Abstract
The Hamilton–Perry method, which uses cohort change ratios (CCR) and child-woman ratios (CWR), has gained acceptance as research has demonstrated its practical value and accuracy in forecasting population composition. Assessments of this method have been based on the usual assumption that CCRs and CWRs developed over the base period are held constant over the forecast horizon. We propose several approaches for modifying CCRs and CWRs over the forecast horizon. These alternatives are averaging and trending these ratios and a synthetic method that bases local CCRs and CWRs changes on state-level changes in CCRs and CWRs. We evaluate the errors for these alternatives against the errors holding the CCRs and CWRs constant for counties in Washington State and for census tracts in New Mexico. The evaluation suggests that averaging or trending CCRs and CWRs are not worthwhile strategies, but the synthetic method reduces errors compared to holding the ratios constant over the horizon.
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Notes
CWRs (children/woman of childbearing years) represent the typical application of the Hamilton-Perry method for forecasting the youngest age groups. Other approaches could be used such as age-specific fertility rates (Swanson et al. 2016) or the ratios of the children at two points in time (Swanson and Tayman 2014).
Smith and Tayman (2003) found that while uncontrolled HP forecasts generally had larger errors than the controlled forecasts for all states and counties in Florida, the pattern of errors by age groups was generally very similar for both the controlled and uncontrolled forecasts.
We analysed separate projections for males and females, but do not report the results here because of space limitations. Forecast errors for males and females were similar for most age groups and the total population. For ages 65 years and older, females generally had greater accuracy and lower bias.
For readers interested in an older terminal age group, we computed forecast errors for persons aged 85 years and older. For both accuracy and bias, the patterns are similar to those seen in the 75+ age group in Table 3. MALPEs for SYN (−0.2%) and CONST (−2.1%) are smaller than those for AVG (−4.5%) and TREND (4.9%), and MAPEs for SYN (10.3%) and AVG (11.4) are smaller than those for CONST (12.1%) and TREND (16.3%).
To conserve space we do not present comparisons of SYN with AVG and TREND. To summarize these results, SYN had smaller APEs in more counties than AVG in six age groups, with percentages ranging from 51.3 to 74.4%. For ages 10–19, SYN had a lower MAPE in 48.7% of the counties. SYN also had smaller IODs than AVG in more counties (64.1%). SYN had smaller APEs than TREND in more counties in all age groups with percentages ranging from 69.2 to 92.3%. In terms of allocation error, SYN had a lower IOD than TREND in 92.3% of the counties.
For persons aged 85 years and older, the levels of bias and accuracy are much higher than for ages 75+ with SYN outperforming CONST. MALPEs for SYN and CONST are 76.2 and 82.3% respectively and the corresponding MAPEs are 106.0 and 110.5%.
We analysed forecast errors by size and growth rate for each age group, but do not present these results to save space. The results for all groups were very similar to those for total population.
We also prepared two other forecasts for Washington’s counties using 1990 as the launch year and 2000 (10-year forecast) and 2010 (20-year forecast) as horizon years. The 10-year forecasts showed CONST with slightly smaller forecasts errors compared to AVG, but the 20-year forecasts showed the errors in AVG are considerably larger than the errors in CONST.
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Tayman, J., Swanson, D.A. Using modified cohort change and child-woman ratios in the Hamilton–Perry forecasting method. J Pop Research 34, 209–231 (2017). https://doi.org/10.1007/s12546-017-9190-7
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DOI: https://doi.org/10.1007/s12546-017-9190-7