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Re: UW Seattle vs UC Irvine
Congratulations on being accepted to these programs. I'm not going to say which I think is better. That would be inappropriate, but I also think you need to figure out which is a better fit for you.
Regarding funding, you need to ask what fraction of 5th year students did not have funding. Ask about the fraction of sixth year students who did not have funding. Ask how many students graduate in 5 years, 6 years, or more than six. Ask if they provide tuition waivers for students who do not get funding. I would ask your program contact, but also ask the current students what their impression is about the availability of funding for 5th and 6th year students.
Nothing sketchy about how UW worded their offer. We professors simply cannot guarantee anything. You aren't signing a contract with the university.
At this point you should ignore the rankings. Econ department rankings are not that precise. They are a popularity contest. US News asks us to rate every school on a 1 to 5 scale. The rankings are just the averages. They aren't based on faculty research, placements, fields, etc. They are useful for getting a broad sense.
You want to be happy and mentally healthy in graduate school. Location and disposable income may matter. But keep it in perspective. You will likely make over $100,000 a year during your first year on a job after graduation. Small differences in the stipend and costs of living shouldn't matter that much.
It sounds like you haven't talked very much to current students. They are a tremendous source of information. Ask for the contact information for five students from each school who are at different points in the program, ideally working in your fields of interest. Ask the students if they are happy, what they like about the program, which professors are good instructors, which are good advisers. Ask who teaches the field classes in your areas of interest and who advises students in these areas. Do students struggle to get time with faculty?