Spreading Imports Thin Does Not Mean Exchange Rates Do Not Matter

I am in the middle of a Twitter debate with J.W. Mason. The starting point for the debate is an empirical paper suggesting that real currency depreciation does not increase real exports, but a real currency appreciation decreases real exports (pdf). Let us see if I can clarify my position that there is an implication that real currency depreciation leads to lower real imports.

Let us suppose there are 101 countries and everyone imports \$100 worth of goods from each of the 100 different partner countries, so that each country imports a total of \$10,000 worth of goods. Now suppose that my current depreciates, say, 10% so that everyone else’s currency appreciates 1% 0.1%. Suppose further that a 1% 0.1% appreciation reduces exports by 0.05%.

At first blush it seems that this implies a 0.05% reduction in my imports. After all, if every partner country reduces their exports to every other country by 0.05%, then my imports must fall by 0.05%– almost too small to measure.

But this ignores the fact that my partner countries exchange rates did not appreciate with each other. When each partner loses 0.05% of exports, that partner reduces exports to me by \$5 and exports to the rest of the world by \$0. Thus, my total imports from all countries falls by \$500, or 5% of my initial imports.

Which is to say, I do not understand the position that the reduction in real imports due to depreciation is “formally correct but practically and empirically irrelevant.”