Saturday, January 7, 2012

Expanding Bob's OLG Example

Bob had a good OLG exposition of the national debt issue here (if you're coming in this late in the game, you're on your own tracing back links). He was also kind enough to send me the excel file that he used to make the diagram so I could expand it by two examples.

But first I want to make a few points about Bob's post.

1. Gene and I have both pointed this out already, but I want to make it very clear: you have to realize that Bob has not disproved Krugman's point anyway. Add up each row sequentially in Bob's OLG model. All of them add up to 200. There is no burden on future generations in Bob's example. None. He can't get a burden with his model. What he has is individual people (in his case, the last person in the chain - Iris) getting screwed and others benefiting (this is what Paul originally called a "different kettle of fish", and a real problem). But within each period we have the same GDP level. In other word, Bob Murphy's example agrees with Paul Krugman. Bob may have changed his mind but so far he has not offered us a model that supports Bob's decision to change his mind. So why did Bob change his mind? I'm still not sure. He's always welcome back over on our side, though.

2. I will still not get into this in my expansion of Bob's example, but let's also remember what Bob doesn't include: growth and investment. This is not a minor issue, and it strains the extent to which we can really go to these models to tell us something about real life human action. Ask yourself - why in the world would you borrow money without some rate of return? It doesn't make sense. However, I don't fault Nick or Bob over that bit of parsimony because we still have a lot to talk about without it. But you should always keep that in mind.

*****


OK - new examples. My contention has always been that the burdens in these models are the burdens introduced by the transfers. Debt does not burden any particular generation. What it can do is make different people bear the burden of a policy. That's an important distinction if you're thinking about the impact of debt on GDP. We saw this in Bob's model. Each generation in Bob's model had the exact same income before and after he added debt. However, Iris had a much bigger burden than anyone else in his example. No effect on GDP - big effect on Iris.

To see how debt and transfers interact, I think it's useful to add two numerical examples to what Bob already has. The first two, below, are his (except I change the title of his second example). The third and fourth are mine. The third example considers the case where the government borrows from Old Al to make a transfer to Young Bob. The fourth example introduces the point of Ricardian Equivalence. Let's say we fund Bob Murphy's initial transfer from Young Bob to Old Al with a tax on Young Bob rather than a deficit.

In the third example, then, we have the same financing method but a different transfer.

In the fourth example, we have the same transfer but a different financing method.



First - what doesn't change? One thing that clearly doesn't change is GDP in period 1 through period 9. That is exactly the same in every row, in every scenario.

Point, Krugman (and whoever else is willing to acknowledge they actually do agree with him and he's not some crazy guy stuck in the 1950s).

What does change? The incidence of the burden. In Bob's transfer example, Iris had the highest burden by far, and everyone benefited a little bit as they earned interest over time. In the third example, everyone bears a small burden, Iris bears a slightly smaller burden than she did in Bob's example, and John earns a large benefit. In the fourth example, Al gets a benefit, John bears a burden, and everything else is the same. So while there is no generational burden there are lots of different burdens on different people depending on the scenario.

Point, Krugman (And whoever else is willing to acknowledge they actually do agree with him and he's not some crazy guy stuck in the 1950s).

What causes what does change? What makes the incidence of the burden change in these different examples? Both the nature of the transfer (we know this causes some of the change because we see a difference between example 2 and example 3) and the financing method (we know this causes some of the change because we see a difference between example 2 and example 4). If you want the burden and the benefit to be borne by people living in the future, finance it with deficits. If you want to spread out the costs and the benefits of the deficit differently, change the nature of the transfer (i.e. - note that example 2 gives out a lot of small goodies and then imposes a big cost at the end, while example 3 gives out a lot of small costs and imposes a big benefit at the end).

Point, well, me, because I don't think anyone made this point in the discussion yet.

