Does the math really add up on these potential solutions to our economic problems?

A number of economists of the liberal Keynesian persuasion have been arguing recently that dollar devaluation is an important step in moving us back toward full employment. In principle, of course, a cheaper dollar should raise US exports and lower US imports. But what's missing from many of these arguments is a concrete, quantitative analysis of how much a lower dollar would raise demand for American goods.

In the interest of starting a discussion, here is a very rough first cut. There are four parameters to worry about, 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. But once we assign values to them, it's straightforward how to calculate the effect of a given exchange rate change. And the values reported in published studies suggest that the level of the dollar is a relatively minor factor in US unemployment.

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's global 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 (2007), -0.93; Crane, Crowley and Quayyum (2007), -0.47 to -0.63; Mann and Plück (2005), -0.28; Marquez (1990), -0.63 to -0.92. (Studies that use the real exchange rate rather than import prices generally find import elasticities between -0.1 and -0.25, which is consistent with 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 value beyond -1. Estimated export elasticities vary more widely, but most fall between -0.5 and -1.

So let's use values near the midpoint of the published estimates. Let's assume import passthrough of 0.33, import price elasticity of -0.75, export passthrough of 1 and price elasticity of -1. 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, the US trade deficit shrinks by 1.9 percent of GDP.

That might sound like a lot. 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 dollar keeps falling. This is less than half the size of the stimulus passed last January. (Although to be fair, increased demand for tradables should have a higher multiplier than the mix of direct spending, transfers and tax cuts that made up the Obama stimulus.) The employment effect would probably be of the same magnitude -- a reduction of the unemployment rate by between 0.5 and 1.0 points.

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So it's not a trivial effect, but it's also not the main thing we should be worried about if we want to get back to broadly-shared prosperity. We should remember, too, that a policy of boosting US demand by increasing net exports has costs that a policy of boosting domestic demand does not.

And what about China? At least as often as we hear calls for a lower dollar, we hear calls for China to allow its currency to rise. How much could that help?

Unfortunately, there aren't as many good recent studies of bilateral trade elasticities between the US and China. And the BEA's published series for Chinese import prices only goes back to 2003, which isn't enough for reliable estimates. But common sense can get us quite a ways here. In recent years, US imports from China have run around 2 percent of GDP, and US exports to China a bit under 0.5 percent. So even if we assume that (1) a change in the nominal exchange rate is reflected one for one in the real exchange rate, i.e. that it doesn't affect Chinese prices or wages at all; (2) a change in the real exchange rate is passed one for one into prices of Chinese imports in the US; (3) Chinese goods compete only with American-made goods, and not with those of other exporters; and (4) the price elasticity of US imports from China is an implausibly high 1.5; then a 20 percent appreciation of the Chinese currency only provides a boost to US demand of less than one half of one percent of GDP in total, spread out over several years.

And of course, those are all wildly optimistic assumptions. A recent Deutsche Bank report uses an estimate of -0.6 for the exchange rate elasticity of Chinese exports. They don't give any estimates for US-China flows specifically, but given the well-established empirical fact that US imports are unusually exchange-rate inelastic, we have to assume that the number for Chinese exports to the US is substantially smaller than for Chinese exports overall. Consistent with that, my own simple error-correction model, using 1993-2010 data and the relative CPI-deflated bilateral exchange rate, gives an exchange rate elasticity of US imports from China of -0.17. If the real figure is in that range, then a Chinese appreciation of 20 percent will reduce our imports from China by just 0.03 percent of GDP -- and of course much of even that tiny demand shift will be to goods from other low-wage exporters. This last point makes a focus on the Chinese peg particularly problematic as an explanation of US unemployment. If you are talking about reducing the value of the dollar against our trading partners as a whole, any resulting shift away from imports has to be to domestic goods. But presumably the closest substitutes for Chinese imports are usually other imports, not stuff made in the USA.

These are rough calculations and only intended to start a conversation. But it's a conversation we very much need to have. Before we launch a trade war with China for the sake of American workers, we need more concrete answers on the size of the potential gains.

Historically-minded critics of China and other surplus countries often quote Keynes' writings from the 1930s and '40s, with their emphasis on the importance of "creditor adjustment". The implication is that it's China's responsibility to reduce its net exports. But this is a misleading reading of Keynes. In fact, his concern was only ever to ensure that no country was prevented from pursuing full employment by the need to earn foreign exchange. The US, as the supplier of the world reserve currency, cannot face a balance of payments constraint; if we fail to pursue full employment, we have no one to blame but ourselves. If Keynes were alive today, I suspect he would be telling American policymakers to forget about China and focus all their efforts on boosting US demand -- by public investment in infrastructure, by unconventional monetary stimulus, by paying people to dig holes and fill them up again if need be. Because he knew that the only reason to worry about the trade balance was to gain the freedom to pursue "a policy of an autonomous rate of interest, unimpeded by international preoccupations, and of a national investment program directed to the optimum level of domestic employment, which is twice blessed in the sense that it helps ourselves and our neighbors at the same time."

J. W. Mason is a graduate student in economics at the University of Massachusetts, Amherst. A version of this post previously appeared at The Slack Wire.