Monday, February 9, 2015

Sam and Janet Learn about Debt

In a recent post on the (non)-importance of debt buildup worldwide, Antonio Fatas makes the point that debt is not necessarily a problem. While I agree with that statement: a great deal hinges on the qualification “not necessarily”.  

Paul Krugman goes further than Antonio. According to Paul debt is “money that we owe to ourselves”. That is at best misleading and at worst;  false. Money is money we owe to ourselves. Debt is money that some of us owe to others. 

In the real world, debt matters; and it matters a lot. Why? Because different generations are not all connected by operative chains of bequests. Government debt is the liability not only of current generations, but also of future generations. An increase in government debt always places a burden on future generations. The right question is: do the benefits of increased government debt outweigh the cost?

Paul, in a separate postinvites us to think of a world where some people (spendthrift Sams) spend more than others (Judicious Janets). I like that model; but lets develop it a little bit further and suppose that Sams and Janets reproduce (asexually since this is, after all, a brave new world). That allows us to think about the real world in which different generations coexist.

In a model that I developed here, there is a stationary population that consists of a bunch of Sams and Janets of different ages.  The Sams spend more than their income when young, and less when old, by borrowing from the Janets. Janets do the opposite. They spend less than their incomes when young and more when old. Sams and Janets are selfish, and although they love their children, they don’t love them all equally. 

Several centuries of social evolution has created a society composed of equal sized populations of Sams and Janets. In each population, there are ancient dynasties and newly created dynasties all of whom are borrowing and lending to each other in amounts that depend on their ages and their types.

Let's expand this idea a little further. Although the incomes earned by Sams and Janets are equal every year (the Scandinavian model) the amount that they each earn fluctuates from one year to the next. In most years, income is high; but occasionally there is a recession and income is low. Since Sams and Janets are risk averse, they insure themselves against these fluctuations by trading in the financial markets. 

Sams and Janets trade two financial assets. One asset, debt, is a promise to pay one dollar next period whether income is high or low. The other asset, equity, is a claim to the future stream of income. Since there are only two events in each period, income my be high or low. The financial markets are complete and Sam and Janet are perfectly insured against fluctuations. But their unloved children are not.

So far so good. Along comes Government Gus. Government Gus issues a boatload of debt that it sells to existing generations of Sams and Janets. Government Gus is in a heated political race with the opposition, and seeking political popularity, he spends the proceeds of government debt creation on pork belly projects that favor existing dynasties of Sams and Janets. Since interest rates are currently low, Government Gus borrows $10 trillion in the form of 1% consols; these are promises to pay $10 billion in coupon payments to the bearers of the securities every year forever. To finance these interest payments, Government Gus introduces an income tax.

Now we can evaluate Paul’s statement that “debt is money that we owe to ourselves”. Not quite. The benefits of  the pork barrel spending have all accrued to existing generations of Sams and Janets. But debt finance has created a perpetual stream of tax obligations that fall not only on current generations of Sams and Janets; but also on all future generations. That is the sense in which Paul’s claim is misleading. ‘We’: are not a homogenous group. Debt benefits some groups at the expense of others.

What about Antonio’s qualification that debt is “not always bad”. That depends on what causes recessions. John Cochrane points out that, if recessions are all supply side events, those pork belly projects are an unambiguous theft from our children. But if most recessions are caused by deficient “animal spirits” as I believe they are and have modeled here, the additional pork-belly spending may increase income (and employment) by shifting the economy into a higher, more efficient, equilibrium. Spending on roads, bridges and Warp drive technology that benefits future generations, as well as current ones, would be even better.

Lets recap; if aggregate income and employment is determined by aggregate supply, government borrowing to finance current expenditure is an unambiguous transfer from future to current generations.

If aggregate income and employment is determined by aggregate demand, government borrowing to finance current expenditure can potentially increase income and employment and make everyone better off. 

Irregardless of whether recessions are induced by supply or demand failures: government debt creation has distributional consequences. A better way of financing expenditure in the midst of a deep recession, (Europe take note), is to create lots of little pieces of colored paper and distribute them to all of the hungry Sams and Janets out there who don't understand why Gus is standing idly by while they go hungry.


  1. Roger, I'm not familiar with the ins and outs of the literature your sunspot paper responds to, but your brief writeup here doesn't explain why Krugman is wrong. Yes, there are perpetual tax liabilities, but there are also perpetual private bondholders. You don't assume a world of only Janets, as Nick Rowe does (so that the intergenerational transfer occurs right off the bat and is transmitted across time periods). Thus it isn't obvious why there should be distributional consequences of debt either across time periods or cohorts. Is this about asymmetric impacts of the changing debt-equity mix on future generations of Sams and Janets? And in the supply-constrained growth model, is debt “bad” if public spending has the same rate of and return to investment as private spending?

    1. Peter: The current generations (both Sams and Janets) get the immediate benefit (porkbarrel spending) but only pay part of the cost. Future, as yet unborn Sams and Janets, must pay taxes to meet part of the interest payments to bondholders born today.

