The equation in the title line is important to understanding Modern Monetary Theory (MMT), but the terminology poses some difficulties. My intent is to share some insights.

Here is the standard explanation from “Understanding The Modern Monetary System” by Cullen Roche, which is a go-to MMT resource:

GDP = C + I + G + (X – M)

C = consumption

I = investment

G = government spending

X = exports

M = imports

Or stated differently;

GDP = C + S + T

C = consumption

S = savings

T = taxes

From there we can conclude:

C + S + T = GDP = C+ I + G + (X – M)

If rearranged we can see that these sectors must net to zero:

(I – S) + (G – T) + (X – M) = 0

(I – S) = private sector balance

(G – T) = public sector balance

(X – M) = foreign sector balance

Notice first that all dollar-denominated accounts are partitioned into three sectors: the public (domestic governmental), the private (domestic nongovernmental), and the foreign (everyone else).

That leaves a lot of questions, e.g., where do you put the state governments, where do you put the Federal Reserve and why, and so forth. The blunt answer is that it doesn’t matter. The equation will be true so long as there are three sectors having these names, and every dollar-denominated account belongs to one and only one of these sectors.

The truth of the equation depends only on the two simple facts:
(1) In every transaction, money comes from somewhere and goes somewhere, and the amount that comes (credits) equals the amount that goes (debits), i.e., the transaction balances. (For the sake of simplicity, we may imagine that in every transaction credits one account and debits another by the same amount.)
(2) If you add up the same numbers two different ways, you’ll get the same answer both ways.

Now the GDP over a period of time is simply a bunch of transactions each of which has a one of four purposes with the amount going to each purpose designated as follows:

T: to pay taxes

C: to purchase consumables (services, food, gas, etc.)

I: to invest in nonconsumables (stocks, bonds, houses, coffee pots, etc.)

(S-I): to save as a non-investment (e.g., in bank accounts, in pockets, in purses, under mattresses, etc.).

Similarly, the money for the transactions that make up the GDP comes from one of four places:

G: government spending

C: the purchase of consumables

I: investments

(X-M): exports minus imports, i.e., our trade surplus, which can be negative

Now from the fact that money-in equals money out we get the equation that: G + C + I + (X-M) = T + C + I + (S-I).

But the most basic algebra allows us to cancel a C and an I from each side, leaving G + (X-M) = T + (S-I).

By subtracting T from each side and flipping the equality we obtain (S-I) = (G-T) + (X-M), which is the equation in the title of this article.

What that says is that, taken over any period of time (e.g., the big bang until now), our uninvested savings (S-I) will equal our national deficit (G-T) plus our trade surplus (X-M). And that will be true no matter how you define each term, just so long as the source-for and the purpose-of each transaction gets classified in one and only one way.

Another way to look at it is: (G-T) = (M-X) + (S-I), which says quite literally that the portion of our national debt that has not gone to covering our foreign-trade deficit is in our money supply, i.e., in the pockets, purses, and bank accounts of the nation’s private sector.

It’s also interesting to note that the money to cover (G-T) is borrowed and/or freshly issued, but it’s mostly borrowed and specifically borrowed from banks including (indirectly) the Federal Reserve, which now owns 11% of our national debt. The good thing about borrowing from the Fed is that the interest paid on that portion of the national debt is considered to be profit of the Fed, most of which gets returned to the Treasury.

So far as issuing new money is concerned, the Treasury is only allowed to spend the profit on newly issued coins, which constitute (pardon the pun) small change in comparison to the annual deficit.

Disclosure: I’m neither an economist nor an MMTer and would appreciate comment from those more knowledgeable in those matters.