Yes. The Census Bureau does collect limited data.
Here are some sources:
The best information source for physicians would be the American Medical Association ( http://www.ama-assn.org/) . It has an inventory of active physicians by speciality broken down further by state and county, which appears in their annual report on "Physician Characteristics and Distribution in the United States."
Some of these data also appear in the Health and Nutrition section of the online Statistical Abstract. Here is an example of a state ranking table (http://www.census.gov/statab/ranks/rank18.html).
The Service Annual Survey provides financial data for receipts, revenue and expenses, and detailed financial data for selected service industries, such as doctors, physicians, dentists, etc (http://www.census.gov/econ/www/servmenu.html). Other findings from the SAS include sources of receipts for
selected industries: such as Medicare payments to medical doctors' offices and clinics, Medicaid payments to medical doctors, and private insurance payments to medical doctors. Sources of receipts data for other taxable firms such as dentists, other health practitioners and nursing-care facilities also are included.
The Census 2000 Equal Employment Opportunity special file contains data on the number of people employed in nearly 500 occupations, from actors to veterinarians. Data cover gender, race, ethnicity, education, age, industry and earnings. In addition, users may find where workers live, where they work and how many who work in one place live somewhere else. Summary geographic levels include the nation, states, metropolitan areas, counties and places with populations of 50,000 or more.
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