* December industrial output falls 2.1 percent vs November * Manufacturing dips, construction falls sharply MEXICO CITY, Feb 11 (Reuters) - Mexican industrial production unexpectedly slumped in December by the most since a deep recession four years ago as factories and builders slowed, bolstering bets that the central bank could cut interest rates. Industrial output fell 2.1 percent in December compared to the previous month, its biggest drop since May 2009, when Mexican factories were dragged down by a U.S. recession. Mexico sends most of its exports to its northern neighbor. Mexico's central bank has said it could lower borrowing costs if inflation continues to cool and growth slows in Latin America's second biggest economy. "The central bank could use this as an incentive to lower rates," said Alejandro Cervantes, an analyst at Banorte-IXE, who is expecting a 50 basis point to 75 basis point cut in March to Mexico's benchmark 4.50 percent rate. Yields on short term interest rate swaps edged lower as the market increased bets on the chance of a 25 basis point cut by March 8 to around 30 percent. The swaps market has fully priced in a cut by April. December's seasonally adjusted output data was below a 0.2 percent rate of growth seen in a Reuters poll and the upwardly revised 1.28 percent month-on-month rate posted in November. Among industrial components, manufacturing contracted 1.07 percent in December from the previous month. Analysts said that a drop in automobile production at the end of last year would likely be compensated by a surge in January's output. Construction slid for its third month in a row, down 2.67 percent compared with November. President Enrique Pena Nieto took office in December and the end of infrastructure projects from the previous administration could have hit building, Marco Oviedo, an analyst at Barclays Capital, wrote in a note to clients. Economists are divided about the chance of an interest rate cut. About two out of five analysts now expect the central bank's next move will be a cut - the same amount who think the next move will be a hike, a survey by Banamex showed last week. Solid U.S. demand has helped support Mexican factories amid sluggish global growth. Mexico's economy is seen slowing from an around 4 percent annual rate in 2012 to 3.5 percent in 2013. "The manufacturing sector will see less demand in the first part of the year, and the appreciation of the peso could further limit exports," Banorte-IXE's Cervantes said. Mexico's peso is trading more than 12 percent stronger from a 2-1/2 year low hit in the middle of last year. The peso's relative weakness since the 2008-2009 financial crisis has helped boost shipments by Mexican exporters. Some analysts think the central bank would like to try and curb peso strength by lowering the yield on Mexican debt. Starved by low interest rates in developed economies, foreign investors have piled up record holdings of Mexican peso-denominated debt and flows are expected to continue this year. Mexico has eschewed the types of direct market intervention and capital controls that other emerging markets have used to protect their exporters from strong local currencies. Compared with December 2011, overall industrial output dropped 1.1 percent, missing expectations for a 2.0 percent rise and worse than November's upwardly revised 2.9 percent expansion.