I have a dataset with mean and median wages for particular geographic areas around the United States. I am interested in calculating the wage premium between some areas. I can already do a simple version of that but I would like to adjust my model for heterogeneous labor markets because the dataset includes data split by industry group for each area. How would I go about doing that exactly?
Consider this example:
+------+-------------+--------------------+-------------------+
| Area | Industry | Mean Annual Income | Number of Workers |
+------+-------------+--------------------+-------------------+
| IL | Medical | $100,000 | 50 |
+------+-------------+--------------------+-------------------+
| IL | Natural Gas | $50,000 | 50 |
+------+-------------+--------------------+-------------------+
| NY | Medical | $150,000 | 60 |
+------+-------------+--------------------+-------------------+
| NY | Natural Gas | $90,000 | 40 |
+------+-------------+--------------------+-------------------+
I could just calculate the wage premium in Natural Gas and Medical between IL and NY, then take a weighted average. But what should the weights be? The proportion of workers in each industry is different for the two areas here.
This looks very similar to textbook price index problems. Could I just calculate a chained price index?