13 Feb 2015

Krugman Defenders 0, Murphy/Rowe 324

Debt 43 Comments

When the nutty Irishmen continue to roll their eyes at Nick Rowe on the debt burden stuff, it would be nice if they didn’t keep committing the same fallacy that Krugman did on Day One of this debate. (Here’s Gene telling Nick that the debt can’t burden future generations because they will inherit the bonds–meaning at that moment, there had been literally zero progress in the debate, even though Gene continues to assure us that he totally gets the obvious little point Nick keeps making.)

The other culprit is Kevin Donoghue, who also assures us he totally gets the obvious overlapping generations stuff, and says that Krugman gets it too–it’s too stupid to even bother mentioning out loud, which is why Krugman has ignored Nick all these years.

And yet, in another of Nick’s posts, Kevin writes this:

Nick, I just took another look at SWL’s “Redistribution between generations” post (link below). I don’t believe Krugman would dispute anything there, or that anything he’s ever written was meant to imply that government debt never involves redistribution between generations. But what comes through very clearly in that SWL post is that there must be a *change* in transfers between the old and the young if that latter are to be ripped off. The level of debt is irrelevant in that context.

Krugman is mostly concerned with refuting people who think that even a closed economy with $10k of debt per person must be more heavily burdened than one with $1k debt, even if the debt is rolled over. It’s quite a different topic.

OK, I am going to now give a simple numerical example–of the same flavor that Nick and I have been cranking out for three years now–to show that the above is totally wrong. Here goes, with my explanation following:

Debt Rollover Still Hurts

In the model above, there are always 200 apples harvested every period; real GDP is always 200 apples. Taxes do not impose any deadweight losses. It is a pure endowment economy; there is no physical investment or depreciation of capital. Each person has a lifetime utility function of SQRT(c1) + SQRT (c2), that is, you take the square root of the apples consumed in the first period and add the square root of the apples consumed in the second period. There is no discount on future utility per se.

Now what happens in the above scenario is that in period 1, the government borrows 50 apples from Bob and makes a transfer payment to Al. There are no taxes, so the deficit is 50 apples and the government’s debt goes from 0 to 50 apples.

Then from periods 2 through 8, the government rolls over the bonds. It taxes the public just enough each period to cover the interest on the debt, which stays fixed at 50 apples, i.e. 25% of GDP.

You can check that (a) Dave through George are worse off compared to a situation in which they consumed 100,100 and (b) Dave through George voluntarily lend the government 50 apples when young in order to get 100 apples paid back when old. Make sure you realize that each individual thinks his future tax burden is given, and then he voluntarily decides whether to lend to the government at a 100% real interest rate.

Thus, Dave through George are hurt, relative to a no-debt scenario, even though the debt is rolled over during these years. Obviously, if the original deficit had only been 1 apple, the burden on them from carrying it would have been lower. I encourage you to go re-read Kevin’s comments quoted at the beginning of this post. It sure seems like he is definitively saying that if we are in years where the debt is merely rolled over, then the people in those years aren’t affected (in the aggregate) by the level of the debt. The example above shows that that isn’t true.

Now at this point, it wouldn’t surprise me if Kevin or Gene or Daniel Kuehn said, “Right Bob, that’s what we’ve been saying for years” but somehow their comments keep suggesting otherwise. At the very least, someone who just read Krugman on this stuff would have absolutely no idea that the above scenario was physically possible.

43 Responses to “Krugman Defenders 0, Murphy/Rowe 324”

  1. OLDKEN says:

    “You can check that (a) Dave through George are worse off compared to a situation …”

    Sorry, I’m slow at this.

    Why aren’t you saying Bob through Iris?

    • Bob Murphy says:

      OLDKEN, yes, Bob through John are hurt, and Al is the only one who benefits. But I wanted to make sure we were just looking at people who were alive when the debt was constant at 25% of GDP, because Kevin Donoghue erroneously concluded that the thing driving the result was the change in the debt.

  2. Tel says:

    Make sure you realize that each individual thinks his future tax burden is given, and then he voluntarily decides whether to lend to the government at a 100% real interest rate.

