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Would someone help me understand the math/accounting behind the following:

"To be precise, the financial balance of the private sector (the excess of domestic saving over domestic investment) must always just equal the sum of the government budget deficit and the net export surplus. "

This says in English that total private domestic savings (S) is equal to private domestic 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.

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.

When there is an external surplus, the public (budget) balance may be in surplus while still permitting the private domestic sector to save. This is the Norwegian situation.

But when private savings desires are strong (and overwhelm the external surplus) as in Japan, then you have to have a public (budget) deficit to support growth.

which says that total national income (GDP) is the sum of total final consumption spending (C), total private investment (I), total government spending (G) and net exports (X – M).

From the uses perspective, national income (GDP) can be used for:

GDP = C + S + T

which says that GDP (income) ultimately comes back to households who consume (C), save (S) or pay taxes (T) with it once all the distributions are made.

Equating these two perspectives we get:

C + S + T = GDP = C + I + G + (X – M)

So after simplification (but obeying the equation) we get the sectoral balances view of the national accounts.

(I – S) + (G – T) + (X – M) = 0

That is the three balances have to sum to zero.

You can also write this as:

(S – I) + (T – G) = (X – M)

Which gives an easier interpretation (especially in relation to this question).

The sectoral balances derived are:

The private domestic balance (S – I) – positive if in surplus, negative if in deficit. The Budget balance (T – G) – positive if in surplus, negative if in deficit. The Current Account balance (X – M) – positive if in surplus, negative if in deficit. These balances are usually expressed as a per cent of GDP but that doesn’t alter the accounting rules that they sum to zero, it just means the balance to GDP ratios sum to zero.

Using this version of the sectoral balance framework:

(S – I) + (T – G) = (X – M)

So the domestic balance (left-hand side) – which is the sum of the private domestic sector and the government sector equals the external balance.

Another basic question on MMT, to help me understand better, if you do not mind:

What are the basic accounting debits and credits that occur when the federal government spends?

From what I have read, bank accounts of recipients are "credited", the Treasury is "debited" and Bank Reserves are "credited." Is that right and if so, where is the other "debit" to balance the accounting?

Crake. When Treasury spends it marks up the deposit account of the supplier and marks down its reserves account at the Fed to clear.

Notice that there is no corresponding liability created in nongovernment when the Treasury spend. The liability is on the side of government. This is why nongovernment NFA increase.

To answer your question, Crake, in order to obtain the reserves it needs from the Fed in order to clear its payments, Treasury issues tsys as a Treasury liability against the asset reserves) receives from the Fed.

Because the Fed is prohibited by law from taking the tsys from the Treasury onto its books, it auctions them and credits the Treasury's reserve account at the Fed with the payments it receives from the PD's. (It's a bit more complicated than this because of the TT&L accounts but this is the basic idea.)

## 11 comments:

Would someone help me understand the math/accounting behind the following:

"To be precise, the financial balance of the private sector (the excess of domestic saving over domestic investment) must always just equal the sum of the government budget deficit and the net export surplus. "

Crake. Sometimes prose is not the best way to describe concepts.

Here you go from wikipedia.

It really is just simple algebra.

http://en.wikipedia.org/wiki/Twin_deficits_hypothesis

I don't want to confuse you. The math in that wiki is correct. The causality is not. Since it doesn't hold true at all times.

So what is correct?

http://www.thomaspalley.com/?p=63

Bill Mitchell:

(S – I) = (G – T) + (X – M)

This says in English that total private domestic savings (S) is equal to private domestic 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.

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.

When there is an external surplus, the public (budget) balance may be in surplus while still permitting the private domestic sector to save. This is the Norwegian situation.

But when private savings desires are strong (and overwhelm the external surplus) as in Japan, then you have to have a public (budget) deficit to support growth.

Thanks. The formulas helped.

(S – I) = (G – T) + (X – M)

seems similar to the GDp forumla of C + I + G + (X-M)

Can you get back to the latter from the former? I assume C is income less S or something.

Crake,

Again from Bill Mitchell:

From the sources perspective we write:

GDP = C + I + G + (X – M)

which says that total national income (GDP) is the sum of total final consumption spending (C), total private investment (I), total government spending (G) and net exports (X – M).

From the uses perspective, national income (GDP) can be used for:

GDP = C + S + T

which says that GDP (income) ultimately comes back to households who consume (C), save (S) or pay taxes (T) with it once all the distributions are made.

Equating these two perspectives we get:

C + S + T = GDP = C + I + G + (X – M)

So after simplification (but obeying the equation) we get the sectoral balances view of the national accounts.

(I – S) + (G – T) + (X – M) = 0

That is the three balances have to sum to zero.

You can also write this as:

(S – I) + (T – G) = (X – M)

Which gives an easier interpretation (especially in relation to this question).

The sectoral balances derived are:

The private domestic balance (S – I) – positive if in surplus, negative if in deficit.

The Budget balance (T – G) – positive if in surplus, negative if in deficit.

The Current Account balance (X – M) – positive if in surplus, negative if in deficit.

These balances are usually expressed as a per cent of GDP but that doesn’t alter the accounting rules that they sum to zero, it just means the balance to GDP ratios sum to zero.

Using this version of the sectoral balance framework:

(S – I) + (T – G) = (X – M)

So the domestic balance (left-hand side) – which is the sum of the private domestic sector and the government sector equals the external balance.

Link_http://bilbo.economicoutlook.net/blog/?p=13959#more-13959

Resp,

Thank you very much. Seeing the forumlas helps me understand it fundamentally.

Another basic question on MMT, to help me understand better, if you do not mind:

What are the basic accounting debits and credits that occur when the federal government spends?

From what I have read, bank accounts of recipients are "credited", the Treasury is "debited" and Bank Reserves are "credited." Is that right and if so, where is the other "debit" to balance the accounting?

Crake. When Treasury spends it marks up the deposit account of the supplier and marks down its reserves account at the Fed to clear.

Notice that there is no corresponding liability created in nongovernment when the Treasury spend. The liability is on the side of government. This is why nongovernment NFA increase.

To answer your question, Crake, in order to obtain the reserves it needs from the Fed in order to clear its payments, Treasury issues tsys as a Treasury liability against the asset reserves) receives from the Fed.

Because the Fed is prohibited by law from taking the tsys from the Treasury onto its books, it auctions them and credits the Treasury's reserve account at the Fed with the payments it receives from the PD's. (It's a bit more complicated than this because of the TT&L accounts but this is the basic idea.)

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