I don't think age plays a factor. You will recieve fewer hammers for a forrest chop the farthur from the city you go. So, while you can chop outside your city cross or even your cultrual boundries, you will get less production from doing so. In fact there is a limit. If you get too far out, then you will get no bonus. I have not figured out the exact distance, after around 10 tiles, you get no bonus.