    I find myself unable to realize that.

    Young Bob must have somehow been expecting someone else to get taxed to pay the interest on the bonds. I can’t imagine anyone being so incredibly stupid as to lend money at interest knowing that they themselves will be paying the interest. I mean that’s what it all revolves around, trying to trick people into believing that the bond creates some future wealth which can be dipped into.

    The entire US Social Security scheme is going the same way, but participation is compulsory so it’s just tax paid now or tax paid later.

  3. Gene Callahan says:

    “Now what happens in the above scenario is that in period 1, the government borrows 50 apples from Bob and makes a transfer payment to Al.”

    Yep, and there is the whole intergenerational transfer mechanism: it is the *transfer* of resources from the young to the old. The *debt* involved here is irrelevant!

    • Bob Murphy says:

      Gene, it’s not really the *transfer* of resources that is hurting the young people; it is the fact that they are eating fewer apples. I mean, we could imagine no government transfers or taxes, and locusts come and eat apples, making the young people get less utility.

      So Gene, I wish you would stop talking about transfers being the issue here, when really it’s “eating fewer apples” that is driving the whole result.

      • Major.Freedom says:

        Ahh, the ol’ Free Advice switcheroo

  4. Daniel Kuehn says:

    Sorry to be dense, Bob, but I have to ask because you pulled me in in the last paragraph – in what sense are Dave through George worse off? I’m not denying they may be I’m just not sure what you’re referring to exactly.

    My position – which I’ve talked about with Bob again recently but for the benefit of other readers – is that the overlapping generations can certainly impose costs on some future individuals relative to other future individuals (I don’t *think* it has to but I’m not 100% sure of that), but it does not make period t+s poorer than period t (unless you bring in some other efficiency or political economy arguments). And since Bob is talking about Dave and George he’s clearly not speaking to THAT claim.

    One additional thought on this in terms of utility – so we have people producing at the same amount in each period but usually these public pension schemes are set up with the idea that income goes down during the older period (sometimes if we talk about public education and an OLG we have income going up but that’s a different model). If income goes down then this sort of transfer can be utility enhancing because it provides some consumption smoothing.

    Obviously we’re not getting into utility here just like we’re considering these pure consumption goods rather than investment goods, but it’s worth bringing up I think.D

    • gienon says:

      They’re worse off because of a decrease in lifetime utility:

      sqrt(50) + sqrt(150) < srqt(100) + sqrt(100)

      • Daniel Kuehn says:

        So you’re saying the whole argument hinges on the assumption that prime age workers would make as much as senior citizens without a public pension system?

        I agree that result would follow that assumption but it has precisely zero to do with debt. That’s the whole point of my third paragraph above.

        Is that really all Bob? Does gienon speak for you on this?

        • Tel says:

          You are welcome to come up with your own model that is a bit more realistic.

          Point is that Krugman says if GDP is constant then by definition utility of the people is constant and thus debt is overall a nett zero. Hence “We owe it to ourselves”.

          Murphy has demonstrated one simple example where this is not the case. If one example exists, Krugman is wrong, but anyway many examples exist.

      • Daniel Kuehn says:

        Ah – I skipped down to the bottom and didn’t see the lifetime utility point. This does seem to be all there is.

        1. This is weak, it has nothing to do with debt, and it’s a bad assumption for talking about social security.
        2. It still doesn’t change Krugman’s point that the only costs to period t+s are distributional.

        • gienon says:

          Just a quick thought pertaining to your 2nd point. The non-distributional effect is present even if we assume simple positive time preference rather than a sqrt(Income_t1)+sqrt(Income_t2) utility function. I’m not categorically saying that this is a crucial assumption, so maybe someone can answer your objection without assuming even that.

          • gienon says:

            Ok, minor correction. I had in mind two consecutive periods taken together, so my point seems to me to be valid for periods t+s,t+s+1.

