I graduated in the recession of 2002. I struggled finding that first job. As mentioned above, absolute catch 22. Very few want to hire a recent graduate, everyone wants an EE with 2-4 years of experience. I got my lucky break and started with a decent salary; nothing mind blowing, but decent.
It's now 11 years later, I carry a Senior EE title and make a little more than double my initial pay and am pretty topped out salary wise as far as I can see. Management is unfortunately the only way up. I've worked at large companies who simply do not even consider hiring an EE (or software developer for that matter) over 50. We were building a team for a new product within an organization and weren't able to consider older candidates. 50 is the end of the rope for anyone with a tech title and without management anything. Jobs can probably be found but pay is not going to be high.
I'm forcing myself to highlight my management experience (be it project, personnel, etc.) as I look for my next position as this is the best way I see to stay relevant and continue the career progressing upward.
Good luck to all EEs out there!