The time period is not specified in The Hunger Games, but it can be assumed to be sometime after the 21st Century. From existing information, it is known that the Games themselves have been going on for seventy-four years at the start of the first novel, and the Capitol and District system had been in place for some years before that. Since the setting is the ruins of North America, and since there is an abundance of new technology such as force fields, the time period is not likely to be earlier than 2100 C.E., and probably much later. Conditions leading to the creation of Panem include uncontrolled Global Warming and nuclear war among nations; the first would take years, possibly centuries to make significant changes, while the second depends on world societal conditions.

The time period of this novel is vague because it needs to be plausible/applicable to any time period.  However, it seems to take place in the future, possibly 20-100 years from now, if not in our time. Dystopian fiction operates on the assumption that the conditions and technologies available to the fictional society will one day or are already available to our societies.  Evidence in the novel indicates that we do not yet have the technology to build the arenas, booby traps, etc., nor do we have the cosmetic talents of the surgeons in the novel.  Therefore, I would go with it being far into the future. I hope this answers your question.