Public deficits = net private savings

Economics Economics Questions
1

I am told that this is taught in macro 101. I took macro 101 many years ago and never learned this accounting identity. I’m currently trying to look up the explanation, but I can’t find the casaulity.

I find that Austrians are better at explaining this stuff than others, so can anybody explain the reasoning?

The best I can find so far is,

The real (inflation-adjusted) national income, Y, is defined as
Y = G + X – M + PX + I

Y = GNP
G = Govt’ spending
X = exports + foreign transfers + property income
M = imports
PX = Private spending
I = Private investment (note, I left this out by mistake the first time. Sorry!)

Subtract T from each side, where T is taxes and government transfers we get

Y – T – PX - I = [G – T] + [X – M]

Private Net Savings = [G – T] + [X – M]

Private Net Savings is GNP - taxes - private spending (PNS is private disposable income less taxes less private spending on consumption less private investment).

Is the assumption that government expenditure constitutes savings?

2

If the government runs deficits, then it issues bonds. It’s generally assumed that private individuals purchase these bonds. Thus, government deficits = private savings. Of course, it isn’t as simple in real life.

3

Probably an attempt to count the “bonds” as private assets or something.

4

If the government runs deficits, then it issues bonds. It’s generally assumed that private individuals purchase these bonds. Thus, government deficits = private savings. Of course, it isn’t as simple in real life.

What about savings held in other forms, like privately issued bonds?

5

From my macro 101 textbooks (which I still have on my bookshelf five years after having taken that class!):

Private savings is income, Y, minus taxes, T, minus consumption, C. So Sprivate = Y - T - C

Public savings is taxes, T, minus government spending, G. So Spublic = T - G

The only way to realize public savings is for the government to not spend more than it brings in as revenue through taxation.

Both public and private savings become national savings, S. National savings, S, can be substituted with the formula Y - C - G.

Then it goes into some gibberish about savings being equal to investments.

6

The definition of Private Net Savings does not include private investment I. I would prefer that instead of Net Private Savings that you bring I to the right side of the equation and define the left side as Gross Private Savings to make government and foreign trade effects on private investment more appearant. So looking at the equation you will see that by simply increasing govenrment spending or restricting imports will in fact increase Net Private Savings. But that increase may not be from an increase in GNP:Y, it could come from a decrease in PX or worse I, or most likely a combination of all 3. This is why most economists are against tariffs and trade restrictions as the accounting of imports means that for every dollar paid out is also a future dollar of private investment or exports. I will grant that the realtionship between government spending and private investment is not as direct but you can see from the latest recession that Net Private Savings (Excess Bank Reserves for example) are up, private investment is down (As shown by the stock market and real estate prices) and private spending is down as government deficit spending has soared and the jackasses in government have devalued money and placed trade barriers on foreign goods.

7

The Keynesian national accounting formulas are often elaborated more in an intermediate level macro class, I wouldn’t be surprised if they weren’t in your macro 101 class. But anyways . . .

National Income Accounting

In a private economy, excluding government:

Y = C + S

Y = National Product or Income
C = Private Consumption (Domestic)
S = Private Savings (Domestic)

Keep in mind the above formula allocates money income between consumption and savings. Introducing the government sector:

Y = C + S + (TA - TR)

TA = Taxes
TR = Transfer Payments (money transfers from one group to another, e.g. welfare, social security, etc.)

Thus money income is also allocated to government taxes, then “refunded” back through transfer payments. Introducing the goods and services side:

Y = C + I + G

C = Private Consumer Goods and Services
I = Private Investment Goods and Services (e.g. capital goods, inventory, etc.)
G = Government Spending on Goods and Services

For now, the external sector (imports and exports) are excluded, so the economy is at autarky. Balancing both sides of the equation:

C + S + (TA - TR) = Y = C + I + G

Left side of the equation is the allocation of money income, while the right side of the equation are the goods purchased with the money income. Think about it this way:

Money Income Goods and Services Explanation
C C Consumption buys Consumer Goods and Services
S I Savings buys Investment Goods and Services
TA G Taxes buys Government Goods and Services

Take the equation and simplify as follows:

C + S + (TA - TR) = Y = C + I + G

S + (TA - TR) = I + G

S - I = G - (TA + TR)

S - I = G + TR - TA

Take a closer look at the last equation:

S - I = (G + TR) - TA

The (G + TR) represents government spending on goods, services, and transfer payments. The TA is taxes.

Balanced Budget

In a balanced budget, government spending is equal to government taxation. In other words (G + TR) is equal to TA, so that:

(G + TR) - TA = 0

Because the economy is in equilibrium, S (which represents Savings) is equal to I (which represents Investments):

S = I

S - I = 0

Therefore, equating the savings-investment side with the government spending taxation side:

S - I = (G + TR) - TA = 0

Budget Deficit

For the government to be in a budget deficit, such that it spends more than it taxes, this would have to happen:

(G + TR) > TA

S > I

Private savings is allocated between the budget deficit and private investment. Move I (for investments) from the left side to the right side of the equation, and this becomes apparent:

S - I = [ (G + TR) - TA ]

S = [ (G + TR) - TA ] + I

Therefore private savings finance the government budget deficit, usually through purchasing government bonds.

No. For the government expenditure to constitute “savings”, there would have to be a budget surplus. In other words, investments are greater than savings.

If it is a privately issued bond, which strictly finances a private good or service, then it is classified as private investment, and thus would not finance the budget deficit.

