Interest rates, growth and the primary balance

Nick Edmonds objects to my assertion that real interest rates should be at or below the real growth rate of the economy (my emphasis):
"Interest payments are just transfer payments, so their impact on stability has to be seen in the context of other transfer payments (principally taxes and benefits). Depending on the structure of these other transfers, there is no reason per se why the interest rate on safe assets has to be below the growth rate. (See for example ) There is no public sector in Samuelson, so you don't get these transfer flows, but by the same token his assets aren't actually claims on anybody, so they can't really be thought of as safe assets. 
"Of course, it may be that excessive interest rates entail tax and transfer rates that are unpalatable, but that's a different issue."

I don't think it's a different issue at all. It's the whole point. Not just "unpalatable", but unsustainable tax and transfer rates are inevitable if real interest rates on safe assets are too high. And this has serious implications not only for the welfare of future generations, but also for economic stability and long-run growth. As Left Outside points out, real interest rates persistently above the long-term expected real growth rate are effectively a subsidy of current generations by future generations.  
The paper Nick quotes in support of his argument that real interest rates above the growth rate is this one by Wynne GodleyGodley's paper does indeed demonstrate that government debt dynamics can be stable with real interest rates far above the real growth rate. But that doesn't mean that the economy as a whole is stable. 
What Godley is saying is that in conditions of full employment, for the government deficit to stabilise after an interest rate shock, government spending adjusted for the new real interest rate must grow at the same rate as the economy. That is eminently sensible - though it is not the situation we have. 

However, from the table of endogenously-determined variables on page 10 and Godley's subsequent mathematical analysis it is clear that maintaining an interest rate persistently higher than the growth rate requires a primary surplus: 
Note that this does not mean the debt/gdp level falls, as it would if government ran a primary surplus with real interest rates at or below the real growth rate. Indeed the debt/gdp level becomes very high, although it does eventually stabilise:
No, it means that a primary surplus is required purely in order to service the interest on the debt.  
National income accounting requires that (assuming external trade is balanced) a persistent primary surplus reduces private sector saving.
Y = C + I + (G-T) + (X-M)
where Y = private sector income net of taxes, C = private sector consumption, I = private sector investment,  G = government spending, T = taxes, (X-M) = net exports/(imports). 
If X-M = 0 (trade is balanced),
Y = C + I + (G-T)      
Clearly if G < T, i.e. the government is running a surplus, C + I must increase if Y remains constant. In other words, the private sector has to work harder to maintain its income. (UPDATE: I have corrected this. Originally said C + I must reduce). 
Private sector saving is the residue of income left after taxes and consumption, and for the purposes of this analysis we assume it is entirely invested in some way (UPDATE. See comments. I have implicitly assumed that trade is not balanced. If S=I, for there to be a government surplus G<T there must also be a trade surplus X>M. However, the next paragraph doesn't really require S = I anyway. The statement that higher T requires either C or S to fall is correct even if S and I are not equal). 
S = Y - T - C = I
So it should be obvious that if T is higher than strictly needed for government spending, then unless C reduces, S must fall. Persistently running a primary surplus means that the private sector must either reduce consumption or dis-save. We assume that labour is taxed more highly than wealth - this is generally the case in Western societies. So to maintain above-growth returns to holders of safe assets, income earners must be taxed more highly than required to meet government spending commitments. 
Godley demonstrates that the required primary surplus becomes stable if interest-adjusted government spending is allowed to grow at the same rate as the economy. But it is still extracting more money from the private sector than it returns as government spending. Admittedly, the difference goes to the holders of government debt, some of whom will spend that money into the economy. If all of them did, it would be a wash. But not all of them will. Many (probably most) will save that interest rather than spending it, either by buying more assets or increasing funds in insured deposit accounts.  It is therefore a wealth transfer from income earners (who are taxed on their labour) to asset holders (who are given a tax credit), most of which does not recycle back to the benefit of income earners but goes to increase the wealth of asset holders. This impedes the desire of income earners to save and causes widening inequality. As income earners tend to be young and asset holders old, it also impoverishes the young and enriches the old. If the asset holders lend their wealth to the young to enable them to buy consumption goods and/or assets, it creates a growing private sector debt burden which is ultimately unsustainable. 
Note also that since S = I, deliberately maintaining interest rates at too high a level reduces productive investment in the economy, since it limits the saving of income earners. The desire of asset holders to have positive risk-free real returns even in a recession therefore impedes recovery and limits the growth potential of the economy. Which is unfortunate, because risk-free real returns above the real growth rate are an open punt on the future growth rate of the economy. In effect, they are saying that although we aren't generating enough at the moment to pay those returns, we will manage to do so in the future even though we are making it damned hard for anyone to invest in order to generate growth in the future.

