Saturday, February 14, 2015

The Great Blog Debate about Debt: A Reading List

I applaud everyone who has weighed in on the Great Blog debate about debt (Simon,  Bob,  me, and others too numerous to link. All of the issues that have been raised on Nick's blog were the topic of frontier research in economics journals in the 1950s -- 1970s.  Nick has links to earlier posts here.

The paper that started all of this (at least in the English speaking world) was by Paul Samuelson. "An exact consumption-loan model of interest with or without the social contrivance of money", Journal of Political Economy 1958, Vol 66 No. 6. The French lay claim to an earlier version by Maurice Allais, but that's another story. 

Samuelson's paper was a revelation to economists because it provided an example where markets don't work. In Samuelson's example, there is an equilibrium, (people optimize taking prices as given and all markets clear) that can be improved upon by a government institution. Samuelson's paper is a good starting point for those who would like to read more about this.

Samuelson provided a model of pure exchange, like the examples Nick has developed. In a pure exchange model there is no production. In 1965, Peter Diamond introduced capital to this model and he discussed the role of government debt in "crowding out" private capital. His paper was published in the American Economic Review, Vo. 55, no 5 under the title "National Debt in a Neoclassical Growth Model". Peter uses a mathematical tool called a 'difference equation'; and if you are sticking with my reading program, you will need to know a little bit about difference equations. There are many good undergraduate books on the topic; I like "Fundamental Methods of Mathematical Economics" by Chiang, but that probably dates me.

The next paper I would recommend in this literature is by a mathematician, David Gale, "Pure Exchange Equilibria of Dynamic Economic Models" Journal of Economic Theory 6 (1973). I include David's paper on the reading list of my first year Ph.D. class. In it, David distinguishes what he calls a "Samuelson economy' from a 'classical economy' and he shows that every overlapping generations model has at least two steady state equilibria; one in which the interest rate equals the population growth rate and one in which the aggregate saving by the young is zero. This divide is the key to understanding when government debt is a burden in the sense we have been discussing.

Throughout the 1960s and 1970s there was a very muddled discussion in the journals, trying to understand why markets can sometimes fail to be optimal. Some people thought that it was because not everybody can meet, due to the one way flow of time. That issue was cleared up by Karl Shell in 1971, "Notes on the Economics of Infinity", Journal of Political Economy, Vol. 79. Karl attributed the problem to what he called the 'double infinity' of people and goods. This is the paper to cite at parties if you want to appear knowledgeable about the topic. It probably won't enlighten you much unless you're enrolled in an economics Ph.D. program.

Any question that you have has, almost surely, been answered already in the literature. How do the conclusions of the model depend on the assumption of no bequests? What happens if some people live forever? What happens if there are multiple goods in each period? Many of these questions are answered in my book "The Macroeconomics of Self-Fulfiling Prophecies".

I'm sorry if the answers are not always obvious, or the papers I have cited seem impenetrable to you. But realize that mathematics is a language and often it is the best language for answering questions of logic. "Everything should be made as simple as possible, but no simpler".

If you think that we are debating esoteric issues that are unrelated to the real world; you are entitled to that opinion. An economic model is only useful if helps us to understand the world. I happen to think that the overlapping generations model contains a great deal of useful insight. If you read, and understand, all of the papers I have cited, you will never again utter the phrase: "debt is money that we owe to ourselves".


  1. Hello,

    I've read some but not all of the articles, and I have a good grounding in mathematics. I understand the models. Even so, I am somewhat happy to say that "debt is money that we owe to ourselves". But to be fair, I have not paid particular attention to the points that have been raised in this latest flare up of this issue, so I may have limited substantive complaints with them. My complaints instead revolve around your appeal to the OLG framework.

    I see four issues with these models.

    (1) OLG models do not appear to offer useful policy insights. I have never seen half of the population keel over simultaneously, which is a prediction of these models. More seriously, fiscal dynamics move far more rapidly than a "generational" view suggests. For example, Spain had a hunky-dory fiscal situation in 2005, and 2015 is a total disaster. I find it hard to believe that 10 years is a "generation", and so this entire shift occurred within less than 1 time increment of an OLG model.

    Since I believe that Functional Finance is the best best description of fiscal policy, the ultimate constraint on fiscal policy is inflation. An OLG model cannot hope to model inflation, and hence offers no policy relevant guidance.

    (2) These models completely ignore the question of distributional effects within a generation. It makes no sense to care about inter-generational equity when there is obvious equity issues amongst the differing income and wealth cohorts.

    (3) Since the consumption basket changes so radically over time, there is no way of comparing the equity of consumption over time.

    (4) Asset holdings are driven by private sector preferences, and policymakers have little control over debt to income ratios once they set an inflation target.

    1. +1 Brian. Exactly. Couldn't have said it better (even though I tried)

      The application of OLG that gets you the debt burden result conflates the roles of creditor and debtor with different generations, with a stupid hidden assumption of how both roles are passed along to other cohorts over time. Plus, debt is just one tiny part of the universe of distributional political and market decisions happening daily.

      "OLG models do not appear to offer useful policy insights". Exactly

    2. Brian:

      1. "An OLG model cannot hope to model inflation, and hence offers no policy relevant guidance."

