BEIJING (Reuters) - Activity in China's vast factory sector shrank for an 11th consecutive month in January, but at a slower pace than in December, a private survey showed on Monday, suggesting the economy was still deteriorating at the beginning of 2016.

The Caixin/Markit China Manufacturing Purchasing Managers' Index (PMI) inched up to 48.4 in January, beating market expectations of 48.0 and a slight pick-up from a reading of 48.2 a month earlier.

The January reading was still below the 50-point neutral level, which separates a contraction from an expansion on a monthly basis.

The Caixin survey focuses more on small and medium-sized private firms, in contrast to the official manufacturing gauge, which focuses more on larger state-owned firms. The official PMI data for January is also released on the same day.

The Caixin PMI new orders sub-index rose to 48.5 in January, the highest reading in a seven-month sequence of contractions.

However, demand from abroad has seen a steep decline as the rate of reduction in new export orders accelerated in January. Overall demand from both home and abroad continued to stand in deflationary territory, forcing companies to lay off more workers in January.

China will expand tax reforms to replace a business tax with a value-added tax (VAT) this year to help relieve heavy burdens on companies. Industries that enter the scheme in 2016 will pay 560 billion yuan ($85.17 billion) less in tax than they did in 2015, according to the country's statistics bureau.

The world's second-largest economy grew 6.9 percent in 2015, the weakest pace of growth in a quarter of a century. Some analysts believe the real growth is even lower, and they expect growth to slow further this year.

Chinese Premier Li Keqiang said last week that the economy was still facing downward pressure, which is unlikely to disappear any time soon.

($1 = 6.5747 Chinese yuan)

(Reporting by Winni Zhou and Nicholas Heath; Editing by Sam Holmes)