Is Government Debt a Burden on Future Generations? Not in Fruitopia.

This blog is in response to the Noble Efforts of Nick Rowe and others to educate the public about OLG and how burdens can be shifted across generations. I want to point out that in these models, the shifting of burdens arises from two aspects:

  • An assumption that Government bonds pay out real goods instead of money
  • An assumption that only the young are taxed.

Neither of these assumptions are very good, and when we drop them we see that debt can be a burden on future generations, but it need not be. It all depends on the taxation policy.

And this is just as true of pay as you go government consumption and pay as you go transfers. In other words, the OLG shifting is not about Debt at all, at least as commonly understood (a promise to pay a nominal dollar, that must be redeemed by the taxation of a nominal dollar, whose tax burden falls disproportionally on the wealthy (in proportion to the amount of bonds that they hold). When the public thinks of debt, they are not thinking of social security transfers, and they are not thinking of wheat futures. It’s important that economists not use their own private language when advocating for public policy. Debts are nominal debts. Taxes involve the sending of money to Washington, not wheat. On the other hand, if an economist said that wheat futures can shift consumption of wheat across generations, no one would be surprised at all. The whole point of wheat futures markets is to allow this, so that firms can hedge the price of wheat. If the economist then concluded that we should not sell more T-bills, many in the public would not be convinced by the wheat futures argument.

More importantly, this is a nice example of the Fiscal Theory of the Price Level, which I think is important, particularly at the zero bound.

Welcome to Fruitopia

Fruitopians live for 2 generations, young and old. Each generation works when young, collecting fruit. They do not work when old. In order to eat fruit in their ripened years, young Fruitopians sell some of their fruit for stones in the fruit-stone market. They then deposit their stones at the Federal Preserve Bank. Old Fruitopians withdraw their stone deposits and sell them for fruit in the fruit-stone market. Let 2N be the total population of Fruitopia, and let N be the total number of stones (although we allow stones to be infinitely divisible).  Each young Fruitopian picks two fruits, has no time preference and log utility. Government has the power to impose consumption taxes on the young and deposit taxes on the old, which are multiplicative (e.g. levied as a fixed percent of fruit eaten while young and stones deposited in the Federal Preserve), so they don’t affect the choice of how much fruit to save. Neither does a change in the stone price of fruit.  In all cases, each young Fruitopian will save 1 fruit in all scenarios. The old fruitopians also have no choice. They withdraw all their stones (net any deposit taxes applied) and sell them in the fruit-stone market, eating whatever fruit they can get.

Assuming no taxes of any kind, this economy rolls along in equilibrium. Because the fruit-stone market clears with no taxes and a constant number of stones, 1 stone will cost 1 fruit, and each old Fruitopian eats their fruit and dies.

Now suppose, in period n, the government digs up a new stone and sells it in the fruit-stone market. With the addition of the new stone, a stone is worth only N/(N+1) pieces of fruit, which is all the private savings of each fruitopian is worth.

  • If the government then divides the fruit it purchased and gives it to the old, then each old person will eat 1 fruit, and each young person will eat one fruit, and the economy will continue as before with 1 stone fetching N/(N+1) fruits in future periods, and no real changes occur to the economy.
  • If the government divides the fruit and gives it to all members of the economy equally, there is a one time transfer of 1/2 fruit from the old to the young in period n, but in no other periods.
  • If the government eats the fruit, then there is a one time income loss of 1 fruit for the old, but no other changes in subsequent periods.

Now suppose that in some future period, the government taxes a stone out of the economy  and throws it away.

  • If the government imposes a deposit tax on the old, then as the young still save the same amount of fruit, all that will happen is that the price of stones (in terms of fruit) increase to their level before the new stone was added to the economy. Both the old and young will  consume 1 fruit each and no change in utility occurs.
  • If the government taxes one fruit from the consumption of the young, and uses it to buy a stone in the fruit-stone market, and then throws the stone away, then there will be a burden of 1 fruit imposed on the young, and a benefit of 1 fruit applied to the old. This is the type of taxation in Nick’s OLG model.

So we see that burdens on the future arise from the taxation policy, and not from the addition of the stone to the economy. Similarly, any burdens incurred when the spending took place arise from what the government does with the fruit that it purchased — consume it, transfer it, give it back.

Stone Coupons

This type of model is used a simple model of money, but there is no transactional demand for money in this model. The only demand for money is as a savings vehicle. Therefore if the government were to sell a coupon that promised to pay 1 stone next period, this coupon would cost exactly 1 stone, as a stone’s own rate of interest is zero. Similarly, in terms of fruit, the young would be indifferent between purchasing this coupon, and depositing it at the Federal Preserve, or purchasing a stone and doing the same.

The introduction of the stone bill is exactly the same as the introduction of a new stone — it causes prices to go up. Really no new markets have been added. The taxation of a stone in order to redeem the stone bill is exactly the same as removing a stone from the economy. In this model, bills are stone-equivalents. Therefore neither the issuance of a new bill nor the redemption of the bill are a burden on any generation, whether present or future. It all depends on what the government does with the fruit, and whether the government taxes optimally to redeem the coupon.

