Does China already have the world’s largest economy? Most economists think not, and there’s a widespread guessing game as to when it will. “Sometime in the next decade” is a common answer, depending on how fast the United States — today’s No. 1 — and China grow. But some economists believe the crossover has already occurred. If so, this would be an event of huge symbolic importance, conferring at least bragging rights to China. But is it so?

In a recent blog post, Arvind Subramanian of the Peterson Institute for International Economics argues that China passed the United States in 2010 or earlier. He says the World Bank and International Monetary Fund, which publish widely used estimates of nations’ output (gross domestic product), have vastly understated China’s economy.

Let’s look at the numbers. In 2010, according to the World Bank figures, China’s economy was about 70 percent the size of America’s. Its GDP totaled $10.2 trillion, compared with U.S. GDP of $14.6 trillion. The trouble, contends Subramanian, is that the United States’s lead is a statistical illusion and that China’s GDP is about 47 percent larger than the official estimates. This would bring the 2010 figure to $15 trillion, slightly ahead of the U.S. GDP. Indeed, says Subramanian, a new study suggests the underestimate could be more than 70 percent. This implies China’s 2010 GDP exceeded $17 trillion.

What are we to make of this?

For starters, keep matters in perspective. Living standards in the United States, as measured by per capita incomes, remain much higher than in China under any of the GDP estimates. Remember that all of China’s production and income are spread over 1.34 billion people while U.S. GDP is divided among 309 million Americans. Using the official World Bank figures, U.S. per capita income totaled $47,153 in 2010, compared with China’s $7,599. Assuming a Chinese GDP of $17 trillion raises per capita income to about $12,700; that’s roughly a fourth of the U.S. level.

Next, understand that the dispute is deeply technical. There are two uncertainties: first, the reliability of Chinese production and price data used to estimate GDP in renminbi (RMB); and second, the conversion of the RMB figures into dollars to permit international comparisons. This second stage, called “purchasing power parity” (PPP), involves finding a common way to measure output in different countries.

To simplify slightly: If an item costs 6 RMB in China and $1 in the United States, the Chinese item would be assigned a value of $1. The problem is that although many items are similar among advanced countries — a Toyota is a Toyota — big differences exist between rich and poor nations. Ways have to be found to measure items that aren’t common everywhere.

This task falls to the World Bank. It supervises the International Comparison Program (ICP) that collects statistics and applies PPP methods to 197 countries and economies. This process establishes an overall relation between local prices in each country and dollar prices in the United States. But the integrity of the results depends upon the accuracy of the local prices. A major complaint about China’s GDP figures is that the surveys underrepresented rural areas, where prices are lower. World Bank economists say any distortion is modest; but Subramanian and others see it as a big source of underestimation.

The issue may not be settled conclusively until the end of 2013; that’s when the latest revision of the ICP, creating new “benchmark” statistics, is scheduled for completion. Meanwhile, it’s interesting to estimate when China might overtake the United States in GDP if today’s official estimates are correct. Assuming China grows 8 percent annually and the United States 3 percent — both assumptions may be a bit on the high side — the crossover would occur in 2018.