But Godley's baseline model (pages 9-10) actually has a real interest rate below the growth rate of the economy (inflation 2%, nominal interest rate 3%, growth 2.5%). And under these conditions, the government needs to run a primary deficit in order to maintain a stable supply of safe assets. This is is because with a balanced budget and positive real growth matched by an equally positive real interest rate, debt/gdp naturally falls over time. The maths to prove this is on pages 11-12 and Godley explains it thus:
" is rather obvious that an increase in the real rate of growth of the economy, accompanied by an equal increase in the real rate of interest net of tax, will lead to a decrease in the public debt to GDP ratio, as long as the propensity to spend out of disposable income is higher than that out of wealth. Only when the growth rate of the economy gets down to nil—the stationary state—should the real deficit become zero and the real budget be balanced."
Godley further shows that under all scenarios, debt/gdp stabilises at some combination of interest rate, growth rate and primary deficit/surplus - provided there is full employment. So debt/gdp does not "spiral out of control" if government produces as much of it as people need in order to save. On the contrary, in my view government creating a plentiful supply of safe assets is essential for financial and economic stability. Deliberately restricting the supply of safe assets by, for example, running a primary surplus in combination with low interest rates (so debt/gdp falls) causes instability: when government doesn't create enough safe assets, the private sector creates faux safe assets, which give the impression of being safe when they are not and are consequently mispriced. When the inadequacy of private sector "safe assets" is exposed, there is a violent crash and a flight to real safe assets, creating bubbles. The 2008 crash was not caused by investors seeking too much risk: it was caused by investors looking for safety, and the private sector attempting, and disastrously failing, to provide it.

But of course we don't have full employment, so our ability to support even the safe assets we already have is curtailed, and lots of people are struggling to maintain essential consumption because their incomes aren't high enough. For these people, saving is a distant dream. Maybe that's what we should be concentrating on, really. 

UPDATE. Ramanan points out (see comments) that in Godley's model the increase in debt/gdp is due to fiscal policy designed to create full employment, and that the fiscal surpluses are a consequence of higher fiscal activity arising from full employment. I don't disagree. But I was looking at the steady-state after full employment is achieved. 

It is distinctly possible that the high interest rates in scenario three are a consequence of the very high debt/gdp level (over 90%) required to achieve full employment. But if that is the case, then government debt in that scenario  can't be considered risk-free: the high interest rate represents the increased default risk associated with such a high debt/gdp level. This is entirely different from Nick's argument that risk-free interest rates can be sustainably above the long-run growth rate. 


  1. Frances, a few things.

    I don't think the condition of full employment is assumed in the G&L model. Rather, the analysis is used to argue that full employment can be potentially achieved using fiscal policy.

    Also the government is hitting primary surpluses in the cases because of higher activity - induced by fiscal policy itself and hence higher tax inflows. So the government is not attempting to tighten fiscal policy to hit those surpluses.

    The intuition of the model is that in the case of closed economy, government deficit is surplus for the private sector and that the debt is an asset, so it is difficult to see a situation (except when there's increasing inflation which is solved by political ways) when debt/gdp keeps rising because private wealth will also keep rising leading them to consume more - increasing economic activity and hence taxes - a bit contrary to the assumed rising debt/gdp.

