Specifically, I find it confusing that your rows do not sum to zero because their elements can be denominated in different currencies under your notation. The whole thing would be much clearer (if also somewhat more cumbersome) if you had each of the three sectors hold both dollar assets and liabilities and reals assets and liabilities, and explicitly settled the FX transactions implied by the foreign and domestic sectors' willingness to hold non-native currency.

To this end, I prefer to treat all foreign trade as being transacted in either the currency of the trade bloc hegemon (for unspecified trade with RoW) or in the currency of the higher-ranking party (in the case of specific bilateral relationships). I believe that this better reflects the actual constraints imposed by the international trade and tribute system than the symmetric treatment you impose here.

However, qualitatively I believe your conclusion rests upon the key assumption that the private sector's FX reserves operate broadly similarly to the strategic FX reserve. This is false: The private sector FX reserve is largely inaccessible during a national solvency crisis, and the strategic FX reserve is largely inaccessible in the daily operations of a non-crisis economy.

This is why prudent central banks should maintain strategic FX reserves on the order of the gross, rather than the net FX debt of their private sector (plus the net FX debt of any other branches of government).

- Jake

Friends come and go. Enemies accumulate.