Wren-Lewis, MMT, and Fiscal Policy with Trees

UPDATE: I did Wren-Lewis a disservice in this post. The post in which he claims that debt can burden future generations was only making the same point that Nick Rowe makes, namely that debt can be involved in an intergenerational transfer. This is easiest to make sense of if you assume that the economy is at permanent effective full capacity. In that case, for the government to give spending power to one group it must take spending power from another group. And with an overlapping generations model such as the one Rowe uses you can see how it can give spending power to a current generation by taking it from a future generation, through the mechanism of deficit spending. Here I was discussing something different, which was a case in which the economy is not at full capacity, and the government borrows to make up for a shortage of aggregate demand. Wren-Lewis does not deny that that can be done without any burdening of future generations. So I apologise to him.


I read Simon Wren-Lewis’s blog post on MMT. The main criticism is that MMT doesn’t say anything macroeconomists don’t already know. That may or may not be; Wren-Lewis cites a paper by Thomas Palley which seems somewhat to miss the point, as I argued elsewhere.

But, as I wrote there, I’m happy with the assertion that MMT doesn’t say anything new. The basic ideas can be found in Joan Robinson’s Introduction to the Theory of Employment or Abba Lerner’s “Functional Finance and the Federal Debt”, which are really just attempts to streamline Keynes’s General Theory.

I’m still not sure that Wren-Lewis really grasps the point that MMT is trying to make, since he has argued in the past that running deficits today can place a burden on future generations. This is important, because such a claim is at the heart of George Osborne’s goal of hitting a budget balance by a certain date in the future, which justifies all sorts of cuts to public services.

Wren-Lewis complains that MMTers don’t like equations very much. That’s not really true, as Billikin mentions in the comments here; one need only glance at Mitchell and Muysken’s book to see that (Mitchell trained as a mathematician). But the equations Wren-Lewis favours, such as the equation representing the government’s ‘consolidated budget constraint’, don’t serve to get across the point that MMT is trying to make. Such equations can represent the final equilibrium arising out of flows over time. But they don’t on their own give a very good sense of the sequences of events that spending operations set off. When I think about those sequences, non-economist that I am, I just don’t understand the claim that deficits today impose a burden on the future.

I’ve tried to make the point in various different formal ways – using balance sheets and different sorts of logical constructions as an alternative formalisation to the straightforward equilibrium-solutions that economists favour. Let me try one more.

I’ll keep the model as simple as possible. Complexity can always be added in later, and if I’ve missed something relevant you can let me know. As I see it, this simple model will be more than sufficient to make the point I want to make.

So we’ll start with a government spending £100. We’ll say, for simplicity, that £10 is taxed out of every subsequent transaction. That’s a massive simplification, but it doesn’t seem out of this world. It means an increasing portion of every transaction is taxed as we progress down the market chain, but this is what you’d expect from a progressive tax system. After all, the further down the market chain a transaction is, the higher the income of the participants is likely to be, since they’ve already received the income from the previous transactions.

I want to represent the ‘multiplier’ on government spending in the form of a tree diagram, a bit like Quesnay’s tableau économique. We start with the government spending £100, and assume that the recipients of that spending use £10 of that income to pay tax, £10 to purchase government securities, and spend the rest, which is £80. So we get this:

Screen Shot 2016-03-17 at 10.21.29

Now we assume that the recipients of that £80 spend £10 paying tax and spend the rest (everyone who wants to purchase securities already did so in the first transaction). So we get:

Screen Shot 2016-03-17 at 10.22.33

The market chain runs on like this until the last £10 people earn is spent paying tax. The whole ‘tree’ looks like this:

Screen Shot 2016-03-17 at 10.23.23.png

If you tally up the totals, you find that the government’s total tax revenue is £90, bonds purchased are £10, and total income for the economy is £460. The tax burden for the economy is around 19% of income.

Now suppose that the government repeats the exact same operation next year. It spends £100 (some of this will now consist of interest payments to the bondholders – an intragenerational distributional issue but nothing to do with intergenerational distribution). £10 of this is spent purchasing new government securities. The rest is spent until it generates £90 of tax revenue for the government and, again, £460 of total income. The tax burden is the same – 19% of GDP. Meanwhile, there is a total accumulation of  £20 worth of government securities. Total debt is rising, while the government’s deficit is staying constant as a proportion of income.

