We Live in Middle Earth

The War of the Rings actually took place in the real world, many years before our current method of recording history, and before our Gregorian calendar system.

Arda was once one large continent. It split during the War of Wrath, and over time, long following the fourth age, the land mass changed heavily into what we know today. 

The western continent, once known as Valinor, is now known as north and south America. The eastern continent split into various pieces. Harad became Australia, most of Middle Earth became Europe, the northern wastes of Forochel formed into Greenland, and Asia was formed from Khand, near the border of Mordor, into Rhún and Hildorien.

The Elves all diminished after sailing into the west, as their time in the world was ending, they spent their final days with their creators. The power of their rings failed with the destruction of The One Ring, causing their lands to wither.

The Dwarves lingered, ever strong and hardy, but they are now few in number, and their secrets and culture are lost in the flow of time. Much breeding with the race of man (now called human) has changed their appearance and diluted their lust for riches. The only remnants of their forgotten language has been confused and intermingled with Sindarin to create Rún, the old Norse runic alphabet.

The Hobbits, like the Dwarves, still remain, but are very few in number. Since The Shire and Ered Luin was mostly destroyed when it was ripped from the west coast of Middle Earth, the Hobbits have survived in few, coexisting in the world of the big folk. In breeding with humans, their height had gradually increased through evolution. But occasionally you will still see a Hobbit whose dormant genetic traits came through.

The Shire, after breaking off from Eriador, eventually floated off and formed New Zealand. The structures, gardens, and Hobbit holes were all destroyed and biodegraded into dirt and dust. Much of the terrain had changed in the catastrophe. But the party tree, the lake, and the hill of Bag End all managed to survive the test of time to this day, and Hobbiton was rebuilt in the early 2000's of our current calendar shortly after its rediscovery.

It is estimated by J.R.R. Tolkien that were we to keep the old Gondorian calendar, we would currently be in the seventh age.

For those of you wondering if this is legitimately canon, a lot of it is not, but the whole thing is a fan theory of mine based on canon material. I think I've made a strong case :P