Yesterday I linked to Dillow’s piece which argued that the government doesn’t choose its deficit; the deficit is chosen for it by the decisions of the private sector to save.

You will be familiar from earlier posts of his (e.g. this one) that GDP can be disaggregated into expenditure components (consumption and investment and net exports), and also income components (wages, taxes, profits, others).   Ultimately, the weird and counterintuitive magic of macroeconomics is that these two need to be brought to equal one another. (Though note: the two are often far apart – see the Economist). It is this sort of insight that causes Nick Rowe to rant* with some justification about the misplaced use of microeconomic techniques in macro.  Certain homespun wisdoms of micro-thinking just don’t work on a macro level.  A classic example is: if you want to have higher savings, then have lower consumption.  It don’t always work that way.

A (very bright) friend noticed that blogpost, and questioned the theory that ‘the government does not control how much it borrows’.    Without being snarky and saying “if they get to choose this, they have made some rather uncontrolled choices in the last 2 years”,  I tried to summon the logic of a naive Keynesian like me into a sentence, and made a hash of it.  So I have tried drawing pictures instead.

This is for my own education as much as anything; I often blurt things out without seeing them through.  It does not constitute a prediction about what will happen if the government cuts now; as a model, it is grossly oversimplified, leaving out prices and the variable behaviour of the various actors (state, households, businesses) in the picture.   It can be extended.

The basic point I have been trying to explain to myself is that GDP as determined by expenditure needs to be brought to equal GDP as determined by income.  This is a picture of how it might happen in equilibrium:

(updated; thanks Ben and Luis below)

In this simple world, I leave out the transfers that government sends straight back to households; I just net them out (see this report).  Government consumption tends to be 20% of so of GDP, not the same as government spending.  For simplification, I assume that businesses reinvest all their profits.  The savings relationship is therefore between households and government: the households save 50, and the government has a deficit of 50.

Now, let’s see what happens in disequilibrium.  The government decides to run no deficit at all.

Now we have a problem: the GDP demanded is now insufficient.  A demand shock: the government has lowered what it wants to spend, and nothing has risen to take its place.   Please note: in that single sentence is buried and second-guessed all of the macro argument, including the possibility of non-Keynesian effects.  If business was investing too little because something about that government spending of 200 was bothering it (it was taking too many resources, bidding up wages, threatening future insolvency, raise interest rates), then the equalization would come through, say, investment increasing.  But in a slump the presumption from a hardline Keynesian is that this does not happen.**

So how is this disequilibrium resolved?  In the Keynesian-depressive account, by GDP falling, household incomes falling, probably unemployment rising and government revenues falling, so the government is forced to run a deficit.  Like this:

Now things match up again.  Household spending has fallen, in order to keep their desired level of savings at 50.  Taxation has fallen – like it does in a recession, much harder than the GDP fall.  Government spending has risen – driven by the GDP fall.  So the government is forced to run a deficit of …. 50, the very deficit it tried not to run.   The situation is just like the first picture – but GDP is 5% lower.

Again, let me reiterate: this is not a prediction about what will happen, just an explanation for my own edification and hopefully some of yours of the logic behind the Keynesian insight.  All of the real macroeconomic meat is in the arrows, not the numbers; how particular relationships make those numbers go up and down.  If I steal a moment tonight, I will post some alternative possibilities.

Does it makes sense?

*I mean rant as nothing but a compliment.  Please read his post.

**And, anyway, even if it did, it would return the same result: what the government chooses is not the point; it is the private sector’s decisions that determine the outcome.


10 thoughts on “Paradox of thrift in pictures

  1. Terrific visualisation (although seems to be two missing zeros in the first diagram, on the original shares of income line – total tax is put at “£15” and business tax as “£5”). I think many people can grasp the concept of how insufficient demand can cause a downward economic spiral, but you show very well how there is great pressure for private saving to be offset by public borrowing.

    1. Many thanks for that Ben, and for spotting the alas undeliberate error. My lame excuse; hurrying back at speed in order to buy coloured stickers, which are meant to make my younger daughter look like a packet of smarties, for Roald Dahl-themed school charity event. I kid you not. Life as a middle class parent is very hell.

  2. (your first box is missing some zeros on the tax items)

    I am never very comfortable with Chris’s posts on this. This is exactly the kind of post I need to clear up my understanding.

    My problem is that accounting relationship is such that you can equally argue the private sector doesn’t choose how much to save; its saving is chosen by government borrowing decisions.

