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Thursday, November 13, 2014

Burden Of Government Debt, Part 2: An Example Of Real Effects

How deficits and debt are interrelated is fairly straightforward, and the message from Evsey Domar – nominal GDP growth reduces debt ratios – is fairly definitive. (This was discussed in the first part of this essay.) The interesting question is how debt and deficits can affect the ‘real economy’ in the long term? There are a lot of potential avenues for government debt to influence economic growth, and the distribution of incomes. Unfortunately, it is also an area of large controversy within economics, and so there are a variety of theories to work with.

I will now give an extended example to show how a long-term effect is possible. The example is based on a scenario that could happen in a modern economy, and it is not based on fables based on the premise of individuals bartering on a desert island. I also aim to make the example agnostic with regards to economic theory, although the lack of theory means that I cannot give an estimate of the size of the effect.

The Example

Assume that the author (a Canadian) managed to win a contract from the Canadian Federal Government which netted him $10,000 after tax in 2015. We also assume that this $10,000 increment in income was viewed as a windfall, and it is added to his retirement savings. The money is deposited into a designated account that invests in Canadian Federal Government bonds, and the holdings are rolled over continuously. And we then assume that my retirement planning was such that I did not need to dip into that trust during my lifetime. In 2115 (one hundred years later), the funds are made available to descendants, who we assume use the proceeds to go on a shopping spree.

I argue that there would be very little effect on the economy until 2115. Although the Canadian Federal Government will need to increase borrowing (initially) by $10,000, this is offset by the additional bond purchases by my investment account. This balancing will continue to hold, even as the nominal amount increases as a result of compound interest.

When the bonds are sold, there will be an effect on the economy. The inheritors will increase consumption then, drawing down available resources. Inventories at retailers would be drawn down, and there would be an impulse towards rising prices (inflation). If we assumed that the government had an extremely sensitive measure of economic activity and it wanted to keep the level of consumption where it was before the bonds were sold, it would have to raise an increment of taxes that would (roughly) correspond to the market value of the bonds in 2115. That amount is $10,000, multiplied by the compound growth factor for interest for the previous 100 years. (For example, if the annual rate of return was 2% after taxes, the holdings would have compounded to around $72,000.)

In other words, one could argue that the $10,000 new debt creates a (potential) obligation to raise taxes in the future, compounding at the interest rate on government debt. (It could have chosen to allow economic activity to run faster than it would have otherwise.) And although some would object to the wording I use, I argue that this logic captures the conventional analysis of government debt. (The concept of Ricardian Equivalence is hinted at within this example, but because I am not attempting to model the exact effect. Therefore, it is unclear whether the mathematical formulation of Ricardian Equivalance holds.)

I am being deliberately vague about the exact effects of this new spending on the economy in 2115. You can think of it as being the same as if the government had increased its spending by that amount in 2115. For example, if you believe that the 'multiplier' on current government spending is 1.2, then GDP will rise 1.2 times this new spending. However, economists do not agree what the exact effects of new spending are, so I do not specify them here. But it appears safe to say that either nominal GDP rises by some amount, implying some inflationary pressure, or taxes rise to offset the impetus of the 'new' spending.  (Note: This paragraph was added to help clarify what I am driving at.)

Critiques I Favour

I will now run through a list of critiques of this example, to explain why I think this logic is only of limited importance in practice.

Size.  The amounts in this example are too small to matter for the Canadian economy. The idea is that you need to scale this example up, so that the author is in some sense representative. The problem with scaling up to a sensible amount is that the hypothetical behaviour is somewhat unusual, and so the spending out of the increased government spending is more likely to hit in 2015. The effect on consumption would mainly happen now, not in 100 years.

No effect on consumption behaviour.  It is very hard to think of examples where I could receive money and it not have an effect on my spending and savings behaviour. A one-time windfall of $10,000 is not going to greatly affect my retirement planning given the uncertainties involved, and so it appears reasonable to pretend that I could receive it without it greatly affecting my habits. But if it were a larger amount, I would realistically start to adjust my spending and savings plans. (Using economist jargon, my assumed marginal propensity to consume out of wealth is zero.)

Taxes. Anyone with a familiarity of the Canadian income tax system would realise that there would be an effect on behaviour before 2115. The interest income would be taxable. If we are to assume that my spending behaviour is unchanged, the account would only be able to grow at the after-tax interest rate.

Federalism. If you looked at the income flows in detail, one would see that Federal spending (the initial amount, and then interest) would incur provincial income taxes. This means that Federal Government spending will almost immediately recirculate back towards Provincial governments, and vice-versa. This creates an automatic “transfer payment” mechanism.

