If you just kept building units, you'd get screwed up. You will need to build buildings in order to keep up at all later on. If your aggresive, several production cities that only builds exp giving buildings and production giving buildings, and then a constant stream of units will be nice. Since your aggresive, you should war a lot, so losing the units in battle will help with not overproducing.
For example, I played the map with Mongolia at a really low difficulty for fun. Ended up building an empire all the way to India by 0 AD. That was easy, but since it gets harder after that as the AI starts to focus more on the army, you need more of your units. Karakorum and Beijing were almost always making keshiks, and my city in korea occasionally did too. That was what kept my war machine going. After capturing Persepolis, I used that as a major keshik site, rarely stopping to make buildings. My other cities occasionally built units because I was going on a rampage all over Asia and Africa, but mostly build buildings to keep my economy in shape.
A bad economy should make you either stop fighting to patch up your economy as if you captured a crap load of cities, your economy should suck, or make you war even more for money from pillaging, capture gold, etc... Ussually its the first one.