      Roger will give better counterexamples than I can, but that just isn't right. Lucas 72 is an OLG model with inflation.

      2. "These models completely ignore the question of distributional effects within a generation."

      Just like in models with infinitely-lived agents, you can either include or exclude intra-generational distributional effects in an OLG model. But OLG models also let you see intergenerational distribution effects.

      3. "Since the consumption basket changes so radically over time, there is no way of comparing the equity of consumption over time."

      Since the consumption basket of changes so radically from one place to another, there is no way of comparing the equity of consumption across places?

      4. What's that got to do with OLG models vs infinitely-lived agent models?

    3. Nick,

      I recognise that academics are churning out DSGE models at a frantic pace, so it is hard to generalise about them. My concern is with OLG models where agents exist for 2 or 3 periods. I have never seen attempt to fit such a model with such extended time steps to real world data.

      3. Yes, I believe it would be difficult to compare my consumption basket to someone in South Africa, and therefore equity comparisons are difficult. However, we lack a world government for which such comparisons are needed.

      4. My view is that demand for government bonds creates supply. If the demand is endogenous to the economy, and varies with things like the income distribution, the government has no hope to guide the debt/GDP ratio over time. OLG models that ignore distribution cannot model these effects.

  2. Great post Roger. I don't have the citations handy, but is it worth bringing in Lerner and Buchanan? The "we owe it to ourselves" comes directly from Lerner, and Buchanan had a snarky article on being a "debt monger" (or something like that) where he showed what Lerner was missing.

  3. What is the difference here between state issued debt and state issued money? I think this analysis implies that money has the same inter-generational implications as debt, but your comments in your previous post ("Money is money we owe to ourselves") suggest you think otherwise.

    1. I don't think many economists have realised that ALL money is a debt. As in a liability for the government. That's where banknotes and deposits get recorded in the accounts - as a liability.

      Which is an indirect way of saying you are right that Roger seems to be holding mutually exclusive views on money and debt.

    2. Cameron: accountants could record the gold produced by goldminers as a liability of those gold miners, but if they don't have an obligation to pay interest on that gold, or to buy it back, it isn't a liability. Is Bitcoin a liability?

      What makes money different is that people will hold money even at zero or negative interest rates, when other assets are paying positive interest rates. You can always run a sustainable Ponzi scheme with money.

    3. Nick,

      Are you saying that the intergenerational transfer cannot be acihieved with money, only debt?

    4. Nick E: I'm not saying anything quite that strong. But r < g is a lot easier to achieve if r refers to the real interest rate paid on money (since it's usually negative).

    5. I see. But I'm not sure what that means in the context of these models as r is generally otherwise determined. So if the state funds with zero (nominal) rate money as opposed to (nominal) interest bearing debt, all that happens is the inflation rates adjusts to preserve r.

  4. With an unbacked, fully fiat currency that floats on the foreign exchange, the only liability the Gov't creates when it spends a dollar into existence is a liability against it's own federal taxes. The USD is essentially a fiat tax credit that accumulates in the accounts of dollar holders. The Federal Gov't could fully insure all deposits and pay a bit of interest on those deposits and the "National Debt" would cease to exist. If Congress just cannot part with it's rule that the Treasury must "sell debt" in order to fund itself, let them sell nothing longer than a 3 month bill, with reserve balances being fully insured as noted above.

  5. Roger,

    Thank you for your always thoughtful and enlightening posts. However, you (as well as Bob, Nick R., or Simon) have not really convinced me that government debt is really a burden for future generations. I cannot give you a precise mathematical reason for my opinion as the papers you cite are probably over my math level (at least at this stage of my life) but I would like to point you to Nick Edmonds’ blog who had some nice posts about OLG models recently. I think he puts my intuition in a more precise and academically acceptable manner. My main criticism is that the examples that you (and the others) give seem to suggest a society can spend out of their savings in real terms. To illustrate this point: Assume a population that has 1 GDP as income solely from labor and holds 2 GDP as government bonds. The examples that I have seen proceed now to have the government tax that labor income to pay down its debt and declaring the people lost out. In reality, they (like Sam and Janet) simply switch from labor income to capital income. They "lost" their financial asset but they still have the same income to pay for the same products that they could have bought before. If "loss of welfare" means reduced consumption I don't see how that is happening. The products are still there as well as the income to buy them at least on an aggregate level.
    Rather than a burden I would call financial assets an "illusion". We like to think that by having amassed savings in the amount of x GDP we could go out at any time and buy the products at current prices. However, any generation can only buy the products they produce at that same point. Increasing spending by drawing down savings will simply lead to higher prices (assuming full utilization of resources) as consumption and production need to net out. When people spend their savings they try to consume more than they produce. What works on a microeconomic level cannot work on a macroeconomic level (imperfections and open economies aside). At a different time and place I once stated that “a macroeconomy can only prepare for the future by spending on real capital to ensure future productivity remains high, not by amassing financial assets”. I still stand by that sentence.

    1. Rather than a burden I would call financial assets an "illusion".

      In that case, I would like to swap my student and credit card debt for whatever balance you hold in your savings accounts.


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