Suppose the government goes on running this deficit for ten years. By the end, £100 worth of government securities will be accumulated. Now suppose that the government wants to balance the budget, retiring all outstanding securities. In addition, it spends, again, £100. The first link in the market chain will look like this:

Screen Shot 2016-03-17 at 10.31.39

The recipients of the £100 of government spending have £200 to spend, since they also have the £100 they receive from the government retiring bonds. Of this, they pay £10 in tax and spend the rest. The rest of the market chain will go on as before:

Screen Shot 2016-03-17 at 10.33.14.png


By the end of the sequence, total tax revenue will be £200 – enough to cover the £100 of new spending and the retirement of £100 worth of bonds. Meanwhile total income will be a whopping £2000. The tax burden will therefore be less as a proportion of GDP than it was for the previous cohorts: only 10%. Far from being burdened by the previous debt, they have done extremely well out of the deal in financial terms.

The final qualifier is important, of course. It might be that £2000 of spending is too much for the economy’s productive capacity, in which case there will be inflation, and the real income of the final cohort will be lower as a result.

But the government can prevent inflation simply by increasing tax rates. Suppose it doubles all the tax rates, so that (in our very simplified system) £20 is taxed out of every transaction. In that case, total income will be £900. The tax burden will be 22% of income. That’s higher than  19%, but not by much. Suppose the tax rates are increased by less, so that $15 is taken out of every transaction. Then total income will be £1050, and the tax burden will be around 19%. If tax rates are severely increased – to £40 out of every transaction – then total income will be £500 and tax will be 40% of income.

The key point is that which tax rate the government needs to set to avoid inflation will depend on the productive capacity of the economy at that time. This is what MMTers have been trying to point out: the government’s constraint is real not financial. With a few simplifying assumptions in place, you could conclude that if the government sets tax rates too low, then inflation will erode away precisely the same value from the income of the future cohorts.

But then there is no financial argument to show that deficits today need to burden generations tomorrow. To prove such a claim, you would need to predict the level of real productive capacity at the time the government balances its budget in the future and compare it with the benefit we are currently getting out of whatever proportion of real capacity we are using today. Good luck with that.

We have, however, forgotten something else enormously important. Is there ever a time where the government will need to balance its budget? The assumption at work here is that there will be a time when people will be spending the principal received from their government securities and not purchasing new securities. There is, as I mentioned in a previous post, a mere assumption among mainstream macroeconomists that this will occur at the point when the economy hits full capacity. There is a rationality presumption at work here: people are assumed to be sufficiently rational to know that the economy is at full capacity and so net saving is pointless, since the attempt to spend the accumulated savings in the future will simply erode away their value.

But what if people aren’t that rational? If people just want to accumulate government securities, in a greater volume than they can ever hope to spend, then the government can’t do better than to keep on supplying those securities. If it refuses to issue those securities, people’s attempt to net save will simply drive paradox of thrift effects and reduce total income. There is no corresponding risk on the other side. There is no inflationary risk, since money that just sits around in securities accounts doesn’t add to total spending. There is no solvency risk, since as long as people keep accumulating securities the government can keep refinancing its old debt while taking on new debt. If people at some point stop accumulating securities, the only tax ‘burden’ on the current generation will be whatever is required to keep spending proportionate to capacity – but that is only the limitation of not being able to purchase what cannot actually be produced.

If this is a ‘burden’, it is a burden faced by every generation. On the other hand, no generation ever gets to face it, since full capacity is never entirely reached. As Neil Wilson puts it, full employment is the ‘light speed’ of economics.

So government ‘borrowing’ today imposes no burden on future generations besides the already existing burden of not being able to purchase what the economy is incapable of producing. So long as people want to accumulate securities, the government can go on borrowing more year on year. If everyone at some point stops wanting to accumulate securities, then at that point people on the whole will have precisely enough money to purchase everything the economy is capable of producing and no more. That is the worst case scenario, and it doesn’t sound all that bad.

I mean the worst case scenario on the assumption that the government behaves sensibly. A worse scenario still would be if the government decides to try to retire all its debt while people still want to accumulate securities. This involves the government doing something unnecessarily harmful, namely what not only George Osborne but also his opposition proclaim as their ultimate intention.

I still don’t understand why. I remain unable to make any sense out of the idea that ‘borrowing’ today imposes a burden of future generations in any sense beyond that of not being able to go beyond full capacity. That’s the question MMTers are asking of mainstream macroeconomists. Any help macroeconomists can offer me is very welcome, and I mean that sincerely.


17 thoughts on “Wren-Lewis, MMT, and Fiscal Policy with Trees

  1. NeilW

    “As Neil Wilson puts it, full employment is the ‘light speed’ of economics.”