Where does the burden come from? Unambiguously it comes from the transfer. We have a burden on someone with and without borrowing, after all. One exercise is to add up everyone's lifetime incomes and calculate the deviation of that lifetime income in each example from the baseline (i.e. - example 1). I've done this in the chart below:



We have burdens on people with debt and without debt. If Bob and I had used real numbers rather than intergers for the bond amounts, it would be clear that the total burden in examples 2, 3, and 4 were all the same. Clearly what adds burdens here is the transfer itself, and all debt or tax decisions do is shift the burden around on different people. This is what Krugman said initially. Krugman's point was that if we're thinking about debt and the prospects for growth and the income of future generations, there is no burden on "our children" together.

Bob demonstrates this amply, and I'm just trying to drive the point home. If you still don't get it, add up all of Bob's rows individually yourself and see what income is with and without the debt.

This is very different from how most people think about the national debt. Krugman is right to highlight this and talk about this in the New York Times op-ed page.

Now, what we've learned is that the real costs or benefits are introduced by the nature of whatever it is government is financing. So can we please put this one to rest and get back to things like "is the stimulus a good or bad idea?" without worrying about financing it with deficits (quite) so much?

35 comments:

  1. Daniel,

    Nice exposition.

    I have a question. Elsewhere, you seem to agree that Nick is correct. But here you write,

    "you have to realize that Bob has not disproved Krugman's point anyway. Add up each row sequentially in Bob's OLG model. All of them add up to 200. There is no burden on future generations in Bob's example. None."

    This is not true. Do you not agree that Nick shows that, assuming future taxes are raised to pay for the debt, future generations bare the burden of current govt expenditure or transfers?

    In Bob's example, per period production is fixed at 200 units by assumption. You cannot appeal to that fact to disprove him, because it is an assumption and not a result. Since production is fixed at 200 per period, the rows will sum to 200 whatever the outcome.

    The model shows that after the chain of borrowing ends and taxes are raised, there has been a (necessarily zero-sum) redistribution of consumption. At the margin, the generation that borrowed must have had higher consumption and the generation that paid the taxes must have had lower consumption.

    I seems hard to make the case that this is in agreement with Paul Krugman's original position. E.g.,

    "the debt we create is basically money we owe to ourselves, and the burden it imposes does not involve a real transfer of resources... as Dean says, talking about leaving a burden to our children is especially nonsensical."

    It's clear that this is contradicted by Nick and Bob's examples.

    ReplyDelete
  2. re: "
    The model shows that after the chain of borrowing ends and taxes are raised, there has been a (necessarily zero-sum) redistribution of consumption. At the margin, the generation that borrowed must have had higher consumption and the generation that paid the taxes must have had lower consumption.

    I seems hard to make the case that this is in agreement with Paul Krugman's original position."


    The first sentence here is Krugman's original position, so I don't see why it's hard to make the case that it's in agreement.

    The second sentence confuses Krugman's point about income in a given period with the lifetime of an individual in the model. Each period has the same amount of consumption before and after introducing debt. People have different levels of consumption if you take their whole life together.

    See the difference? It's the difference between my second table and adding the rows.

    Krugman says the second table may change, but adding the rows won't change (you don't have to make Bob's assumption of 200 in income in each period to get that).

    That's exactly what I'm trying to highlight here - that you can't act like adding up people's lifetime consumption and adding up the rows are interchangable. They're not.

    And yes - as I said originally - people who act like they're interchangable are actually agreeing with Paul. For some reason they're just loathe to admit it.

    ReplyDelete
  3. "The first sentence here is Krugman's original position"

    That doesn't seem right, though. I quoted from Krugman's original post:

    "The burden [the new debt] imposes does not involve a real transfer of resources... talking about leaving a burden to our children is especially nonsensical."

    That flatly contradicts my claim that, assuming taxes are raised, the debt redistributes consumption across generations. It obviously does involve a transfer of real resources (which you seem to agree with, at times), and it's not at all nonsensical to talk of the debt burdening our children.

    Each period has the same amount of consumption before and after introducing debt.

    But we already know that. The question we want to answer is does debt affect the intergenerational distribution of real resources. Paul Krugman claimed that it does not and that it is nonsensical to say that it does. That seems unambiguously wrong.