Distributional issues. There is a large amount of analysis of the “inter-generational equity” of government spending. That is, are policies fair from the standpoint of different generations? My example shows that a sub-division by generational cohorts makes little sense. The initial government spending benefited me, and if there is a burden, it is on the rest of Canadian society, as resources that could have gone to them went to myself (or my heirs). They either paid taxes (in the present or in the future), or experience a higher price level (inflation) in order to allow resources to be transferred. And since the initial hypothetical payment is in exchange for work on a hypothetical contract, that resource transfer was in exchange for a service. Whether or not the exchange is “fair” is a determination that would have to be made by Canadian voters. (Note that the same logic is true even in the case of transfer payments. Transfer payments, such as welfare payments, are made to further economic and social aims. We can only judge the fairness of transfers by taking those objectives into account.)

External Sector. If I were an American, there would be a reasonable expectation that my heirs would be similarly American. In this case, the unwinding of the account would be associated with selling Canadian dollars on the foreign exchange markets. Although many economists worry about the effects of foreign-held debt, I would lump this effect in with the inflationary effect of government spending.

To summarise what I see as the effects, it is only possible for government debt to have a long-term effect if we assume that the holders have an unusually low tendency to spend out of the flow of income they receive from the government. In the next section, I will list some effects that I do not think are important, but others are concerned about.

Some Further Possible Long-Term Effects

The following effects have been suggested as a mechanism that create a long-term effect from debt.

Crowding Out. In the example, I assumed that since there is an equal increase in buying and selling of government bonds, the yield on those bonds is unchanged. Although I disagree, some argue that increasing the amount of government debt outstanding will raise the yield on those bonds. (This effect would augment the total return of the bonds I hold, and would thus increase the dollar amounts that would be spent in 2115.) Since government bonds act as a benchmark for other lending rates, long-term interest rates faced by private sector borrowers will also increase. This is supposed to have the effect of lowering investment, and therefore reducing long-term potential growth rates. It should be noted that the size and even the existence of this effect has been disputed. But for the question at hand, I believe that it is largely immaterial. Reducing private sector investment in 2015 is only going to have a measurable effect on the economy in 2015 and for a few years later. By 2115, the investments will have long depreciated, and the state of the economy will depend upon the structure of the economy at that date. In other words, "crowding out" only really matters for the existing generation.

Rollover Risk. A related issue is supposed increased probability of default as the size of government debt increases, which is described as “rollover risk”. (Even if the amount of debt outstanding is fixed, governments need to issue new bonds to replace maturing bonds; in market parlance they are “rolling over” the debt.) This effect matters if the government is borrowing in a foreign currency, but I am not interested in discussing that case. In most instances, the chickens from foreign currency borrowing come home to roost relatively quickly, so it is the current generation that pays for this mistake. Otherwise, this effect will just show up in the form of raising bond yields now, and so it is embedded in the previous explanation. However, there have been no relevant cases of such failed “rollovers” in comparable government debt markets (as defaults amongst developed countries generally are associated with fixed exchange rate systems, such as the Euro or the Gold Standard). As a result, my view is that increased debt levels will double the probability of default as a result of financial reasons – from 0% to 0%.

Threshold Effects. Fiscal conservatives are attracted to the theory that high debt-to-GDP levels have bad effects on the economy (beyond the not easily measured alleged effect on the level of interest rates). For example, it was argued that a debt-to-GDP ratio exceeding 90% caused growth to slow (although that study turned out to be based on error in a spreadsheet).  I believe that this theory is dubious, but if some variant of it were true, then there would be an effect if debt grew beyond some magic threshold.

Fiscal Theory Of The Price Level. The Fiscal Theory of the Price Level is an interpretation of modern DSGE models that implies that the price level would rise in response to increasing debt levels if fiscal policy was assumed to not tighten. This theory is complex, and I discuss it elsewhere. In any event, the effect appears now, and not in the future.

Politicians' Preferences. Interest spending is a line item in the budget, and politicians would be happy to replace it with more congenial items, such as building infrastructure that is named after politicians. Future politicians will have greater freedom of action if debt levels are lower. But since interest charges immediately rise, it is unclear to me why this is a greater burden on future generations than the present one.

Concluding Remarks

Although adding to the stock of government debt now can have long-term effects, it requires fairly strong restrictions upon behaviour. The debt has to pile up on the balance sheets of entities that have no intention of liquidating those additional assets to fund expenditures within the domestic economy. Moreover, government spending transfers resources between contemporary entities within the nation; they do not transfer resources across generations. Therefore, analysis using "overlapping generations" models tells us very little about fairness of policies.

