A commentator called Nick asked on the blog:
I've seen you use the national income identity repeatedly when talking about MMT:
Y = C + I + G + (X-M)
Where Y = GDP, C = consumption, I = investment, G = government spending and X-M = net exports.
But it is also true that:
Y = C + S + T
where S = private saving and T = taxes paid
Equating, this gives:
C + S + T = C + I + G + (X-M)
Rearranging you get:
I = S + (T-G) + (M-X)
Where T-G is public saving and M-X is capital inflow.
Which states that investment I equals the sum of public and private saving, plus net capital inflow. Which suggests tha investment is directly linked to saving.
However, in your blog above you say that:
“There is no tie between investment and saving”
Which is incorrect, given these accounting identities. So is this statement you have made wrong, or are the accounting identities wrong, at which point they would also be wrong when applied to MMT.
Which is it?
That's a good question and so it deserves an answer. But let's be clear in the first instance that the answer is in the question. If, as example, S = 0 (and that is quite possible) then, of course, there would be no link between I and S (investment and savings).
But let me expand another term forst. As I (and Stephanie Kelton, and Bill Mitchell, with slight variation on the theme in his case as I recall it) have all argued:
G = T +∆B + ∆F
where G and T are as above, B is government borrowing and F is government-created money (or funding)and ∆ simply represents the change in the stock over a period, so measuring a flow.
In that case:
G - T = ∆B + ∆F
Since G - T can be a negative or positive sum the ordering in which they are written is inconsequential: the same is then true of ∆B and ∆M, which can both have positive and negative value in the same period and need not be similarly signed.
In that case it is possible to rewrite your rearranged formula as:
I = S + (∆B + ∆F) + (M-X)
For the sake of argument hold foreign flows constant: it just makes the formulas eaier to follow and the assumption could be realxed if desired but the same conclusion would be reached.
No let's assume the savings ratio is zero (which is entirely plausible).
So:
I = ∆B + ∆F
In other words, it's entirely possible that if the overseas sector holds constant and that savings do too then investment is all funded by net governmment flows.
I make the point for a simple reason. There could be a relationship between I and S. But you have to make assumptions to make that relationship. And the fact is that if, as has been the case of late the savings ratio has been small or even negative, then investment can be financed by the government, or by government-created money or by overseas interests (to relax that condition, once more). In other words, there is nothing that says there is an immutable relationship between S and I. There is just a funding mix and it is my suggestion that the relationship is weak at best, and that other factors can be and almost certainly are more powerful, and that can and should now include government-created money to be used for this purpose.
And quite specifically, investment need not be funded by saving, at all. Hence my claim, which I think holds true.
Other opinion is, of course, welcome.
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Right, but you have made the assumption that S = 0
Problem is S has NEVER been zero.
https://www.ons.gov.uk/economy/grossdomesticproductgdp/timeseries/dgd8/ukea
So your claim is true ONLY if S = 0, otherwise it is false. There is a link between S and I, given S has over the last 50 or more years has always been positive.
The claim I made is true for all values of S
S = O was just an extremist example where there is no link
But when S = anything there is no proof at all that S = I because there are far too many other variables in the equation
You can only say S = I when ∆b, ∆F, X and M all are 0 or net to zero and there is much less chance of that then S = 0
So S ≠I holds true except in a very freakish circumstance
It’s true there is a relationship between S and I
But that does not make S = I
And the household savings ratio can be negative
You made the claim that there is no link at all between savings and investments, if I understand it correctly.
This is clearly false. Just by looking at the accounting identity, which states there is a link…..
I don’t think Nick was claiming that S = I either, just that there is a direct link between the two (when you are saying there isn’t one). They are correlated and linked (by the equals sign), but not directly equivalent.
Likewise there is a relationship between the other variables and I as well.
That said, you are trying to pull a bit of a fast one. You have rearranged the government saving term (T-G) to be G-T, then said the terms can be negative. In this case the term G – T would stand for government net borrowing. Then you simply substituted G-T for T-G, without changing the sign, which incorrectly changes the accounting identity.
So you should really write government net saving as:
T – G = – (dB + dF)
So it follows that
I = S – (dB + dF) + (M-X)
T-G is negative when the government is running a budget deficit, I would hope you agree. Which means that if the other terms (S and X-M) are zero then I will also be negative. In other words, by this accounting identity more government borrowing or printing money (both which would be positive terms) would means LESS investment. You are trying to switch the term over to show more government borrowing increases investment – which is incorrect given the accounting identities. I guess you were hoping nobody would spot that little switcheroo.