    In my view you are right to ask about the particulars of the expenditure or transfers. It might very well be the case that the growth rate of the economy is higher than the growth rate of the debt, it might be the case that the govt is financing productive investment, or it might be the case that even if it isn't, it might be the case that the chain of borrowing never ends, or it might be the case that the borrowing is welfare enhancing anyway. For example, imagine that each generation is less productive in the terminal period of its life--then every period the older generation can borrow from the young generation to smooth lifetime consumption.

    But these are conceptually distinct issues. As a first order point of principal, Krugman is wrong to say that borrowing cannot burden future generations.

    ReplyDelete
  4. But you keep talking about "generations" and keep citing numbers on "individuals".

    Which is it?

    I think you're demonstrating my initial point that Bob and Nick and Don are essentially saying the same thing as Krugman they just don't realize it.

    ReplyDelete
  5. I'm not sure I follow you--I don't know where I've cited any numbers, sorry. I think Bob's example is unnecessarily complicated given its purpose, but in the table above each individual represents a particular generation or cohort.

    I don't think that it's the case that Nick and Paul Krugman are saying the same thing. Krugman has said that there cannot be an intergenerational redistribution of real resources. Nick has shown that there can. I don't think that there is any ambiguity there.

    ReplyDelete
  6. I'm not sure how else to explain this. Perhaps Gene can help.

    Like I said several posts back - I think this is almost entirely semantics.

    ReplyDelete
  7. It's certainly not semantics. The two competing claims are mutually exclusive:

    Either debt can redistribute real resources across generations (Rowe, Murphy), or it cannot (Krugman, Baker).

    At times you seem to agree with the former and at times the latter. But they can't both be true.

    ReplyDelete
  8. Again - what do you mean by "generations" exactly? I think I have been pretty clear and I think Krugman was pretty clear about where there would be redistribution and where there wouldn't be. I'm still not sure exactly what you mean by it. Sometimes you seem to agree with Krugman and I and sometimes you don't.

    Which is why I think this is semantic. The disagreement hasn't seemed to be over the model. The disagreement has been over the interpretation of the model and the interpretation of Krugman (alas - since he's at the AEA conference I don't think I'm going to get an answer from him).

    ReplyDelete
  9. I do have a track record of correctly interpreting Krugman and DeLong when others have attributed pretty strange things to them.

    ReplyDelete
  10. Daniel,

    You are confusing periods with generations. Look at your post:

    "My contention has always been that the burdens in these models are the burdens introduced by the transfers. Debt does not burden any particular generation.

    (...)

    Each generation in Bob's model had the exact same income before and after he added debt. However, Iris had a much bigger burden than anyone else in his example. No effect on GDP - big effect on Iris."

    Each period in Bob's model had the same income, not each generation. Iris and other names were placeholders for different generations who coexisted in different periods.

    ReplyDelete
  11. The politics of transfers has me worried (e.g., the scenario I've seen outlined before where future divisive politics center on an increasingly Latino base of payors into Social Security being led to worry that white retirees will make it insolvent), and I think that as long as it's the natural thing for people to think of it in terms of micro, that is the argument we are going to keep being pulled back to. You don't have to believe in micro terms to be scared by the MMT-style pat responses, either (though I think they make more sense than the deficit hound view by far).

    Also troublesome is the insistence on the zero-sum assumption. Are we to hold that deficit expenditures, which have as a certain cost inflation (but perhaps at a very manageable level, especially if the real economic base is increased from those expenditures), do not have a multiplier effect? How in a democratic society do we get our preferred policy outcomes if we are dependent on non-democratic decision-making processes about wealth, dependent on angel investors and other sources of wealth for a few crumbs of infrastructure?

    Mike Norman makes this point well here:
    "Even if it were true that deficit spending merely 'transfers money from one group to another' (which is not true under fiat regimes) then it would still serve a purpose; that purpose being countering the savings 'leakage' to demand. As the late William Vickrey noted: 'deficits, sufficient to recycle savings out of a growing gross domestic product (GDP) in excess of what can be recycled by profit-seeking private investment, are not an economic sin but an economic necessity.'"

