I have found state-level, monthly unemployment data for 2014/2015, and I have found national monthly youth unemployment data for 2014/2015. However, I need all four together; State-level, monthly youth unemployment data for 2014 and 2015. In addition to scouring their website, I have called the Bureau of Labor Statistics and they were not helpful, unfortunately. Alternatively, state-level monthly unemployment data on low-wage earners for 2014/2015 would work as well. Basically, I want to find the effects of the state-level minimum wage changes occurring in January 2015, and these affect primarily youth and other low-wage earners. If I could find this data at the yearly level for 2014 and 2015 instead of the monthly level, that wouldn't be too bad. It wouldn't be quite as useful as monthly, but I could still run the regression and get some results. The other elements are pretty crucial though.
state level, yearly:
i know that is not the ideal set you wanted, baffled at how bls can't help, but not surprised. i would see if they are on github and try and ping some developers.
also, considering how they collect the data (monthly by state) its beyond ridiculous that they aren't helpful. perhaps show them this document, or find out who created it, and that will lead you down the right trail:
i'd also contact each state's labor/economics department...that's not a fun task, but seems like they should have this information.
summer youth data
this is a crapshoot, but you could pick through this:
if none of this helps, just let me know and i'll delete the answer. i realize pointing you in places and saying "look here" can be a) wrong and b) really cumbersome.