data2 = data.frame('population by age' = seq(3, 24, by = 1),
                   '2008' = c(145391,
                              140621,
                              136150,
                              131944,
                              127968,
                              124209,
                              120650,
                              117163,
                              113674,
                              110207,
                              106871,
                              103659,
                              100398,
                              97017,
                              93584,
                              90240,
                              86957,
                              83783,
                              80756,
                              77850,
                              75003,
                              72226
                   ),
                   '2009' = c(148566,
                              143943,
                              139367,
                              135083,
                              131052,
                              NA,
                              123628,
                              120213,
                              116826,
                              113381,
                              109915,
                              106574,
                              103346,
                              100058,
                              96644,
                              93175,
                              NA,
                              86455,
                              NA,
                              80192,
                              77279,
                              74422
                   ),
                   '2010' = c(152330,
                              147261,
                              142555,
                              138172,
                              134071,
                              130214,
                              126559,
                              123099,
                              119825,
                              116538,
                              113134,
                              109669,
                              106320,
                              103075,
                              99760,
                              96312,
                              92805,
                              NA,
                              NA,
                              82733,
                              79661,
                              76739
                   ),
                   '2011' = c(156630,
                              151387,
                              146491,
                              141905,
                              137593,
                              133545,
                              129737,
                              126124,
                              122678,
                              NA,
                              116093,
                              112666,
                              109174,
                              105791,
                              102505,
                              99159,
                              95699,
                              92193,
                              88759,
                              85373,
                              82123,
                              79065
                   ))


data7 <- data2 %>%
  gather(key = year, value = value, -`population.by.age` )%>%
  group_by(`population.by.age`) %>%
  nest
library(imputeTS)
impute_nas <- function(df, var, fun, ...) {

  df[[var]] <- fun(df[[var]], ...)

  return(df)
}
imputed <- data7 %>%
  mutate(
    interpolation = purrr::map(data, impute_nas, var = 'value', fun = imputeTS::na.locf)
    ) %>%
  select(-data) %>%
  unnest

imputed <- imputed %>% spread(key = 'year', value = 'value')
as.data.frame(imputed)

impute_from_previous <- function(ds) {

  for (i in 2:length(colnames(ds))) {
    rows_missing <- which(is.na(ds[[i]]))
    ds[rows_missing, i] <- ds[rows_missing, i - 1]
  }
  return(ds)
}

data3 <- impute_from_previous(data2)