Winner of the New Statesman SPERI Prize in Political Economy 2016

Friday 24 October 2014

Redistribution between generations

I ought to start a series on common macroeconomic misunderstandings. (I do not watch zombie films.) One would be that the central bank’s balance sheet normally matters, although this nice comment on my last post does the job pretty well. Here is one that crops up fairly regularly - that government debt does not involve redistribution between generations. The misunderstanding here is obvious once you see that generations overlap.

Take a really simple example. Suppose the amount of goods produced each period in the economy is always 100. Now if each period was the life of a generation, and generations did not overlap, then obviously each generation gets 100, and there can be no redistribution between them. But in real life generations do overlap.

So instead let each period involve two generations: the old and young. Suppose each produced 50 goods. But in one period, call it period T, the government decides that the young should pay 10 goods into a pension scheme, and the old should get that pension at T, even though they contributed nothing when young. In other words, the young pay the old. A fanciful idea? No, it is called an unfunded pension scheme, and it is how the state pension works in the UK. As a result of the scheme, the old at T get 60 goods, and the young only 40, of the 100 produced in period T. The old at T are clear winners. Who loses? Not the young at T if the scheme continues, because they get 60 when old (and assume for simplicity that people do not care when they get goods). The losers are the generation who are old in the period the scheme stops. Say that is period T+10, when the young get to keep their 50, but the old who only got 40 when young only get 50 when old. So we have a clear redistribution from the old in period T+10 to the old in period T. Yet output in period T and T+10 is unchanged at 100.

That example did not involve any debt, but I started with it because it shows so clearly how you can have redistribution between generations even if output is unchanged. To bring in debt, suppose government taxes both the old and young by 10 each period, and transforms this 20 into public goods. So each generation has a lifetime consumption of 80 of private goods.

Now in period T the government says that the young need pay no taxes, but will instead give 10 goods in exchange for a paper asset - government debt - that can be redeemed next period for 10 goods. In period T nothing changes, except that the young now have this asset. In period T+1 this allows them (the now old) to consume 50 private goods rather than 40: the 40 it produces less tax and the 10 it now gets from the government by selling the debt. Their total consumption of private goods has increased from 80 to 90. How does the government obtain these 10 to give the now old? It says to the young: either you pay 20 rather than 10 in taxes, or you can buy this government debt for 10. As people only care about their total consumption, the young obviously buy the debt. They now consume 30 in private goods in T+1, but 50 in T+2 when they sell their debt, which gets us back to the original 80 in total lifetime consumption.

This process continues until period T+10, say, when the government refuses to give the young the choice of buying debt, and just raises an extra 10 in taxes on the young. So the debt disappears, but the young are worse off, as they only have 30 of private goods to consume this period. Their total lifetime consumption of private goods is 70. We have a clear redistribution of 10 from the young in period T+10 to the young in period T enacted by the government issuing debt in period T.

If you are thinking that these redistributions need not occur if the debt is never repaid or the pension scheme never wound up, then we need to get a bit more realistic and bring in interest rates and growth (and the famous r<>g relationship), which these posts of mine (and these at least as good posts from Nick Rowe) discuss. But the idea with this post is to get across in a very simple way how redistribution between generations can work because generations overlap.

Nick Rowe

The burden of the (bad monetary policy) on future generations


  1. I think this is the clearest post I've seen so far on this issue.

    "That example did not involve any debt, but I started with it because it shows so clearly how you can have redistribution between generations even if output is unchanged."

    In the process, ISTM you've shown that the debt is beside the point. As Krugman pointed out during a previous blogfight about this, when people get anxious about the burden of debt, this isn't what they seem to have in mind: "a debt inherited from the past is, in effect, simply a rule requiring that one group of people — the people who didn’t inherit bonds from their parents — make a transfer to another group, the people who did. It has distributional effects, but it does not in any direct sense make the country poorer."

  2. Why do the old in T receive pensions while they're still producing goods? Pensions are for retirees and they don't produce goods.

  3. You are talking specifically about redeemable debt here. Do you think it changes anything if we replace that with government issued money? Presumably that involves an equivalent redistribution across generations. Or does it come down to how we look at the r<>g point?

