HONG KONG—Higher commodity costs drove China’s factory-gate prices to rise in August by their fastest pace in 13 years, defying aggressive moves by Beijing to tame a rally in metals prices.

Robust demand for coal, steel and other raw materials pushed China’s producer-price index 9.5% higher in August from a year earlier, the fastest increase since August 2008, when it rose 10.1%, according to China’s National Bureau of Statistics. The result beat the 9% forecast by economists polled by The Wall Street Journal.

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