Noah Smith asks: Do government deficits equal private surpluses? The answer is actually rather simple. When the government runs a deficit (spends more than it taxes) they sell a T-bond to Peter who supplies his bank deposits to the government who then spends those bank deposits into Paul's account. The deposits get redistributed and the T-bond is a new financial asset for the non-government sector. That T-bond is technically a liability of the US Treasury so the US Treasury's new liability is the owner's asset (the Treasury has a new liability and Paul owns the T-bond which is an asset). Said differently, the government's deficit results in surplus for the non-government (some of this surplus could be held by the foreign sector or even the Fed so we really shouldn't say "government deficits equal private surpluses" or the accounting nerds will have our necks!). This is a net financial asset (NFA) because there is no private sector corresponding liability.
That's all pretty obvious. What's more confusing is the way some people use all of this to describe how the monetary system works. For instance, the sectoral balances equation can be broken down from the GDP equation where:
GDP = C + I + G + (X - M)
Where C = consumption, I = investment, G = government spending, X = exports & M = imports
Or stated differently;
GDP = C + S + T
Where C = consumption, S = saving, 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
Where (I - S) = private sector balance, (G - T) = public sector balance & (X - M) = foreign sector balance.
Take that a step further:
(S - I) = (G - T) + (X - M)
Close the foreign sector out and you get:
In other words, the private sector's balance is equal to the public sector's balance. But this view is saving NET OF INVESTMENT. If you view the world through this lens then the private sector can't NET save without government spending and NFA issuance. But is it best to net out investment when trying to understand how the monetary system works? After all, the private sector is built largely on the back of private investment. Using (S-I) to describe private saving is not only misleading in my opinion, but a lot less interesting than some people might have you believe. A really simple example might help clarify this point.
Let's say you borrow $100 to build your dream home and the homebuilder banks at your bank. The bank ends up with a $100 asset and a $100 liability (the loan and the deposit - loans create deposits). The homebuilder will end up with $100 in retained earnings and you will end up with $100 in debt. If you net out the investment (you made $100 in residential real estate investment) then the private sector has no change in financial assets and you might presume the private sector is no better off than it was before. Remember, your $100 investment resulted in $100 in saving for the homebuilder. But are we actually no better off than we were before? Of course not. You have your dream house, the corporation has $100 in profit and the bank will presumably make a profit on its loan. We are all actually better off! In a credit based monetary system this process can go on in perpetuity, but the problem is that a capitalist economy will tend to veer towards disequilibrium. So we don't just build 1 house. We build 1 million houses and then prices get euphoric and then lenders make more loans than present incomes can pay off those loans and you get something like 2008. You don't need government in all of this, but it sure can help if used properly.
For instance, the government can step in like it did in 2008 and provide net financial assets to help improve balance sheets, but that's not really the point here. The point is that (S-I) tells us a very incomplete story about the private sector so focusing too much on it misses the point. Netting out investment is essentially netting out the most important piece of the entire economy. After all, it is investment that makes all of the wonderful things in this world that help us live a better standard of living (in a pure financial sense).
If you wanted to more accurately portray how the private sector saves you might take a step backwards and say:
(S - I) = (G - T) + (X - M)
S = I + (G - T) + (X - M)
Which rearranges to:
S = I + (S - I)
Why do we do this? Well, private investment is the backbone of private sector equity. So the net worth in US households of roughly $70 trillion is largely built on the back of private investment. If you just took (S-I) = (G-T) you might presume that we are all just sitting around sucking our thumbs waiting for the government to spend money and issue bonds so we can live our lives. But that doesn't accurately reflect reality. Net out investment and you've missed the most important piece of the economic puzzle. It's better to start to understand the monetary system by focusing on private investment and thinking of government as an important facilitating piece. Get that backwards and you'll build a world view that gets the relationship precisely backwards by assuming that the monetary system starts with the government.