Comparing cost of living of one state with that of other states In the past I read something like this:


  If basic expenses for family went from 100€ to 200€ but its wage
  went from 200€ to 400€ it can expend more than before.
  
  Weighting the costs of living in state X, in the median wage in state X,
  is the best way to compare state X's COL with COLs of other states.


I assume that weighting COL in MW particularly is better than weighting COL in average wage (AW), because, although there are few families with extremely high wages, their wages bias AW extremely upwards, while MW is less effected from such extreme cases.

Is weighting COL in state X in MW in state X the most accurate way to compare that COL to these of other states?
Quality of life matters too. This sometimes appears in the labor economics literature as "compensating differential". So it's probably not enough to weight cost of living by median or average wage unless you can objectively determine that all other factors are identical (e.g, tax structure, quality of transportation networks, population density, greenspace, etc.).

These factors are in general not likely to be pecuniary, so they are usually treated as a residual - if MW/COL in state A is less than MW/COL in state B, then the difference must be due to improved amenities in state A.  This is obviously unsatisfactory, and as a result there's a lot of active literature in this area.  And they will, of course, be highly subjective.