Institutions are likely having a permanent effects as they create path dependency which implies that even temporary shocks would have permanent effect. At least that is what is argued by many developmental economists including Acemoglu and Robinson (see Why Nations Fail). Furthermore, they claim that this hold not just for development itself but that the political institutions are themselves path dependent and reinforcing.
However, permanent effects and path dependency should not be confused for some sort of historic fatalism. Just because some countries had (or were imposed on them) extractive (i.e. in Acemoglu and Robinson's view 'bad') institutions does not mean that they are forever doomed to be underdeveloped. It just means that the loss of welfare that occurred as a result to the 'shock' (i.e. adoption of extractive institution itself) wont be recovered.
For example, below I simulated an example of an one time adoption of extractive institution. I tried to simulate the sort of extractive institutions imposed by the king Leopold II on Congo which arguably both affected the production capabilities of Congo and its growth.
Below you can see that the effect is permanent even if country will eventually grow and attain the level of output it had before the extractive institution was implement.
Even if the old institution will be reversed and replaced by better one the effect of the old institution will be still permanent as you can see the simulated examples of growth where the old extractive institution was replaced by inclusive (left picture) vs where extractive institution was never in place (right picture) but inclusive was implemented show that the GDP per capita will be permanently affected.
Hence to sum up, if you buy into the theory that development is path dependent which Acemoglu and Robinson do then the answer is that the effect of those institutions is permanent. Thus you can trace the effects as back as recorded history goes. Even some ancient event such as the Bronze Age Collapse or the fall of Roman Empire (or as Brian mentions in his +1 comment even ancient road network patterns) and changes in institutions caused by those have still significant effect today as if we could avoid them today's output would arguably be significantly different.