Home > Main > “Chapter 2: In Which the Traders Crucible slays the Intertemporal Government Budget Constraint, and Mr. Rowe demonstrates his Worth

“Chapter 2: In Which the Traders Crucible slays the Intertemporal Government Budget Constraint, and Mr. Rowe demonstrates his Worth

April 29, 2011

There has been lots of confusion lately over at Brad Delong’s place by the usually unconfused Brad.  Nick Rowe of the incorrectly named Worthwhile Canadian Initiative jumped in.  (why incorrectly named? Should be named “Essential Canadian Initiative” – the dude is freakin’ smmmmaaaarrt, and you’ll see why later.).

But this is about the budget constraint.  The Intertemporal Government Budget Constraint has a single, seemingly innocuous assumption of no Ponzi for government spending. The no Ponzi assumption is that the net present value of our spending/debt must equal the net present value of future taxation.  The books must balance across generations. If this doesn’t hold, the currency must go to zero.  Sounds prudent right?

There is only one problem with this assumption.  We cannot know if it is being violated or not with much certainty at all.  We cannot see the future.  We do not know with perfect knowledge if this constraint holds. We cannot know if the no Ponzi criteria is being held with certainty, because we cannot see the future.

And it gets worse, much worse.  We cannot tell if the no Ponzi criteria is being violated within a rather large band of certainty.  In fact, anyone who says we conform to the no Ponzi criteria must be lying, given the history of governments.  But then, anyone who says we are not conforming to the no Ponzi assumption is lying too.  They ignore hard empirical data from today, right now, given todays data, and given history of the United States.   So far, the U.S. has held to the no Ponzi quite well.

All the data points to that the U.S. holds to the no Ponzi over time. And yet we are foolish to assume we can hold to it

This to me sounds like a paradox.  There is no reasonably certain correct answer.

Is Observation the Key?

Still, We can only know what we observe today.

All we can know today is what people think about the value of their money.  If the no Ponzi assumption holds or does not hold, we have to look to current inflation rates to tell us the opinion of what people think is the ultimately unknowable answer.  There is no other way to tell other than inflation rates today, because the future is obscured to our observation.

It turns out the assumption is irrelevant for this reason.

The no Ponzi assumption is irrelevant

The no Ponzi assumption kinda sorta ignores the fact that any violation of the assumption has to be observable today.

We know this because the conclusion of the no Ponzi assumption says words like “We would see rates of inflation increase to levels that make g < r if people think the no Ponzi assumption is being violated.”  But then people forget we cannot know the future with much certainty, so there is this eternal hand wringing over current inflation rates.

These people cannot know if there is a Ponzi violation.  It’s a guess, at best. It’s mad-cap speculation at worst.  How can we ever really tell?

Future Ponzi violations or no violations are impossible to know information. They are not falsifiable for any current levels of real growth or real interest rates.  Nobody knows, or can know, what the future levels of primary deficits will be 20 or 100 years or 1000 years from today.  Anyone can always say “Well, future levels of spending might be too high and spur hyperinflation,” and there nothing anyone could ever say that will prove that statement false.  Those levels of future spending might turn hyperinflationary or not, and we cannot know.

Of course they could also say “We are going to be so rich in the future when we  energy that costs 5% of current costs that these current deficits are trivial”.  How can you tell?

Todays evidence shows we are within the bounds of any reasonable no Ponzi assumption given by Scott Fullwiler.  But who in the hell knows? We cannot know the future.

So how does can the no Ponzi assumption help us manage policy real world policy in any practical way?  It doesn’t. It’s a myth, a spook story economists tell their kids at night. “Spend too much, and the Intertemporal Government Budget Constraint will get you.”

The only way we can possibly guess if this assumption is being violated is through current inflation rates, real interest rates, and rates of real growth.   Even then, these observable rates change all the time.  Over the course of decades, these observable rates are all over the place.

Still we have some guidance here with observable market prices of things.  All violations of the no Ponzi assumption must be observable. If we don’t have significant inflation, the no Ponzi cannot be being violated as far as we could ever know.

Inflation is the observable change in the price of money in real world goods, services, and transactions, including all financial assets.  In other words, the overall market for money will show us the violations of the no Ponzi assumption.

Violations of the no Ponzi assumption must be observable otherwise the EMH is false for the largest, most transparent, most liquid market possible 

If the violations of the no Ponzi criteria are not observable for the most liquid and transparent possible market in any economy, then the EMH must be wrong. No EMH in the market for money has devastating consequences.

