This is certainly an interesting use of archaeological data, and the authors should be applauded for it, but I can't really say I buy into their conclusions.
Increase in coin hoards may be a sign of dead owners who never recovered them, but it may also be a sign of more owners, or even more criminals due to overpopulation, leading owners to hoard their wealth.
Even if internal strife was responsible for the data, there is no reason to think that population numbers declined, as the demographic decrease due to losers' deaths could be made up for by the demographic increase due to winners' taking over properties and a stream of immigration making up for loss of life.
Coin hoards speak of population declines in Ancient Rome
Peter Turchina, Walter Scheidel
In times of violence, people tend to hide their valuables, which are later recovered unless the owners had been killed or driven away. Thus, the temporal distribution of unrecovered coin hoards is an excellent proxy for the intensity of internal warfare. We use this relationship to resolve a long-standing controversy in Roman history. Depending on who was counted in the early Imperial censuses (adult males or the entire citizenry including women and minors), the Roman citizen population of Italy either declined, or more than doubled, during the first century BCE. This period was characterized by a series of civil wars, and historical evidence indicates that high levels of sociopolitical instability are associated with demographic contractions. We fitted a simple model quantifying the effect of instability (proxied by hoard frequency) on population dynamics to the data before 100 BCE. The model predicts declining population after 100 BCE. This suggests that the vigorous growth scenario is highly implausible.