Beijing may relax the country's one-child policy by the end of 2013, say China watchers, following local media reports in the recent days that the government is mulling changes to its highly unpopular restriction that has been in place for three and a half decades.

"China's one-child policy could be eased around end-2013. We believe that the reform-minded president Xi and premier Li will use the opportunity of abolishing the one-child policy to build up their authority, show their determination in making changes and convince the Chinese people that they do have a roadmap for reforms," Ting Lu and Xiaojia Zhi, China economists at Bank of America Merrill Lynch (BoFAML) wrote in a note over the weekend.