As an analyst, do you get paid more your second year out of school?

If they paid the same YoY, I would immediately freshen up the resume. 
 

my analyst days saw 5-10k increase in base and like a 10-15% bump in bonus.

I would hope so.

My experience with pay bumps as a 2nd year pretty much echos the above comment. I started with no experience, 6 months in got a $5K base and 5 percentage point bonus inc. A year later got a $15K base and 10 percentage point bonus inc.

For reference, I’m at a small-ish (20+ employee) family shop with $800 million AUM. Small aside since family shops can be hit or miss, but I’m incredibly happy that no family members actually work at the company (they’re board members), thanks to the founder barring family employees before he died in the 80’s.

You should minimally expect a COLA. I'm also curious about salary bumps for experienced roles, I started working at my small firm in Oct (got a prorated bonus which was unexpected and nice) and am curious what other people see for associate/post-MBA roles. 

I would expect at least something each year. At minimum, 5% increase.

I calculated my initial salary out of school until now, and it's about an 18% CAGR.