How much a tag of a premier B-school (IIM's) matters than a B-school (TAPMI, KJ, and LIBA) five years down the line?

There are two schools of thought on the same. The proponents would say that it matters a lot since the older your institute gets the more your alumni base spreads across the industry and in today’s corporate world connections are everything. Hiring managers ask for recommendations. Every college has its reputation in the market that has been built over a period of time by its students, faculty, and staff. But we also have people who dont believe in this concept and would like you to believe that only matters to an extent. Well that might be true for some but it takes a lot of effort to not be seen as a part of your institution