    In any case, I think that this is one of those areas where MMT shines: If you can forestall deficit demagoguery, the "transfers" happen between institutions that want stable financial instruments (i.e. debt) and the government, which is only on the hook for inflation (which, as we see from the liquidity trap, isn't actually guaranteed to end up "paying" for lending banks the privilege of buying the government guarantee), so in effect there is no zero-sum of transfer from one account to another.

    The stock response ("the gov't heats up the economy more than will be sustainable") doesn't make sense here, because we know that the balance of the unemployed workforce is as capable of productivity as any from previous decades or centuries, and if they could be employed the economy would undergo a real expansion. In this case it is clear that appealing to the reduced requirements of a given firm is nonsensical because that argument is appealing to a shrunken private sector as the real gauge of an economy's real growth potential, rather than the real productive assets.

    ReplyDelete
  12. I had the same idea http://s1.directupload.net/images/120108/qvuiio7l.jpg haha

    ReplyDelete
  13. "Add up each row sequentially in Bob's OLG model. All of them add up to 200. There is no burden on future generations in Bob's example."

    What is your definition of the word "generation"? Is it everyone who happens to be alive at a given time? Or is everyone who, as time passes, happen to share the same age?

    ReplyDelete
  14. For anyone who cares, Dean Baker here (and remember, Krugman quoted Baker with approval) and Paul Krugman here seem to be quite unambiguously claiming that it is literally impossible for people alive today, to increase their real standard of living through deficit financing (that will require future taxation to service/retire), at the expense of EVERYbody after some future date T, unless you add in the issues of deadweight loss from income taxation etc.

    If Daniel admits it would be wrong for someone to think this, great; I believe him. But if he says Krugman and Baker aren't misleading people with their discussion, I can't follow him down that path. I myself would have made the mistake three weeks ago, and I am quite sure that Baker and Krugman are making that mistake now. (Or, they were making it when they wrote those blog posts, and in light of the controversy might have silently changed their minds and will be more careful going forward.)

    ReplyDelete
  15. It's safer to use the word "cohort".

    ReplyDelete
  16. 1)AARP lobbies congress to tax everyone who's under the age of 55 at their current rate plus 10%. And then use that tax money to bolster SS and Medicare.
    The youth freak out.

    2)Bolster SS and Medicare through deficit financing.
    No one notices because we owe it to ourselves.

    Let's skip 1 and try 2. Youth A eschews private sector investment for govt debt. The feds give the money to the elderly. The youth are later taxed to pay Youth A after elder buckets have already been kicked.

    The youth don't initially notice the foregone private sector investments or the fact that their taxes will be higher when they're older as servicing the growing debt becomes more onerous. They will be taxed more to pay back people who could have invested in a better tomorrow, but instead invested in backdoor taxation of their own cohort. Servicing the current, giant debt is the first budget priority. Paying the troops is secondary.

    The demands on government are limitless. The one thing stopping govt growth is resistance to higher taxes. Debt is a tool to feed limitless greed of the politically active/connected.

    ReplyDelete
  17. Daniel,

    Vimothy has it completely correct. You are using an assumption implicit within their models to try to prove Murphy and Rowe incorrect. And, even more importantly, Vimothy correctly points to your misconception of what a future cohort is.

    In addition, I will point you back to your example three above where the government was borrowing from the old. You are slipping a different assumption in there, though I don't think you quite realize what it is since you didn't mention it at all.

    ReplyDelete
  18. What do you mean I didn't mention it? That was the whole point of example 3 - to switch the nature of the transfer from Bob's #2 and demonstrate that that would change the burden. That was the only thing I changed - why do you think I even have a #3 in there?

    ReplyDelete
  19. To make sure I follow: Your chart, "Where does the burden come from?" shows that

    1) The need for a "burden" is always caused by a transfer
    2) the "burden" is always taxation, and what makes it a burden is that it is not volontary
    3) with no debt the "burden" is always in the same time period as the transfer
    4) with debt it is possible to push the "burden" into a later period than the transfer


    Is that correct? Isn't that what Bob has been saying all along, that deficits allow the burden of a transfer to be pushed into he future ?