We know that the government has been running a budget deficit for most of the last 50 years, which makes the (T-G) term a negative number.
https://tradingeconomics.com/united-kingdom/government-budget
We also know the savings rate since 1963 from the data I provided in my first post – which has NEVER been negative, contrary to your claims. M-X varies a lot more, given UK is a net importer of goods (so capital outflows) but is also has huge net inward FDI.
Helpfully the total M-X is also a measured statistic:
https://tradingeconomics.com/united-kingdom/capital-flows
So, given the data, we know that S has been positive since 1963, T-G has mostly been negative and M-X has been a bit of both, but since 2000 mostly positive.
Going back to:
I = S + (T-G) + (M-X)
It very much looks like positive I is mostly driven by S and M-X, with T-G having a negative effect on investment.
Given all that, I think it is fair to say that I is linked to and positively correlated with S, which you claim is not true.
It is also not true that investment is financed by the government – given the accounting identities government borrowing reduces investment, not the other way around.
You are wrong
I did not say there was no link
I said there is no necessary link that is causal
And the question here – as others have pointed out is what is I?
If a government deficit reduces saving in equities is what you’re claiming, so what? Frances Coppola certainly thinks I does include that I note. But that’s pure nonsense, as I have already noted
Bit if it does then all you’re then saying is bonds substitute for equities, and I would agree. That would be true
If we’re discussing real investment what you’re suggesting makes no sense
And you’re ignoring ∆F, I should add. You’re I think only considering ∆B and are assuming ∆F is a constant. Since so far ∆F and ∆B tend to be oppositely signed that changes matters somewhat
How am I wrong? All I have done is use the same accounting identities you and MMT rely on.
I have read the above post and the original post, and in the latter you say “There is no tie between investment and saving”, though now you have stepped back from that incorrect statement and instead say things like “There could be a relationship between I and S. But you have to make assumptions to make that relationship.” and in your reply above “I said there is no necessary link that is causal”.
The equals sign in the relationship means causality, by default. It doesn’t mean a linear relationship, but it does imply that one is dependent on the other.
I don’t know where you are going with the talk about bonds and equities, because they amongst other things are just vehicles for saving. The term S doesn’t differentiate between any – it is just total private savings.
Where you have again gone wrong though is with dF. You will notice that in the accounting identity above, dF and dB have the same sign. If you increase dB, or in other words, increase government debt issuance, you are reducing investment. Likewise, if you increase dF you decrease investment. For dF to increase investment, it would have to be negative – the government would have to remove cash from the system rather than print it.
Reading between the lines, I think Nick was trying to make two points.
1. The accounting identities can’t be correct when applied to MMT but at the exact same time be incorrect when you say that savings are not linked to investment.
2. MMT makes the claim that by printing money and spending it you can increase investment and GDP. Following from the accounting identity above (I am going to drop the deltas because you are using them incorrectly, this is not a partial differential equation, it is a static relationship):
I = S – (B + F) + (M – X)
Which means increasing B and/or F being positive, meaning the government issuing debt OR printing money reduces I.
Now if you go back to the original GDP identity:
Y = C + I + G + (X-M)
We can substitute for G, which we know is G = T + B +F
To get Y = C + I + T + B +F + (X-M)
Now doing the same for I (see the equation above) we get
Y = C + S – B – F + (M-X) + T + B + F + (X-M)
Which itself reduces back to what we expect: Y = C + S +T
From this we can see that increasing B or F will increase the term G, but decrease the term I by exactly the same amount. In itself this suggests that there is a significant problem with MMT if it relies on these accounting identities – which it does. It also tells us that printing money (increasing F) doesn’t create value in GDP terms, contrary to what you and MMT tells us.
And I have already explained that all that means is a change of savings medium
But not a change in real investment
Which was my point all along
I is not now in what most think of as investments – call it equities if you like – but in bonds
I’m not sure what you are talking about. The savings medium (or indeed investment medium) doesn’t have any relevance to these accounting identities – not least because these identities cover ALL saving and ALL investment.
It really doesn’t matter if that investment at a micro level is in bonds, equities, cash or anything else. Thee is no separate term for investment in equities, for example.
I am not sure why you are trying to make such a point, when it is clearly irrelevant to the matter in hand.
It would be good if you could answer the two questions I asked above though. But to the main point, either you are incorrect in saying that saving aren’t linked to investment, or the accounting identities are wrong, which means that MMT is in itself wrong, given it relies heavily on them.
