I need to find data regarding the migration of the elderly population by state for each year. Can someone help me
In IPUMS-USA, you can find migration variables here. Specifically, the variable MIGPLAC1 reports the state (or foreign country) where the respondent lived 1 year ago. This variable is available for years 2000-2012, as well as 1950. To limit to elderly persons, you can use the AGE variable to filter the data.
Keep in mind that IPUMS provides microdata, which you can use to produce estimates of national population figures. If you are interested in summary tables, the NHGIS project, which is also housed in the Minnesota Population Center, offers many of the official Census tables going back to 1790 at several geographic levels. While NHGIS is primarily focused on mapping data, the summary tables can be extracted independent of shape files as .csv files with optional descriptive headers. Additionally, the Census’ American FactFinder site is another source for Census tables.
I hope this helps.