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Referring to this question and this one

Imagine you had a closed economy with two people and they both started off with $100 dollars. How would net savings in aggregate ever not be zero? Anything spent, net, by person 1 would be a positive savings for person 2, and a negative savings for person 1. The same is true vice versa.

I understand that if person 1 and person 2 both produced 10 bushels of wheat and then ate only 5 of them, and then ground up the other five and used them as fertilizer (bad example, I know) that they would have 'saved' and 'invested' 10 bushels of wheat in aggregate. However, in monetary terms, the personal savings rate in aggregate would still be zero because they didn't sell the wheat to anyone and thus had no personal income (again, in dollar/monetary terms).

So, to sum up, my first question is, in monetary terms, in a closed economy will aggregate savings always be zero?

Second, how does the BEA get a positive savings rate, and how do we have positive gross national savings, in addition to running a trade deficit?

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I think this boils down to misunderstanding what saving in macroeconomics is. Saving does not cancel each other out. In closed economy, private saving is difference between income (which is by definition equivalent to output so I will be using output and income interchangeably) and consumption $S=Y-C$ and public saving is difference between government spending and taxes $T-G$. In your case there are only private individuals so let us assume there is no government so that $T=G=0$ and consequently national identity will be given just by $Y=C+I$ (also note this shows that investment and saving must be equivalent since $Y=C+I \implies Y-C=I \implies S=I$). See Blanchard et al Macroeconomics a European Perspective for further explanation of those identities.

  1. You you can't just save without having income. The money you saved in previous time periods would be part of your net wealth. For example, if in 2010 nothing is produced and sold both individuals have no income and thus cannot form any new saving. In this example saving for 2010 would be 0. The money they hold from previous time period would be their net wealth. However, note in this case there cannot be any consumption either and consumption will be zero. Why? If there is no income and production there cannot be any consumption as well. If something would be produced in 2009 and it was not consumed in 2009 so that it is still avaiable for purchase in 2010 it would be recorded as an inventory investment. So in your example, no matter what those people do $Y, C$ and $I$ are all zero $Y=C=I=0$.

  2. If they actually produce something saving is totally possible. Consider the following trivial example, suppose the person A produces in 2010 $\\\$75$ worth of widgets and person B produces in 2010 $\\\$50$ worth of food. This means that the national income in 2010 will be $Y=50+75={\\\$}125$. Now let us suppose person A buys all food from person B for $\\\$50$ and person B buys $\\\$50$ of widgets from person A. In this case consumption for B is $C={\\\$}50$ and B has zero savings since for B we have $Y_B-C_B=0$. However, A will have some saving since for A income was $Y_A={\\\$}75$ and consumption was $C_A={\\\$}50$ so there is $S_A=Y_A-C_A={\\\$}75-{\\\$}50={\\\$}25$ which on national accounts will turn up as and inventory investment. So everything balances since $Y=C+I$ holds as we have $Y_A+Y_B ={\\\$}125$

  3. Note it makes no difference whether everything is expressed in purely monetary units or real terms. In above I assumed all those quantities are expressed in nominal, so monetary terms, but I could as well just make them real by deflating those prices by some deflator. The equality would still hold equally well.

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    – 1muflon1
    May 7 at 8:39
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To answer your first question: You are correct. Financial saving is always zero. Every new financial asset must have a corresponding financial liability.

The reason why overall saving is reported as a positive number is that this saving included non-financial saving -i.e. saving in tangible goods. Non-financial saving is equal to the level of investment.

Hope helpful

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System of National Accounts

This 117 page reference is an introduction to the outdated standard called 1993 System of National Accounts:

https://www.imf.org/external/pubs/ft/pam/pam56/pam56.pdf

Table 1 on page 20 is shown below:

1993 SNA Framework

The Capital Account is supposed to accumulate the net increase of non-financial assets and this equals the difference between aggregate total income and consumption spending. There is a statistical error however when making efforts to measure investment in nonfinancial assets and measure income and consumption via flow transactions. Anyway this is the idea that saving income really means spending for investment in nonfinancial capital. This is a tautology or economic definition of "saving" "investment" and "consumption" in the system of national accounts (SNA).

The financial accounts are efforts to measure aggregate net lending and borrowing. These are flows of credit some of which are linked to the production of nonfinancial capital (so-called saving equals investment) and some of which are linked to refinancing capital that already exists in the opening balance sheet. In theory net financial saving is zero because for every financial asset there is a matching liability.

The aggregate economy should have a financial identity which I approximate as follows:

N = F + K - L

where if the economy is closed domestic variety then financial assets F equal liabilities L and national net worth is given by N = K which is the valuation of nonfinancial assets, in monetary terms, stated in the opening and/or closing balance sheet.

If there are net exports or imports financed by net lending and borrowing via the respective domestic and foreign financial sectors then there is a net lending and borrowing factor in the net worth of the respective nations in addition to the valuation of nonfinancial assets.

The advocates of so-called Modern Monetary Theory (MMT) argue that a fiat Sovereign government that runs a persistent budget deficit provides net financial assets to the other domestic sectors. Bill Mitchell shows these financial assets accumulating in the non-government tin shed in an illustration on this blog page: http://bilbo.economicoutlook.net/blog/?p=381.

In the United States flow of funds the concept of the "balanced budget" shows up as follows:

Ns = Fs + Ks - Ls = 0

where the federal government (sovereign) kept net worth roughly equal to zero in the Integrated Macroeconomic Accounts (SNA-IMA) prior to going off the gold standard in 1971. However since then the federal government has accumulated negative net worth shown in the official published statistics. This means the government can simply debit its net worth Ns for a decrease when issuing liabilities Ls which are in demand by the investors who store financial assets in the nongovernment tin shed.

The net worth of the United States is to some degree an accounting fiction because vast tracts of federal land are given no valuation and because financial assets and nonfinancial assets are recorded at historical cost. The world seems to be content, for the time-being, to allow the federal government of the United States to provide cash flow insurance to the world financial system independent of its stated net worth.

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