You can find out by dumping a lot of your espionage budget into them until you can look in their city, and then you will see.
What I'm wondering is: why are you not smashing their ships as fast as you can? I had a game once where I wound up building about 60 Privateers and had most of the world blockaded. I got 3 GGs before I ever declared a war! They also seemed to help get me vassals, as a bunch of them begged me for lordship around the time it was becoming impossible to keep them all out there (dang Indians kept hunting them down with Frigate fleets).
Part of this rush to be vassals was definitely due to the economic hit they took. While I continued to get stronger, they didn't, so I got higher power ratios against them. I suspect another part of it was the kill ratio; even though they didn't "know" I was whacking their boats left and right, I think I still got scored up on the kill ratios, and that made them want to be my pets. Made sense, I suppose, since I promptly withdrew my Privateers from their waters.
I probably built more Privateers in that one game than all previous ones combined - I had a really good tech lead and beelined them.
I found that everyone else started beelining for Frigates once the skull and crossbones flew over their waters. Dang Indians got them early, so I didn't get to hit them hardly at all. And in the meantime, they built tons of Caravels and kept most of them safe in the cities, but wouldn't use them unless they had like a 10-to-1 advantage (and even then they were hesitant).
I wound up having to do a three-tiered system. One tier was pretty much there to blockade. The second hunted down anything it could find. The third made use of Medic promotions to heal the second tier. Both first and third tiers were needed to supplement the second when a battle went less-than-well or when there were a lot of boats begging for doom.
The Dutch seemed to be a good choice for this strategy. First, the Dutch do better with lots of water, not least of all because of Willem being Financial. Second, they need to beeline Astronomy for their UU, and while you're there, you may as well get Chemistry before beelining your UB. And though the AI doesn't build Privateers (yet), if they ever do, your UU probably won't get attacked by them (equal strength).