(Shaking head) Noah Smith is a professor of finance and he doesn't know the answer to this — although granted it is not very clearly stated as "government deficits equal private surpluses," as Jan Hatzius does, whom Noah quotes.
It is clearer to say that the government fiscal deficit equals the consolidated nongovernment fiscal surplus in aggregate, since the government balance plus the consolidated domestic private sector balance plus the external balance must sum to zero as an accounting identity. Transposing, the government balance will be the inverse of the consolidated nongovernment balance in aggregate.
If the external balance is zero, then the government balance and the domestic private sector balance must sum to zero, therefore, must be in inverse relationship. In this case, if government net spends by running a deficit, then the domestic private sector saves the same amount in aggregate wrt net financial assets. And vice versa.
If the both the external sector and the government sector are in balance, then the domestic private sector must also as an identity. There can be net savers but not net savers in aggregate, since accounts within the sector must balance, i.e., net to zero.
Hint to Noah: Read Godley and Lavoie,
Monetary Economics for an explication of stock-flow consistency in sectoral balance accounting. Jan Haztius learned this from Wynne Godley, and it is the basis of MMT SFC macro modeling. This is really simple when you do the accounting properly.
While accounting identities don't say anything about the causality, they do reveal what is necessary and what is impossible in terms of stock flow consistency. Mixing up stocks and flows is a novice error.
Noahpinion
Thinking out loud: Do government deficits equal private surpluses?
Noah Smith | Assistant Professor of Finance, Stony Brook University