Effect of census errors on the measurement of net migration
Authors: Hamilton C. Horace 
Published: March 2007

Summary
This paper traces the history of the use of vital statistics, survival rates, and ratios in the estimation of net migration from one decade to another. Net migration studies by Hart (1921); Baker (1933) ; Hamilton (1934); Thornthwaite (1934); Lively and Taeuber (1939) ; Henderson (1943); Hamilton and Henderson (1943); Hamilton (1951); Siegel and Hamilton (1952); Lee and Bowles (1954); Price (1955); Lee, Miller, and others (1957); Hamilton (1959); Zachariah (1962); Tarver (1962); Shryock (1964); Eldridge (1965); Hamilton (1965); and the United States Census Bureau are cited as the principal users of various residual methods of estimating net migration. All these demographers have either implicitly or explicitly recognized that errors in census enumeration and in the registration of births and deaths have been reflected in errors of estimated net migration.
The underlying characteristic of all the methods used by these demographers has been the estimation of net migration as a residual obtained by subtracting natural increase in an area during a decade from the population change during the same decade. This method has been most generally stated in the classic formula {fx394-1} This formula has been used both with total populations and with aging cohorts. The principal variations of the basic formula have involved the use of life table and census survival ratios as a means of measuring natural increase (B − D), or of estimating “expected” populations assuming no migration. The main points of controversy have involved life table v. censm survival ratios, assumptions regarding the similarity in national and state census enumeration errors, and ways and means of estimating the errors involved in estimates of migration and of migration rates by the various methods.
Daniel O. Price (1955) and Zachariah (1962) made important mathematical contributions and attempted to evaluate the errors involved in the me of census survival rates. Eldridge (1965) discovered that, in the United States between 1950 and 1960, the use of the census survival rate method usually gave much lower estimates of net migration than did the classic vital statistic method. Hamilton (1965), using some suggestions by Hope T. Eldridge, developed a mathematical theory or explanation of not only why the CSR estimates were usually lower than the VS estimates but also why the CSR estimates would usually give closer estimates on the true net migration than would the EVS method, which itself is subject to errors of census enumeration and of underregistration of births and deaths. The author also discusses the effect of improvement in census enumeration between 1950 and 1960 on estimates of net migration and derives a generalized formula which takes the timing of migration into consideration.The author acknowledges with sincere appreciation important constructive suggestions made by Dr. Hope T. Eldridge, Population Studies Center, University of Pennsylvania, and the authors of the many papers used as original material. This paper is a revision of a paper read before the annual meeting ot the Population Association of America, Hotel Roosevelt, New York, New York, April 29–30, 1966. Contribution from the Departments of Sociology and Experimental Statistics, North Carolina Agricultural Experiment Station, North Carolina State University. Published with the approval of the Director of Research as Paper No. 2227 of the Journal series.