrows to invest in e.g. schools that benefit cohort C, they pay the higher taxes but also benefit from a better education. If the benefits exceed the costs, there is no burden *on net*.

    2. *Maybe*, though you really need some sort of model with multiple equilibria and not just a simple Old Keynesian model, government borrowing and spending acts to "kick-start/pump-prime" the economy out of recession, and once out it stays out, even if the government increases taxes again. Cohort C gets the extra taxes, but they also get jobs.

    3. If the rate of interest is less than the growth rate of the economy (as it would be if there were no easy way to save for retirement, as you mention above), there never is a cohort C. You can just keep on rolling over the debt+interest forever, because it still grows more slowly than the economy. All cohorts benefit, until the end of time.

    BTW: If I had been wrong, Brad deLong would have nailed me. The fact that he didn't write a post saying "Nick Rowe is wrong for saying Paul Krugman is wrong" tells us something.

    1. Ah, yes. He's actually pretty good at that. his response (August 6, I think) to Arthur Laffer's WSJ piece was as thorough a beatdown as I ever see on the blogs.

      More on our topic here this weekend. I'm being distracted by my day job...

  4. Replies
    1. I'm not abandoning the discussion, Craig, but my day job has been kicking my behind for the last few days, and will for the next few too. I'm sitting in a hotel in Hampton right now.

      Also, I've been thinking about Prof. Rowe's model a bit, and on the difference in approach that it implies---difference from the approach I started with in the post above. I have to draw some pictures to describe that, and I don't know how to put pictures in the comments section. I guess I'll have to write another post on this. But I don't think I'll have time until the weekend.