Reagan DID decrease tax rates. I have no idea what these tax increases would be, and if true, I am surprised that I've never seen mention of it. On the face of it, it makes no sense. Why reduce tax rates and increase others?
Reagan reduced MARGINAL tax rates, that is, the tax on the next dollar you earn. If you earn 30,000 and pay 5,000 in taxes why would you sacrafice to earn 35,000 if you wind up paying 10,000 in taxes? Marginal tax cuts stimulate. If Reagan raised Federal gasoline taxes it would tend to drag on the economy but not change anyone's behavior. If marginal tax rates are raised the potential is for everyone to change their behavior and avoid the next brackett. I know I faced that a couple of times.
Also the TEFRA act of 1982 where Congress promised Reagan $2 of spending cuts for every $1 tax increase. Congress passed it, renegged on the agreement and we just got the tax increase.
There was the 5-cent a gallon add'l gas tax passed for "infrastructure improvements" around 1983 also (that we still pay today) in addition to Clinton's add'l 5-cent-a-gallon tax from 1993.