What would dollar depreciation bring?

From the National Bureau of Economic Research, here is the latest on the J-curve:

The pattern of international trade adjustment is affected by the continuing international role of the dollar and related evidence on exchange rate pass-through into prices.  This paper argues that a depreciation of the dollar would have asymmetric effects on flows between the United States and its trading partners.  With low exchange rate pass-through to U.S. import prices and high exchange rate pass-through to the local prices of countries consuming U.S. exports, the effect of dollar depreciation on real trade flows is dominated by an adjustment in U.S. export quantities, which increase as U.S. goods become cheaper in the rest of the world.  Real U.S. imports are affected less because U.S. prices are more insulated from exchange rate movements — pass-through is low and dollar invoicing is high.  In relation to prices, the effects on the U.S. terms of trade are limited: U.S. exporters earn the same amount of dollars for each unit shipped abroad, and U.S. consumers do not encounter more expensive imports. Movements in dollar exchange rates also affect the international trade transactions of countries invoicing some of their trade in dollars, even when these countries are not transacting directly with the United States.

Here is the paper.  This asymmetry is no accident but rather stems, in large part, from the central role of the dollar as a reserve currency and a medium for invoice pricing.  When an Asian export is priced in terms of dollars in the first place, exchange rate movements lead to less pass-through.  In other words, to the extent we would see an improvement in our trade balance, from dollar depreciation, it would be vis-a-vis the countries with the highest propensity to consume more American exports.  It would not be with the countries whose exports we are most likely to consume.  This also means that we cannot in every way extrapolate European currency experience to the United States.