    Are you agreeing with, or still disputing

    ReplyDelete
  20. Right rob.

    I've never really challenged Bob's arguments or model or that interpretation of the model. I'm just saying the model agrees with the points that Krugman has made.

    I haven't been disagreeing with Bob.

    Bob has been disagreeing with Krugman.

    So I guess you could say I'm "disagreeing with Bob" insofar as I'm trying to show him how nothing he's said disagrees with what Krugman has said.



    I don't know why, but I often find myself in this position. People used to think my 1920-1921 paper was disagreeing with ABCT. It wasn't! In fact I had a lot of nice things to say about ABCT in the paper. I even said it might be a good explanation for 1920-1921! The paper was a critique of bad arguments against Keynesianism. It wasn't an argument against ABCT.

    ReplyDelete
  21. This way of looking at "critiques" as the same as "refutations" is a very dangerous mindset, I think. It's not new with the blogosphere by a long shot, but it's certainly facilitated by it.

    ReplyDelete
  22. Thanks for the clarification and I agree with your last comment.

    ReplyDelete
  23. So at the risk of stating the obvious

    1. When the govt makes a transfer that increases one person's consumption someone one else has to reduce their consumption in that period.

    2. It is possible for the govt to compensate someone for giving up that consumption by offering them more consumption in the future

    3. If the conditions do not exists for the government to roll over the debt for ever then eventually the govt must either default on the debt (in which case the loanor loses his promise of higher future compensation) or the govt forecably reduces other people's consumption to meet the debt and the loanor increases his consumption in that period.

    4. If the model was changed so that the apple endowment increased greater than the rate of interest then the debt could be rolled over for ever. Its size would increase in apples but as this was a reducing % of total apple endowment this would be sustainable.

    5. This means we understand how the "burden" of govt transfers can be distributed through time. The big ticket items is then "is govt debt ever a good idea, and if so when?"

    ReplyDelete
  24. 1. As long as we're abstracting from free lunches below full employment of the factors of production, this sounds right.

    2. I don't see why not. Keep in mind, after all, that all the period 1 bond issues are voluntary here.

    3. Sounds right - we could even think of this as a second transfer decision by the government in the interest of maintaining its credit-worthiness.

    4. Yes - this is the Samuelson (1958) point.

    5. Yes, that sounds like a good way of putting it. But the essential point that Krugman makes is that debt transfers the burden through time by generating new assets and liabilities - so that when you use debt to push the burden onto certain individuals in the future you don't burden the entire community in a given time period in the future.


    So that all sounds good to me - but as we've found in this debate, what person X thinks he has asserted and what person Y thinks person X has asserted are often two quite different things!

    ReplyDelete
  25. Daniel,

    If you borrow from the old, there must a bequest of bonds. You didn't mention that at all.

    ReplyDelete
  26. "But the essential point that Krugman makes is that debt transfers the burden through time by generating new assets and liabilities -so that when you use debt to push the burden onto certain individuals in the future you don't burden the entire community in a given time period in the future."

    This is true even if austerity measures and higher taxes on the entire community in the future become necessary just to service the debt? Are future creditors not worse off even though they're being repaid partially by their own taxes instead of by corporations that aren't allowed to tax them?

    ReplyDelete
  27. Daniel,

    One additional question.

    What role does OLG play in all this ? I think (or at least I hope) that I have a good understanding of what is being discussed without really having looked into what OLG is all about (and Bob never mentioned it in any of his posts).

    Can you explain the relevance of this model to this discussion ?

    ReplyDelete
  28. Oh sorry - that is basically the model that Bob offered. OLG is for overlapping generations. Bells and whistles are added - obviously it gets more interesting when there's investment so that borrowing decisions are weighed against rates of return. It was developed by Samuelson, Diamond, and those guys. It's a pretty standard way of talking about the impact of fiscal policy positions in a growth model.

    ReplyDelete
  29. Daniel's example 3 closes the case. It is the transfers that matter, not the debt.