It’s crazy to suggest that the accounting identities are right some of the time, but then wrong when you need them to be wrong. All we are trying to do here is find out who is making the mistake – you or MMT.
I consider I have answered the point
You think not
How baffles me when the identities show S ≠I
And a simple addition shows that government credit creation changes everything but I have published your disagreement and am now wasting no more time on disagreeing knowing full well from your tine that your are not seeking to either understand or agree
You haven’t answered the point at all. If anything, you have steered away from it at as much as possible whilst putting forward totally meaningless and incorrect waffle instead.
You have said S and I are not linked. It is very clear (from the equals sign in the equation) that they are. Linked does not mean exactly equal, which is what you are trying to use as an escape route to avoid answering.
This means that either you are wrong, and S IS linked to I, or MMT is wrong, given it relies on the very same accounting identities.
You now refuse to answer this question. Are you wrong or is MMT? Could you answer that for us all please?
Then you go on and dissemble again and start talking about credit creation. As I have shown above, government issuing bonds OR printing money changes nothing. They reduce the term I, thus reducing investment, but increase the term G by exactly the same amount, meaning that the GDP term Y is unaffected. Which rather looks to me like a massive problem for those claiming that MMT means that we can print money to increase GDP.
I did not say S and I are not linked
I said lots of things, including S and I are linked
And I pointed out that there are limi8trs ti the model -0 which is, by a long way, not all that MMT is about
But because you have but one goal you persist
And in the process you forget something very important which is that all models are wrong, but some are useful
This model is wrong if used to say S = I (which requires a cash flow definition of I that has no economic meaning)
If it is used to explain cash flows it works
But I was talking economic substance
Very clearly you do not get the difference
Nor very obviously do you understand how disruptive ∆F is
Oh, and MMT does not say printing money raises GDP. Not once has it ever claimed that
It says providing liquidity does release real economic activity
If you don’t get the difference then you really are not worth debating with
It is neo-classical orthodoxy that insists that fluctuations in interest rates equate S and I at full employment.
Basic Keynesian macroeconomics suggests instead that I depends more on expected future returns than on interest rates, and that S depends more on income than on interest rates. So any equilibrium between S and I is brought about not by a change in interest rates, but by a change in income.
Because S=I can take place at income levels that fall below those needed for full employment, G needs to exceed T if income levels that ensure full employment are to be restored.
What I like about this exchange is that even though some see maths as a language, good at reducing the complexity of complex concepts, you still need good English (or French, or German or Mandarin) to put it in its place, to humanise it.
Maths as a form reduction is useful, but is also heavily abused – as we found out in 2008. Nor is maths as neutral as it claims to be – which is why it needs to be used in conjunction with another language so that – with luck – a healthy debate can ensue and light is shined on the matter and the truths considered, choices made (hopefully the rights ones).
For example, I’m sure that there is an equation behind a credit default swap. But even ‘credit default swap’ or ‘collateralised debt obligation’ still needs unpicking in plain English/Dutch/French/Whatever.
It may have been inferred in what you wrote but was not obvious to me, but it is surely also the case that investment can also be funded by bank lending which is not dependent on savings as acknowledged in the 2014 BoE report.
You are absolutely right
I added a money creation element to the model for this (∆F) but it is incomplete
The problem here is one of definition and measurement. Accounting identities deal in numbers real investment deals in things.
Y = the amount of things within a geographical area controlled by a state entity where Y represents the amount of real things produced either physical goods for consumption or capital goods or services. Investment can be defined as the increase in physical inputs of real things that increase the supply of available goods in an economy, preferably beneficial but not necessarily so. These inputs could be additional labour caused by population growth or immigration or a technological innovation which increases the supply of goods and services. Investment can thus be defined in terms of real things. In order to satisfy the accounting identity the increase in things has to be given a money value in order to give I.
Savings on the other hand cannot be defined in terms of things. An economy does not deliberately hoard labour or hold back a technological improvement to use at a later date. Because National income is an accounting identity and represents accounting/economists attempt to measure NI in terms of a number and so add up different outputs S has to be derived as I for the purpose of balancing double entry bookkeeping. Savings thus flow from an increase in physical things and not from presumed block of things that have been hoarded and are then used to boost output. Savings are a monetary phenomena arising from putting a money value on the increase of outputs. In this way I=S but S does not mean savings in the way we as humans traditionally think of it. S is simply a number because of the value economists place on I.
