Does China control the fate of the U.S. labor market? Fred Bergsten, the distinguished director of the Peterson Institute for International Economics, writes that persuading China to boost the value of its currency would be "by far the most cost-effective possible step to reduce the unemployment rate and help speed economic recovery" in the United States.

He claims that "such a trade correction would generate an additional 600,000 to 1.2 million jobs." In this claim he actually underbids competitors such as Paul Krugman (1.4 million jobs) of the New York Times and Rob Scott (2.4 million) of the Economic Policy Institute. Praiseworthy as Bergsten's moderation may be, how does one get a number like his?

Here is his chain of assumptions:

• China will revalue its currency significantly. Bergsten estimates that the renminbi is undervalued by about 40 percent against the U.S. dollar.
• Chinese revaluation will cut the U.S. trade deficit (i.e., increase exports relative to imports).
• Cutting the U.S. trade deficit will bring American jobs.

Every single link in this chain is weak. Let's take them in turn.

Weak link No. 1: While estimates may vary about how much China ought to revalue, there is less quibbling about how much China is likely to revalue. I agree with Gary Hufbauer, also of the Peterson Institute, who writes:

The period between July 2005 and July 2008, when China temporarily abandoned its peg to the U.S. dollar, suggests the maximum extent and pace the Chinese might allow the yuan to appreciate. During that period, the yuan increased 20.15 percent against the dollar; on a per month basis the average increase was 0.52 percent."

So the most likely outcome is a modest appreciation of the renminbi. But even if the United States could compel a 40 percent overnight appreciation, China would be left reeling from the magnitude of the economic shock. It would be unlikely to turn into a vibrant source of demand for Western goods.

Weak link No. 2: If we think that China will reproduce past behavior with a new appreciation policy, we might look at the same time period for guidance on results. As Dan Ikenson of the Cato Institute notes, when China appreciated from 2005 to 2008, "the trade deficit, according to the trade statistics compiled by the U.S. Census Bureau, nevertheless increased to $268 billion from $202 billion." Those are numbers for the economically-meaningless but politically-potent U.S.-China bilateral trade deficit.

How could that move in the wrong direction? For one thing, we live in a multilateral world and U.S. and Chinese trade balances with other countries can shift in offsetting ways. Furthermore, exchange rates are only one determinant of trade balances; changes in consumption and productivity can also matter.

Weak link No. 3: Suppose we nevertheless managed to cut the overall U.S. trade deficit through Chinese reform; at least this would create jobs, right? Here Bergsten bases his argument on some particularly dubious economic reasoning, which claims 6,000 to 8,000 jobs for every billion dollars of exports. That comes from reports like this one yesterday from the Commerce Department.

The model they use roughly works like this: Suppose a firm with 12,000 employees sells $2 billion of manufactures every year and exports half ($1 billion). The analysis assumes that half of the employees are supported by exports, hence 6,000 jobs per billion of exports.

But if you get beyond the headline section of the Commerce report, you hit the cautions from the economists: this does not tell you what the next $100 million of exports will get you. Imagine that the firm exports $100 million more, but cuts its domestic sales by the same amount. That means more exports but probably no more jobs. Or imagine it leaves its domestic sales unchanged, but just asks existing workers to work harder. That, in fact, is what we've seen in this recession, as firm productivity has increased (more output with fewer workers). At annual rates, U.S. manufacturing output per hour worked in the last three quarters of 2009 increased by 6.6 percent, 14.8 percent, and 6.6 percent, respectively.

In normal times, economists routinely scoff at the idea of trade setting the overall number of jobs. The Federal Reserve sets monetary policy to target ‘full employment,' a rate that depends on factors such as the characteristics of the labor force and employment regulation. Trade helps determine the types of jobs, but not the overall number.

Of course, these are not normal times. The Federal Reserve is struggling to boost the economy. Perhaps the old truths do not apply? Perhaps in these difficult times, a cut in the trade deficit will boost jobs?  We can check empirically. From July 2008 to February 2010, the U.S. monthly trade deficit with the world shrank from $65 billion to $40 billion. By Bergsten's reasoning, that should have created 150,000 jobs per month, or 1.8 million at an annual rate. In fact, we lost 7.2 million jobs over the same period.

One might object to this sort of empirical refutation: of course there were other things going on! You cannot just assume that trade explains everything or rely so heavily on a rule of thumb calculation. We need a more sophisticated model.

Just so. We have a more sophisticated model, from Ray Fair, a macroeconomist at Yale. With careful econometric estimation, he finds that, on balance, China's currency undervaluation in recent years was a slight positive for U.S. job creation. This is the opposite of Bergsten's contention.

As I have argued at length elsewhere, China ought to revalue its currency, but this should not be seen as a major U.S. jobs program