    Not so much full employment, but full real capacity output. We can have full employment without reaching our full real capacity output, because there is always overtime that can be done, weekends that can be worked, improved intensity of capital assets, improved speed of operation.

    And that’s before you hire me to enrich jobs and streamline and automate processes 🙂

  2. synchretist

    There appears to me to be a flaw in the scenario when you pay down the debt. You show the debt paid down on the right side of the tree, but there is no source for that – you just add it to the income branch. Should there not be a relationship with the left branch, say, – 20 instead of – 10 until the right branch is retired over ten iterations?

      1. axdouglas Post author

        The top £100 is new spending. The -£100 in the bonds column represents the retirement of bonds. Since the tax revenue generated by that spending ends up adding up to £200 in any case, you can see that both parts of that spending are ‘funded’.

    1. axdouglas Post author

      Read what comes after that diagram. The total tax revenue at the end of the market chain turns out to total £200, which is enough to pay for the £100 of new spending and the retirement of £100 of debt. That’s true whether you set the tax rate to £10, £20, £30, £40, or whatever amount out of each transaction (up to £200, obviously).

  3. Billikin

    I think that Wren-Lewis’s idea that MMTers do not like equations has to do with his taking laymen who comment on his blog as representative MMTers, instead of people like Bill Mitchell.

    1. axdouglas Post author

      That’s a really good point – so good I’m going to edit my post to mention it.

      If Wren-Lewis means to say that Bill Mitchell doesn’t like equations then that’s hilarious.

    2. IDG

      Is a fallacious argument anyway, argument from authority. This is what people does when they feel their position is threatened by critics.

  4. Frances Coppola (@Frances_Coppola)

    Alex, you touch on an important point here, which is the responsibility of government to accommodate the desire of ordinary people to save safely for their future. I think government “debt” should be more correctly seen as a savings scheme and bonds as certificates of deposit. Bill’s objection to government debt is its use as what he describes as “corporate welfare”, but in my view that is a reason to repurpose it, not eliminate it. We agreed that government should provide savings vehicles for citizens, though Bill says he would prefer a deposit scheme such as the UK’s NS&I over bearer bonds.

    1. andy blatchford

      I seem to remember commenting on your blog that it’s better off calling it national savings but that should be it for it’s own citizens only, export orientated countries collecting interest bearing bonds can sod off.

    2. NeilW

      There are only two options. You either accommodate the excess savings of the non-government sector, or you confiscate them. That’s it.

      In a system that is promoting compulsory pension saving with the private sector rather than increasing the availability and generosity of the state pension via a SERPS then it is very difficult to see how a confiscation system can work in a growing economy.

  5. grkstav

    The assumption that “that the economy is at permanent effective full capacity” is not a simplifying assumption, it’s a bogus assumption. No matter how sophisticated and ‘elegant’ the theory one builds on its basis, it’s not going to matter.

    S.W-L. simply refers people to ‘standard’ macroeconomics (premised on those bogus assumptions) whenever presented with a critique. That’s not science, in even the Continental sense of ‘disciplined inquiry’.

    Therefore, I am reading the finale of the update,

    “Here I was discussing something different, which was a case in which the economy is not at full capacity, and the government borrows to make up for a shortage of aggregate demand. Wren-Lewis does not deny that that can be done without any burdening of future generations. So I apologise to him.”

    as a bit of self-deprecating trolling. If so, well done! 🙂

  6. Jerry Brown

    I want to give Simon Wren-Lewis a little credit here. Even though I disagree with his post, it is through the comment section on his blog that I found your blog here. I have been reading through your posts over the last several days and they are excellent! You describe many of these issues with a clarity in thought and writing that is exceptional. I have read back through August now and am dreading getting to the point where the blog begins. So thank you Simon. And Thank You Dr. Douglas!

    Oh, and I agree with grkstav above about the completely unnecessary nature of the update you wrote for this post.

  7. Billikin

    I think that your apology to Wren-Lewis may have been premature. Rowe’s point, laid out in a long scenario some years ago, was not just that spending power was transferred from later generations to earlier ones, but that each generation received more spending power from the next generation than it had transferred to the previous generation, and that the net difference was greater than the growth of the economy between generations. It is that imbalance that caused the transfer system to eventually break down.

    Now, any such transfer system can break down if it comes to an end. But for the economy to come to an end in the way that they do come to an end, the break down of the transfer system is one of the least of the things to worry about.

  8. Pingback: Apologising to Simon Wren-Lewis and Nick Rowe | Origin of Specious

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