    ReplyDelete
  30. So the OLG part is saying that the govt can sell you a bond when you're young that makes you defer consumption, but then when you're old they may tax you to pay off the bond and hence deprive you of the extra consumption you were due.

    Your lost consumption goes to those who are old when you are young (whose bonds holding the govt buys and sells to you).

    I think I finally fully understand Bob's story now.

    However I'm a little underwhelmed. My original understanding was that the taxation in the last period caused a loss to match the gain from original transfer (and the bond-activity , being voluntary ,was neutral) still seems more interesting.

    Is the consensus that this is the version that Krugman et al have believed all along, and the only new bit Bob was adding was this OLG piece ?

    ReplyDelete
  31. Daniel, Gene is quite happy about your example 3. When Gene described it on his blog--namely saying that you apparently used my framework to get the later generations to benefit at the expense of the earlier ones--I couldn't figure out how you could make such a thing work.

    So I come here and now see that you have introduced altruism. Well, that gets really tricky, because now our intuition breaks down. How do I tell if certain people are better or worse off, because now their utility depends not just on their own consumption, but on the consumption of other people in the model.

    So: Can you try to get this effect, if you just assume everybody has utility functions of U=sqrt(a1)+sqrt(a2)? I don't think you can.

    If you think I'm making it impossible with that requirement, OK fine, but please give us actual utility functions so we can check your work. I'm not claiming your result is impossible, I'm just saying I would like you to "show your work."

    (If you want to see an example of what I mean, at 6am Monday morning I will have a post that gives a precise numerical example where I have the first 5 people benefiting and the last 5 people losing. So I'd love to see you flip that result, if it can be done. Like I said, I don't think it can, if we assume people aren't altruistic.)

    ReplyDelete
  32. Suppose there is only 1 period of time.

    Suppose there were 9 different types of apples. A1,A2,A3,....A9. Each person can only produce 2 types, and can only consume the same 2 types. Just like in the spreadsheet.

    Now suppose the government imposes a tax of 10 type A1 apples, on Iris, and gives them to Al.

    Exactly the same spreadsheet can be used to explain the trades Iris uses to buy the 10 type A1 apples to give to the government.

    The government taxes Iris 10 current apples and gives them to Al.

    ReplyDelete
  33. I think I lost you Nick.

    But if it's a way of saying that Iris bears a real cost, I've always agreed she does.

    As I've maintained from the beginning I think you and Bob are trying to establish a different point, and in doing so you're not contradicting Krugman's point. I understand you disagree with me on this.

    ReplyDelete
  34. Daniel: It's a way of saying that debt imposes a burden on future taxpayers in exactly the same way that taxes impose a burden on current taxpayers.

    If there were a non-overlap between generations; or if generations 5 on switched to being carnivores, neither producing nor consuming apples, then it really would be impossible to put a burden on future taxpayers.

    And that none of those things are revealed by saying "we owe it to ourselves" and "you can't eat next year's apples today".

    All that Abba Lerner stuff totally misses the real issues, that are only revealed in an OLG model.

    ReplyDelete
  35. Right - debt is not a free lunch in these endowment economies. If you transfer income you're not going to negate that transfer by debt-finance. This is Diamond's distinction between balanced budget incidence and differential incidence.

    The Krugman point is that the way it generates burdens on future taxpayers is by generating benefits for other future taxpayers.

    re: "All that Abba Lerner stuff totally misses the real issues"

    I wouldn't go that far. How many men-on-the-street can reassuringly note that burdens are pushed into the future by generating benefits for others in the future and that an overlapping generations model that shows burdens on future taxpayers will have no net effect on national income in any given period?

    Abba Lerner's point communicates all this quite well - and it's a point that's worth communicating, say, in the Op-Ed pages of the New York Times.

    But I agree - man cannot live on Abba Lerner alone. Thank goodness we don't have to, and we also have Buchanan, Barro, and Samuelson at our disposal.

    ReplyDelete

All anonymous comments will be deleted. Consistent pseudonyms are fine.