The Universities mentioned by the panel are all highly regarded and very well known in India.
Why should this hold for second-tier schools like NYU and Rutgers?
Rankings do matter and make a difference.
Why? You have to provide an argument (I may agree with you, but by the "principle of sufficient reason" you're still obliged to list reasons). What if the rankings are crud?
Who decides on the rankings, and on what basis? If the argument for the MFE ranking is that it's the consensus of those hiring, were they extensively polled?
So, prospective students do keep a track of it and they do notice Univs which are making improvements leaps and bounds (Baruch for instance).
How? Particularly in the face of crud rankings? Conversely, I'm aware of one Midwestern university, with a good second-tier math department, which recently started its own program. The program is crud. The program has no real faculty except "industry experts." The syllabus hasn't been carefully designed. Yet they manage to con international students into signing up based on the general strength and reputation of the math department. I'm sure others here can list their own examples (e.g., Fordham).
but the strength of the IIT depends on the quality of the students it is able to attract
Only partly. Good students are a corollary of the general strength of an institution. That strength derives primarily from the strength and activity of the faculty and its commitment to research and graduate education. Take Dan Stefanica out of Baruch's MFE and the program will start drifting downhill. On the other hand, replace the current students with a less stellar lot, and the reputation won't take a major hit because of the strength of the program itself. I suspect you're thinking of the IITs, which serve as effective filters for the best India has to offer, and which churn out a reliable if unspectacular product. Yet the IITs are not known for outstanding faculty and don't register on the radar screen with regard to research. Universities like Harvard,
MIT, and Cambridge do. Which brings me back to the point that assessing their strengths is a complex business: strength of faculty, nature of research, quality of graduate education, quality of facilities, and -- where relevant -- placement information.