I heard from an administrator of a different grad program than mine that TA salaries are in fact negotiable -- a little known fact to be aware of.
Given this tip, how can I effectively negotiate my pay for the classes I will TA for, before signing my contract with the human resources department?
Unlike in industry, I don't have TA salary information from, say, other schools around our campus location to make an effective argument for more money.
In general, TA salaries are not negotiable, but are instead set by a department or school for all students. There may be some "wiggle room" in special cases: for example, if you have already served as a TA and have experience, there may be a higher level of pay available under such circumstances.
In the event that your school allows for negotiations, I would say in any case that you would have to provide a solid argument for why you deserve more than the standard salary. Do you already have teaching experience? How much? Where?
As with any job in just about any industry, salary negotiations are tricky, however the basis for it depends on your experience and skill set. If you have experience being a TA prior (and perhaps with a good track record) then that is something you can bring up in your negotiations. If you are TAing for classes that require a certain skillset or knowledge that not a lot of TAs have, then that's another advantage. If the negotiations are in person, then the conversation might go something like this:
Based on my prior experience, along with the skillset and knowledge needed to be a TA for these classes, I would like to ask for an increase of $x to what you are offering.
If it's over email, then something similar. Nothing is guaranteed, but that would be a start for your negotiations.
As other responses have pointed out, most programs don't have any flexibility about this. But a few do. They might also have other points of flexibility, such as teaching load, auxiliary funding (e.g. travel), or one-time recruitment awards. Your leverage is more your desirability as a student than your teaching experience.
The good news is that as long as you're not a jerk about asking them to improve their offer, you're not in danger of having it rescinded. (At least I've never heard of this happening.) So you have nothing to lose by trying.
