Suppose, a prospective PhD student doesn't have money to self-finance his PhD in the USA.
Is it possible for a PhD student to survive in the USA only on TA/RA money?
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Agnostic of institution, each of which has its own set of policies governing TA/RA pay (more or less depending on the institution), a short answer is yes. There are also, of course, different costs of living depending on where your institution is located (e.g., the cost of living in New York is much higher than in, say, the midwest). In any case, you will be paid a livable wage, but don't expect to be living any sort of lavish lifestyle.
Personal experience: I've been living off of TA/RA pay for the past 3 years. The pay offered by the R1 institution I attend and work for is located in the Midwest and, relative to other schools in our conference, offers one of the best stipends. As such, I've had enough money to not only live, but support my hobbies and enjoy a [non-extravagent] leisurely life during my non-working, non-academic hours (of which there are not usually a ton haha).
The answer is usually yes, but it varies, and some people need to take out loans or get financial help from their families. For example, the graduate students' union at Yale is organizing around issues such as inequities in pay, lack of access to affordable childcare, and general difficulties in making ends meet when living in New Haven. http://www.nhregister.com/general-news/20170125/yale-university-graduate-students-in-9-departments-given-right-to-hold-union-elections
Students in the humanities are often less generously supported than those in the sciences, even at the same university. Fields that attract federal grant money do better than those that don't.
Think carefully about decisions such as your type of housing and whether to sell a car that you own before you start school. If you have more than one school to choose from, check carefully for differences in the local cost of living, which can easily be a factor of two or more between a small college town and a city like San Francisco or New York. In cities such as San Francisco with very high rents, make sure you have an affordable option for housing, such as on-campus housing or a subsidized university-owned apartment.
Health care is not free in the US, and although schools will usually provide health care to PhD students, there may be costs that are passed on to the student. Coverage may not include things that are included in other countries' national health services, such as birth control, drugs, and mental health care.
This question is relatively vague, in that the US is a big place and remuneration for RA/TA positions is not equivalent across institutions.
However, I believe that the answer should explicitly address that the cost of living in the US varies considerably across the country.
Can a single person survive on the income provided by a typical stipend in the Midwest United States or the South? Yes.
Can a single person survive on the income provided by a typical stipend in the West or East Coast? Probably not.
Anecdotally, I have survived wonderfully in Indiana on a typical stipend. Upon moving to Boulder, Colorado for a PhD however, that stipend (same dollar amount) is not enough to pay for the basic living expenses and I have had to work an additional job to make ends meet.
TL;DR: Yes - but this may often require you (and us) to fight for this collectively.
This question sheds light on the outrageous exploitation of junior researchers and teachers at universities in the US. A PhD candidate - and I mean the kind who does research and teaching throughout the week on campus, helps his/her research group and/or advisor with various projects and tasks, and is generally at the disposal of the advisor, research group, department or university - is a full-time employee. And not just any employee, but a skilled and meritotious one, which outside of academia would be gainfully employed. (Of course, salaries and job opportunities differ greatly between, say, an Electrical Engineering graduate and a graduate of a Semitic Language Philology, but still). Even if their work as PhD candidates also has the aim of earning a degree, that does not detract from their benefit to their employers: Universities are institutes which spread knowledge by teaching and ehnance knowledge and understanding by research, and PhD candidates promote these ends, devoting some of the best and most productive years of their lives. For this reason it is just and proper that they be paid a good salary.
Instead, what we (or rather, you; I work in the Netherlands where things are much better in that respect) have is a system in which many PhD candidates (and, again, I'm talking about the kind I described above) are not paid salaries at all, or are paid meager 'stipends', or paid for just their teaching / just their research, as though they work a small fraction of a full position, which is oviously not the case.
It is utterly infuriating that PhD candidates should worry about "surviving" their PhDs financially, rather than asking "Will I be able to put a down payment on an apartment or a house with my salary?". And let's not get started on how employers in the US and elsewhere used the entrance of women into the workforce over the last 50 years to increase downward pressure on wages so that if a couple wants to have children they have to choose between holding two jobs or near-poverty (and PhD candidates are very typically in that age range).
