Mean Square Error Confidence Intervals for Measuring Uncertainty in Intercensal Net Migration Estimates: A Case Study of Arkansas,1980–1990

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.