Working paper

Forecasting mortality in New Zealand

Deaths Demographics New Zealand
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In Forecasting mortality in New Zealand: A new approach for population projections using a coherent functional demographic model, we summarise the investigation of a new method for formulating mortality assumptions (ie forecasting mortality) that was implemented in official New Zealand population projections in 2012.


Long-term (100-year) forecasts of male and female age-specific death rates are produced using a coherent functional demographic model developed by Hyndman, Booth, and Yasmeen (2013). This method builds on the functional demographic model of Hyndman and Ullah (2007), which is itself an extension of the Lee-Carter model widely used in mortality forecasting. The research of those authors and Booth, Hyndman, Tickle, and de Jong (2006) shows that FDM forecasts are more accurate than the original Lee-Carter method and at least as accurate as several other Lee-Carter variants. The advantage of the coherent functional demographic model is that it ensures male and female forecasts do not diverge over time. This method uses smoothed historical mortality data to fit the model, which is then forecast using ARIMA and ARFIMA time series models. We used Hyndman's demography package for R to carry out the forecasts.


We fit the model to the last 35 years of data, 1977–2011, so the forecasts reflect this period of sustained mortality reductions. A fitting period of 35 years is short relative to our 100-year forecast period and results in underestimation of uncertainty bounds. To achieve more realistic uncertainty bounds, an ARIMA(0,2,2) model was used in place of the usual ARIMA(0,1,1). This results in only small changes to the forecast age-specific death rates, but more realistic uncertainty bounds.

Another adjustment to the forecast death rates was necessary due to an obvious disjuncture between the death rates in the final year of the fitting period and the first year of the forecast, with males having a sudden decrease and females a sudden increase in life expectancy at birth. This bias is sufficiently large to result in unrealistic forecasts of death numbers which are particularly obvious for the first few years of the forecast. We therefore applied adjustments to the age-specific death rates in 2012 to give a shift in life expectancy at birth of approximately +0.7 years for males and –0.2 years for females. These adjustments were amortised (smoothed in) over the 100-year forecast period so that the 2111 life expectancies at birth are the same as those produced directly from the model.


The coherent functional demographic model gives an empirical basis for forecasting mortality for use in population projections, and a model that can be replicated by others. The coherence of male and female death rates, with modelled prediction intervals, are important aspects of the method. Further refinements to the model are expected in future, especially in the derivation of the uncertainty bounds.

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