So the big story of the day is that China has overtaken Japan, moving up to become the world's second biggest economy. Please forgive me if I manage to contain my excitement. You see, the media stories about China's economy leap-frogging Japan's are based on the latest quarterly figures for gross domestic product. And GDP figures are slippery things at the best of times. Sure, according to numbers released yesterday, Japanese growth all but stalled over the three months to the end of June. As a result, Japan's GDP - its total output of goods and services - for the quarter came to 119 trillion yen (HK$10.72 trillion). At the average exchange rate for the quarter, that equals 8.8 trillion yuan, which is clearly lower than China's economic output of 9.1 trillion yuan (HK$10.39 trillion) over the same three-month period. Hooray! China has surpassed Japan at last. Except that the story is hardly big news. A quick look back at the past data shows that this is not the first time China's quarterly output has overtaken Japan's. According to the raw numbers, China's GDP also topped Japan's in the fourth quarter of last year (see the first chart below). Then in the first quarter of this year, China's output slipped back, and Japan regained its second place. The trouble is that raw quarterly GDP numbers are a terribly unreliable indicator of relative economic development. For one thing, they are massively distorted by seasonal variations. In China, for example, the lunar new year holiday drags down first quarter data, while quirks in the local business environment tend to exaggerate output in the last three months of the year. As a result, the raw numbers frequently show fourth quarter GDP exceeding first quarter output by 50 per cent or more. And for another thing, the latest quarterly numbers are little more than rough preliminary estimates. Although China's number-crunchers have traditionally avoided admissions of fallibility, rarely making revisions to their initial announcements, Japan's statisticians have no such hang-ups. Their revisions are frequent and often large, so that final GDP numbers often bear little resemblance to the preliminary figures announced six weeks after the end of each quarter. As a result, if you want a guide to different countries' positions in the economic pecking order, it's better to wait for the full-year figures. On that basis, there is no doubt that China's economy will be shown to have overhauled Japan's when the full-year figures for 2010 are finally declared. Even so, China's achievement will hardly be hot news. In reality, China's GDP overtook Japan's years ago. The numbers cited above rely on market exchange rates to compare the size of the two economies. But most economists believe that Japan's currency is trading well above its fair value, while the Chinese yuan is deeply undervalued; a discrepancy which severely distorts the relative output of the two economies. Many analysts believe you get a better picture of GDP by adjusting for differences in the domestic purchasing power of different currencies. These can be enormous. According to a recent study by brokerage house CLSA, the Japanese yen is currently overvalued against the US dollar by 54 per cent, while the yuan is 31 per cent undervalued. As a result, measured on a purchasing power parity basis, China has been the second-largest economy in the world for years, with a GDP more than twice the size of Japan's in 2009 (see the second chart below). But even based on market exchange rates, China has almost certainly been the world's second largest economy for several years now. We can be fairly confident of that because of deficiencies in China's data gathering methods, which tend to be biased towards measuring the output of state-sector heavy industries while missing much of the more service-oriented private sector. As a result, China's economy is almost certainly bigger than official figures indicate. But working out how much bigger is tricky. In 2005, Beijing's statisticians revised up China's GDP by 17 per cent overnight following a new survey which captured more of the private sector's output. Even so, it is likely they are still missing a great deal of activity. According to an independent survey of household incomes published this month, China's GDP in 2008 was fully 10 per cent greater than official figures indicate, and even that may be understating the importance of China's grey market. So, whichever way you look at it, China's economy is bigger than the official data imply, and has certainly been bigger than Japan's for a long time now, despite what the headlines might tell you.