    If you make every decision endogneous, the only way of determining the state of the system (say, deficit outcomes) is to go back to the initial conditions of the system before somebody pressed “go”. And you can appeal to “shocks”. If you want to grant certain actors scope of exogenous decisions, and make everything else ultimately a reaction to those decisions, you grant those actors implausible power (this is like the first-year econ Keynesian model where the level of output is determined by the exog government expenditure decision).

    How much scope to allow for exogenous action is a headache. Obviously (to give one example) if the private sector decides to try and save en mass, the government “has” to borrow, in the sense that there will be a recession on. But the government does face decisions (taxation and expenditure) that “could be otherwise” (i.e. are not completely endogenous). We don’t believe those decisions don’t matter. These decisions do (partially) determine the borrowing requirement. I’ve never read a story about how those decision feedback, via economic activity in the private sector, to ensure all those accounting relationships still add up, that I’m satisfied by (they are always merely one story among many possible stories). If we knew how the private sector will respond to these government decisions, then the government would be choosing the deficit, via those responses.

    I may be missing the point, but that’s precisely my problem: I’m never really sure what the point is.

    What arguments / beliefs does Chris refute? Some people may believe the government deficit is something it chooses like we choose what shirt to put on in the morning, but these people are idiots. Are these posts addressed to those people?

    1. I don’t think at all that this is incoherent stream of consciousness, and in fact the whole endogenous vs exogenous language is one I wish it had occured to me to use; I had instead (earlier post) plumped for ‘what is the tail, what is the dog?’ Except, of course, the dog wags the tail wags the dog … I have before raised with Chris the way accounting identities do not PROVE causal identities, and I know he knows this – I think he favours educating people about the unusual angle in this case. And I think there is a case for saying in a demand recession it is definitely the spending that drives the income that drives the saving, while in other situations more resembling crowding out, it is the saving that enables the investment that enables the income that produces the saving.

      What drove me nuts last year is that these two different versions of how the world works were argued against and utterly past one another, without either party recognising how it is situational.

      I intended to use this evening to post some spreadsheet models showing either way of looking at things; holding household behaviour constant (not particularly unreasonable) and then positing various different equations for the behaviour of business investment, as the variable that drives everything else. But I forgot the file name of the spreadsheets, so darn it I have to have a relaxing evening instead!

      BTW the only thing I would disagree with is ‘idiots’, although I must concede that my language re. Redwood at times has verged on that. When he complains of private virtue being undermined by public profligacy, I get sorely tempted.

  3. sorry I got a bit lost towards the end there, and stopped making sense … I know this post isn’t addressed to idiots or trying to refute any particular position. Here you are setting out one example of how “GDP as determined by expenditure needs to be brought to equal GDP as determined by income” in response to a decision to change spending behavior on the part of one actor, because as you say, it’s hard to get these stories right. Please regard my first comment as stream of consciousness on this general topic, rather than as a direct response to this post.

  4. Government borrowing = private saving is an account identity except insofar as there can be lending from abroad (or lending to abroad). So I guess one question is why a huge shift to private sector surplus didn’t see a capital outlow and exchange rate appreciation? [of course this too might cause a recession]

    1. Why appreciation ? Would the private sector not be bidding up foreign assets and therefore the pound lower?

      For currency movements, I think no rule ever works. Sushil Wadhwani’s letter to the FT on this was v good. So I felt relatively relaxed leaving out the external sector in this thingie – it doesn’t do what it’s meant to. Darned furriners …

  5. Money – a necessary refinement to the model?

    Assume money supply is fixed, then, (for Keynes?) that initial fall in national income will mean that savings and transaction money fall, speculative money increases so people buy bonds, driving up their price, bond yields fall, investment cut-off falls, investment expenditure increases – as a result the gap between savings and investment leads to income rising until the equilibrium point is again reached.

    Adding a variable money supply (and going back to my old hobby horse) suppose Gov finances more of its spending from bank lending to the public sector, the money supply rises. Since (for Keynes?) we already have enough transaction money the whole of the extra goes into speculative money which leads to bigger demand for bonds and so a rise in their price/fall in the yield. The investment cut-off falls so there’s more investment expenditure. Now I greater than S so income rises until the two are made equal again.

    1. Hi Bill

      It is obviously very very partial – an illustration rather than a model – all quantitites and also prices. But I would disagree about what might happen. Yes, excess savings means rates fall, but so do expected prices, and so as a result business investment falls (who is going to buy my stuff?). I am knocking up a few excel models to show a few scenarios ….

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