          • Daniel Kuehn says:

            Let me clarify on my point 2. So Krugman is saying that in every period we owe the debt to ourselves. He’s always said that doesn’t mean we like the outcome every time because of potential distributional problems. So if the debt changes the distribution at period t+s from 100,100 to 50,150 then you just need diminishing marginal utility and a willingness to engage in interpersonal utility comparisons (not always a given in this comment section) to say that that makes people worse off. But that’s a distributional point, not a debt point.

            • gienon says:

              I’m happy to have understood the point correctly.

              I’m not sure about the necessity for interpersonal utility comparisons or, by extension, intrapersonal comparisons in different periods. It seems logically preferable to have 100 apples at one’s disposal at a young age rather than the 50,150 alternative, assuming consumption of apples from period 1 can take place in period 2. When assumed otherwise, one could make an argument that utility derived from the additional 50 apples in later stages of one’s life justifies the diminishing by 50 in earlier stages.

            • Bob Murphy says:

              Daniel, I’m not making any interpersonal utility comparisons.

              • Daniel Kuehn says:

                Bob – right to arbitrate your point it’s not necessary. To arbitrate Krugman’s point on a utility basis you’d have to though.

            • Tel says:

              Actually, there’s inter-generational distribution happening as well, Bob had other examples of this.

              If government debt grows in “apple land” then during the growth phase they all get more apples, but during the inevitable shrinkage phase they all get less apples.

              • Daniel Kuehn says:

                Tel – the result depends on how you’re using the word “generation”. For certain definitions, yes.

              • Tel says:

                I linked to a worked example below. Four consecutive generations end up better off than they would have if they had merely consumed exactly what they produced. After that one generation breaks even and eight consecutive generations end up worse off.

                I don’t think there’s any ambiguity in that, full details are provided.

  5. Daniel Kuehn says:

    I’ve said it before and I’ll say it again – your answer, and all the disagreements on this question – turns on what you mean by “generation”. Specificity is key. Are we talking about people born in t+s as opposed to t+s-1, or are we talking about t+s vs. t+s-1.

    Both are intelligible, I’m not knocking the former (which is what Nick and Bob always focus on). But “we owe it to ourselves” is clearly a reference to a particular point in time, not to a cohort.

    • Tel says:


      Antonio Fatas, commenting on recent work on deleveraging or the lack thereof, emphasizes one of my favorite points: no, debt does not mean that we’re stealing from future generations. Globally, and for the most part even within countries, a rise in debt isn’t an indication that we’re living beyond our means, because as Fatas puts it, one person’s debt is another person’s asset; or as I equivalently put it, debt is money we owe to ourselves — an obviously true statement that, I have discovered, has the power to induce blinding rage in many people.

      I think it’s pretty clear how Krugman is using the word “generations” here, and what specific claim he is making. He is saying that government debt NOW cannot possible make future generations worse off SOMETIME LATER.

      Krugman’s claim is demonstrably wrong, a whole bunch of future generations will be worse off as that debt unwinds.

      The whole balance sheet can be displayed right down the the individual numbers.

      • Bob Murphy says:

        Right Tel. Krugman isn’t getting the overlapping generations thing. I would’ve agreed with him wholeheartedly in the passage you quoted, before Nick Rowe blew up my world.

  6. Daniel Kuehn says:

    And I guess I get frustrated with them on this because they treat Krugman as some kind of backwards thinker. Granted, Krugman thinks that of other people too, but he is not talking about people like Nick and Bob who are running through OLG models and talking about effects on cohorts. He’s concerned with the general public who misses Lerner’s fundamental point (which is a pre-OLG point about a point in time).

    • Bob Murphy says:

      Lerner’s fundamental point is extremely misleading at best, and wrong at worst, Daniel. Krugman has quite clearly led people to believe that the absolute level of government debt in the year 2100 can only affect the distribution of resources in the year 2100, and so if it makes some people in 2100 worse off, it must do so in a way that is exactly offset by making other people in 2100 correspondingly better off.

      But nope, that’s utterly wrong. In my example in this post, Al is the only one who benefits. Every other person is hurt, for generations to come.

      • Daniel Kuehn says:

        But see in this comment you’re not doing things consistently again, Bob. You start the comment talking about “people in 2100” and then you end the paragraph talking about individual experiences across multiple periods.