So, while for some (many?) universities, the RA/TA salary is enough to get by, it's almost universally much much lower than it should be (either the salary itself or the FTE fraction at which you're employed, or both). Occasionally you can sort of maneuver yourself into better wages by leaning on your advisor or obtaining some external source of funding for your research group; but that's the exception.
The rule is that without graduate researchers and teachers organizing in unions, without resolute industrial action, and without solidarity from older/tenured researchers and teachers - the answer to your question would be "no". So I urge you to join one or participate in forming one. I have (although, again, not in the US). You may not get all you want - but with Herculean effort, a measure of personal sacrifice and a bit of luck you might get some of what you need; and it won't be just you personally, but rather everyone at your university. So go to it; it is probably no less important than your actual research work.
By the way, there's recently been a landmark NLRB ruling buttressing the legal right to collective bargaining of graduate student-employees, in NLRB case 02-RC-143012 (The Trustees of Columbia University and Graduate Workers of Columbia, UAW; main decision here).
As others have said, cost of living can vary considerably from one city (and region) to another. I think this deserves a very concrete comparison as it is important not to just have a vague understanding that the costs in one place might be more than another.
Let's start with Champaign, Illinois (home of the University of Illinois's flagship campus, a top research university) which is very much a "college town"—the metro area has a little more than 200,000 residents and a large portion of them are connected to the university. This is the type of place that, all else being equal, would be among the most realistic types of locations for there to be both a PhD program of repute and a cheap cost of living.
Now let's compare that with living in New York City, home of many research institutions and other colleges. According to Sperling's Best Places, the cost of living in New York City is twice as high as Champaign. And maybe more important, the cost of housing in New York City is over three times as high as Champaign.
I have lived in neither location, but have visited them when considering under- and post-graduate programs. PhD students in a social sciences field that I met in Champaign sometimes shared housing, but many of them shared houses (1500+ sq. ft.) in which each person had their own bedroom and usually there were multiple bathrooms. They were also usually quite close to the campus, though for some people/situations not walkable (for some, a walk that takes 20-30 minutes is unfathomable). In a place like New York, it's more likely you find yourself splitting a rather small apartment for similar or larger costs. For some, this is not a big factor...but for others, the ease of getting around, having one's own personal space, etc. are immensely important for their emotional wellbeing. More than one person I met in that program ended up even purchasing a home during their time there, though in both cases they were in a student-student marriage.
Universities, disciplines, and departments all vary in their ability to fund graduate students through the summer months. There are basically three tiers:
I will say that it is not always easy or straightforward to find summer work that even rises as high as a grad student stipend. More important is that most employers aren't dying to have an employee who will be leaving in 2 or 3 months. International students are also generally not permitted to work and may either need to go home or maintain a savings to get through the summer.
I have also been in a situation in which summer pay was the norm, but the pay was different/less. We were hired as lecturers or lab assistants rather than graduate assistants, placing us on a different payscale and under different hiring rules. We earned roughly 10-15% less in gross pay and the net pay was roughly equivalent (no student fees paid over the summer, but we were required to pay into a public pension program).
Many graduate programs cover a large portion of health insurance premiums, perhaps sometimes all of the premium. This is a major expense to reckon with, so be sure you know how it works. When a program tells you how much they are paying, the number you get will be how much you get before various costs are taken out, including your health insurance premium. At my institution, 85% was covered and I paid somewhere between $25-$45/month for the premiums (spread across only 9 paychecks).
Another "gotcha" can be student fees and associated costs paid to the university. While tuition is customarily waived, many universities will still require graduate students to pay "student fees." At my institution, the supposed purpose of these fees included things like a public transportation pass, access to the fitness facilities, and some other "activity fee" kinds of things. Over the course of the year, I usually spent about $1000 on this and it is not optional. It was taken out of my paycheck post-tax, if I recall correctly. This isn't always going to be the case—both the requirement to pay fees and the amount—but you should be asking questions when figuring out if the costs will add up. If you drive to campus, you will probably need to pay for parking.
To answer the question directly, the answer is "under the right circumstances." If the balance of the program's compensation, the cost of living, the auxiliary costs/benefits, and your own wants and needs sync up, then it will work. And I think there are many people who can have that balance work out, though it is probably not nearly a majority of graduate students.
I will note that my operating assumption is that living "only" on stipend money means that the person is not using student loans to pay some of the expenses.