<p>I went to two of the top grad schools (probably each the top 1 depending upon how you sliced the field) when getting my PhD and was a professor for a while and I would not give the unequivocal answer that all of the respondents seem to give. What matters, I believe, is the quality of the person and high quality people can be found all over. But, being able to discern who is high quality is hard and people use shortcuts to figure that out. So, a recommendation from a professor whom they know can count for a lot, if that person is well-known and has produced good students in the past. Undergraduate admissions are one pass at filtering for quality, but there are a lot of other things going on there: athletics, legacies, URMs, leadership, … that grad schools may not care about (well, they may care about URMs). A person who isn’t at a school with well-known faculty can still get and (and they do) but the barrier is a little higher. They may have to publish a paper (or papers) or otherwise demonstrate talent and creativity – good grades and a good recommendation will mean less. </p>
<p>Let me give you a couple of data points from my experience. My undergraduate advisor was a genius and a great man of American academia who was rather eccentric and apparently it was difficult for undergraduates to work with him. His recommendations, apparently, seemed negative but anyone that he gave a semi-positive reference to was a shoo-in everyplace. I later read a letter from him written when I was applying to be a professor. Apparently I had gotten better significantly better results on my undergraduate thesis than he thought technically possible (it was published in the top journal in the field). The most positive thing in the letter was apparently the statement that I had some talent, which meant that I got a full ride at each of the top 5 departments (no teaching or RA duties, just full support to get on with my work). I could have been the same kid at a lesser school and it wouldn’t necessarily have been so obvious. The critical thing, though, is working with a well-known guy, not going to a name school. However, there is often a correlation between well-known professors and name schools.</p>
<p>Second data point. I took a year off in the middle of grad school and was interviewing for a job at a firm run by Wharton professors. I had lunch with two of them and one was grilling me on what I knew, etc., and the second turned to the first and said, “He’s Princeton magna, Jerry” and Jerry said, “So, why do you want to work for us?” I didn’t work for them, but I think they knew what the label meant, and if I had wanted to study in grad school with them, it would also have been easy.</p>
<p>Nothing I wrote above is meant to imply that not going to a name school means that one won’t or can’t go to a highly-ranked program. I had classmates in grad school from UBC, University of Washington, Pomona, Hampshire, SUNY Albany, as well as Harvard, Princeton, and Chicago. But, I think the folks from the name schools probably found it a little easier to get in.</p>