    1. Ramanan,

      I did read that paper rather carefully, actually. I'm not using the whole model but rather the bit that Nick used to support his argument. And I have quoted exactly what it says. In the particular bit that Nick used, full employment is assumed in all three scenarios. Godley himself said the fact that the model showed debt dynamics did not explode when interest rates were far above the growth rate was a surprising conclusion. My point though is that the wider economic effects of real interest rates so far above the real growth rate are unstable over time.

      If trade is balanced then by definition a fiscal surplus is taxing the private sector more highly than is justified by spending commitments. That impedes private sector saving. If it is done in order to give high returns to asset holders then it is regressive, since increasing private wealth at the expense of labour income causes inequality. And if it is sustained then over time it will impoverish and/or indebt the younger and poorer and enrich the older and richer.

    2. Frances,

      I will rephrase my previous comment on full employment. It is written in the context of full employment but it is not by itself needed to show the sustainability. A lot of population can eat grass and yet the debt dynamics be sustainable. That is, the condition full employment itself isn't crucial for the model to have sustainable dynamics. And because NAIRU is not useful concept, even full employment doesn't blow the debt ratio - the story is that way.

      So full employment is not crucial to achieve sustainability. Rather the story is that even with fiscal policy targeting full employment, the debt ratios don't blow.

      I am not sure of your worries - total taxes are high because of private sector has high income. It is not as if the government is supertaxing them. In fact the tax rate is held constant in the model.

      In the abstract this phrase is the key "...even when the government is not targeting primary surpluses ..."

  2. Hi Frances,

    Thank you for devoting a whole post to my comment.

    A few points on your accounting:

    If Y is GDP, we would normally write Y = C + I + G, rather than Y = C + I + ( G -T ). That latter equation suggests that Y is private sector disposable income, rather than GDP.

    More importantly, you do not have a separate item for interest income. I know that is often done for simplicity, but where it is, T needs to be understood as net taxes and transfers, not just taxes. This includes the interest payments. Otherwise the equation S = Y - T - C won't balance. This means that G - T must be understood as the actual deficit, not the primary deficit.

    Generally, this emphasises the point that government debt service payments are just another form of transfer payment like taxes, benefits and pensions. Now I agree with what you say about the importance of transfer payments in terms of the allocation of resources between rich and poor and young old. I have written a lot on this myself. But the point is that you can't conclude anything about the implications of a particular rate of interest without also knowing about other things like how progressive the tax system is and the extent of pension provision. You can have an interest rate above the growth rate without these effects; it just depends on the structure of the other transfer payments.

    I appreciate that there may be plenty of good reasons why we might not wish to apply taxes and benefits in particular ways. But this is a different issue from that implied by Ponzi scheme arguments.

    1. Re accounting: oops, yes you're right. I wrote this very late at night after a glass of wine. Probably shouldn't have.

      I'm afraid otherwise I disagree with you though. Over the long run, a sustained primary surplus diminishes private sector saving. And giving returns persistently above the long-run growth rate causes inequality. Other transfers may mitigate that effect but they can't eliminate it.

    2. I think we'll just have to agree to disagree on the sustainability point. But for the record, I'm not saying I think it's better for the interest rate to exceed the growth rate, much less that anybody has a right to expect such a return on risk-free assets. I'm just making an observation on dynamics.

    3. This comment has been removed by the author.

    4. Frances,

      The context of the analysis is to show that there is no reason to reject r>g nor is it necessary to contract fiscal policy to achieve primary surplus as economics textbooks claim. In fact the paper shows an expansionary route to achieve primary surpluses.

      Also primary surplus doesn't translate into total surplus because the government is in deficit, only the primary balance is in surplus in the long run.

      The model has less to say about income inequality and private investment but you can try to easily think of more realistic scenarios when r>g. Something like: there's a fair system of taxation and as you move forward in time income inequality is reducing as high income earners are taxed and government expenditure is aimed at more welfare - low income earners are accumulating more wealth including government bonds etc. Also saving is equal to investment plus total deficit, so people are able to save.

