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Monday, February 25, 2013
JKH — Briefly Revisiting S = I + (S – I)
Drilling down deeper into S = I.
I suggest commenting over at MR in order to keep comments together. JKH is very generous in responding to comments and questions there.
Yes, saving is a terrible word in that context because it leads really, really smart people to torture the simple concept of "all spending equals all income for a closed sector" until they've tied themselves in knots.
"Oh man... what are you guys doing? I don't even know where to start. But look: you're confusing an accounting statement for a behavioral equation. Joan Robinson always took the neoclassicals to task for this. Okay, I'm going to be brief:
"S = I + (S – I)"
This is true. In the same sense that saying: "2 = 2 + (2 - 2)" is true. Yeah, pretty stupid thing to say, right? That's what we call a tautology. What you've "derived" in your manipulations is a tautology. Great. Okay.
"And that is the equation in question. It says that private sector saving is the amount required to fund investment I plus a residual amount in excess of that, equal to (S – I). "
Yeah, since I=S, that "residual" is zero. Let's run through that:
I = S
Put I and S at 5.
5 = 5
Now substitute that into your above "residual":
(S - I)
Ready?
(5 - 5) = 0
There's your "residual".
Congratulations. Another tautology. But then you're deriving some bizarre behavioral ideas from this. This is like the old Pre-Socratic debates. Look them up. They're more interesting than the above..."
"you're confusing an accounting statement for a behavioral equation"
S=I+(S-I) is just the basic sectoral balances equation, as described in any number of MMT/other texts on the subject.
As the MMT Wiki says (courtesy of Bill Mitchell):
"The sectoral balances equation says that total private savings (S) minus private investment (I) has to equal the public deficit (spending, G minus taxes, T) plus net exports (exports (X) minus imports (M)), where net exports represent the net savings of non-residents.
Another way of saying this is that total private savings (S) is equal to private investment (I) plus the public deficit (spending, G minus taxes, T) plus net exports (exports (X) minus imports (M)), where net exports represent the net savings of non-residents."
In other words:
S=I+(G-T)+(X-M)
or in other words:
S=I+(S-I)
(S-I) simply denotes domestic private sector net saving.
So we can re-state S=I+(S-I) as:
private sector saving (S) = private sector investment (I) + private sector net saving (S-I).
(S-I) equals (G-T) + (X-M)
Mitchell continues:
"All these relationships (equations) hold as a matter of accounting and not matters of opinion.
Thus, when an external deficit (X – M < 0) and public surplus (G - T < 0) coincide, there must be a private deficit. While private spending can persist for a time under these conditions using the net savings of the external sector, the private sector becomes increasingly indebted in the process."
Suppose private investment is zero, then S= (G-T)+(X-M). The private sector then decides to spend 10% of its income on constructing houses (an investment). That 10% is simply a payment by one section of the private sector to another and not to G,T,X or M. So now 0.9S= (G-T)+(X-M).
No, because investment precedes and creates savings. You have it the wrong way round.
One could say that saving is the financial record of investment as firm expenditure on capital as real growth, since firms are owned by households.
In a closed economy w/o govt
Y = GDP (Household) Income in aggregate = (Firm) Expenditure in Aggregate
C + S = C + I
simplifying
S = I
S and I are records of flows., so this just says that households in aggregate increased stock of savings by the same amount that firms invested, that is, spent that did not go toward producing consumables, thereby growing equity, which is owned by households, in that period.
So saving can only not be equal to I if something changes to increase or decrease net saving of households in aggregate and that some thing is the addition of government, and in an open economy also the current balance.
As Bill points out, the identities say nothing about causality as identities, but they can be interpreted causally in terms of a theory and then these assertions of causality can be investigated empirically by formulating testable hypotheses.
Investment only precedes saving in the sense that that an increase in firm equity through expenditure in the period gets reflected the income statement of the owners has an add to their equity.
