It might surprise many that governments have routinely spent more than they take in from taxes. In ancient times, governments simply minted more coins to fund their operations, they did not generally borrow. Some Greeks borrowed from the temples to fund wars and did default. However, typically, tax revenues amounted to only about 80% of expenditure.
Records have survived as well as dies from which coins were struck. Pictured here, you will see an actual Roman die from the Republican period which has survived. Each die was hand carved so we can distinguish between dies and as such, the fact that the average number of coins produced before a die breaks is about 15,000. Here is a coin struck from this issue that this die represents. Since we can catalogue the number of known dies, we then can reasonably estimate the annual production of money in the Roman Republic as well as the Imperial era.
The above chart demonstrates the annual production of coinage during the Roman Republic 155-66BC. We can differentiate periods of contraction (deflation) from inflation. We can see that some periods were clearly deflationary and there emerged a shortage of money at times. The Roman Emperor Tiberius, who followed Augustus in 14AD, was notoriously frugal. We find private coinage appearing as tokens to make up the difference for such period of deflation.
The private token issues during the period of Tiberius (14-37AD) are reminescent of the Great Depression when hundreds of cities issued Depression Scrip. We also find private token coinage produced during the American Civil War. They even issued Postage Currency whereby stamps were exchanged as money.
If we then can ascertain the annual production of coinage with a reasonable degree of accuracy, adding up those annual production figures will give us a look at the total money supply. We are then able the also reasonably ascertain that the Roman government collected only about 80% of its total expenditure from taxes. The rest was not borrowed, but simply produced.