  4. I disagree with this representation for a number of reason, which are mostly contained in this post of mine

    Let's be clear about what you are saying.

    In all periods prior to T there are two identifiable unique cohorts of people that can be considered so similar they can be aggregated based on their age into 'young' and 'old'. They each produce (according to the system of political, legal, economic, property relations that exist at that point in time) 50 units each per period, providing an aggregate output of 100.

    In T+1 the system changes so that the young must give 10 units to the old each period. That is all that changes. The young produce 50 and consume 40. The old produce 50 and consume 60.

    You also mention that the scheme stops, there will be a 'losing' generation. If in fact it does. Which it doesn't need to. And remember that losing and winning are conditional on the fact that nothing else changes in the system. No other welfare changes. No interest rate changes. No nothing. Which is fine for this exercise, but if you want to pretend that you are capturing some phenomena that really has occurred in real life, then ignoring these changes is a problem.

    Consider the reverse - youth welfare payments. The same OLG model says that when they are introduced the old generation at that time miss out.

    So if welfare and pensions are introduced together, we all win. Thinking in terms of some identifiable old and young cohort makes no sense anymore, and we then talk in terms of high and poor cohorts. Which we ignored before. Maybe we should have rich old, rich young, poor old and poor young. Or maybe keep adding arbitrary groupings until we realise there is a big bad distribution system out there constantly changing.

    But what about debt? I side with Abba Lerner on this. It changes nothing in the OLG model. The model doesn't even have money in it. Only resources. And in resource terms EXACTLY the same thing happens.

    You don't even need to complicate the story with the 20 units of public goods. Just say that instead of being taxed 10 units each period to directly give to the old, you buy a bond worth 10 from the government who uses the money to give to the old generation.

    The same balance occurs - in period T the young produce 50 and get 40 (but know the own this 10 asset) and the old produce 50 but consume 60.

    In the T+1 period the young are now old, and there is a new young cohort. They sell their 10 asset to the young to fund their pension.

    The T+1 balance is that the young produce 50 and get 40 (but know the own this 10 asset) and the old produce 50 but consume 60.

    It is all exactly the same. That there is interest on debts mean nothing in this situation - there are just another transfer to consider.

    Your last sentence also makes no sense, even when the whole system reverses (which neither must do, because you can consider exactly the reverse argument of starting with pension scheme, removing it for 10 periods, then reinstating it. There is no baseline except of your choosing).

    We did not have a distribution from young in T+10 to young in T. We had a distribution from young to old in T, and old to young in T+10, but only if you measure it relative to the immediate prior T.

    You can't explain it your way because the system never has to reverse, and hence a future young cohort need never 'lose'. Goods don't travel through time, and the existence of debt does not change anything.

    1. My post shows how, even though goods do not travel through time, a generation today can still take resources away from a generation in the future because generations overlap. Nothing you say disputes that possibility. So saying - as many still do - production in each period does not change and therefore debt (or a pension scheme) has no intergenerational implications is wrong - period.

    2. But in your simple model, all you are saying is that any group with political-economic power (you call the groups generations but as others have observed they could be classes, or even ethnic groups) can take current resources from another group. The time dimension could equally be spatial or virtual.

      The interesting question is surely whether saving for (funding) a pension is economically sound and this is much less clear cut. If I save 10% of my annual income over 30 years I will have a nice little pension pot. BUT this pot consists only of claims on other people's production unless I have literally squirrelled away enough necessities for my declining years. I will therefore be relying on the future (post-retirement) economy to respect my claims and satisfy my expectations.

      Note that this is not only a question of legal obligation but also of a set of assumptions concerning which assets will be productive, what the tax and interest regimes are/will be and so on. Moreover, there are a host of macro and micro implications of my past decisions to consume less and save more, which may, or may not, have had the effect of increasing the total future pie (to mix the kitchen metaphors). After all, I think we can agree that increasing savings, even for pension purposes, in the midst of a recession (as Americans were urged to do by those clamouring to 'fix' Social Security) will probably have a depressing effect on future consumption.

    3. A very interesting point David, and also touched upon in a post by Frances Coppola:

      The question is - what exactly are savings for? Particularly if we seem them for what they are - just a claim on the future economy.

