One of the less commented upon themes of both parties' conventions was a fear of the U.S. economy being overtaken by China. President Obama bragged that his administration had "stood up to China on behalf of our workers" and railed against education cuts that make it harder to "compete with the scientists and engineers coming out of China." Mitt Romney attacked Obama's energy policies, saying his "assault on coal and gas and oil will send energy and manufacturing jobs to China," while Sen. Rob Portman (R-Ohio) alleged that the administration wasn't doing enough to fight Chinese currency manipulation.

But a new IMF study suggests that industries in Europe are, if anything, more vulnerable than those in the United States.

Right now, European machinery and textile workers are sufficiently more productive than Chinese counterparts. While China has lower per-person labor costs, the lower-tech equipment the country uses reduces productivity. At the end of the day, the final cost of the products they make isn't that much lower than for European-made textile and machinery products.

But that dynamic could change. Fund economists Uffe Mikkelsen and Esther Pérez Ruiz built a model to predict what would happen to different European economies if Chinese workers were to quickly grow more productive. A sudden boost in productivity for textiles would lead prices and GDP to drop across the board in Europe. The economy of Portugal would shrink an astonishing 2 percent, and over 7 percent of Portuguese textile workers would leave the industry. The overall results for the countries studied show a 1 percent drop in GDP and prices, and 2 percent of textile workers leaving the industry:

Source: International Monetary Fund

The results for the machinery industry are less extreme, but more uniform across Europe. Here's what happens if the Chinese machinery industry suddenly gets more productive:

Source: International Monetary Fund

The most dramatic results for GDP and prices are in Germany, a country whose manufacturing industry has been praised as a model for the United States. But if these results are correct, then a more productive China could put at least the machinery manufacturing sector in Germany in serious trouble, with 4 percent of workers leaving the industry (and 3 percent of workers across Europe leaving).

So this is bad news, right? Not necessarily. For one thing, GDP and prices fall by roughly the same amounts in most countries observed, so in real terms, GDP doesn't change much. What's more, the usual worry with falling prices — that they'll lead to a "deflationary spiral" that pushes down production and wages and leads to a prolonged recession — seems ill-placed here, as in most countries, greater Chinese productivity actually leads to an increase in real wages in European countries:

Source: International Monetary Fund

Some countries are hard-hit, like Portugal, Greece, and Italy in the case of textiles, but most countries actually come out ahead.

So is rising Chinese productivity good? To quote Sam Shakusky, who's to say? Portuguese workers certainly don't seem to win from an increase in textile productivity. But most European workers actually come out ahead. What's more, productivity growth will also almost certainly lead to rising wages in China, lifting hundreds of millions of people out of poverty and raising the standard of living considerably in the world's largest country. That may be the most important factor here.