It’s at this point where I raise the head of the IGBC and proclaim the dragon slain.  Either you believe the inflation rate as the only way to tell if people believe the IGBC is holding, or go back to believing in crystal balls telling the future.  If you insist on a strong belief in magic, then I hand over the head of the EMH.

As an aside, even if the violations are not observable, it would be foolish to act in any way but to accept the EMH as true in the market for money – which as far as i can tell, is the largest, most transparent, most liquid market possible within current human experience.

This might sound astonishing, but I am not over yet.  Living in a no Ponzi world has incredible consequences.  Nick Rowe knows exactly what I am talking about.  We are living in a world where g is greater than r, nearly all the time, except when some normal business cycle pushes g below r.   

Next up, “Chapter 3, in which Mr. Rowe proves his worth.”

  1. Detroit Dan
    April 29, 2011 at 7:19 pm

    This I have to see…

  2. vimothy
    April 30, 2011 at 8:32 am

    The no Ponzi game condition is not the same as the govt’s intertemporal budget constraint. You have them confused here.

    • TC
      April 30, 2011 at 9:24 am

      The no Ponzi constraint defines the budget constraint. If the no Ponzi doesn’t matter, then there is no budget constraint other than what we are willing to accept as inflation, because the budget constraint uses the no Ponzi condition as the key condition.

      If Ponzi is allowed, then there is no budget constraint. We can ponzi all we want, meaning spending is not limited by any levels of g or r.
      If Ponzi is not allowed, then we need to have some real world, observable way of seeing a violation for it to be meaningful or useful.

      That real world way of seeing violations must be the current level of inflation, otherwise the EMH does not hold for money, and therefore you’re a Keynesian at minimum.

      If you can see violations through inflation, we live in Nick Rowe’s bubble land. Where bubbles are demanded by the economy, or conversely during recessions, become Richard Koo’s blackholes.

      Fortunately we can control T, the treasury rate, which then dictates r, the real rate. Which allows us to live in bubble land whenever we desire, bounded only by a much higher rate of inflation and the risk of pushing real rates too high by high spending. Thats chapter 3 about Nick Rowe.

  3. vimothy
    April 30, 2011 at 11:27 am

    The no Ponzi game condition says that the limit of the present value of govt debt is zero. You could have a positive quantity of government debt in the limit, but that would mean that at least one individual holds a strictly positive quantity of govt debt and therefore can increase their utility by selling the debt and consuming more. I.e., the economy is not at an equilibrium, by non-satiation.

    • wh10
      April 30, 2011 at 12:25 pm

      Vimothy, I appreciate your presence in the MMT blogosphere. Checks and balances are a good thing. However, I rarely can understand or see the logic in anything you write. It could very well be my thin formal background in economics. Can you please restate your above post and perhaps spell things out a bit more?

      • TC
        April 30, 2011 at 5:28 pm

        The no Ponzi math is in the heart of the derivation of the Budget Constraint Math. It is the crucial step in the Walsh derivation. The point is not about the NPV, it is about being able to tell if there is no Ponzi violations.

        Look to Walsh Monetary Theory and Policy (2003) 4.11 if you have any doubts about the no Ponzi game being a key assumption of the IGBC.

      • vimothy
        May 4, 2011 at 1:10 pm

        If the public is holding some government debt, that must mean that someone has not consumed all of their income, which means that the economy is not at an equilibrium.

        • TC
          May 5, 2011 at 8:05 am

          lol. Little steps.

  4. studentee
    April 30, 2011 at 11:03 pm


    vimothy’s purpose around here is to undercut heterodox challenges. he’s a professional economist working within the orthodox tradition. he’s understandably irritated that there are schools out there who say his paradigm is bogus

    • vimothy
      May 4, 2011 at 12:57 pm

      Er, no I’m not. I’m currently a student. I read a lot of MMT & PKE stuff (among other things) before I decided to go back to school to study economics. It seemed to me that a lot of what I read from the MMT camp criticising other economic schools was mistaken and misguided.

      • vimothy
        May 4, 2011 at 12:59 pm

        “It seemed to me that a lot of what I read from the MMT camp criticising other economic schools was mistaken and misguided.”

        It seemed to me, after doing some study, that etc…

        • vimothy
          May 4, 2011 at 1:11 pm

          Also, I find hetero schools plenty interesting, which is why I’ve spent so much time reading about them and debating with their proponents online.