        Yes, definitely those two have different answers.

  7. gienon says:

    What I think Mr. Murphy’s point is, is that the physical amount in one period is constant (100+100=150+50) but across generations there are differences in levels of consumption (Al consumes 250, John – 150). The burden for other participants of the above scheme stem from diminished lifetime utility, despite a maintained consumption of 200 apples.

    Perhaps the chart could use one more period before and after the current ones, because the fact of Al consuming more than others and John consuming less than others did not jump out right at me.

  8. Transformer says:

    In each period you can distribute consumption however you want but you can only ever affect the lifetime consumption of living cohorts, You can never make a change that will have a binding affect on a future (unborn) generation’s consumption.

    You can build a narrative ,such as the ones involving debt and bonds ,that make it look like the living are creating burden on the unborn – but that is not actually what is happening.

    Further , you can never prove if the changes you make are good or bad in a given period. If you change the assumed utility function to SQRT(c1) + (c2) then the transfer payment make everyone better off in Bob’s model (if my math is OK).

    • Yancey Ward says:

      You are overlooking something. Living cohorts arise out of the still to be born cohorts, too. Yes, the people of a future time can indeed say, “We will stop playing this game.” However, what that future time cannot do is undo the effect the scheme had on those who are living and lived parts of their lives with the scheme in place, or on those who must, necessarily, act in order to ameliorate the effect on such people. For example, if the scheme ends after Young Iris has lent, but before young John buys the bonds, then Iris is the one who bears the burden.

      • Transformer says:

        Yes, but it is still the cohorts alive at the same time as Iris who would have consumed what she had lost, not Al.

        I agree though that once the initial imbalance has been created (period 1 in Bobs example) then the only way to correct it is to have someone lose out. No-one can ever get back Old Als extra consumption, and to get back to the period 0 distribution someone would have to consume less by an amount equal to his surplus. But in theory this could be delayed forever, and ultimately would be down to a decision made in the future present , not the past.

        • Yancey Ward says:

          then the only way to correct it is to have someone lose out. No-one can ever get back Old Als extra consumption,

          Precisely. The debt incurred in the past burdened the future. The only out, as you wrote, is to assume a sustainable Ponzi. I would have no problem with Krugman’s argument if he would precisely state just that. At least then, we would be debating whether or not something can continue in a truly infinite way.

  9. Michael says:

    There is not a real interest rate of 100% here or even a nominal rate of 100%. There is a discount bond at 50 Apple cents to the Apple that pays off an Apple a full generation later. Hey you stole my apple is a false argument. One could make a number of reasonable utility equations for Young and Old in a generation that gave all kinds of implications for the voluntary lender, even if the debt/ tax/ hekicoptor apples were not mandatory.

  10. Bob Murphy says:

    Transformer, Krugman (and Kevin Donoghue who unfortunately fell prey to Krugman’s fallacy, which he in turn got from Lerner) is NOT making the Gene Callahanian point that it’s the future taxes that hurt our great-grandkids, rather than the debt per se.

    No, Krugman thinks that in the future, if the government levies a big tax on some of our great-grandkids to service the debt, then necessarily it will confer an exactly offsetting benefit to other of our great-grandkids, since they are holding the bonds.

    All of that is true in the model in the OP. And yet, there is a very real sense in which Al benefits at the expense of the next 9 generations.

    • Transformer says:

      Al benefits from Bob. As a result Bob (for legal or psychological reasons) may be more likely to arrange a transfer from from Christy (and so down the generations) but there is nothing predetermined about it.

      On Krugman: Does he really not recognize that the distributional effects of transfer payment may also affect overall utility ?

  11. Michael says:

    Well sure. Everyone except lucky Al has to lend apples for a generation at an after tax return of zero (if I understand correctly: my loan of 50 apples will net me 50 apples after tax a generation later). Clearly Al is better off. Al just gets to eat apples that G gave him. And the cost is always punted forward.

    But why in your model is Bob also better off with debt as you state further above? Why is Bob in a different position than Dave relative to the no debt world? They seem to be confronting the same rules both when young and when old? And what if all interest were not taxed away from old x, or the only child of old x?
    would that matter?

