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I am using data from selected zip codes in California for 1980 to 2000. How can I tell if the boundaries for these zip codes have remained the same?
There is no easy way to determine if the boundaries have remained the same. Zip codes are not census geography so the normal equivalency files that allow one to see if the definitions of a geographic area have remained the same do not exist.
However, you can start with a crosswalk of zip code to census tracts based on 1991 boundaries:
Restrict the state to California and select 1991 zip code as the SOURCE and census tract/BNA as the TARGET.
You can then use a 1980 to 1990 comparability file from the Census Bureau to see if there were any changes in census tract definitions in the previous decade. This file can be found at ICPSR as study 9810. If you need to go back to 1970, there is a 1970 to 1980 comparability file (ICPSR 7913).
For further description of the complexities of zip codes over time, see the following resources: