A further question: the change happened around the election of Reagan. Was Reagan the cause of this change or was he a result of it?

I would make the claim that it largely had to do with Reagan and Carter as well as the positioning of both major parties. In addition, I might use the message from the 1992 Bill Clinton campaign—It's the economy, stupid.

By the end of his term, Carter was becoming increasingly unpopular due to his positions being hard to swallow by many Americans. He was preaching conserving and making due with less and the economy was faltering under his watch and under the watch of the Democrats. It might also be noted that the Democrats had held control over both houses since the mid-1950s and had a large impact on the political trends in the country.

As the 1970s moved on, the American people saw what was becoming a failure in maintaining the economy as unemployment and inflation shot upward and our foreign policy led to the energy crisis. Carter symbolized tightening our belt buckles—see his speech on economic malaise and the Crisis of Confidence. Reagan, on the other hand, was able to break the hold by the Democratic Party and his economic policy created fairly substantial growth—the ~4% growth under his administration and the new Republican majorities has still been held as a standard to which administrations are held today.

As an historian who has largely focused on political and societal institutions, I believe that the substantial growth of people identifying Republic and the sudden drop in people who identified Democrat can be largely chalked up to the success of the parties' policies. Reagan's new Republican movement spurred growth the country hadn't seen in decades—note specifically that those were decades of Democratic control. When Reagan and the Republicans were able to grab both the Senate and the Presidency and push through his policies, we saw an economic boom that was associated with the Republican Party.