    • Bob Murphy says:

      Michael, in this particular example, Bob is in the same boat as Christy through Iris. The reason I didn’t include Bob in the discussion is that the debt was increasing when Bob was alive, and Kevin Donoghue (erroneously) thought that the debt burden stuff could happen, but only when the levels of debt were changing. So I wanted to focus just on the people who lived through a period of constant debt, and show that they too were all hurt by the scheme.

      Bob is hurt by the whole scheme. However, *given* that in period 2 Old Bob is going to be taxed 50 apples, and given that in period 1 the government is offering to borrow 50 apples from him at a 100% real interest rate, here are Bob’s two options of apple consumption:

      Option A: Consume 100 apples in T=1, and 50 apples in T=2,

      Option B: Consume 50 apples in T=1, and 150 apples in T=2.

      Given the utility function I made up (but it would work for a general class of reasonable preferences), Bob clearly prefers Option B. So Bob voluntarily lends his money to the government at T=1. The government uses coercion on Bob, but not until T=2 when it taxes him.

  12. Major.Freedom says:

    Once again I see the fallacy from the “it is only about the transfers costs” crowd.

    Even if everyone agrees that debt burdens future generations because of “transfers” costs, and even if everyone agrees that purely redistributional taxation burdens future generations (ignoring the impossibility of purely redistributional taxation, since those doing the taxing must consume a portion of the taxes) because of “transfers” costs, then it would still be wrong to say that what burdens future generations in the case of debt is not the debt per se, but the transfers costs associated with it, the same as redistributional taxation.

    The reason why it is still wrong is because it still ignores of the opportunity costs to real production that are UNIQUE to government debt. The unique costs associated with government debt are the opportunity costs to forgone investment. When government borrows, it borrows out of the pool of SAVINGS. It does not borrow out of consumer driven revenues. But it can tax consumer driven revenues.

    See where this goes?

    When government borrows, the pool of savings is redirected away from private investment of goods and services. That makes the economy’s capital accumulation permanently smaller. This reduction is not observable by history alone, no more than the counterfactual world of no world war one or world war two is observable.

    Right now as we speak the entire world’s population has been burdened by decades of prior government borrowing that has made the total supply of capital smaller than it otherwise would have been. We could have been living with a much higher standard of living today had it not been for that government borrowing. That counterfactual reduction cannot be be replicated with redistributional taxation. It might resemble it in certain respects, but exactly? Not a chance.

    The intragenerational model is only true to the extent the above is true. Unfortunately the model assumes unchanged “capital” for both the factual and counterfactual.

    • Major.Freedom says:

      There is more to borrowing money than money changing hands. There are real goods implications.

      • Major.Freedom says:

        Sorry, unique is too strong a word. I meant between taxation and debt, there are opportunity costs to debt that differ from taxation. If borrowing and taxation are the only options, the there are opportunity costs unique to debt. I was making the point within that narrow box of the debate.

  13. Tel says:

    For what it’s worth… same rules, every generation collectively creates and consumes 200 apples, individuals are modelled in three life phases [1] young, produce only 50 apples, [2] adult, produce 100 apples, [3] old, produce only 50 apples. At any moment in time three generations overlap (one young, one adult, one old).


    Using the same sqrt() utility function, we get a base utility of sqrt(50) + sqrt(100) + sqrt(50) for an individual if they don’t borrow or lend = 24.1

    Early generations can do considerably better than that, but (obviously) it isn’t sustainable, as the debt unwinds later generations are worse off.

  14. Michael says:


    Thanks very much for taking the time to answer my question, and providing such a clear answer. One follow up: is there any added utility to being more secure that the coercively obtained transfer mechanism at least protects me from hunger if things don’t go so well for me as I am jumping from the young to the old cohort. That is, does the square root or log utility function as you and Nick create it overstat the loss of total utility? Do I get any utility as a young person from the knowledge that this transfer I would not voluntarily undertake does at least give me some utility?

  15. Michael says:

    I meant …give me some comfort.

Leave a Reply