  5. TC
    May 1, 2011 at 12:04 pm

    In case you don’t have a copy:


    Page 142. The last term of the math in 4.10 needs to go to zero otherwise it is unbounded for the NPV calculations. The no ponzi condition must be met for the budget constraint math to work.

    And the only indications that people think this condition is being met is current inflation, current real rates, and current growth, no matter what the projected levels of future debt are or might be.

    • vimothy
      May 4, 2011 at 1:08 pm

      I have that textbook. Of course there are others. But anyway, think of it this way. Say that we all agree that currency is a stable Ponzi, i.e. that the government will never pay back the debt represented by cash, but will continue to roll it over forever. (Which seems reasonable). Does this imply that the government does not face an intertemporal budget constraint?

      • TC
        May 4, 2011 at 1:16 pm

        Now that is a real question. I think I answered in my post on Insolvency vs. Debasement. That government doesn’t face a “constraint”, it faces some level of inflation or deflation at which it can make decisions. Not saying they will be good decisions or bad decisions. But any other way of looking at this particular problem and taking action is “here be dragons” style action, cloaking itself as prudent or even moral behavior.

        • vimothy
          May 4, 2011 at 1:24 pm

          If you want the govt to be to repay its debt in anything other than paper, then the constraint is real and the only question is how to represent it.

  6. Peter D
    May 2, 2011 at 11:02 pm

    Nice. If I am understanding you correctly, you’re saying that the IGBC is an ex post condition and as such worrying about it ex ante should be done only insofar as there is an observable that tells us whether we’re violating it or not. If there isn’t one, then who cares, more or less. If there is one – such as inflation rate – then this is the only thing we should be concerned about, which bring us back to your posts about solvency vs. inflation.
    Seems to me similar to the metaphor I always use when thinking of MMT: it is like driving a car according to the road conditions. No need to think that somewhere down the road there might be a downhill while right now you’re going uphill. Worrying about unforeseen changes in the road conditions beyond the basic prudence of not driving too fast is counterproductive, as you might not even scale the current uphill.

    • TC
      May 3, 2011 at 7:00 am


      This is a great way to say it very concisely. Thanks.

      The no Ponzi criteria relies on ex post knowledge of the windup of the government. What can we tell our conformance or non conformance ex ante? Less than nothing.

      We can see inflation ex ante, and Inflation is something we have to deal with anyway, IGBC or no IGBC.

      And you are exactly correct about the the relationship to the “Solvency vs. Inflation” debate. I wrote this post because Brad Delong, Nick Rowe, and Paul Krugman threw up “Hey, all this MMT seems great, but they forgot about the IGBC.” Well, the IGBC is irrelevant considering we only have ex ante knowledge of conforming to the assumption.

      Nice metaphor btw.

      • Peter D
        May 5, 2011 at 10:35 pm

        A very apropos video of a Quantum Computing pioneer David Deutch. Go to the 17mins mark and listen to him eloquently argue that we shouldn’t worry about things we cannot control and observe and that we just need two “commandments”: (1) Problems will happen and (2) Problems can be solved. He talks about it in the context of climate change and related stuff, but it applies to our debate about IGBC beautifully.

        • TC
          May 5, 2011 at 11:08 pm

          Absolutely great stuff. My background is in physics a long time ago. Also read tons of Bucky fuller – and “observable” is one of his guiding lights.

          Can you go engage this guy and show him the light?


          MIT phd, thinks the GBC is knowable. I just started to engage him on it.

  7. vimothy
    May 4, 2011 at 1:16 pm

    Here’s another way to think about it: Imagine that a govt made promises to one sector of the polis that exceeded the real wealth of the entire country (i.e. the PV of its real GDP). Here we would have liabilities > assets in a very straightforward sense.

    • Peter D
      May 4, 2011 at 11:24 pm

      vimothy :
      If you want the govt to be to repay its debt in anything other than paper, then the constraint is real and the only question is how to represent it.

      Why would I want the govt to repay its debts in anything other than paper? Does it promise anybody anything other than paper?

      • vimothy
        May 5, 2011 at 6:13 am

        Because you can’t eat paper. Money is only useful in so far as it trades for other stuff in the economy. Let’s say that the govt gives everyone £1bn tomorrow. On paper, we are all a lot richer—fabulously rich—but in reality, there was no increase in wealth, because all the gains were paper, which is to say, illusory.

        • TC
          May 5, 2011 at 8:12 am

          This is an argument based on something that will never happen with the Pound at its current relative value. I can make arguments like that too. Maybe the government will give us all eternal life tomorrow – then we have major problems, eh?