    2. In your model each individual maximizes the utility of lifetime consumption and could die with net positive or negative assets only because of uncertainty, yes? This means that all net purchases of bonds by those alive at the time of the Great Borrowing are, stochastically, discharged by net sales to all those unborn at that time. These future kids will buy their bonds, meaning they acquire no net PV from them (aside from income smoothing etc.) and they are still stuck making payments on the bonds of oldsters who haven’t kicked off yet. I get that. But in the real world (Piketty’s for instance), a significant proportion of bonds are bequeathed. That changes the age structure of payments in periods after the death of the founding generation, such that the intergenerational distribution can no longer be assumed. I would understand Krugman’s claim as being net of any particular special case involving this age structure, such as the zero bequest motive in your model.

    3. Not quite. My model has perfect annuities markets so that borrowers take out life insurance and lenders earn a higher rate of return than the market in return for leaving their assets to the annuities company. This is pretty basic stuff that was developed in 1985 by Olivier Blanchard in his classic paper Debt Deficits and Finite Horizons. No I don't assume zero bequests: that's why I talk about dynasties and not people. Debt is a redistribution between generations. Period. All I need, for this result to go through, is that some children are unloved. There is another classic piece in this literature by Philippe Weill Love Thy Children that makes this point. This seems to be one of the rare times when Krugman is genuinely confused. Nick Rowe sent me this link which makes the same point, published back in 2011. Nick is right. PK is wrong.

  2. Roger, you write:

    > debt finance has created a perpetual stream of tax
    > obligations that fall not only on current generations
    > of Sams and Janets; but also on all future
    > generations.

    But Roger: that same debt also creates a perpetual stream of payments to the bond holders. That benefit to future generations precisely offsets the burden, and nets to zero. Why are you only looking at one side of the coin? How can this stream of payments be a net burden to future generations?

    1. You are seeing the world through the lens of Ricardian equivalence. The world is not Ricardian. We live, we die; but the government goes on forever. The government borrows and gives the money to Sam and Janet. Janet buys the debt. Sam spends his transfer on a party and dies young. Future generations now have an obligation to Janet from which they received no benefit.

    2. Roger, thanks for the answer. But I am still baffled.

      > Future generations now have an obligation to
      > Janet from which they received no benefit.

      But Janet (or Janet's heirs) receive a benefit. There is future redistribution for sure, from taxpayers to bondholders. But there is no reason to think that that ongoing redistribution makes the people alive at that later time collectively worse off. Our children are not collectively poorer. The children who don't hold bonds will be poorer, and the children who hold bonds will be richer, and it nets out to exactly zero. This is Krugman's point, and I still believe he's right. If there is ongoing transfer from "future generations (except for Janet)" to "Janet", and assuming everyone consumes according to their income, then total future consumption is identical with or without the debt, because for every dollar of consumption that future_generations_except_for_Janet forgoes, Janet_or_heir consumes an extra dollar's worth.

      You may not like that redistribution (from future taxpayers to future bondholders). There might be good reasons not to like it. But collective wealth is identical with it or without it. Aggregate consumption is identical.

      Yes, there are elaborate schemes that redistribute consumption generationally (one is called "social security"), and these can continue ad infinitum that has the net effect of distributing consumption from people who won't be born for years (when social security collapses) to people alive today. But this form of making parents-richer-children-poorer has nothing to do with debt and everything to do with fiscal policy (taxing the young, sending the money to the old). Nick Rowe goes into great detail in how they can be set up. But debt is neither necessary nor sufficient for intergenerational redistribution.

      I hate being so at odds with famous economists, when I'm just a lousy old computer programmer, but I guess I can feel good about being in company with Peter Doorman above as well as Krugman.


      Kenneth Duda
      Menlo Park, CA

    3. Let me try an even simpler example. In the beginning of the world there is one old person and one young person. The old person dies at the end of the first period. The young person lives for two periods and then dies. Every period there is a new generation of people who live for two periods and in every period there is always one young person and one old person.

      Everybody has ten apples when young and ten apples when old. Society always has twenty apples. There is no borrowing and lending because the young person has no-one to lend to.

      The initial old person sets up a government. The government sells a perpetuity to the initial young person and, in return, the young person gives the government five apples. The government gives these five apples to the initial old person. This person gets to eat fifteen apples and the young person, voluntarily chooses to eat only five.

      In period 2, and in all subsequent periods, the government takes five apples from the young in taxes and gives it to the old as interest on the perpetuity.

      Every period, the young person buys the perpetuity from the old generation. In return, he receives interest when he is old and he passes the perpetuity on to the next generation. Remarkably; this allocation can be supported as a competitive equilibrium with markets.

      The initial old guy is clearly better off. He got to eat fifteen apples instead of ten. Everybody else in the infinite future is worse off. Even though they still get to eat twenty apples over their lifetime, the allocation between youth and old age is distorted. There is a huge literature on this model dating back to Samuelson in 1958. The clearest piece I know of is by David Gale.

