We have had one recession during that time, which was due to the First Gulf War and Bush I renegging on his "no new taxes" pledge and raising taxes. Bingo...recession, but it lasted only a few months. We are not in a recession at this time.
The "Bush 1" recession was from July of 1990 to March of 1991.
The budget that contained the tax increases was passed October of 1990, so saying that the tax increases caused the recession is not acurate, as the US had been in recession for a full three months by the time the budget was passed. The tax increases didn't go into effect until the following year.
Desert Shield started in August of 1990, and the shooting didn't commence until January of 1991. So the war was not the cause either.