Lots of economists of the liberal Keynesian persuasion (Paul Krugman, Dean Baker, Robert Blecker  -- very smart guys all) think dollar devaluation is an important step in getting back toward full employment in the US. But have any of them backed this up with a quantitative analysis of how much a lower dollar would raise demand for American goods?
It's not an easy question, of course, but a first cut is not that complicated. There are four variables, two each for imports and exports: How much a given change in the dollar moves prices in the destination country (the passthrough rate), and how much demand for traded goods responds to a change in price (the price elasticity.)  We can't observe these relationships directly, of course, so we have to estimate them based on historical data on trade flows and exchange rates. Once we choose values of them, it's straightforward to calculate the effect of a given exchange rate change. And the short answer to this post's title is, Not much.
For passthrough, estimates are quite consistent that dollar changes are passed through more or less one for one to US export prices, but considerably less to US import prices. (In other words, US exporters set prices based solely on domestic costs, but exporters to the US "price to market".) The OECD macro model uses a value of 0.33 for import passthrough at a two-year horizon; a simple OLS regression of changes in import prices on the trade-weighted exchange rate yields basically the same value. Estimates of import price elasticity are almost always less than unity. Here are a few: Kwack et al., 0.93; Crane, Crowley and Quayyum, 0.47 to 0.63; Mann and Plück, 0.28; Marquez, 0.63 to 0.92.  (Studies that use the real exchange rate rather than import prices almost all find import elasticities smaller than 0.25, which also supports a passthrough rate of about one-third.) So a reasonable assumption for import price elasticity would be about 0.75; there is no support for a larger value than 1.0. Estimated export elasticities vary more widely, but most fall between 0.5 and 1.0.
So let's use values near the midpoint of the published estimates. Let's say import passthrough of 0.33, import price elasticity of 0.75, and export passthrough and price elasticity both of 1.0. And let's assume initial trade flows at their average levels of the 2000s -- imports of 15 percent of GDP and exports at 10.5 percent of GDP. Given those assumptions, what happens if the dollar falls by 20 percent? The answer is, US net exports increase by 1.9 percent of GDP.
1.9 percent of GDP might sound like a lot (it's about $300 billion). But keep in mind, these are long-run elasticities -- in general, it takes as much as two years for price movements to have their full effect on trade. And the fall in the dollar also can't happen overnight, at least not without severe disruptions to financial markets. So we are talking about an annual boost to demand of somewhere between 0.5 and 1.0 percent of GDP, for two to three years. And then, of course, the stimulus ends, unless the depreciation continues indefinitely. This is less than half the size of the stimulus passed last January (altho to be fair, increased demand for tradables will certainly have a higher multiplier than the tax cuts that made up a large share of the Obama stimulus.) The employment effect woul probably be of the same magnitude -- a reduction of the unemployment rate by between 0.5 and 1.0 points.
I would argue this is still an overestimate, since it ignores income effects, which are much stronger determinants of trade than exchange rates are -- to the extent the US grows faster and its trading partners grow more slowly as a stronger US current account, that will tend to cancel out the initial improvement. I would also argue that the gain to US employment from this sort of rebalancing would be more than offset by the loss to our trade partners, who are much more likely to face balance of payments constraints on domestic demand.
But those are second-order issues. The real question is, why aren't the economist calling for a lower dollar providing quantitative estimates of its effects, and explicitly stating their assumptions? Because on its face, the data suggests that an overvalued dollar plays only a modest role in US unemployment.
 I was going to include Peter Dorman on this list but I see that while he shares the IMO misplaced concern with global imbalances, he says, "Will a coordinated dollar devaluation do the trick? Maybe, if you can get coordination (no easy feat), but it is also possible that US capacity in tradables has deteriorated too far for price adjustment alone to succeed." Which is a more realistic view of the matter than the one Krugman seems to hold. On the other hand, Dorman was also writing just a couple years ago about The Coming Dollar Crash. That dog that didn't bark is something I'll hopefully be writing about in a future post.
 Many studies collapse passthrough and price elasticity into a single measure of real exchange rate elasticity. While this is a standard approach -- about half the published papers take it -- I would argue it's not the right one for either analytic or policy purposes. Analytically, the real exchange rate elasticity doesn't distinguish between the behavior of buyers and sellers: A low value could mean either that consumers are not responsive to price, or that sellers are holding price stable in the face of exchange rate changes. And on the other side, it's the nominal, not real, exchange rate that's accessible to policy. Policy-induced movements in the nominal exchange rate only translate into movements in the real rate if we assume that price levels (and real wages, if we're deflating by labor costs) don't respond to movements in the exchange rate, which is not generally a safe assumption.
 Price elasticities are all negative of course. I'm omitting the negative sign for simplicity.