Affiliations: [a] Arkansas Institute for Economic Advancement,
University of Arkansas at Little Rock, 2801 S. University Avenue, Little Rock,
Arkansas 72204-1099, USA | [b] Center for Rural Mental Healthcare Research,
University of Arkansas for Medical Sciences, 4301 W. Markham, Little Rock,
Arkansas 72205, USA | [c] Operating Sciences Department, General Motors
Research Laboratories, 30500 Mound Road, Box 9055, Warren, MI 43090-9055,
USA
Abstract: Estimates of net migration are virtually always constructed from the standpoint
that the mortality underlying a survived population is not stochastic and the
census counts framing the intercensal period are error free. There is compelling
evidence, however, that mortality should be viewed as a random variable and
census counts contain systematic errors. This evidence suggests that net
migration accuracy is affected both by random error and bias. We explore the
estimation of net migration accuracy by placing “Mean Square Error” (MSE)
confidence intervals around 1980–1990 net migration estimates for Arkansas made
using the Forward Life Table Survival Method. This type of confidence interval
measures accuracy by incorporating both bias and random error. We provide
empirical and theoretical justifications for the use of this type of confidence
interval over the more commonly-found typed based solely on random error, Since
bias can affect probability levels, we provide a simple adjustment that
preserves the desired level of probability for the MSE confidence intervals and
produces an unbiased estimator. For the illustrative age-gender-race net
migration data for Arkansas, we construct 66% MSE confidence intervals and note
that they become wider as random mortality variation increases. They also become
wider as the differential between 1980 and 1990 net census undercount error
increases for a given cohort. We argue that the MSE intervals provide an
accurate description of the uncertainty in net migration estimates and that they
have useful applications.
