MortCast-package {MortCast}

MortCast: Estimation and Projection of Age-Specific Mortality Rates

Description

Age-specific mortality rates are estimated and projected using the Kannisto, Lee-Carter and related methods as described in Sevcikova et al. (2016) <doi:10.1007/978-3-319-26603-9_15>.

Details

The package implements methodology described in Sevcikova et al. (2016) that is related to estimating and predicting age-specific mortality rates. The main functions are:

• cokannisto: Extrapolates given mortality rates into higher ages using the Coherent Kannisto method. The original Kannisto method (with sex-independent extrapolation) is avalable in the function kannisto.

• lileecarter.estimate: Estimates the coherent Lee-Carter parameters for male and female mortality rates (Li and Lee 2005), i.e. sex-independent parameters a_x and k_t, and the coherent parameter b_x. In addition, it computes the ultimate b^u_x for rotation (Li et al. 2013). The underlying sex-independent estimation is implemented in the function leecarter.estimate.

• mortcast: Using estimated coherent Lee-Carter parameters and given future sex-specific life expectancies, it projects age-specific mortality rates, while (by default) rotating the b_x parameter as described in Li et al. (2013).

Functions contained in the package can be used to apply Algorithm 2 in Sevcikova et al. (2016) as shown in the Example below. It can be used for both, 5-year and 1-year age groups.

Other methods for forecasting mortality rates are available:

• pmd: pattern of mortality decline

• mlt: model life tables

• logquad: log-quadratic mortality model

• mortcast.blend: combining two different methods

A life table can be constructed using the life.table function.

Author(s)

Hana Sevcikova, Nan Li and Patrick Gerland

References

Li, N. and Lee, R. D. (2005). Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42, 575-594.

Li, N., Lee, R. D. and Gerland, P. (2013). Extending the Lee-Carter method to model the rotation of age patterns of mortality decline for long-term projections. Demography, 50, 2037-2051.

Sevcikova H., Li N., Kantorova V., Gerland P., Raftery A.E. (2016). Age-Specific Mortality and Fertility Rates for Probabilistic Population Projections. In: Schoen R. (eds) Dynamic Demographic Analysis. The Springer Series on Demographic Methods and Population Analysis, vol 39. Springer, Cham. Earlier version.

Examples

# This example applies Algorithm 2 in Sevcikova et al. (2016) 
# on data from WPP2017 for China
#
data(mxM, mxF, e0Fproj, e0Mproj, package = "wpp2017")
country <- "China"

# extract observed mortality rates for male and female
mxm <- subset(mxM, name == country)[,4:16]
mxf <- subset(mxF, name == country)[,4:16]
rownames(mxm) <- rownames(mxf) <- c(0,1, seq(5, 100, by=5))

# Step 1: extrapolate from 100+ to 130+ using Coherent Kannisto
mx130 <- cokannisto(mxm, mxf)
 
# Steps 2-5: estimate coherent Lee-Carter parameters
# (here ax is computed from the last observed period 
# and smoothened over ages)
lc.est <- lileecarter.estimate(mx130$male, mx130$female, 
            ax.index = ncol(mx130$male), ax.smooth = TRUE)
        
# Steps 6-9: project future mortality rates based on future 
# life expectancies from WPP2017
e0f <- as.numeric(subset(e0Fproj, name == country)[-(1:2)])
e0m <- as.numeric(subset(e0Mproj, name == country)[-(1:2)])
names(e0f) <- names(e0m) <- colnames(e0Fproj)[-(1:2)]
pred <- mortcast(e0m, e0f, lc.est)

# plot projection for the first and last future time period
plot(pred$female$mx[,"2015-2020"], type="l", log="y", 
    ylim=range(pred$female$mx, pred$male$mx), xaxt="n",
    ylab="mx", xlab="Age", main=country, col="red")
axis(1, at=1:nrow(pred$female$mx),
    labels=rownames(pred$female$mx))
lines(pred$male$mx[,"2015-2020"], col="blue")
lines(pred$female$mx[,"2095-2100"], col="red", lty=2)
lines(pred$male$mx[,"2095-2100"], col="blue", lty=2)
legend("topleft", legend=c("male 2015-2020", "female 2015-2020",
    "male 2095-2100", "female 2095-2100"), bty="n",
    col=rep(c("blue", "red"),2), lty=c(1,1,2,2))