Money Financed Deficits Have the Same Future Tax Obligations As Bond Financed Deficits

Over at Worthwhile Canadian Initiative, Nick Rowe wonders how much of a deficit would need to be money-financed as opposed to bond-financed. I say it doesn’t matter how you finance the deficit, what matters is the time path of interest rates (which is independent of how the deficit is financed).

To see why, assume that in one scenario, a government sells B bonds, sold as short term bills. Each period, the debt will compound by (1 + r_i), where r_i is the nominal rate in that period. That debt will continue to compound until the government decides to pay it off (say with a lump sum tax).

On the other hand, suppose that the government sells B bonds, and then the central bank purchases those bonds, holding them as excess reserves. Now for the central bank to maintain a positive interest rate, it must pay interest on reserves at a rate (1 + r_i) each period, and those reserves will compound just at the same rate as if the government issued bonds.

Nick suggests that currency demand will ultimately reduce the excess reserves to zero — e.g. banks will purchase currency with their reserves as NGDP grows, decreasing the quantity of interest paying reserves and increasing the quantity of non-interest bearing currency. The issuance of non-interest bearing currency is seignorage income, but the Government could just as well use the same seignorage income to retire a portion of the bond debt, by having the central bank gradually expand its balance sheet and purchase a portion of the debt as currency demands increase. If the currency demand comes from high inflation, then it makes no difference whether a debt is inflated away, or whether excess reserves are converted into currency as a result of high prices. The same drawbacks apply to both approaches.

When will currency demand a.k.a. seignorage income really eliminate all the excess reserves? Currency demand should grow at most as fast as NGDP, i.e. at a real rate of g. This means that the crucial test is the difference r – g, where r is the real rate. This is exactly the condition for whether government debt must be paid off or whether we can ‘outgrow it’. And as the seignorage income can be equally applied to retire the government debt or to retire the excess reserves (or to provide for goods and services if no action was taken), the present value of the future taxes necessary to eliminate the excess reserves is the same as the present value of the future taxes necessary to eliminate the debt.

But will the time path of interest rates be higher if the central bank replaces an interest bearing bill with interest bearing reserves (both paying the policy rate)? Why should a household care if it holds a bill or a deposit paying the same amount? I.e. if the act of selling the debt causes interest rates to settle on a rate r, then buying the debt with reserves that pay an interest rate of r is not going to cause the equilibrium rate to change.

I think the confusion stems from a belief that central banks issue currency (which does not pay interest) rather than reserves. When the interest rate is positive, there is an incentives for banks to deposit their currency with the central bank, converting the currency into reserves and earning a positive interest. This makes banks compete for currency and deposits belonging to households. In this way, even if the central bank were to make all of its QE purchases with $2 Bills, as soon as rates become positive all of the bills would end up back at the central bank converted from currency into interest bearing excess reserves. Therefore whether rates are positive or negative, there is no difference between reserves and short dated bills, and so there is no difference between financing a deficit by issuing more short dated bills or financing a deficit by issuing more reserves.

It’s very odd how nervous commentators are about the central government expanding its balance sheet yet the same group enthusiastically urges the central bank to do whatever it takes.  The bank can just keep paying more and more interest on reserves that swell geometrically in size with no concern about whether r > g, no discussions of “sustainability”, “future generations”, etc. In other words, functional finance applies only to the bank, not to the government, even though both are under the same constraints — pay interest of r_i each period on your liabilities net of seignorage income.

Money Financed Deficits Have the Same Future Tax Obligations As Bond Financed Deficits

11 thoughts on “Money Financed Deficits Have the Same Future Tax Obligations As Bond Financed Deficits

  1. Market Fiscalist says:

    I think your argument is:

    If the deficit is funded by bonds sales to the public the govt has to eventually pay off the debt via tax or seignorage (or just roll it over)

    If the deficit is funded .via bond sales to the CB then tax or seignorage will be needed to eliminate the new money the CB created.

    So its a wash which is used. Is that correct ?

    If so, I’m not seeing the 2 cases as similar in regards to the liability created. In both cases money is distributed to the public via fiscal policy. If and when this policy needs to be reversed then tax and/or seignorage will be needed to reverse it.

    In the case of bond sales to the public tax and/or seignorage will be needed to eliminate this too. But f the CB bought the bonds they can just hold them for ever can’t they (or until they need to be sold to the public as part of monetary policy), so tax and/or seignorage will not be needed.

    1. The CB needs to pay interest on reserves, just as the Government pays interest on bonds. It is the same interest (if the government sells bills) on the same amount, so the NPV is the same.

      In terms of whether the tax can never be paid, that is a question of r, g for both the CB and Govt.

  2. Market Fiscalist says:

    OK, I see.

    The choice is between paying interest on bonds or paying interest on reserves.