What then are savings based on our usual view as something that is kept for later? In my view savings represent a transfer of wealth within society of the physical things that are produced within an economy by use of the money system. Savings once transferred can be used for consumption or used to transfer consumption to others in return for physical labour say in the form of wages. In this way savings can form part of investment but does not necessarily equal investment from the definition of the accounting identity. Governments can increase investment by creating money and using it to buy labour from outside to increase national output or to reallocate resources from one part of the economy to another say like from coal mining to green energy production by the use of subsidy and taxation. Individuals can do a similar thing by borrowing from banks (which produce money under licence from the state) to see if they can increase output for themselves and move money wealth from one part of the economy towards them. This may increase overall national wealth but doesn’t necessarily do so as it could just move wealth from one part of the economy to themselves the surplus being savings.
So my answer to the question does S=I is yes in a narrow accounting sense but no as part of the real world. Savings (S) in the equation are not the same as savings as people normally view them.
See my reply to John
I agree with you that this discussion opens up the limitations in the accounting
My problem with this analysis is more fundamental. The reliability of the equation depends on the fixity, the uniformity, the precision of the secure identification of the underlying data the equations actually depend on – entirely; and the variables that are reduced to a ‘C’, an ‘I’, or an ‘S’. We can do this for particles, secure in their reliability, although in some cases only through statistical or quantum mechanics; i.e, not through direct observation or traditional analytical dynamics. We can do it for molecules, but for ‘GDP’; for ‘Consumption’, for ‘Investment’? Just how stable are the equations in economic? How good are the ‘facts’? Just how precise is the measurement, how consistent the definition of the variable, indeed over time how reliable the data that is being followed?
I suspect MMT will require of economics a more fundamental overhaul of the econometrics than is contemplated. Much more effort, and education should go into the problem of observation and measurement than the discipline of economics has ever bothered to contemplate. Here is an area in which accountants begin with an advantage. They actually have to contemplate counting real stocks. In economics there has been too much theory, not enough concentration on the basic facts, their availability – and the methods of measurement.
Please do not take the last remark I now wish to make here as intending to be patronising, it is not; but having made my most important point, I do not wish to participate further in this discussion, save as an interested observer; and to ask everyone who intends to contribute here; to provide some basic information I at least would wish to see clarified; where does the capital repayment of a loan appear in the above equations? Thank you.
You are right: the equation represents form but nit the substance of what is happening
And macroeconomics has never got its head around stocks or money
This needs reappraisal
Adding in delta F blows it apart, for a start….
Further up in the text Andy advocates dropping the use of delta (∆). But is it not the case that when writing equations which include symbols depicting flows, in conjunction with others that depict stocks, it is essential to include some symbol that acknowledges the presence of this fundamental difference? If we fail to do so, is it not the case that we lose dimensional integrity and potentially sow the seeds of much possible confusion? Surely Richard’s use of ∆ served that purpose quite functionally? If nothing else, its a reminder that we are in the terrain of differential equations (dynamics) as contrasted to simple algebraic ones (imagined equilibrium).
You are right
Stocks are not the same as flows
Businesses which are making money, but not investing for various reasons including static demand, must either save more and/or take any profit out of the business. In other words, it seems to me that private sector savings is not always equal to household savings, so the ONS data is not the whole story.
I understand your algebra Richard, but I’m not clear if this makes a difference to the algebra, or whether it might affect the conclusion.
Can you please explain for a non-wonk?
The implication to make S = I is that savings that fund investment are not all household saving
Clearly I is funded by government and the overseas sector as well (investment can also be overseas)
The only real implication is that money and reality are loosely related
Richard
As you say, if you set private saving S and net foreign flows to zero, then investment is funded by net government flows:
I = T – G = -dB – dF
But this means that if investment is positive, the government is running a budget surplus: T > G, and net bond/money issuance is negative!
What you may have in mind is the classic Keynesian situation, where desired private sector saving (at full employment) is too BIG relative to investment opportunities: then the government can run an offsetting budget deficit. Net bond/money issuance is then positive and it is ‘absorbed’ by the private sector.
[…] of ISAs was to encourage savings. The logic was that this helped fund investment in the economy. This is not necessarily true. Savings have, however, been seen to be virtuous and so to be rewarded by generations of […]
I agree with those that cast doubt on mathematics to resolve the issue.
I also agree it is about putting values on future implications of immediate actions.
Therefore what it boils down to is whether people trust the Bank Of England/ government in its economic policies and monetary actions.
Exactly the same actions may provoke different responses depending on the context e.g. A neoliberal chancellor seeking to save capitalism, or a Corbynite chancellor seeking another answer to macroeconomic policy.