          There was never any promise to pay in anything but paper or gold (which you cannot eat either) in the first place.

          Also, until you get that everything – and not just paper money – is defined in value by the other objects available, you’ll be constantly bummed out by paper money. Paper money is not a special case. Everything has only a relative value, and not an absolute value. Wheat flour I can buy at the store for pennies a pound. Yet, in a famine, it would be among the most valuable objects I could purchase. Its all relative, even gold and silver. Gold is valuable until you have to eat it. Then, not so much.

        • TC
          May 5, 2011 at 8:25 am

          Also, watch Schilnders list. Specifically, the end and the scene where the German officer swallows the diamonds.

          “I could have got more”

          “This pin. Two People. This is gold. He would have given me two more. At least one.”

          And he is devastated, because it a damn pin, and worth 2 peoples lives. In normal times, a tiny gold pin is not worth someones life. It’s worth a mans custom made suit, which is worth about 2 weeks of work for an average person, which is worth a few days of food in a famine…

          I hope you move to understanding this point.

        • vimothy
          May 5, 2011 at 8:56 am


          I am not bummed out by paper money at all. Gold is irrelevant; I’m not sure why you’re bringing it up here. The point is that the value of money is defined by what you can purchase with it, which you obviously agree with, hence your digression on marginalism.

          And this is something that is actually already a problem in the States, where the govt has large amounts of unfunded liabilities relating to health and social security programmes. Of course, the government can print as much money as it likes and hand it out to pensioners. But since they cannot eat money, it won’t do a terrific amount of good. The govt really needs to somehow print a load more output. But, alas, it cannot.

  8. Peter D
    May 4, 2011 at 11:32 pm

    vimothy :
    Here’s another way to think about it…

    As I often find with you, it is not an intuitive or illuminating way – at least to my untrained eyes.
    Suppose the govt promises to pay a retiree $X. Just like with any other govt spending, if such payment causes inflation, then it may need to be “neutralized” by taxes. Note that this needs to be done ex post, not ex ante.

    • vimothy
      May 5, 2011 at 8:15 am

      I take a lot of pride in being unintuitive!

      Think about your example. Our argument is about whether the government can possibly make promises that it cannot keep. Suppose the government promise to pay a retiree $X, where X is larger than the entire GDP of the country. What would it mean for someone to receive this payment?

      • Peter D
        May 5, 2011 at 10:42 pm

        No, that’s your twisted interpretation of our argument. Our argument is whether nominal obligations of the govt can ever cause it to default (no) and what could be the possible consequences (inflation). The govt never promises anybody $X>GDP, but if it did, it would only have to print $X, and then watch it being inflated away (unless the payees are all misers and put most of the money under the mattress). $X can be greater than GDP[t] but it won’t be greater than GDP[t+1] (all nominal, naturally)

        • vimothy
          May 6, 2011 at 2:53 am

          It’s not an interpretation of anyone’s argument–it’ a thought experiment.

        • art
          June 20, 2011 at 8:31 am

          Gents, Vimothy isn’t saying anything too radical here. MMT’ers agree that (1) a sovereign govt’s promise to pay in something other than its currency imposes real constraints (that’s sort of the point of the “M” in MMT) and (2) if it runs deficits or promises real benefits beyond the capacity of the economy to produce them, it will induce inflation (and in the case of benefits, and/or relative price shifts, which means there are also potential opportunity costs; Levy Inst writings on SS and Medicare say essentially the same thing).

        • TC
          June 20, 2011 at 9:06 am

          But he is trying to do it in such a way that he can make silly claims about the logic of MMT.

  9. jamdox
    June 9, 2012 at 9:42 pm

    I admit I’m not up to date on the entire conversation, but:

    1) the gov’t doesn’t promise to pay in anything other than it’s own currency (if it’s not Greece). Indeed, FR Note “greenbacks” are claims against US Treasury debt held by FRB… this shouldn’t be news but somehow I think it is… Regarding Art’s point 2, I’m not sure what he’s saying… “deficits…beyond the capacity of the economy…” what?

    2) all it takes for the no-ponzi condition to fail is for real debt issuance to be higher than the level of inflation. The only constraint is that REAL DEBT SERVICING COSTS ARE SMALLER THAN REAL OUTPUT. That’s it.

    So Vimothy is confusing debt servicing costs and debt itself. Claro?

    Oh, wait this is from 2011… lol

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