    But couldn’t you have a workable model where the CB never pays interest on reserves ?

    1. It might help to view the CB policy rate as the rates that banks pay when borrowing and lending reserves to each other. From that, the other rates are set. Therefore if you flood the system with excess reserves, this rate falls to zero. In order to maintain a positive interest rate, you pay interest on reserves.

      Said another way, whatever “problems” a government has in paying interest when rates go up, those same problems will be applied to the central bank with a large amount of excess reserves when rates go up. Therefore buying bonds with reserves doesn’t hide or reduce the overall costs of the deficit spending.

      1. Market Fiscalist says:

        OK. At the ZLB when the CB attempts QE then IOR would hinder its effectiveness. But when the ZLB is passed there may then be excess reserves in the system that the CB needs to manage via IOR to stop NGDP overshoot.

        But if the CB bought wisely in the QE program why can’t they just sell those assets back to the market again ? (in theory the assets they bought for QE may not be govt debt at all , so interest payment are irrelevant once sold back)

        if rather than QE the govt had sold bonds to the CB for newly created money (money-financed deficit), then I suppose excess reserves would still exists and when out of the ZLB the monetary authorities would be faced with a choice between 1) paying IOR 2) selling the bonds to the public to eliminate excess reserves and paying interest on them or 3) using taxes or seignorage to eliminate excess reserves (and the govt buying the bonds back from the CB with the budget surplus or seignorage profits).

        But wouldn’t option 3 be totally consistent with the fiscalist approach that money-financed deficits were part of ?

  3. “But if the CB bought wisely in the QE program why can’t they just sell those assets back to the market again ? (in theory the assets they bought for QE may not be govt debt at all , so interest payment are irrelevant once sold back)”

    Let’s forget about “investing wisely” and assume the CB bought risk-free bills. Yes, they can sell some of them back each period. How many? Whatever is necessary to support growing currency demand. I.e. this is the seignorage income that reduces the stock of excess reserves over time, but this same seignorage income can be used to retire some bonds in the non-deficit financing case (remember that CB net interest income is owned by the Government). Therefore it is not “cheaper” to reserve-finance or debt-finance. The use of seignorage income in both cases will retire some of the debt, but whether it is enough to fully retire the debt depends on r > g or r < g. In any case, it's a non-issue as to which financing approach has a lower future tax burden relative to the other.

  4. Market Fiscalist says:

    During QE the CB increases in balance sheet and the amount of excess reserves builds up. The issue is what happens when QE is no longer needed.

    As NGDP increases over time then 2 things are possible

    1) The excess reserves get converted into cash as demand for it increases. This is seignorage
    2) The level of reserves and the CB balance sheet is kept the same and the additional cash needed for the increase in NGDP is provided via purchases by the govt of existing bonds for new money.

    In as much as there is always a trade-off between CB balance sheet and govt indebtedness at all levels of NGDP and as either IOR or interest on govt debt will have to be paid it doesn’t matter what combination of these things is used in terms of “burdens on future generations” etc.

    This is an interesting idea and I need to think about it some more.

    1. Ignore seignorage income, as the government gets receives this income in all cases (even if no deficits are run). Bringing in seignorage income, or sales tax receipts, just muddies the water when estimating whether reserve-financed deficits incur more cost than bond-financed deficits.

  5. Market Fiscalist says:

    I’m trying to understand how one might compare the costs of reserve-financed deficits rather than bond-financed deficits.

    To keep it simple, lets assume:

    – No growth and NGDP growth is 0% (remove g and seignorage from the story)

    – The authorities need to take action in year 1 to address a fall in velocity that then slowly corrects itself in the next few periods.

    Reserve-financed deficits = vary the size of the CB balance sheet to meet NGDPT
    Bond-financed deficits = vary size of national debt to meet NGDPT

    So for reserve-financed deficits the CB balance sheet first increases then declines as V dips and then recovers

    And for bond-financed deficits the national debt first increases then declines as V dips and then recovers

    The cost of the debt-financed option is the tax needed to reduce the debt
    I am not clear what costs are attached to reduce the CB balance sheet for the reserve option. Am I missing something ?

    In both cases it would be possible to use IOR as a way of reducing bond-financing costs , but it seems irrelevant if interest payment are made on bonds on reserves other than that one counts as fiscal and the other monetary.

    So unless I am missing some costs on reserve-finance, that one seem optimal (as long as it works at ZLB!)

    1. Market Fiscalist says:

      Actually just realized I missed something important…

      For the reserve-finance option, if the deficit was funded by the govt selling new bonds to the CB then as the CB reduces its balances sheet the national debt will increase and the govt will need to use tax to eliminate it, just as in the case of bond-finance.

      So I now agree it makes no difference.

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