      (In fact in the models saving is endogenous and depends on consumption of households out of income and wealth, so it is not as if the government is holding saving down).

    5. Ramanan,

      If safe assets were mostly held by lower income people then r>g would to a degree be redistributive - although the poorest, who can't afford to save at all (but are often still being taxed), would still lose out.

      My point though was that Nick's use of this paper to support his argument that interest rates well above the growth rate were sustainable over the long run was fundamentally flawed. It doesn't show any such thing.

    6. Actually, I never said anything about rates "well above" the growth rate - it was more that there's no sudden switch in consequences at r = g, as there is with the issue of whether Ponzi schemes are sustainable. I'd agree with the general proposition that the bigger the gap between interest rate and growth rate, the harder it is to correct for it.

  3. First of all, interest rates cannot possibly be transfer payments. If they are, then effectively, so are profits.
    Interest rates, like all other prices indicate time preference and therefore the propensity to consume and save.Today's interest rates have unfortunately been distorted beyond comprehension by central banks so the prices suffer the problem Mises and Hayek pointed out... problem of economic calculation. So the level of interest rates today doesn't tell how much savings are in the system and therefore doesn't give us proper information on people's time preference... but that is another argument altogether.
    Lastly, I thought the cure for high prices is high prices and the cure for low prices is low prices. If interest rates get too high, people will prefer to save more and this will push down interest rates as amount of loanable funds exceeds the available investment opportunities.
    To put it simply, I totally disagree with the basis of your hypothesis.

    1. Oh that's old style accounting terminology of Meade and Stone to call government interest payments on public debt as transfers. .

    2. Oh dear Johnson - you are arguing from a "loanable funds" mindset. You realise that the concept has been repudiated? Read some Basil Moore if not.

  4. I'd really like to hear your opinion on Wicksellian theory of natural interest rates...

    1. Well, I sort of covered it in my "Weird is Normal" post at Pieria. But I might do another post on it.

  5. "Clearly if G < T, i.e. the government is running a primary surplus, C + I must reduce if Y remains constant"
    Not necessarily true. Y can grow as a result of lower G and lower T that boosts work ethic which is a dynamic that the general equation can't capture.

    1. Within the conditionality that I set - i.e. constant Y - what I said is true. I have not argued that Y cannot increase.

      I don't necessarily agree with you that lowering G and T would increase Y. After all, some people think that RAISING these in a recession would increase Y because of multiplier effects - "some people" in this case now including the IMF.

  6. "Note also that since S = I, deliberately maintaining interest rates at too high a level reduces productive investment in the economy"
    The problem with this statement is that it represents a disconnect between financial sector and real sector. The return on investment is generated in the real sector not in the financial sector. This is because investors invest on the basis of available investment options not on the basis of abstract numbers...

    1. "a disconnect between financial sector and real sector".

      No. The financial sector is not represented in this equation at all. S is the savings of the real private sector, I is investment in the real private sector. I made the classical assumption that all private sector real saving is productively invested in real enterprise. In practice this may or may not be the case at any point in time: during a recession, I would expect S to exceed I, the difference being investment in unproductive (but "safe") assets. And indeed currently that is the case. But I've discussed this elsewhere and don't really want to repeat it here - hence the simplification.

  7. " The desire of asset holders to have positive risk-free real returns even in a recession therefore impedes recovery and limits the growth potential of the economy."
    This begs the question, what is a recession? I think it is when unprofitable businesses are liquidated. So the desire for positive real interest rates during a recession conserves capital as opposed to investing it to sustain failing businesses... i.e. essentially, throwing good money after bad.
    This would become clearer with a robust theory of capital... one that views capital as heterogeneous and not homogeneous. This means that investment in a plant that produces 100,000 units per annum in a 30,000 units per annum market is a bad idea and a waste of capital. In the event of a recession, the hitherto profitable investment is exposed for its profligacy.

    1. Strictly, a recession is a period of negative growth. But following Keynes, I would say that recession is characterised by an excess of saving over productive investment (i.e. S > I).

