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Estimating current job openings by income level

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Are there any open data sources estimating the number of current job openings by income level?

I've attempted to go through a variety of government and Federal Reserve sites to put together some combination of data series that might be joined in such a manner to calculate such an estimate but not even JOLTS (Job Openings and Labor Turnover Survey) disaggregates by income level nor by occupation code. It only disaggregates by industry just as "General Medical and Surgical Hospitals" which would include everything from 7-figure brain surgeons to minimum wage support staff, so it does no good trying to use industry averages. (Although medians might be marginally less useless, the medians aren't available at the industry level either.)

For obvious reasons, this is a highly sensitive political topic, which may explain why no government sources permit putting together these kinds of estimates, but one would hope that NGOs might offer such estimates. Even though NGOs are frequently politically biased, one would expect a variety of such estimates representing different biases from which one might discern some general picture.


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