      People presume that savings are "hard", and therefore economic policy is directed to ensure that they are hard - low inflation, reduced government deficits This might be a laudable aim - but then it might not..

      Remember, savings (and pensions) are a relatively modern invention.

  5. "We have a clear redistribution of 10 from the young in period T+10 to the young in period T enacted by the government issuing debt in period T."


    "We have a clear redistribution of 10 from the old in period T to the old in period T+10 enacted by the government issuing debt in period T."

    Think about it.

    1. Cameron: OK. I have thought about it.

      Your sentence should read: "We have a clear redistribution of 10 from the old in period T to the old in period T+10 enacted by the government issuing NEGATIVE debt in period T."

      The government needs to *lend*, not borrow, in period T. Tax 10 from the old in period T, and lend 10 to the young in period T. And then stop rolling over the loan in period T+10.

      Is that what you wanted me to think?

    2. Nick, I'll be honest, your negative debt idea is confusing me.

      What does this mean "The government needs to *lend*, not borrow in period T"

      It is doing both simultaneously (as it must) - lending to the old and borrowing from the young. That is a transfer, and independent of any specific financing arrangement.

      It need never reverse the situation. Indeed, you could equally model the opposite. Prior to period T there is a specific institutional arrangement giving the old 60 and the young 40 (including a fully funded pension system). Then we use debt to transfer 10 from the old to the young in order to undo the pension scheme. Oh no! That's unsustainable because in period 10 we will have some kind of interest obligation we can't meet. We can't undo a pension scheme using debt, that's unsustainable and leaves a burden on future generations!

      Make sense? The model can apply to any transfer from any baseline between any cohorts. They way it is applied - that using debt to create the transfer means that the the transfer must be reversed in the future - makes no sense at all. The T and T+10 period are unrelated. The debt and plain old transfer situations are identical in terms of complete rights and obligations by government and citizens.

  6. This post reminds me of the Baby Boomer retirement effect and how non-funded pensions are a bit like a Ponsi scheme.

  7. What happens if only 0.01 percent of the country owns all the government bonds, and then passes them on, as inheritance, to the next generation. And what happens if all taxpayers are on the hook for guaranteeing the interest payments on those bonds, which are now owned by the second generation of 0.01 percenters? Does that mal distribution change anything of what you write?

  8. My wife's shared rental house with friends accidentally did this. Each person paid a $500 security deposit when moving in and got $500 back when moving out. Except at some point before her time the "pot" of money got spent on parties and groceries so that it was now the newcomer's $500 that funded the payout to the person leaving, except no one saw this clearly because of their incompetent house accounting. Right before my wife moved out, they figured it all out and by majority vote decided that this system is wrong, and has to stop sometime so that actual deposits can be accumulated, so she got nothing back. She made an "intergenerational" transfer to fund a few big house parties that happened 10 years before she moved in.

  9. Market Fiscalist24 October 2014 at 18:32

    I see the logic in what you are saying but is this truly redistribution between generations or merely a series of redistribution between people in the same generation that may end up leaving some generations in an OLG model worse off than others ?

    This may be a subtle distinction - but if you don't make it you may end up as giving the impression that redistributive actions in one generations somehow can also have re-distributional consequences across different generations. Assume that in any given generations the government has the power to distribute the available income as it sees fit - then no distributive decision in any one generation necessarily has any effect on distributive decisions in future periods

  10. Simon: I am very chuffed. Thank you!

    Good post. I hope you do write a post on central banks' assets. My theory: they hold 100% assets mainly to stop accountants freaking out.

  11. Another complication is if the young save for when they are old in assets. A tax on the young then also falls on the old through decreased assets values as the young can't pay as much. In this, it can revert to being intragenerational.

  12. Market Fiscalist25 October 2014 at 14:12

    "We have a clear redistribution of 10 from the young in period T+10 to the young in period T enacted by the government issuing debt in period T"

    I think I disagree with this.

    In period T and T+1 the govt distributes income so that the young in period T get more than average income.

    In period T+10 and T+11 the govt distributes income so that the young in period T+10 get less than average income.

