The type of government that existed in Rome during the time of the Pax Romana (a time when Rome enforced peace over a large part of Europe and the Middle East) was an empire. It was an autocracy in which the Emperor held final authority.
The Pax Romana started at the same time that Rome became an empire. This was in 27 BC when Augustus Caesar came to power as emperor. It is generally said to have ended in 180 AD -- this was almost 200 years before the "fall" of the Roman Empire. During this whole time, Rome was ruled by emperors. Therefore, it is correct to say that an empire or an autocracy was Rome's form of government during this time.