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Population projections are judged primarily by their accuracy. The most commonly used measure for the precision component of accuracy is the mean absolute percent error (MAPE). Recently, the MAPE has been criticized for overstating forecast error and other error measures have been proposed. This study compares the MAPE with two alternative measures of forecast error, the Median APE and an M-estimator. In addition, the paper also investigates forecast bias. The analysis extends previous studies of forecast error by examining a wide range of trend extrapolation techniques using a dataset that spans a century for a large sample of counties in the US. The main objective is to determine whether the choice of summary measure of error makes a difference from a practitioner’s standpoint. The paper finds that the MAPE indeed produces error values that exceed the robust measures. However, except for situations where extreme outliers rendered the MAPE meaningless, and which are rare in real world applications, there was not a single instance where using an alternative summary measure of error would have led to a fundamentally different evaluation of the projections. Moreover, where differences existed, it was not always clear that the values and patterns provided by the robust measures were necessarily more correct than those obtained with the MAPE. While research into refinements and alternatives to the MAPE and mean algebraic percent error are worthwhile, consideration of additional evaluation procedures that go beyond a single criterion might provide more benefits to producers and users of population forecasts. Copyright Springer Science+Business Media B.V. 2007Forecast accuracy, MAPE, Error measures, Population projections,

Population forecasts entail a significant amount of uncertainty, especially for long-range horizons and for places with small or rapidly changing populations. This uncertainty can be dealt with by presenting a range of projections or by developing statistical prediction intervals. The latter can be based on models that incorporate the stochastic nature of the forecasting process, on empirical analyses of past forecast errors, or on a combination of the two. In this article, we develop and test prediction intervals based on empirical analyses of past forecast errors for counties in the United States. Using decennial census data from 1900 to 2000, we apply trend extrapolation techniques to develop a set of county population forecasts; calculate forecast errors by comparing forecasts to subsequent census counts; and use the distribution of errors to construct empirical prediction intervals. We find that empirically-based prediction intervals provide reasonably accurate predictions of the precision of population forecasts, but provide little guidance regarding their tendency to be too high or too low. We believe the construction of empirically-based prediction intervals will help users of small-area population forecasts measure and evaluate the uncertainty inherent in population forecasts and plan more effectively for the future.

Projections of future populations are integral to many planning applications, yet are often poorly understood. This analysis focuses on the implications of the choices planners make when they construct projections. Specifically, it examines the impact of length of base period, analyzes the error structure of projection techniques for counties in the aggregate and by size and growth rates, investigates the role of averaging, and compares the performance of trend extrapolation and cohort—component methods. The article concludes by discussing forecast complexity, data quality, the role of assumptions, and other considerations of forecasting in a planning context.