    These 2 sets of event are entirely unrelated. This would be the case whether the redistribution is effected by taxation, issuing bonds, or whatever means is used.

    I do not see any sense in which anything is redistributed across generations, all redistribution is within a single period and the inter-genertional effect is a sort of optical illusion, IMO.

    1. He's distinguishing between generations and times. Simplify the case to consist of only one time T. The government passes a law requiring the young at time T to give 10 goods to the old at time T. Then Armageddon comes. As a result there has been a net transfer of 10 goods from one generation to another. But that intergenerational transfer takes place at a single time.

      But I believe you are right that this has nothing to do with debt instruments. If at each time starting with T the government requires a transfer from the young to the old, and there is a last generation T10, then the generation that consists of the young at time T10 is the net loser, whether debt instruments are involved or not. It has nothing to do with a transfer of wealth across times, but a succession of transfers within times. It's easy to tell stories where some generations turn out to be net losers and some generations turn out to be net winners when such transfer schemes are extended across times.

      But one thing that is left out of this discussion, and that tends to get left out of many of these discussions, is that the nature and ultimate direction of any transfer depends on the employment of the transferred goods. These cases are usually presented in such a way as to suggest that the purpose of the mandated transfers is to increase the consumption of the old. But suppose instead the taxed goods in each generation are taxed from the old and used to build public works, like schools and playgrounds. Then you can easily tell a story in which there is a net growth of these forms of public wealth over time, where the per capita consumption of public goods by the young rises over time to ever higher levels. And where the generation of young at the last time T+10 is the biggest net winner.

    2. Market Fiscalist27 October 2014 at 14:02

      I think people who see inter-generational transfers may be looking at it something like this : Take a OLG model with n generations. n-2 generations have average consumption. generation 1 has above average consumption and generation n has below average consumption (by the same amount) - therefore there must have been a transfer between n and 1.

      This seems the only explanation at first.

      But (as this is OLG) there are 2 generations (0 and n+1) that are left out of that story. Generation 1's gain and generations n's loss can just as easily be explained by transfers that didn't happen in the periods before and after the model begins and ends.

      So saying "its a transfer between non-consecutive generations in the model" still seems to me like creating an interesting narrative out of series of events that don't actually completely fit the storyline - there is much more simple explanation that has been overlooked.

  13. The theory in the above article holds far as I can see, however it is of limited relevance to the real world. First reason is that no one envisages that pension schemes will come to an end in period T+10 or any other period.

    Second, the above theory is sometimes used to make the claim that the sacrifice made in one year or by one generation to fund a public investment can be spread across generations if the investment is funded by government debt. The problem there is that even if for some bizarre reason no investments were made at all, people would still want pay as you go pensions, and they’d organise pensions of the size they wanted (public or private). And that would cause a fair amount of re-distribution between generations. If a public sector investment is then made and funded by public debt, people are not going to want any increased amount of intergenerational re–distribution, i.e. they aren’t going to want extra pension and less pay during their working lives. Ergo pension funds will just, to a greater or lesser extent, cut down on the pay as you go element in pensions and increase the “government debt” funded element. Net result is that the fact of funding public investments via government debt does not have much effect on inter-generational transfers – unless I’ve dropped a clanger.

    1. Ralph: you haven't dropped a clanger. You are invoking a (slight) variant of Barro-Ricardian Equivalence.:

      Barro said the people care about their kids' welfare, and will increase their bequests to their kids to offset any transfer between generations.

      You are saying (I think) that kids care about their parents' welfare, and will reduce their gifts to their aged parents to offset any transfer between generations.

      But remember, under Barro-Ricardo Equivalence, bond-financed tax cuts do not increase AD.

  14. There's a rather important point that is often missed.

    Yes, public debt reflects redistribution between generations, BUT that doesn't mean that the (real) level of public debt causes the redistribution between generations. It's just as valid, if not more so, to say that the private sector's natural redistribution (evidenced by the spending and saving patterns of different generations) determines the level of government debt.

    After all, in the example here, the debt only arises because the young in period T decide to save (although it sounds like they have little choice - save or be taxed!)

