Exploring Mortality Differentials in the CenSoc-DMF Demo Dataset

Summary: This vignette gives an overview of the CenSoc-DMF Demo dataset and presents two stylized examples on state variation in longevity and wage income. The goal of this vignette is to give users a high-level overview of working with CenSoc data, including the use of weights, the specification and visualization of regression models, and the use of the WAGEINC variable in the 1940 census.

The CenSoc-DMF Demo dataset was constructed by (i) linking the CenSoc-DMF dataset to the IPUMS 1940 1% census sample and (ii) selecting a set of 20 mortality covariates from the 1940 census. The smaller size of the file — approximately 1% of the records in the full CenSoc-DMF dataset — makes it easier to work with but precludes the high-resolution mortality research possible with the full CenSoc-DMF dataset.

## Library Packages
library(tidyverse)
library(statebins)
library(broom)
library(knitr)

## make sure to update the path to your CenSoc file
censoc_demo <- read_csv("/data/censoc/censoc_data_releases/censoc_dmf_demo/censoc_dmf_demo_v2.1/censoc_dmf_demo_v2.1.csv")

## state strings
state_strings <- read_csv("/data/censoc/miscellaneous/ipums_bpld_usa.csv")
names(state_strings) <- c("bpl", "bpl_string")
censoc_demo <- censoc_demo %>% left_join(state_strings, by = "bpl")

## set seed for reproducibility 
set.seed(16)

## Look at a handful of people with a non-missing wage
censoc_demo %>% 
  select(byear, dyear, death_age, race, educd, bpl, incwage, urban) %>% 
  sample_n(6) %>% 
  filter(incwage < 99999) %>% 
  kable()

byear	dyear	death_age	race	educd	bpl	incwage	urban
1918	1992	73	1	26	3900	22	2
1913	1995	81	1	60	2100	1620	2
1913	1996	82	1	60	1700	120	1
1919	1988	68	1	50	2500	250	2
1913	1992	79	1	110	3600	2300	2
1910	1995	85	1	60	46500	1000	2

Note: For the CenSoc-Demo dataset, we converted the IPUMS numeric codes into meaningful character value labels (e.g., “Male” = 1, “Female” = 2). Before using a variable in your analysis, it is a good idea to learn more about its coding schema. Check out the terrific documentation from the IPUMS-USA website.

Examples with OLS Regression

Using OLS Regression on age of death with fixed effect terms for each year of birth is a straightforward method for analyzing CenSoc mortality data. There are a few specific considerations for using regression on age of death to analyze the CenSoc Mortality data. The CenSoc-DMF file only includes deaths occurring in the window of 1975-2005 (the period with high death coverage). As the left and right truncation ages vary by birth cohort, it is important to include fixed effect terms for each year of birth. Models of the form:

\[ Age\_at\_death = birth\_year\_dummy + covariates\_of\_interest \]

provide estimates of the effect of the covariates on the age of death in the sample, controlling for birth cohort truncation effects. In this example, we work with the cohorts of 1900-1920, so we need to include a fixed effect term for year of birth.

As the truncated window of deaths excludes the tails of the mortality distribution, any measurement of the average difference between groups will be downwardly biased. The coefficients in our OLS regression model will underestimate the size of the true effect. For a more detailed discussion of mortality estimation with truncated data, see the “The Berkeley Unified Numident Mortality Database” working paper.

Mortality Differentials by State

Geographic heterogeneity in levels of health and mortality is well documented. Can we see any state-level variation in life expectancy at age 65 in the CenSoc-DMF Demo dataset?

The code below runs an OLS model with year fixed effects. It then extracts the regression coefficient for each state and plots it using the statebins package, which provides an alternative to state-level choropleth maps. For the example below, we use Maine’s 1910 birth cohort as the reference group, although the example will work with other state/birth cohort parameters.

The CenSoc-DMF file is already restricted to deaths occurring in the “high-coverage” period of 1975-2005. We further restrict this analysis to the birth cohorts of 1900 to 1920 and deaths for persons 65+ (these are the birth cohorts and ages at death for which we have the best death coverage).