Basically firms make consumables that households consume and firms invest in additions to capital which is owned by the households that own the firms.
That's the total of (household) income = (firm) expenditure, or Y = GDP in a closed economy w/o govt.
Since (G-T) and (X-M) both refer to a flow of funds over some period into or out of the government and external sector, it follows that (S-I) must also refer to a flow of funds over some period into or out of the private sector.
But I (investment) does not necessarily refer to a flow of funds out of the private sector (particularly in the case of house building). Thus the units employed on one side of the equation are not the same as the units employed on the other, which makes a nonsense of the equation.
It’s a bit like saying a car going at 100 miles an hour in some sense equals a bit of furniture which weights 100 kilos.
In contrast, if we define S as simply the flow of funds into or out of the private sector, and leave investment out of it, then the equation makes sense, as I pointed out a year ago here
Put another way, you claim that investment is part of the definition of savings. OK: in that case, what’s investment doing in the equation as a separate entity? It shouldn’t be there, should it?
If S and I increase by the same amount, then quantity (S - I) is unchanged. E.g., let /a/ be the increase in both S and I, representing new real estate investment or whatever. Then,
(S + a) - (I + a) = (S - I) + (a - a) = (S - I)
If I = 0, then quantity (S - I) reduces back to S, regardless of the magnitude of a.
But I (investment) does not necessarily refer to a flow of funds out of the private sector (particularly in the case of house building)
Investment does not refer to a flow of funds out of the private sector _at all_. Funds flow *into* investment. Investment is a /use/ of funds.
Accumulation(S) = accumulation of real assets (I) + accumulation of financial assets (X)
ReplyDelete=> X=S-I. QED
There is no information about causality that can be inferred from that equation alone however many words one wishes to write about it.
It seems the word "saving" is a word that gives everyone trouble.
It seems the word "saving" is a word that gives everyone trouble.
ReplyDeleteThat's an understatement.
Thanks for the input. Nice to see you here.
Yes, saving is a terrible word in that context because it leads really, really smart people to torture the simple concept of "all spending equals all income for a closed sector" until they've tied themselves in knots.
ReplyDeleteStop linking to this... My response:
ReplyDelete"Oh man... what are you guys doing? I don't even know where to start. But look: you're confusing an accounting statement for a behavioral equation. Joan Robinson always took the neoclassicals to task for this. Okay, I'm going to be brief:
"S = I + (S – I)"
This is true. In the same sense that saying: "2 = 2 + (2 - 2)" is true. Yeah, pretty stupid thing to say, right? That's what we call a tautology. What you've "derived" in your manipulations is a tautology. Great. Okay.
"And that is the equation in question. It says that private sector saving is the amount required to fund investment I plus a residual amount in excess of that, equal to (S – I). "
Yeah, since I=S, that "residual" is zero. Let's run through that:
I = S
Put I and S at 5.
5 = 5
Now substitute that into your above "residual":
(S - I)
Ready?
(5 - 5) = 0
There's your "residual".
Congratulations. Another tautology. But then you're deriving some bizarre behavioral ideas from this. This is like the old Pre-Socratic debates. Look them up. They're more interesting than the above..."
"you're confusing an accounting statement for a behavioral equation"
ReplyDeleteS=I+(S-I) is just the basic sectoral balances equation, as described in any number of MMT/other texts on the subject.
As the MMT Wiki says (courtesy of Bill Mitchell):
"The sectoral balances equation says that total private savings (S) minus private investment (I) has to equal the public deficit (spending, G minus taxes, T) plus net exports (exports (X) minus imports (M)), where net exports represent the net savings of non-residents.
Another way of saying this is that total private savings (S) is equal to private investment (I) plus the public deficit (spending, G minus taxes, T) plus net exports (exports (X) minus imports (M)), where net exports represent the net savings of non-residents."
In other words:
S=I+(G-T)+(X-M)
or in other words:
S=I+(S-I)
(S-I) simply denotes domestic private sector net saving.
