Forecasting the U.S. Population with the Gompertz Growth Curve

Abstract

Population forecasts have received a great deal of attention during the past few years. They are widely used for planning and policy purposes. In this paper, the Gompertz growth curve is proposed to forecast the U.S. population. In order to evaluate its forecast error, population estimates from 1890 to 2010 are compared with the corresponding predictions for a variety of launch years, estimation periods, and forecast horizons. Various descriptive measures of these forecast errors are presented and compared with the accuracy of forecasts made with the cohort component method (e.g., the U.S. Census Bureau) and other traditional time series models. These models include quadratic and cubic trends, which were used by statisticians at the end of the 19th century (Pritchett and Stevens). The measures of errors considered are based on the differences between the projected and the actual annual growth rate. It turns out that the forecast accuracies of the models differ greatly. The accuracy of some simple time series models is better than the accuracy of more complex models.