First, as promised, will show the very simple but not arguable math on which this is based.
We learn in Econ 101 (51 years ago for me!), we learn that:
GDP = C + G + I + (X - M), or
GDP = Consumption + Government + Private Investment + (Exports - Imports)
This is the Sources side. There is an equivalent Uses side:
GDP = C + S + T, or
GDP = Consumption + Savings + Taxes, so:
C + G + I + (X - M) = C + S + T
Strike out the Cs', transpose, and you have:
(G-T) + (X - M) = (S - I)
The left side is the Sources - Deficit plus Current Account Surplus
The right side is Uses - Net Private Savings
Sources must equal Uses, or Sources and Uses must net to zero.
And here is this described in some detail by the Pragmatic Capitalist :
To see this in the context of the teeter-totter model, let’s initially hold the public sector’s balance constant at zero (i.e. let’s assume the government is balancing its budget so that G = T). With the government budget in balance, Uncle Sam is a “weightless” entity on the teeter-totter, so that the private sector’s financial position will simply reflect the “weight” of the capital account. Suppose, first, that the current account is in surplus (i.e. the capital account shows an equivalent deficit):
The image above depicts the benefit (to the private sector) of a current account surplus (a.k.a a capital account deficit), and it is the outcome that many of you accused me of sidestepping in my previous post. Of course, the U.S. does not have a current account surplus, so let’s address that point before moving on. (And lest anyone begin to hyperventilate, I’ll also address the fact that G ≠ T). First, the current account.
Sticking with (G = T) for the moment, we can show how a current account deficit impacts the private sector’s financial position. As the capital account moves from deficit (diagram above) into surplus (diagram below), we see that the private sector’s financial position moves from surplus into deficit.
But does this all of this hold true in the real world, or is it some kind of economic chicanery? Let’s check the facts.
Equations  and  above are not based on economic theory. They are accounting identities that always “add up” in the real world. So let’s firm up the discussion about the implications of government “belt tightening” by running through some examples using the real world data found in the table below (Hat tip to Scott Fullwilir for sharing the file. All of the data comes from the National Income and Product Accounts (NIPA) and the Flow of Funds.)
Let’s begin with the data from 1998 (Q3), when the public sector deficit was just 0.01% of GDP and the current account deficit was 2.56% of GDP. Plugging these numbers into equation  above, the identity tells us (and the data in the table confirm) that the private sector’s balance must have been:
 Domestic Private Sector’s Balance = 0.01% + (-2.56% )= -2.55%
Here, we can see that the private sector’s financial position was deteriorating because it was making large (net) payments to foreigners. Because this loss of financial resources was not offset by the public sector, the private sector’s financial position deteriorated.
To see how a bigger government deficit would have improved the private sector’s financial position, let’s look at the data from 1988 (Q1). As a percent of GDP, the current account balance was 2.59%, nearly the same as before, while the government’s deficit came in at a much higher 4.2% of GDP. We can use Equation  to see effect of the larger budget deficit:
 Domestic Private Sector’s Balance = 4.2% + (-2.59%) = 1.61%
In this period, the private sector ends up with a surplus because the government’s deficit was large enough to more than offset the negative effect of the current account deficit.
Again, this is simply a property of the sectoral balance sheet identities. Whenever the government’s deficit is too small to offset a deficit in the current account, the private sector will experience a net loss. The result my ruffle your feathers, but it is an unimpeachable fact.