See Also:

(c) Brian Romanchuk 2014


  1. I find myself agreeing with almost everything you write. I only differed in the emphasis on the need for the CB to raise future taxes when the money was spent 100 years hence. I would assume that existing taxes at that time would show unexpected revenue increases but these increases would only last until some other person (or many persons) again saved the money (which restarts your 100 year rest period).

    Now, turning to you conclusions, I think that conditions for long term withdrawal obviously exist in the U.S. and in Japan. These two countries continue to amass government debt which must be owned by private holders.

    To extend your example a little, we could assume that the children 100 years hence cashed the bond and bought farm land. This plausible example points to the property aspects of money. The Canadian Government, by initially giving the author the opportunity to have $10,000 after taxes to spend, inadvertently (intentionally?) allowed children 100 years hence to buy farm land valued at $10,000.

    Thanks for another informative post.

    1. There is an embedded assumption that when the heirs "go on a shopping spree", they are buying goods and services for current consumption, and so final domestic demand rises. If they buy an asset from someone, we have to determine what the recipient does with the money. If the sellers of the asset spend the money on goods and services, the end result is almost the same thing. The idea is that the "new money" is bouncing around the economy like a hot potato. If this was the case, the taxes paid would rise automatically since the amounts of value-added taxes would go up.

      This could be thought of in terms of functional finance, or mainstream financial-based fiscal analysis ("Ricardian Equivalence"). I want the example to be agnostic about theory, so I am vague regarding the details.

  2. The main point missing is the tendency for the economy to net-save over time. It tends towards net-accumulation. So those saving tend to outnumber those spending.

    So when your heirs come to spend their spending is offset by a whole load of people saving.

    In other words the aggregate dissaving that people panic about doesn't tend to happen, if it does then government can tax it out or let inflation rot the dissaving, and what you did for the Canadian government today is a public good (because that's what Government buys) and therefore increases the capacity of the economy in the future to produce output - directly or indirectly.

    Net Saving is merely voluntary taxation and like all taxation it makes space for government to invest.

    1. Your point about aggregate net saving over time is embedded in my comment about the marginal propensity to spend out of assets. Even if I do not spend out of this particular segregated set of assets, what matters is the aggregate behaviour.

      I will go into those details later, as they become less "theory agnostic". (This article is a first draft of a longer document I am writing about fiscal policy, so some of the context of why I am writing about a particular topic may be missing.)

  3. Another good piece Brian-

    I would think that one problem with the spending analysis by your grandkids 100 years from now is that someone else would be taking their place wrt to holding the Govt securities.

    In other words, unless the Govt runs budget surplus, the stock of savings cannot change, only the distribution.

    If I let my Govt securities mature and then proceed to spend that money, the Govt is issuing new securities of an equivalent amount that someone else is then saving.

    In the same way we know reserves cant leave the Fed's computers, neither can the money (in aggregate) in securities accounts.

    Which is why the size of the debt (stock) is largely irrelevant to economic activity (flows), and the the years deficit is the operative factor.

    1. The idea is that the spending from the heirs resembles a new flow of demand, which is roughly equivalent to a contemporary deficit. From the point of view of my explanation, I should split this example into two cases, the first where I spend the money on consumption goods immediately, the second where it sits in an account, and then acts as "new" demand in 2115.

      The reason I wanted to avoid discussing what happens if I spent the money in 2015 is that the Canadian economy is below potential, and so the "new spending" would be soaked up without causing much in the way of a "burden".

    2. "The idea is that the spending from the heirs resembles a new flow of demand, which is roughly equivalent to a contemporary deficit."

      Right, but for the cycle to be representative of the real world, we need to take into account the fact that someone else is losing their ability to spend at the same time.

  4. Brian,

    I calculate that each new dollar presently results in about 1.4 dollars of new GDP. I am working on a new post to explain how I arrive at that figure.

    If that number is correct, then the future spending of $10,000 will have a $14,000 impact on future GDP.

    The potential GDP increase caused by a new $10,000 block of money is infinite. The reason that only a small amount of GDP increase is predicted is because it would take an infinite number of transactions to cause infinite GDP from a small block of money..

    1. The size of the multiplier would depend upon the chain of transactions that occur in response to the new spending. This becomes model-dependent.

      One small point - the future spending would be larger than $10,000; it depends upon the total return of the bond investment. A 4% compound return would mean that the amount is around $505,000. I will update the text to make that more clear.

  5. Brian,

    I have a new post at

    that references this post. I expand on how I arrived at the $14,000 figure (which is incorrect) for future GDP expansion.

    Thanks once again for this well written post.

    P.S. Off topic but you might take a look at this post by Frances Coppola at

    1. Thanks. It's an empirical question how fast spending will recirculate. For example, the recipient can just save the money for a considerable period, or could instead run out immediately and buy something.

      The Coppola post was interesting. I made a few of the points here:


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