So I have a Masters in Economics and am currently working at NITI Aayog. In applying for various jobs within and outside India, here is what you can expect (roughly).
Economic Consulting- The Big 4, Compass Lexicon, RBB Economics, London Economics and Frontier Economics are some companies that operate in London. There are others as well. They mainly work in completion policy and regulation. They look for candidates with a strong microeconomics background along with industrial economics. Usually hire from the Masters level. Salaries range from 25-35k pounds per annum. You have to have gone to one of the top Universities to even get an interview at some of these firms. And sometimes that is not enough either. Visa issues also.
Investment Banks
The usual suspects hire Masters students in the UK. Don't know about America. There are opportunities at the research side of things as well. It really depends how geared your studies are towards financial markets. I'm of the opinion that if I wanted to get into investment banking I was better of with an MBA than a Masters in Economics.
Government Organisations- Ministries/Departments offer positions on a contract basis.
Department of Economic Affairs is hiring consultants with 3 years of experience for around 80k a month.
NITI Aayog hires economists at Young Professional(entry level) and Officers on Special Duty(experienced) levels. Masters needed for entry level. There are a few PhDs as well.
I've seen Ministry of Commerce and other related Ministries having similar arrangements.
International Organisations
IMF, World Bank, ADB, UN, Commonweallth etc - entry level is through Young Professional or Economist programs. You need 5 years of experience and a Masters or a PhD.
Contract positions are offered as well, but you need to keep checking their respective websites. Masters plus some experience is required.