Optimal Taxation

The rule of thumb that you shouldn’t tax savings because you might as well tax labor income assumes that all savings come from *someone’s* labor income and therefore this amounts to double taxation. The problem being when a new service is introduced that must be paid for with a new tax. If only the young are taxed, then the old get the service for free. Therefore in steady state, you *can* only tax the young, but when there are changes, and debt redemption is one such change, you need to tax the old as well. Therefore any model which only taxes the young is going to have the feature of inter-generational transfers (unless one introduces a device such as bequests). That is true of any new pay-as-you-go provision just as much as it is true of any debt redemption. It is the inefficient taxation, and only the inefficient taxation, that is responsible for the canard that “Debt *is* a Burden on Future Generations”. One can only say that debt *might* be a burden on future generations, if the taxes used to redeem the debt are applied inefficiently. But debt is really not a burden in some fundamental, or inevitable sense. It’s the government consumption of output that is a fundamental burden, not the financial adjustments of bond issuance or bond redemption.


The main problem with this economy is flexible prices. If prices are “stuck”, then the necessary deflation will not occur as a result of austerity. In real world economies, austerity is a real burden, but not because of the flexible-price OLG models, but because of price-stickiness. One can also argue that the central bank will undo any deflation arising from austerity by cutting rates, using sticky prices as an advantage. But at the zero bound, this no longer holds. More importantly, adding a central bank that creates stones “out of thin air” doesn’t change the results at all — e.g. we can assume the stones deposit pay a positive rate on stones, and this will immediately transfer to the stone rate of coupons, but the young will continue to save the same amount of fruit and taxing the old will have no effect on consumption. I.e. the central bank is only relevant in so far as we assume sticky prices. With flexible prices, a central bank has no effect on the economy. In this model, it is flexible prices or market clearing in the stone-fruit markets, and not the zero bound, which prevents the central bank from converting the non-burden of taxation into a burden on a particular generation.

In any case, it’s important to see where in the standard non-Ricardian OLG arguments the “debt is a burden” result is coming from. It’s not coming from debt, but from a very idiosyncratic modeling of bonds and suboptimal taxation to redeem the debt.

Is Government Debt a Burden on Future Generations? Not in Fruitopia.

8 thoughts on “Is Government Debt a Burden on Future Generations? Not in Fruitopia.

  1. Good post.

    Preliminary thoughts:

    1. In your model, when the government issues a new stone (or a new paper stone), the real value of the stock of stones (including paper stones) stays the same. (Though this would only be true, I think, if people expected it to be a permanent increase in the stock of stones.) If you doubled the nominal debt, but kept the real debt constant, it’s not surprising there would be no burden on future generations.

    2. In your model, if there were no stones, the equilibrium real interest rate would be very negative. With a constant stock of stones, the interest rate rises to 0%, which is the same as the growth rate of the economy (right?). So we have r = g, which is exactly the borderline between r > g (Ponzi finance bad and unsustainable).

    3. My simple models are normally non-monetary models. Because I’m simply trying to get the point across that we *can* use bonds to impose a burden on future generations, by way of simple examples. These are counterexamples to those who say it’s impossible. If we added money, we could think of the debt as indexed bonds, or we could consider cases where actual and expected inflation were the same. (Unexpected inflation would indeed change things, by transferiing wealth away from current bondholders towards future taxpayers, in an r > g world.) If we have bonds and money, we need to distinguish between the r on bonds and the r on money, and between bond-finance and money-finance.

    1. 1. The real value of 1 period debt in any OLG model is whatever the young save. Because we are using Log utility, real savings are independent of taxation and interest. That is not specific to my example.

      Optimizing: ln( (real labor income – real savings)*Tax_Factor) + ln(real_savings*Gross_Interest_Rate*Tax_Factor)

      Means that real savings = 1/2 real labor income regardless of the other factors (which are per-period constants)

      That’s why financial shennanigans like adding stones or paper promises to pay stones, or removing the stones, or removing the promises aren’t going to affect any generation’s consumption. They will only mess with the price level. You need a transfer or having the government buy a fruit in order to affect consumption.

      Taxing the young is a burden here because the government has to tax a fruit from the young (they have no stones) and then sell the fruit for a stone for the old. So taxation is a transfer from the young to the old — when the young are taxed. But it is not a transfer when the old are taxed. In Barro’s model the old are not taxed.

      I still believe that for any nominal debt and assuming flexible prices, there exists an optimal taxation policy so that no generational shift occurs when debt is repaid. With more complicated utility functions and if the young also had stones (say with inheritance), then you would want to tax the young as well as the old and the math would get a bit messy. Log utility is great because the choice functions are so simple when you have multiplicative interest and taxation.

    2. 2. I’ll do another version with time preference/growing population. I don’t think that matters but it’s a fair point. Log utility is also very special but I wanted to point out what was driving the transfers in others’ models, because the moment I read Barro’s paper, I remember saying to myself “Well, duh, he’s only taxing the young, so of course there is burden on the young.”

      3. Well, all forms of government spending as well as government transfers can be a burden on future generations. It is not an intrinsic property of Debt that it is a burden on future generations as opposed to pay-as-you-go spending: If you only tax the young to pay for government spending in your OLG model, then it doesn’t matter whether you borrow or not, any government spending is going to be a burden on younger generations.

      So stop saying “Debt is a burden on future generations”. How about a more neutral statement like “Debt repayment can have distributional consequences, and we need to be aware of those”.

      And then you have Roger Farmer making strong statements like “An increase in government debt always places a burden on future generations.”, even though he has no such universal result. And these types of statements are made with great confidence, as if it was obvious and well known that debt is a burden on the future — you end up appealing to the public’s sense of a household economy when making these statements whereas Krugman’s “we owe the debt to ourselves” is an appeal for macro-thinking to avoid these types of errors.

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