      We've crossed swords before on the subject of malinvestment. Let's not reopen old wounds.

    2. "I would say that recession is characterised by an excess of saving over productive investment (i.e. S > I)"

      do you mean an excess of private saving over private domestic investment? If so then the US has been in recession for majority of the time since 1947:

    3. "Characterised by" doesn't mean it exclusively happens in recession. I did say a recession was a period of negative growth. Clearly, the US hasn't been in negative growth for most of the time since 1947.

  8. If a government is running a surplus over an extended period, would we expect the currency to rise relative to countries which aren't?

    1. Intuitively I would say "yes, to some extent". But many things influence the exchange rate, both domestic and global factors. And it probably depends most on the monetary policy stance.

  9. "Y = C + I + (G-T)

    Clearly if G < T, i.e. the government is running a primary surplus, C + I must reduce if Y remains constant"

    Clearly it is not the case. Confusion, confusion. You confuse rates of change with levels. If G-T<0 you only know that C+I>Y, you don't learn anything about *rates of change*. To infer anything about rates of change, take a derivative and ipose the condition that Y is constant (dY/dt =0):
    0=dY/dt = d/dt(C+I)+d/dt(G-T). Now if d/dt(G-T)>0 then d/dt(C+I)<0, so if G-T *grows*, C+I reduces to keep Y constant. But you didn't say G-T *grows*, you said it was negative, an unrelated attribute. So your conclusion doesn't follow.

    Also, if S=I then G=T in a closed economy, you cannot have G<T and S=I, so none of your analysis follows. Eg. if you assume at any point that 1=0 you can prove a lot of "interesting" results like 100<20 or 4=1000. You won't be taken seriously with such basic errors.

    I think you understand finance and have a lot of experience but you cannot analyze the economy with math because you make too many basic mistakes to be successful this way. Please feel free not to publish this comment, it is just FYI.

    1. Two points.

      1) if I were discussing rates of change I would have done as you have done and used the derivative. But I was actually discussing levels, not rates of change. This equation should be expressed as a time series really, but I didn't want to complicate things.

      2) it is absolutely possible for S=I and G<T in a closed economy. Have another look. All that happens is that either C or S is less than it would be if the budget were balanced. If S is less, then so is I. However, I did say it was a simplification. In practice S is not usually equal to I.

    2. 1) no, you were not discussing levels. "Y stays constant, C-I must reduce" are statements about changes it time. You can use time series, whatever, it won't change the logic.

      Consider a statement. "Amazon makes profit on book and non-books. Book-sales profit was negative, so for the total profit to stay constant, the other component must grow". This statement is false. It is enough for the book-sales loss to decline.

      2) False. Read on national accounting. In a closed economy S-I=G-T, end of story. If G<T, S cannot equal I. It is grade school arithmetic.

    3. PeterP,

      1) I've had another look at what I wrote. It's not my maths, it's my English that is wrong. For Y (private sector income) to remain constant C + I must increase not reduce.

      In fact as I am talking about private sector income, I shouldn't really have assumed that Y is constant. When government runs a surplus, the private sector runs a deficit, so for Y to remain constant the private sector has to work harder to maintain its income.

      Your example is wrong, though. If Amazon's profit is made up of books & non-book sales:

      P = Pb + Pnb

      If Pb is positive in time period t and negative in time period t + 1, then for P to remain constant, Pnb must increase.

      2) Ok, fair enough. If you eliminate G-T from the equation completely then I = Y - C which is S. I have implicitly assumed without stating it that the economy is not closed: for G<T and S=I both to be true there must be a trade surplus. My apologies.

      I don't think it is appropriate to tell me that I make "too many basic mistakes" so should never use maths in my posts. You've actually identified one mathematical error and one English error. Kudos to you for noticing them, but anyone can make mistakes. Indeed John Cochrane, a far better mathematician than me, published a post recently with several errors in the maths which were pointed out by friendly people in the comments, none of whom suggested he should stop using maths because of his errors. I need to check my work more carefully before posting. And you need to be more polite.

