It's true in practice, because of the practical ways in which large-scale capital flows are manifested. The stronger point, that it's true in all cases, is mad

It's true in practice, because of the practical ways in which large-scale capital flows are manifested. The stronger point, that it's true in all cases, is made by Pettis somewhere deep in his blog... and it boils down to the idea that other edge cases diffuse the allocation of debt, investment, capital -- but the identity must still hold true at the level of abstraction of the nation / currency area. Those edge cases tend to look starker (and harder to explain) in toy models, though. I can't really do his argument justice, though. Sorry! I'm simply nowhere near sophisticated enough. But... the case where it's not re-lent, there is still exchange-rate pressure, but the 'missing' capital (say it's not stuck under a mattress, but is instead burned in a furnace) effectively deflates the remaining capital in the economy. The identities still balance. Again, the exact allocation of debt etc doesn't matter to the identity, and it's easy to construct a situation where the capital somehow disappears, or the underlying mechanism (or lack of mechanism) obscures the overall identity. This all works because currency is effectively meaningless, it's a derivative of actual 'value' in an economy, as measured by the total output of goods and services. I'm going to stop here before I butcher it any worse; but if you find this at all interesting, Pettis is a much better source than I.