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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?

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It all depends on how you define the 'wage premium between different areas'.

The average NY resident makes $51,000 more per year than the average IL resident.

There are 110 medical workers and 90 natural gas workers in NY and IL combined, so you could try weighting the wage premium of medical workers by 110/200 and the wage premium of natural gas workers by 90/200 to give a combined wage premium of $45,500. This will tell you how much more or less a person chosen at random from the whole population will earn if they work in the same industry that they are currently working but in a different area.

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