      Is collective wealth the same? In a sense yes. In another sense no. Society always has twenty apples. But the wealth (defined as net present value of lifetime endowment) is lower because the interest rate has gone up and because future endowments are taxed.

      You say that social security has nothing to do with debt. That is incorrect. Social security and debt are essentially the same thing. You are correct to point out that the issue is one of redistributing resources between generations. That is what government debt is: a redistribution of resources between generations. And when the interest rate is greater than the growth rate; debt makes everyone except the current generation worse off.

    4. Thank you again Roger, you are very generous with your time.

      I think I fully understand your model of intergenerational transfer and agree completely that the government is capable of transferring wealth and consumption arbitrarily far across generational timelines.

      Thank you.

      Kenneth Duda
      Menlo Park, CA

  3. "Debt is money that some of us owe to others." - This I understand.

    "Money is money we owe to ourselves." - This I don't.

    Your paper looks interesting. I look forward to going through it in more detail.

  4. in regards to the burden debt puts on future generations, should we damn our parents for the government debt they passed on to us? i was born into a country with a debt to GDP ratio of 120% coming out of world war two…should we argue that our parent’s generation should have fought the war on a pay as you go basis? and during the 50s, the government ran deficits to educate the returning soldiers and to build the interstate highway system…to avoid adding to the debt, would the country have been better off using the roads we had at the time, and without the GI Bill?

    1. "should we argue that our parent’s generation should have fought the war on a pay as you go basis" Obviously not. Infrastructure projects and wars are examples of expenditures that benefit future generations as well as current generations. They are good examples of when we should be using debt.

  5. I think you are being a bit unfair to PK. I don’t think he is claiming that debt is neutral. Indeed, he is specifically addressing situations where insufficient demand creates positive externalities to government spending. He is not claiming that borrowing now is always and everywhere justified simply because, "it is money that we owe ourselves". He is not claiming that government debt can never make us worse off. He is railing against the claim that increasing government debt is bad, just because. When he says, "debt is money we owe ourselves," he is including future generations in "we" to make this statement trivially true. Also, he acknowledges
    this burden will have real negative effects in the future.

    You yourself point out that there are conditions under which future generations benefit from current government borrowing and spending. Infrastructure and defense are public goods. Anything that governments can do that increases current real income is also beneficial to future generations. To argue that a government can engage in a redistribution scheme to transfer income from children to parents is hardly an indictment of Paul Krugman's claims. He is not advocating a debt financed increase in transfers to old people.

    1. Ben, you totally nailed it. Krugman is making a simple point (that $18T in debt does not make our children $18T poorer). This point is so obvious to professional economists that they can't even understand that's all PK is trying to say. PK expresses the idea as "debt is money we owe ourselves", which in typical Krugman form, is clever, true, and also a stretch/oversimplification. The pros like Roger and Nick Rowe and Simon Wren-Lewis then protest the implication that government debt is always and everywhere 100% benign, and around we go, lost in side issues like whether it's possible to have "crowding out" at the ZLB, or whether it's possible to transfer "flows" across generations or only "stocks", etc., and missing the larger and much more important question of: what *is* the right way to deal with the output gap? How can we build consensus behind a sensible reaction to the ZLB, which, in my opinion, is two things:

      (1) monetary policy that can raise aggregate demand at the ZLB, such as NGDP level targeting;

      (2) automatic countercyclical fiscal stabilizers, which hopefully aren't needed if NGDPLT does its job, but are still there in case it doesn't.

      I believe the above to be the sensible and practical reaction to the lesser depression, yet it's amazingly hard to build consensus around that.

      Kenneth Duda
      Menlo Park, CA

  6. "Government Gus borrows $10 trillion in the form of 1% consols; these are promises to pay $10 billion in coupon payments to the bearers of the securities every year forever."

    Don't you mean $100 billion coupon payments?

  7. Roger, the USD is a fully fiat currency that floats on the Foreign Exchange. It's essentially a fiat tax credit and the only liability that the Federal Government incurs when it creates a dollar is a dollar of liability against it's own taxes. Why would we have even bothered to create a fiat regime if there we still owed somebody something for having created an increasing amount of our national currency. Although some nations peg to our currency on the fx (or use a currency board) the USD has no intrinsic value and floats on the fx. Currently, we "sell debt", but there's really no need to do so, the Treasury could just create the money directly. If Congress can't set aside it's own rules about this, let us insure all deposit accounts, pay a smidgen of interest if necessary and sell nothing longer than a 3 month bill. That should drive the point home that the so called "National Debt" is nothing more than the surplus of fiat tax credits sitting in private accounts, that the Federal Government has not yet clawed back via taxes. This Private Sector surplus of USD-denominated tax credits will never be an intergenerational burden.

  8. That should have been "...let us fully insure all deposit accounts..."


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