  15. This is outside the government-funded pension and healthcare plans for seniors but, what about the wealth that accrued to one generation that was the result of the exorbitant privilege (at the expense of developing nations that sacrificed with slave-labour wages, selling their oil for pennies on the dollar in regards to its true value, and having their savings bring down the interest costs of the citizens of developed nations for the last 35 years)?

    And, as a result of declining interest rates, the baby boomer generation have seen their assets become excessively inflated at the expense of the generation that follows them.

    This generation must now deal with the loss of the exorbitant privilege, interest rates that are no longer falling, AND wages that are lower than those enjoyed by their parents. Add to it the labour market adjustments that must now come with the loss of exorbitant privilege.

    Not to mention the adjustments that must come as a result of technological advances that now seems to leave us with an oversupply of labour.

    Yes, this wealth will eventually be passed down, so I guess that is how the wealth redistribution comes full circle. But, it will definitely not result in a "fair" redistribution of wealth.

  16. The same point, but from an alternative perspective.


  17. RE: "... Suppose the amount of goods produced each period in the economy is always 100. ... ..."
    • Here is the first problem Professor. If there are unemployed folk in the economy (excess resources), the sovereign can issue the currency (print) and put the people to work producing public sector goods and services. They than spend and business people go waky waky and hire more people and produce private sector goods and services. That's goods and services up the you know what. So the point of a Job Gty as part of a Full Employment Fiscal Policy is keep the economy producing at peek production at all times. See the Doggy's blurb:

    RE: "... The losers are the generation who are old in the period the scheme stops. ... ..."
    • Why would the scheme stop? The US government debt is not a problem in any way shape or form. In fact, it can be repaid tomorrow without a negative repercussion.

    RE: "... how you can have redistribution between generations even if output is unchanged. ... ..."
    • Yes indeed. But think of of it this way. Not in dollars or pounds but in resources. What do geezers consume in actual resources: an apartment, shuffleboards (in Florida USA), cable subscriptions, cat food. Yes if we were at peak pruduction at all times one cn say: :"OOOhhh!!!! We are at full employment in shuffleboards! Our shuffleboard line is going 24/7! We have no resources!!!!!! to support our geezers!!!!! Then I might have sympathy for your intergenerational sacrifice - but not much because every generation will have some percentage of their population as geezers with low productivity. But that is just resources. If its currency, its not a sacrifice. Becasue the Federal Debt is irrelevant.

    RE: "... refuses to give the young the choice of buying debt, and just raises an extra 10 in taxes on the young. ... ..."
    • Why would it need to do that? It can issue the currency and have the young maintain the income. But what about inflation you say. Inflation is easily addressed: When you can:
    - tax,
    - spend,
    - buy/sell securities, and
    - manage interest paid on reserve deposits -
    you don't worry about inflation. You manage it. The trick is to make a tax, for example, a fair across-the-board tax to avoid a controversial redistribution (within that gneration). A sudden income, VAT, and asset tax will stop inflation in its tracks without involving a reduction in curreut consumption in the least.

    RE: "... a bit more realistic and bring in interest rates and growth (and the famous r<>g relationship) ... ..."
    • When you own a printing press and have the powers, discussed above, to modulate inflation, these stats are irrelevant. They are simply reading tea leaves.

  18. The reasoning is flawed and does not demonstrate anything except for the obvious fact that the government can redistribute or worse. Regarding the last part:
    1. If the government starts taxing older generation from T+1 20 instead of 10 and younger 0 instead of 10 then generation Y_T+0_O_T+1 (young at T old at T+1) has a lifelong consumption of 80 instead of 90 and there is no shift. At period T+10 young need to pay 10 in taxes while old (Y_T+9_O_T+10) still need to pay 20 while 10 is redeemed by selling the bonds. The system reverts back to its original setting.
    2. The so-called inter-generational transfer from Y_T+9 to Y_T+0 can be achieved without bonds, let's imagine that from T+1 young pay 20 while old pay 0 until T+10. Then Y_T+0_O_T+1 have livelong consumption 90 instead of 80 and the consumption pattern Y 30, O 50 with lifelong consumption 80 persists until generation Y_T+9_O_T+10 who pay 20 as young and 10 as old with lifelong consumption 70.


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