testing whether the mortality component of a sullivan decompo ought to be same for different prev scenarios

sullivan_decomp_mort_check.R

# Testing whether mort component should be identical in decomps where
# only prev swaps out
library(tidyverse)
library(HMDHFDplus)
library(DemoDecomp)

mlt <- readHMDweb("USA", "mltper_1x1", username = Sys.getenv("us"), password = Sys.getenv("pw"))
flt <- readHMDweb("USA", "fltper_1x1", username = Sys.getenv("us"), password = Sys.getenv("pw"))

mx2Lx <- function(mx){
  # (lazy-man's approximation)
  # we're not sacrificing too much precision here. just pretend...
  lx <- c(1, exp(-cumsum(mx)))
  (lx[-1] + lx[-length(lx)]) / 2
}

mxm <- mlt |> filter(Year == 2000) |> pull(mx)
mxf <- flt |> filter(Year == 2000) |> pull(mx)

sully <- function(mx, prev){
  Lx <- mx2Lx(mx)
  sum(Lx * prev)
}

sully_vec <- function(pars){
  dim(pars) <- c(111,2)
  sully(mx = pars[,1], prev = pars[,2])
}
prev_f_1 <- seq(0,.5,length=111)
prev_m_1 <- prev_f_1 * .8

prev_f_2 <- seq(.2,.6,length=111)
prev_m_2 <- prev_f_2 * .9

cc1 <- horiuchi(sully_vec, c(mxm,prev_m_1), c(mxf,prev_f_1), N = 20)
cc2 <- horiuchi(sully_vec, c(mxm,prev_m_2), c(mxf,prev_f_2), N = 20)

dim(cc1) <- c(111,2)
dim(cc2) <- c(111,2)

# first element is the mortality contribution
colSums(cc1)
colSums(cc2)

# no I'm curious what the mort-only difference is
mx2ex <- function(mx){
  sum(mx2Lx(mx))
}
mx2ex(mxf) - mx2ex(mxm)
horiuchi(mx2ex,mxm, mxf, N = 1000) |> sum()