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Q:  

Where can I find a digital version of birth data for Michigan counties, for the 1950s and 1960s?

A:  

There are two possibilities. One is the net migration files for available from ICPSR as study 8493. Net migration estimates are based on births and deaths. The drawback is that these data are reported in 5-year intervals as that is how net migration data reported. So, this resource has the number of births in 1950-1954, 1951-1955, 1952-1956, etc. for all counties in the United States. That’s not all bad as the data for many Michigan counties ought to be cumulated over a 5-year period for more robust results.

The other source is from the National Bureau of Economic Research (NBER). A researcher had a table from the Natality published volumes for 1940 – 1968 transcribed. It has single year of data for all counties in the US:

Vital Statistics Births 1940-1968

If that’s not the exact table you want, here’s an interactive index to the published natality volumes from 1931-1968:

Interactive Index to Vital Statistics Births 1931-1968

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