The war induced provincial governments to establish their own system of free public employment offices.
I am trying to say that at the time of the war, provinces each established a system of employment offices. These offices aided in the distribution of labour for the war effort. The provinces did this on their own, they felt there was a need for such a system. They were obviously not the same, but had one key element that was common: they were labour exchanges that distributed man power.
The way I have written it sounds weird to me, esp. the part "their own". It kind of feels that using "their own" somehow conveys that the federal govt. beforehand set up these offices FOR the provinces. I will explain their purpose in following that sentence. Can someone help me figure out a way to restructure this please?