So we can re-state S=I+(S-I) as:
private sector saving (S) = private sector investment (I) + private sector net saving (S-I).
(S-I) equals (G-T) + (X-M)
Mitchell continues:
"All these relationships (equations) hold as a matter of accounting and not matters of opinion.
Thus, when an external deficit (X – M < 0) and public surplus (G - T < 0) coincide, there must be a private deficit. While private spending can persist for a time under these conditions using the net savings of the external sector, the private sector becomes increasingly indebted in the process."
Suppose private investment is zero, then S= (G-T)+(X-M). The private sector then decides to spend 10% of its income on constructing houses (an investment). That 10% is simply a payment by one section of the private sector to another and not to G,T,X or M. So now 0.9S= (G-T)+(X-M).
ReplyDeleteAn blatant self contradiction.
No, because investment precedes and creates savings. You have it the wrong way round.
ReplyDeleteNo, because investment precedes and creates savings. You have it the wrong way round.
ReplyDeleteOne could say that saving is the financial record of investment as firm expenditure on capital as real growth, since firms are owned by households.
In a closed economy w/o govt
Y = GDP
(Household) Income in aggregate = (Firm) Expenditure in Aggregate
C + S = C + I
simplifying
S = I
S and I are records of flows., so this just says that households in aggregate increased stock of savings by the same amount that firms invested, that is, spent that did not go toward producing consumables, thereby growing equity, which is owned by households, in that period.
So saving can only not be equal to I if something changes to increase or decrease net saving of households in aggregate and that some thing is the addition of government, and in an open economy also the current balance.
even if you don't accept the idea that I "precedes" S the sectoral balance equation still holds nonetheless. As Bill says:
ReplyDelete"these relationships hold as a matter of accounting and not matters of opinion"
I think he might have missed an "as" ;)
ReplyDeleteAs Bill points out, the identities say nothing about causality as identities, but they can be interpreted causally in terms of a theory and then these assertions of causality can be investigated empirically by formulating testable hypotheses.
ReplyDeleteInvestment only precedes saving in the sense that that an increase in firm equity through expenditure in the period gets reflected the income statement of the owners has an add to their equity.
ReplyDeleteBasically firms make consumables that households consume and firms invest in additions to capital which is owned by the households that own the firms.
That's the total of (household) income = (firm) expenditure, or Y = GDP in a closed economy w/o govt.
Y,
ReplyDeleteSince (G-T) and (X-M) both refer to a flow of funds over some period into or out of the government and external sector, it follows that (S-I) must also refer to a flow of funds over some period into or out of the private sector.
But I (investment) does not necessarily refer to a flow of funds out of the private sector (particularly in the case of house building). Thus the units employed on one side of the equation are not the same as the units employed on the other, which makes a nonsense of the equation.
It’s a bit like saying a car going at 100 miles an hour in some sense equals a bit of furniture which weights 100 kilos.
In contrast, if we define S as simply the flow of funds into or out of the private sector, and leave investment out of it, then the equation makes sense, as I pointed out a year ago here
http://ralphanomics.blogspot.co.uk/2012/02/alternative-sectoral-balance-equation.html
Put another way, you claim that investment is part of the definition of savings. OK: in that case, what’s investment doing in the equation as a separate entity? It shouldn’t be there, should it?
Yours, confused.
Ralph,
ReplyDeleteIf S and I increase by the same amount, then quantity (S - I) is unchanged. E.g., let /a/ be the increase in both S and I, representing new real estate investment or whatever. Then,
(S + a) - (I + a) = (S - I) + (a - a) = (S - I)
If I = 0, then quantity (S - I) reduces back to S, regardless of the magnitude of a.
But I (investment) does not necessarily refer to a flow of funds out of the private sector (particularly in the case of house building)
Investment does not refer to a flow of funds out of the private sector _at all_. Funds flow *into* investment. Investment is a /use/ of funds.