Definition

The wage of workers at the 90th percentile divided by the wage of workers at the 50th percentile.

This is a common measure of wage inequality/dispersion among economists.

Calculating Percentiles in R

In the example below we show you how to get the percentiles for any distribution using the quantile function.

We’ll do this with some sample data combining a normal distribution for the bulk of our employees plus a sprinking of high earners because wages within an organization are not typically normally distributed.

set.seed(42) # so we can reproduce our wages
# sample data with multiple distributions combined for some extra high earners
wage <- c(rnorm(n = 2000, mean = 60, sd = 15), rnorm(150, 200, 30 ))

# Love them distributions

hist(wage, col = 'red3', border = 0)

# Getting the percentiles for the 90 and 50

quantile(wage, probs = c(.90, .50))

##      90%      50% 
## 86.79506 61.01537

# Percentiles by 10% chunks to illustrate another use 
quantile(wage, probs = seq(0, 1, .1))

##         0%        10%        20%        30%        40%        50% 
##   9.423914  41.587057  47.724970  53.056375  57.200956  61.015370 
##        60%        70%        80%        90%       100% 
##  65.214898  69.995150  75.792010  86.795063 270.071026

# Calculating the 90/50 ratio
# using as.numeric to drop the 90% and 50% labels from quant
quant <- as.numeric(quantile(wage, probs = c(.90, .50)))
quant[1]/quant[2]

## [1] 1.422511

This result with our sample data shows that those at the 90% percentile earn 142% percent of those at the 50% percentile.

Note: Please do not look into this number as a benchmark; it is only illustrative of the method.

Why You Should Care

Wage inequality is perhaps the biggest topic in current socio-economic discussions in the United States.

To the extent that an individual organization begins to ask questions about wage inequality within its own walls, you can have confidence that the 90/50 wage ratio will provide you one commonly used indicator of wage dispersion.

References

• Mind the Productivity Gap to Reduce Inequality
  • This is a great article although you’ll need a subscription
• Performance pay and within-firm wage inequality
  • Not for the faint-hearted. See esp. pg 17 for some measurement approaches
• Does Automation Affect Employment and Income Inequality?
  • Great tidy paper from the Federal Reserve of St. Louis