The exact time period is never explicitly stated in the books, but it's implied to be far in the future after a devastating event called "The Dark Days" that destroyed much of the continent.
Here's what we know:
* The Capitol: The seat of power, located in the former Washington, D.C., is described as a gleaming city of luxury and technological advancement.
* The Districts: The 12 surrounding districts are divided based on their primary industries, with each district contributing to the Capitol's wealth and prosperity.
* The Dark Days: The event that led to the creation of Panem, these are referred to as a time of "great destruction" and "disaster" that resulted in the collapse of the old world.
So, while the specific year is unknown, we can say that Panem exists in a post-apocalyptic future based on what was once North America.