8

Btw, the definition of “bond” in finance is a loan with collateral. So, there is no such thing as a government bond.

9

If the government runs deficits, then it issues bonds. It’s generally assumed that private individuals purchase these bonds.

Isn’t the cenral bank (or other reserve institution) supposed to purchase these bonds if private lenders are not enthusiastic? I thought this is part of the concept of “lender of last resort” (the other being bailing out of other insolvent institutions).

10

Btw, the definition of “bond” in finance is a loan with collateral. So, there is no such thing as a government bond.

The texts which I studied define bond simply as securitized debt.

On the other hand, government bonds are frequently used as a collateral for other loans. For example, a government G issues a bond (“G will pay the holder of this instrument 1M of USD on 01.01.2011”), a bank B buys the bond at a discount (say, for 800K USD), then uses the bond as a collateral to get a loan from a cental bank C (800K USD, to be repayed as 900K USD on 31.12.2010). This way, if you look at the cash balances, C has virtually lended 800K to G, using B as a middle man (C has -800K, G has +800K, B has 0). When 2011 arrives, the loan and the bond mature, and the final balance is C +100K, G -200K, B +100K - the banks have earned interest (C on the money it “printed”, B on the money it got from C).

Disclaimer: I am not an expert, so you should take this scenario with a grain of salt. Any comments from experts are highly appreciated.

11

I guess the definition in some circles changed after securitization was invented. Point is, you can’t take anything from the good ol’ gov if they don’t pay up.

12

I guess the definition in some circles changed after securitization was invented.

I just intended to demonstrate how different can be definitions. In scope of this thread I am using the definition compatible with the one on Wikipedia (basically an IOU).

13

If it is a privately issued bond, which strictly finances a private good or service, then it is classified as private investment, and thus would not finance the budget deficit.

Ok, so as per the thread’s title public deficits =/= net private savings. Or, are how are net private savings defined?

14

Technically, net private savings can equal the budget deficit, but it does not have to. Here is why. Introduce the external sector with international trade:

(S - I) - (X - M) = (G + TR) - TA

X = Exports
M = Imports

Let’s assume domestic savings is equal to domestic investment, then S - I = 0, so that:

M - X = (G + TR) - TA

Therefore, given that domestic savings is equal to domestic investment, a trade deficit (M - X) can finance the budget deficit at 100%, with no net private savings supplied by the domestic private sector.

Net private savings can be stated as (at budget deficit with government public dis-saving):

S - I = (G + TR) - TA

Net private investment can be stated as (at budget surplus with government public saving):

I - S = TA - (G + TR)

From my perspective, net private savings would be defined as private savings in excess of private investment.

15

I took many Keynesian classes in the last 3 yrs.

The accounting framework you used is the expenditure side of GDP. Based on this (assuming government does not finance deficits with new money) we can see the flaws of Keynesian thought.

BUT

If instead you had used the income side, although still illogical the outcome could have been different.

Yet another formula for GDP by the income method is:

GDP = R + I + P + SA + W

where R : rents
I : interests
P : profits
SA : statistical adjustments (corporate income taxes, dividends, undistributed corporate profits)
W : wages

AGGREGATION IS JUST STUPID.

Jonathan M. F. Catalán wrote the following post at Wed, Jul 14 2010 9:14 PM:

I am told that this is taught in macro 101. I took macro 101 many years ago and never learned this accounting identity. I’m currently trying to look up the explanation, but I can’t find the casaulity.

I find that Austrians are better at explaining this stuff than others, so can anybody explain the reasoning?

The best I can find so far is,

The real (inflation-adjusted) national income, Y, is defined as
Y = G + X – M + PX + I

Y = GNP
G = Govt’ spending
X = exports + foreign transfers + property income
M = imports
PX = Private spending
I = Private investment (note, I left this out by mistake the first time. Sorry!)

Subtract T from each side, where T is taxes and government transfers we get

Y – T – PX - I = [G – T] + [X – M]

Private Net Savings = [G – T] + [X – M]

Private Net Savings is GNP - taxes - private spending (PNS is private disposable income less taxes less private spending on consumption less private investment).

Is the assumption that government expenditure constitutes savings?

16

From my perspective, net private savings would be defined as private savings in excess of private investment.

This is the answer then. It’s just a lack of understanding of the definitions. My initial reaction was based on the idea that “net private savings” was all private savings, and so I didn’t see the causality between deficits and net private savings. But, now that I understand that “net private savings” exclude savings that have been invested by the private sector, there’s no more confusion.

So, net private savings simply refers to savings held by people financing government debt, minus the capital surplus(?).

17

This is Keynesian theory, so we’re not concerned about capital. :slight_smile:

But honestly, I’m not too clear what you meant by “capital surplus”, so perhaps you can clarify?

18

i.e trade deficit. I meant capital account surplus.

19

Net private savings would be an increase in government debt privately financed minus the capital account surplus, within a given time period.

This can be otherwise stated as:

S - I = [ (G + TR) - TA ] - (M - X)

S - I = Net Private Savings (private domestic savings minus private domestic investment)
G + TR = Government Spending
TA = Taxes
M - X = Current Account Deficit (contra Capital Account Surplus)

20

This is apparently the source for the fuss about “net private savings”:

http://krugman-in-wonderland.blogspot.com/2010/07/is-deflation-enemy-or-is-it-inflation.html

There’s someone posting some arguments, which frankly, don’t make any sense, even from a Keynesian point of view. I will take a look into this.