Models for Estimating Intrinsic r and the Mean Age of a Population at Stability: Evaluations at the National and Sub-national Level

Abstract

Using Canada’s provinces and territories in conjunction with the “Cohort Change Ratio” approach to generating a stable population, I test the accuracy of two regression models constructed from national-level data designed to estimate two factors of a population at stability from initial conditions at the sub-national levels: (1) its constant rate of change, denoted here by r'; and (2) mean population age. In a test of accuracy at the national level I find that these models provide reasonably accurate estimates. In the tests at the subnational level, the accuracy, as expected, is less, but the results indicate that the national level models provide estimates that are useful. The models are useful because they are tractable and provide information not available from the traditional analytical approaches. Evaluating these models also provides the opportunity to look at Canada’s provinces and territories from a stable population perspective. The findings support the use of: (1) The Cohort Change Ratio approach in examining stable population concepts; and (2) the two regression models for estimating r' and the mean age of a population at stability. They also show that there are connections between initial conditions and stability that have been overlooked. This knowledge gap may be due to the fact that widespread knowledge and acceptance of the ergodic nature of the “age structure factor,” have served to mask the possibility that ergodicity does not always apply to other factors. Further exploration of these potential linkages appears to be in order.