Most western economies currently show large public deficits. Whether they are sustainable is subject to much debate, and if they are not there is also much debate when action should be taken, and how radical it should be. One important part of the debate is the measurement of public deficits and debt, which makes any discussion of possible scenarios difficult. And these scenarios have to make heroic assumptions about the future evolution of the economy, which may in fact be endogenous to policy. All this is very complicated, and pundits do not help at all in this.
Richard Evans, Laurence Kotlikoff and Kerk Phillips take a different approach. Take the current policies, assume they persist forever. Calculate the fiscal gap, that is, the tax rate required to balance the current debt plus the sum of discounted future non-interest liabilities less future taxes. Feed this into a DSGE model and see when it violates feasibility (when the current generation has incomes lower than the tax necessary to close the fiscal gap. In their simulations, it takes a century for the US economy to reach its fiscal limit, although there is a 35% chance this could happen within 30 years. This results fits well within Kotlikoff's decade-old message that every economy is on an unsustainable fiscal path, message he repeats on his platform as a candidate for the US presidency.
Getting back to the model at hand, I do not quite understand the result. To me, this implies that there is somewhere a dynamic inefficiency, or some transversality constraint is being violated. But I do not see where this would happen in the model economy. There is a lump sum transfer from the young to the old in each generation that corresponds to 32% of wage income. To it corresponds a promise for future transfers that may be more difficult to satisfy were the economy to be hit by adverse shocks. Thus, it seems difficulties arise accidentally when the economy is hit by a series of bad shocks and continues forging ahead without any adjustment. That seems unlikely to me.