Michael Darda pointed me to the following statement from Larry Summers (in reply to Ben Bernanke):
Successful policy approaches to a global tendency towards excess saving and stagnation will involve not only stimulating public and private investment but will also involve encouraging countries with excess saving to reduce their saving or increase their investment. Policies that seek to stimulate demand through exchange rate changes are a zero-sum game, as demand gained in one place will be lost in another. Secular stagnation and excess foreign saving are best seen alternative ways of describing the same phenomenon.
The middle sentence sure looks like reasoning from a price change. Whether currency depreciation is a zero sum game depends entirely on the reason why the currency depreciated. In fairness to Summers, he probably had in mind currency depreciation caused by non-monetary factors. In that case, it may well be a zero sum game.
Nonetheless, I'm not willing to entirely overlook the problem here, for two reasons:
1. The examples of currency depreciation that are currently on everyone's mind are the recent sharp declines in the yen and the euro. In both cases, expansionary monetary policy almost certainly played a major role. One reason we know this is that the respective exchange rates tended to depreciate on statements made by monetary policy officials, and were often accompanied by new policies such as aggressive QE. All you have to do is look at the reaction of global equity markets to realize that monetary stimulus by major economic powers is very much a positive sum game, at least when the global economy is depressed.
2. Summers referred to "policies that seek to stimulate demand through exchange rate changes," which almost all readers would naturally assume applies to monetary policy. Furthermore, this claim occurs in a post that insists that fiscal stimulus is the only solution to "secular stagnation." And of course (like most progressives) when Summers talks about fiscal stimulus, he doesn't have in mind tax cuts to generate growth in the private sector.
When viewed in context, I would guess that about 99% of readers would have assumed that Summers claim applied not just to non-monetary currency depreciation (say due to more government saving) but also to the recent currency depreciation that occurred in Japan and the Eurozone.
Either Larry Summers is mistakenly reasoning from a price change, or he is not doing a very good job in communicating his actual views.
PS. What if Summers claimed monetary stimulus was ineffective due to the zero interest rate bound? In that case monetary stimulus would also fail to depreciate a currency. And that's pretty clearly not the case with the yen and the euro.