Here is Krugman’s long and complex post, do read it carefully. Here are a few points:
1. Bernanke said that non-secular stagnation in other countries might cause capital outflows and thus exchange rate depreciations in the potentially ss (secular stagnation) countries, thereby boosting their exports and demand.
2. Krugman argues in return that those real interest rate differentials will be offset by expected exchange rate appreciation, so the capital outflows won’t be so profitable. Why switch funds from a stagnating Europe to a non-stagnating India, if expected euro appreciation will wipe out potential profits in India from the point of view of an investor in Europe?
3. I think that is the wrong comparison of interest rates and the wrong metric of expected currency appreciation.
4. Rather than looking at real interest rate differentials, take the market’s implied prediction for the euro to be the forward-futures exchange rates. These futures rates match the differences in nominal rates on each currency across the relevant time horizons. Those equilibrium relationships hold true with or without secular stagnation, whether in one country or in “n” countries, and from those relationships you cannot derive the claim that expected currency movements offset cross-border differences in real rates of return.
4b. (It is the nominal rate here because, from the point of view of a European investor, your final real return in terms of your own unit of account depends on a combination of the nominal rate abroad, combined with expected future currency conversion rates. Got that?)
5. In that setting, rates of return in non-ss countries still will drive capital flows toward those countries (and an exchange rate depreciation, and thus higher exports, for the origin country, in this case the eurozone.)
6. The best way to speak of the non-ss countries, for international economics, is that their corporate sectors offer nominal expected rates of return which are relatively high, compared to their nominal government bond rates. Once you see this as the correct terminology, it is obvious that capital still will flow outwards to the non-ss countries, even with expected exchange rate movements. The excess profits are there, capital flows out, the euro weakens or appreciates less strongly, and eurozone exports are stimulated, as Bernanke had analyzed.
7. Theory aside, some of the empirics suggest exchange rates often are close to a random walk (pdf), as opposed to being predicted by nominal interest rate differentials. This still supports the Bernanke hypothesis.
8. Yes, I am familiar with the Frankel (1979) strand of the literature on how real interest differentials can forecast currency changes, but it is actually a theoretical puzzle that domestically measured real interest rates (sometimes) have had this explanatory power. And most importantly in this literature high real rates of return tend to predict currency appreciation, not depreciation, so funds should flow all the more to the higher return venues. It is not a rigorous relationship in any case. And on top of that Mishkin (1984), among others, has shown such an equalization on the real interest rate, across borders, is rejected by the data.
9. So I agree with Bernanke. We should not think of real interest rate differentials as being washed out by expected currency movements. And then the flow of investment abroad can break the secular stagnation chain of reasoning.
10. Bernanke is not arguing that “currency movements and export boosts will set everything right.” I take him to be suggesting “if the problem were so fully one of the demand-side, currency movement and export boosts could set everything right.” But since it seems they can’t set everything right, we should infer it is not a problem of the demand side only. That is a subtle but important difference in argumentation.
11. Personally, I favor supply-side over demand-side analysis for the long run.