## Prepare dataset for modeling
## Restrict to birth cohorts of 1900-1920
## Years of death already restricted to "high-coverage" period of 1975-2005
censoc_state_model <-
  censoc_demo %>%
  filter(byear %in% c(1900:1920)) %>% 
  filter(dyear >= 65) %>% 
  filter(bpl_string != "Hawaii" & bpl_string != "Alaska" & bpl_string != "Puerto Rico") %>% 
  mutate(byear = as.factor(byear)) %>% 
  mutate(byear = relevel(byear, ref = "1910")) %>%
  mutate(statefip = as.factor(bpl_string)) %>% 
  mutate(statefip = relevel(statefip, ref = "Maine")) 

## Linear model predicting age at death from State and byear 
## Use both IPUMS and CenSoc weights
state.lm <- lm(death_age ~ statefip +  byear,
                     data = censoc_state_model,
                     weight = weight*perwt) 

## Put model results into a data.frame 
state.lm.df <- tidy(state.lm)

## Select coefficients and ZIP Codes
state.lm.df <- state.lm.df %>%
  select(term, estimate) %>% 
  filter(str_detect(term, "statefip")) %>% 
  mutate(state = substr(term, 9, 35)) %>% 
  select(state = state, estimate) %>% 
  add_row(state = "Maine", estimate = 0) ## add Maine as zero value 

## Plot using State Bins Package
mortality_differentials_by_state <- ggplot(state.lm.df, aes(state=state, fill=estimate)) +
  geom_statebins() +
  coord_equal() +
  scale_fill_distiller(palette = "RdYlBu", 
                       direction = 1,
                       name = "Mortality Differential (Yrs)")+
  labs(title="Mortality Differentials By State") +
  theme_statebins() +
  theme(plot.title=element_text(size=17, hjust=0)) 

## Display Plot
mortality_differentials_by_state

Our figure indicates that the Mountain and Southwest States have a relative mortality advantage while the Southern States have a relative mortality disadvantage. While these patterns may be real, we should keep in mind disaggregating by state significantly reduces our sample size. This introduces a lot of noise and uncertainty into our regression model — which our visualization does not capture.

Mortality Differentials by Relative Wage Income

The association between relative income and mortality in the United States is well documented, as well. Can we see this association in our CenSoc-DMF Demo dataset?

To answer this question, we will use the INCWAGE variable. The variable is limited: census enumerators in 1940 were instructed to “not include earnings of businessmen, farmers, or professional persons who depend upon business profits, sales of crops, or fees for income and who do not work for wages or salaries,” leaving only salary and wage workers in the dataset. For more information, check out the 1940 census’ instructions to enumerators. We will account for the discrepancy in our analysis by only including persons with non-zero wages — other researchers may take a different approach.

## Calculate income deciles
## Restrict to cohorts of 1900-1920
censoc_incwage <- censoc_demo %>% 
  filter(byear %in% c(1900:1920)) %>% 
  filter(dyear >= 65) %>% 
  filter(incwage > 0 & incwage <= 5001) %>% ## INCWAGE is topcoded at $5001; higher values denote NA/Missing
  mutate(wage_decile = ntile(incwage, 10)) %>% 
  
  mutate(wage_decile = as.factor(wage_decile))

## Run linear model 
## Use both IPUMS and CenSoc weights
test <- lm(death_age ~  wage_decile +  byear + as.factor(race),
                     data = censoc_incwage,
                     weight = weight*perwt) 

## Put model results into a data.frame 
test.df <- tidy(test, conf.int = T)
  
## Select coefficients and standard errors from OLS model
test.df <- test.df %>%
  select(term, estimate, se = std.error) %>% 
  filter(str_detect(term, "wage_decile")) %>% 
  mutate(quantile = as.numeric(substr(term, 12, 15))) %>% 
  select(quantile, value = estimate, se)

## Plot 
income_decile_ols_coefficients <- ggplot(data = test.df) + 
  geom_pointrange(aes(ymin = value - se, ymax = value + se, y = value, x = quantile)) + 
  theme_bw(base_size = 15) + 
  labs(title = "Income pattern of Longevity at Age 65",
       x = "Wage Income Decile",
       y = "Additional Years of Life")

## Display Plot
income_decile_ols_coefficients

The plot shows an association between relative wage income and longevity. The reference group for this plot is the first income decile. When interpreting these mortality differentials, we should keep in mind that they are calculated from a truncated window of deaths and understate the differences in life expectancy at age 65.

Exploring Mortality Differentials in the CenSoc-DMF Demo Dataset

Casey Breen (caseybreen@berkeley.edu)

2023-12-07

Examples with OLS Regression

Mortality Differentials by State

Mortality Differentials by Relative Wage Income

Conclusion