The politburo was informed in 1979 in a super secret session that the economy could no longer support the arms race and the USSR was broke. Nothing much seems to have come out of it, except that one young Comrade Mikhail Sergeyevich Gorbachev was in attendance. Some believe that this was the moment he started planning the changes needed for the USSR to survive.
As to Reagan his true contribution was his willingness to negotiate with the USSR. Thatcher had to point out to Reagan that Gorbachev was a willing negotiating partner. After a hesitating start Reagan got the message and bought full in on the negotiations. This was his contribution, not increase in spending, not the speech in the Berlin Wall, not his deficit increasing tax cuts.