After the 1980 Census, New York State sued to compel the Bureau of the Census to adjust the population counts, using a regression model. The appropriateness of such models is considered in this paper.
"Regression Models for Adjusting the 1980 Census." Statist. Sci. 1 (1) 3 - 11, February, 1986. https://doi.org/10.1214/ss/1177013804