Quick note: Earnings inequality and aging

By Matt Nolan 02/07/2014

Note:  I know I’m not replying to comments right now, I’m very sorry.  It isn’t you, it is me – this time of year is always pretty full on for me!  Keep an eye out – in the next couple of weeks I will find time to turn around and comment back.  Post will be a touch lighter as well – but I will try to have at least three things up a week!

Via Twitter came this cool graph from Wiki New Zealand.

I’m going to quickly note something from that graph.   If you have a peek at it, you may notice that the ratio of the average wage to the median wage rises over time (the average gets relatively higher).  This implies that the “wage distribution” is getting more (right) skewed – so that the right tail is “longer” (eg there are more/larger “high” incomes, relative to the average in the age group, cropping up).

Why is this the case?  Well a common explanation is that it takes time, effort, and investment for a firm to discover how productive a worker is – or on the other side for a worker to invest in their human capital.  When we are young, we are “relatively” similar – so our labour input is “relatively” homogeneous.  However, as we get older this investment, experience, and reputation effects begin to have a larger and larger role, pushing up wages.

This explains why the average and median rise with age (at least for the first 20/30 years), but why does this lead to such a greater dispersion and skew in the distribution?  Well, workers characteristics (their inherent skill, their preference regarding sacrificing consumption now to invest in human capital for the future) are either revealed (eg their natural skill level) or built up (eg their investment in human capital) through time, so the spread in wages increases as this information is revealed and people’s choices to invest begin to pay off!

Ok, I’m still ignoring the skew – we have a reason why the average/median rises, and why incomes become more spread/dispersed with age.  But why do we have this “skew”?  Since Pareto (at least) we have known that there is a big skew in wages, with the income distribution out of labour income looking like a “parade of dwarves with a few giants”.  However, here we know that the skew increases with age as well as its existence, so is there any story we can tie together to explain these facts?

This is an excellent question.  There are a few of answers I commonly hear:

  1. Power structures ensure that a few people are able to extract rent,
  2. The revealed marginal product of workers is right skewed,
  3. Individual characteristics of individuals are normally distributed.  However, when they are combined they form a log-normal distribution with relation to the workers ability to produce.

All three of these potential explanations could easily play a role, for our two stylized facts here:  The income distribution is right skewed, and this skew appears to rise with age.

Is that interesting!  Well I think so ;)