DURING his state visit to America last week, President Hu Jintao of China offered some familiar banalities and worthy pieties, as this week's Banyan remarks. But he also made a couple of hard, quantitative claims. In a speech on January 20th, President Hu said that cheap inexpensive imports from China had saved American consumers $600 billion over the past decade (2001-2010) and that exports to China had created over 14m jobs around the world.

Those figures were probably provided by the Ministry of Commerce, but I've no idea how they were calculated. (The figure of 14m jobs made an earlier appearance in a 2009 piece in the People's Daily.) In this blogpost and a sequel, I'll see if I can make sense of President Hu's arithmetic.

I've received great help in this endeavour from Raphael Auer of the Swiss National Bank and Princeton University. In a paper* last year with Andreas Fischer, also of the Swiss National Bank, Mr Auer estimated the impact of low-wage competition on 325 American manufacturing industries—everything from cat food to artificial funeral wreaths.

Isolating the effect of foreign competition on prices can be tricky. If American demand goes up, for example, it will drive up prices and suck in imports. One might therefore falsely conclude that more imports equals higher prices.

After dealing with this problem, Messrs Auer and Fischer estimate that whenever Chinese imports increase their market share by 1 percentage point, American producer prices fall by 2.5%, a more pronounced effect than many previous studies had found.

According to Mr Auer, China claimed a 3.7% share of the average market in 2001, rising to 8.6% in 2006, when their data end. Imports from the Middle Kingdom have grown by about 28% in the four years since, even as America's total imports have grown by only 4%. So let's assume that China has enlarged its share of America's manufacturing markets to 10.6%.

That would mean that China's penetration of American markets has increased by 6.9 percentage points from 2001 to 2010 or 0.69 points a year. If each point reduces prices by 2.5%, then this expansion has cut prices by about 1.7% a year.

What does that add up to in dollars and cents? American manufacturing sales averaged $4,512 billion a year in the last decade, according to the Annual Survey of Manufactures, including over $13 billion of cat and dog food in 2005. The calculations above suggest these shipments might have cost $4,590 billion if China had failed to encroach on these markets. This implies savings of about $78 billion a year, or $780 billion over the decade.

This is all heroically back-of-the-envelope stuff. But by this reckoning, President Hu's estimate looks quite plausible, even conservative. In my next post, I'll look at his claim that exports to China have created more than 14m jobs around the world.

* "The effect of low-wage import competition on U.S. inflationary pressure," Journal of Monetary Economics, May 2010