> Are you stating that cost of living impacts your skill level?

Not at all. If all things are equal except the cost of living difference then a company can get X units of value at a discount by hiring the person with the lower cost of living at a lower salary. The discount is equal to the cost-of-living difference.

Of course in the real world things are rarely "equal" except for cost-of-living and so the effect is only going to be seen in the aggregate.