Reagan specifically put into place a strategy aimed at raising the stakes financially, thinking the empire would crumble.  He did, and they did.  he also took a much more confrontational stand on the issues with the leaders of the USSR.  In his own style of humor, he put the Cold War strategy as, "how about we win, they lose".

Now of course it's possible that this fall would have happened anyway.  And though I don't know the %'s, it is true that CIA estimates significantly overstated the economic power of the USSR.

I imagine history books will give Reagan credit, for at least hastening the fall.  But I doubt this is an argument that will be resolved in our lifetimes, though it certainly has been, and will be, argued strongly.