A Long Term Test of the Accuracy of the Hamilton-Perry Method for Forecasting State Populations by Age

Abstract

The Hamilton-Perry method is a variant of the Cohort-Component population forecasting method that has minimal data input requirements. It only requires the age distributions for a population at two points in time, which generally are two successive census enumerations. Although the method has gained acceptance, tests of its accuracy are limited. In this chapter we evaluate the forecast accuracy of the Hamilton-Perry method both in terms of age and total population (obtained by summing up the forecasted age groups). This evaluation is based on a sample of four states (one from each of the four census regions) and decennial census data from 1900 to 2010, which yield 10 census test points (1920, 1930, 1940,…, 2010) that provide a wide range of characteristics in regard to population size, growth, and age-composition that affect forecast accuracy. We conclude that the results are encouraging and suggest that the Hamilton-Perry method be considered when either a 10-year forecast of state populations by age or a total population are desired and components of change are not required.

Appendices

Appendices

1.1 Appendix A.1: Hamilton Perry Method and the Fundamental Demographic Equation

In this Appendix we demonstrate that the Hamilton-Perry method satisfies the fundamental demographic equation. We begin by restating the fundamental demographic equation as follows:

$$ {\mathrm{P}}_{\mathrm{i},\mathrm{t}+\mathrm{k}}={\mathrm{P}}_{\mathrm{i},\mathrm{t}}+{\mathrm{B}}_{\mathrm{i}}{\textstyle }-{\mathrm{D}}_{\mathrm{i}}+{\mathrm{I}}_{\mathrm{i}}{\textstyle }-{\mathrm{O}}_{\mathrm{i}} $$

(A.1.1)

where,

• P _i,t  = Population of area i at time t (the launch year),

• P _i , _t+k  = Population of area i at time t + k (the forecast year),

• B _i  = Births in area i between time t and t + k,

• D _i  = Deaths in area i between time t and t + k,

• I _i  = In-migrants in area i between time t and t + k, and

• O _i  = Out-migrants in area i between time t and t+

then,

$$ {}_{\mathrm{n}}{\mathrm{CCR}}_{\mathrm{x},\mathrm{i},\mathrm{t}}=\left({}_{\mathrm{n}}{\mathrm{P}}_{\mathrm{x}{\textstyle \hbox{-}}\mathrm{k},\mathrm{i},\mathrm{t}{\textstyle \hbox{-}}\mathrm{k}}+{\mathrm{B}}_{\mathrm{i}}{\textstyle }-{\mathrm{D}}_{\mathrm{i}}+{\mathrm{I}}_{\mathrm{i}}{\textstyle }-{\mathrm{O}}_{\mathrm{i}}\right)/{}_{\mathrm{n}}{\mathrm{P}}_{\mathrm{x}{\textstyle \hbox{-}}\mathrm{k},\mathrm{i},\mathrm{t}{\textstyle \hbox{-}}\mathrm{k}} $$

(A.1.2)

Expressing Eq. (A.1.2) in terms of Eq. (A.1.1):

$$ {}_{\mathrm{n}}{\mathrm{P}}_{\mathrm{x}+\mathrm{k},\mathrm{i},\mathrm{t}+\mathrm{k}}=\left(\left({}_{\mathrm{n}}{\mathrm{P}}_{\mathrm{x}{\textstyle \hbox{-}}\mathrm{k},\mathrm{i},\mathrm{t}{\textstyle \hbox{-}}\mathrm{k}}+{\mathrm{B}}_{\mathrm{i}}{\textstyle }-{\mathrm{D}}_{\mathrm{i}}+{\mathrm{I}}_{\mathrm{i}}{\textstyle }-{\mathrm{O}}_{\mathrm{i}}\right)/\left({}_{\mathrm{n}}{\mathrm{P}}_{\mathrm{x}{\textstyle \hbox{-}}\mathrm{k},\mathrm{i},\mathrm{t}{\textstyle \hbox{-}}\mathrm{k}}\right)\right)\times \left({}_{\mathrm{n}}{\mathrm{P}}_{\mathrm{x},\mathrm{i},\mathrm{t}}\right) $$

(A1.3)

where x + k > = 10, then,

$$ {}_{\mathrm{n}}{\mathrm{CCR}}_{\mathrm{x},\mathrm{i},\mathrm{t}}=\left({}_{\mathrm{n}}{\mathrm{P}}_{\mathrm{x}{\textstyle \hbox{-}}\mathrm{k},\mathrm{i},\mathrm{t}{\textstyle \hbox{-}}\mathrm{k}}{\textstyle }-{\mathrm{D}}_{\mathrm{i}}+{\mathrm{I}}_{\mathrm{i}}{\textstyle }-{\mathrm{O}}_{\mathrm{i}}\right)/{}_{\mathrm{n}}{\mathrm{P}}_{\mathrm{x}{\textstyle \hbox{-}}\mathrm{k},\mathrm{i},\mathrm{t}{\textstyle \hbox{-}}\mathrm{k}},\mathrm{and} $$

since N_i = I_i – Oi, where x + k ≥ 10, we have

$$ {}_{\mathrm{n}}{\mathrm{CCR}}_{\mathrm{x},\mathrm{i},\mathrm{t}}=\left({}_{\mathrm{n}}{\mathrm{P}}_{\mathrm{x}{\textstyle \hbox{-}}\mathrm{k},\mathrm{i},\mathrm{t}{\textstyle \hbox{-}}\mathrm{k}}{\textstyle }-{\mathrm{D}}_{\mathrm{i}}+{\mathrm{N}}_{\mathrm{i}}\right)/{}_{\mathrm{n}}{\mathrm{P}}_{\mathrm{x}{\textstyle \hbox{-}}\mathrm{k},\mathrm{i},\mathrm{t}{\textstyle \hbox{-}}\mathrm{k}}. $$

(A.1.4)

Equations (A.1.2), (A1.3) and (A.1.4) show that the Hamilton-Perry method is not only consistent with the fundamental demographic equation, but also closely related to the cohort-component method. The Hamilton-Perry method simply expresses the individual components of change—births, deaths, and migration—in terms of CCRs (Cohort Change Ratios). An important reason for a demographic forecasting method to be consistent with the fundamental demographic equation is to minimize the potential errors associated with hidden heterogeneity (Vaupel and Yashin 1985).

1.2 Appendix A.2: Population by Age, 1900 to 2010 by Decade (Tables A.2.1, A.2.2, A.2.3, and A.2.4)

Table A.2.1 Population by age, 1900 to 2010, Georgia

Table A.2.2 Population by age, 1900 to 2010, Minnesota

Table A.2.3 Population by age, 1900 to 2010, New Jersey

Table A.2.4 Population by age, 1900 to 2010, Washington