>>37429940His actual age is 16, as can be determined by the number of christmases and other seasonal festivals (which have been in correct order with few gaps) and his increase in height compared to adult characters of consistent fixed height. Certain pokemon like his Lapras have also grown. Also, let's face it, he's still a kid, but hes definitely gotten a lot more mature since his early days as well.
Both mattpat and satoshipedia have done the maths, with different approaches, and arrived at the same answer.
The japenese has yet to say his age since initially leaving Pallet. However the english dub has repeatedly said 10 a bunch, basically at the start of each new region.
That said though, we've seen trainers visibly younger than him receiving their pokedex, and we know the trainer license minimum is 10 years. And some cases of know time passage have occured. For instance, Dawn said a year had passed since she was in the Wallace Cup. The magnet train took a year to build. That sort of thing. So we know that time IS passing, as a definite, even if we haven't been told exact year numbers.
Personally, I'm siding with the evidence. He's 16.5 at the end of XYZ.
NOW, that said, in Sun Moon, Misty and Brock are back to their original clothing styles. He mentions having traveled with them and he mentions having dealt with Tauros before, so SunMoon definitely takes place after original series, but we've yet to see any evidence it's on the same timeline as anything else, it may not even include orange islands, EXCEPT that pikachu's movepool still includes iron tail from AG, and at the start of SM Electroball from BW.
So until more callbacks are made in SM to other series, it's anybody's guess as to what's going on with it.