Ok, not to be picky, but as President, Reagan owned the bill regardless who wrote it.
In fact, Reagan threatened to veto anything that did not reflect his wishes so in a sense you could say Reagan wrote the bill.
He did a bit more than just sign it.
And so what. Doesn't matter if threatened to nuke Kansas unless the Bill was written ITS CONGRESS WHO WRITES THE BILLS. And then it must be passed by BOTH houses. AND you will find that the Lower House was CONTROLLED BY DEMOCRATS all of Reagans Presidency. So when Obama and his asswipe buddies complain about Reagan doing this and doing that and exploding the Debt in reality the DEMOCRATS are the ones who had to initiate everything that happened during his Presidency.
Same as when they claim Billybob Clinton Balanced the Budget. HE DID SQUAT. It was the Republican Congress that did the deed. Billybob just signed the Bill!