The Accuracy of Hamilton–Perry Population Projections for Census Tracts in the United States

Abstract

In a first-ever nation-wide census tract evaluation, we assess the accuracy of the Hamilton–Perry population projection method for 65,221 census tracts. We started with 73,607 census tracts but eliminated those for which zeros appeared in age/sex groups. The test uses 1990 and 2000 census tract data by age and gender to construct cohort change ratios, which are then applied to 2000 census tract data to generate 2010 Hamilton–Perry projections that are evaluated in an ex post facto test against the reported 2010 census tract data by age and gender. The projections include: (1) uncontrolled age and gender projections; and (2) age and gender projections controlled to a projection of the population total by census tract. Mean Absolute Percent Error (MAPE) is used to evaluate precision and Mean Algebraic Percent Error (MALPE) is used to evaluate bias. We find that controlling the Hamilton–Perry projections by age for each tract to the linearly projected total population of each tract reduces both MAPE and MALPE within age groups by gender and for total females and total males. As this result suggests, simple linear extrapolation provides more accurate projections of the total population than does the Hamilton–Perry Method. However, even with controlling we find the Hamilton–Perry projections by age to be biased upward. Finally, we use MAPE-R (MAPE- Revised) to evaluate the effect of extreme outliers and find that high MAPEs in the uncontrolled projections are largely driven by extreme errors (outliers) found in less than 1 percent of the 65,221 census tracts used in the study.