China’s factory-gate prices extended a record stretch of declines, with the sharpest drop in two years in December, suggesting room for further monetary easing. The producer-price index slumped 3.3 percent from a year earlier, the National Bureau of Statistics said in Beijing Saturday, compared with the median projection for a 3.1% decline in a survey of analysts by Bloomberg News. The slide has yet to be fully reflected in consumer prices, which rose 1.5%, matching the median estimate. Tumbling oil and metal prices have extended the run of producer-price declines to a record 34 months, adding to deflationary pressures worldwide as China’s export prices drop.