    4. Frances,
      "1) I've had another look at what I wrote. It's not my maths, it's my English that is wrong. For Y (private sector income) to remain constant C + I must increase not reduce."

      This is still a bit wrong. The initial condition would have to be that the government surplus is *growing*, not merely that it is positive. If it is positive and falling (G-T is negative but increasing towards zero) then C-I may be falling and Y will be constant. You still mix up levels and changes. You cannot deduce *anything* about *changes* in Y from the *level* of G-T. Read Billy Blog on this. He says: there is a good deficit and bad deficit. Bad deficit is when the automatic stabilizers are too weak to close the output gap, the deficit grows due to the economy falling into an abyss. So deficit grows and Y falls. But a good deficit would be a deficit large enough to satiate the desire of the private sector to hoard financial assets. The the deficit grows and Y possibly starts growing. So an increasing deficit can coincide with growing and falling Y, accounting allows both possibilities. So you cannot say which will happen just from the accounting. You have to look at the economics: private debt, deleveraging, who gets the assets generated by govt. deficits etc, which makes it more interesting!

      So your example about P=Pb+Pnb is correct because you use changes for both Pb and Pnb. In your initial example, you used levels for G-T and tried to deduce about rate of change of C-I, not doable with the available information.

      2) Cochrane is driven by ideology, just like most of orthodox people. Yes, they should stop doing economics altogether, they use their smarts to further their ideology. So no wonder that he makes mistakes, because he knows beforehand which result he "wants" to get. Also read billy on Mankiw on deficits - his math was correct, his conclusions garbage.

      About you using maths: I seriously think that you should avoid it, because you are stronger without it. By using it you arrive at conclusions that seem iron to you but are not supported at all, just a result of a bunch of mistakes. No offense, but you seem to lack basic intuition and ability to analyze equations. But you are very good about how financial institutions work.
      I think that we need the strongest weapons to battle the cluelessness of monetarists and neoclassicals and by doing maths you are throwing away your best weapons and reaching for weapons that can hurt you more that help you. Or maybe check your reasoning by running some tests/simulations in excel? I do that often. You would see that G-T negative can coincide with constant Y and growing or falling C-I, simply depends on whether G-T grows or falls, NOT on its sign.

      You are right that I am bad at being polite, I apologize, that is my weak point. I am terrible with words and lack debating skills. You handled it well in spite of that!

    5. Peter,

      I do see what you mean. You're basically saying that I am confusing stocks and flows. Yes, maybe - though I didn't think I was (I'm usually pretty strict about that).

      I agree with Bill Mitchell about "good" and "bad" deficit. You can't deduce from the accounting alone whether or not it is a problem. The same could be said about a government surplus, too - a surplus caused by the economy growing faster than government spending can be a good sign. Really that's the point Ramanan is making further up the comments thread.

      I'm fast reaching the conclusion that economic indicators - inflation and deflation, for example - are not of themselves "good" or "bad": we need a narrative to explain their cause and their consequences in order to determine whether they indicate positive or negative trends. Deflation, for example, which we go to such lengths to avoid, can actually be a good sign if it arises from rapid technological change (David Beckworth made this point recently in a research paper about America after the Civil War).

      I appreciate your remarks about me and maths. I would be the first to admit that maths is not my language. I don't "think" in mathematical terms, though I do think logically. And I don't notice mistakes in the way that I notice spelling mistakes in English (they look wrong) or wrong notes in music (they sound wrong in my head - I don't need to physically hear the music, I only need to look at the written notation). For me, using maths is like writing in a foreign language. I wrote about this a while ago.

      Having said all that, I'm actually comfortable with financial maths (discounted cash flows, compound interest, cost of capital etc.), no doubt because I spent a lot of my working life doing those sort of calculations. In fact financial maths underpins quite a bit of my writing. For example, the Pieria post that precedes this one, "Weird is Normal", is all about discounting: There is no actual maths in the post, but the whole thing is really a particular application of financial mathematics.

      So maybe I should stick to what I know and leave the algebra to others.



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