Saturday, September 27, 2014

Wage inequality vs. compensation inequality

Some of my fellow grad students at Clemson are doing research on wage inequality. At a seminar yesterday one of them stated that wage inequality between high skilled workers and low skilled workers, where skill is measured by educational attainment with a bachelor's or more being considered high skilled, is still increasing but since the 1990's is doing so at a declining rate. The diagram below shows what this looks like:

The Y axis is the ratio of a high skilled person's wage to a low skilled person's wage. The X axis is time. Two things could be happening to cause this trend; either the high skilled wage could be decreasing over time or the low skilled wage could be increasing over time.

My criticism of wage inequality is that it measures the wrong thing. No economic actor, neither workers nor firms, cares about wages. Firms care about the total cost of hiring a worker and workers care about the total compensation they receive for their labor. Any analysis that ignores other forms of compensation such as health insurance, paid vacation, paid sick leave, paid maternity leave, and other pecuniary and non-pecuniary benefits is incomplete and could be very misleading.

For example, let's just look at compensation as the sum of the wage and the portion of a worker's health insurance premium that is paid by the employer, W + H. Also, let's assume that the insurance premium is not correlated with skill type, but instead only varies by the personal health and family characteristics of the worker. What this means is that a firm will pay the same health insurance premium for a high skilled male who is 50 years old, makes $150K/yr, doesn't smoke, and has 2 teenage children living at home as it will for a lower skilled male in the same circumstances except the low skilled person only makes $45K/yr. I think this is a reasonable assumption, as risk pooling is done based on the risk factors of the individual, not their degree or IQ (of course if IQ is strongly correlated with healthy living this may not be true, but I don't think that is the case).

The wage inequality between these two workers, 150/45, is 3.33. If we set the portion of health care paid by the employer at H = $8K/yr, which appears to be on the low side, then the compensation ratio is 158/53 =  2.98. The addition of a fixed cost to each worker that does not depend on their wage or value added to the firm makes the low skilled worker relatively more expensive than the high skilled worker and decreases the inequality measure that real people actually care about. If health insurance costs to the firm are increasing over time, as the Forbes article linked to above shows, then over time we would expect to see inequality decreasing when total compensation is used instead of wages.

What this means is that inequality may not be as high as people think. The addition of other forms of compensation that stay relatively constant across skill levels decreases the real inequality of the two skill levels.

Some people are probably thinking that most "low skilled" people e.g. high school graduates do not get insurance, paid vacation, sick days, etc. and this is true. So let's think about adding a third category, medium skilled. These are white collar or high skilled blue collar workers who have technical degrees, associates degrees, or bachelor's degrees but are not on an executive management track and earn between $35K/yr and $80K/yr with little prospect of ever earning above the high end of that scale. They are solidly in the middle class and often receive health insurance, paid vacation, etc.

Let's use the $150K for the high skilled worker, $60K for the medium skilled worker, and $30K for the low skilled worker. Let's assume that only the high skilled and the middle skilled receive compensation other than wages. So the high skilled/medium skilled wage ratio is 150/60 = 2.5 and the medium skilled/low skilled wage ratio is 60/30 = 2.

Now let's add insurance and calculate the compensation ratios. The high skilled/medium skilled is 158/68 = 2.32 and the medium skilled/low skilled is 68/30 = 2.27. So when insurance is included the medium skilled worker has become more expensive relative to both the high skilled worker AND the low skilled worker. The addition of other forms of compensation makes medium skilled workers the most expensive workers of the firm from a value added perspective.

If this is happening it can help explain the hollowing out of middle income jobs. Middle income jobs have not recovered since the recession but both low and high skilled have. Employers may have been waiting for an opportunity to reduce their middle income workforce because of the compensation dynamics I just described above and the recession presented the opportunity to do so. Now they are reluctant to create those jobs again because they are relatively more expensive than both high and low skilled jobs due to the fixed forms of compensation that stay relatively constant across skill level.

I am not claiming that this is precisely what happened but it is one story. I would like to see some more evidence but unfortunately there is not much data available on total compensation which is why nearly all of the inequality studies use wage. But that is an incomplete measure and ignores the story I just told.


  1. When you compare middle to low wages with and without fixed compensation, you forgot to add insurance pay to the low skilled worker, which then gives you the ratio of 68/38. This implies middle-wage workers are less expensive relative to low-wage workers when adding in a fixed cost uniform across wage levels.

    Also I think it's a stretch to say non-wage consumption is uniform across wage groups. If you look at the average 401(k), where an employee contributes a portion of his/her income to a tax free account, the firm usually matches this amount up to a certain percent...implying higher wage earners are getting larger non-wage benefits.

    1. I kept the H out of the low skilled worker's compensation on purpose.

      "Let's assume that only the high skilled and the middle skilled receive compensation other than wages."

      And the reason is that many low skilled jobs are part time and worker's do not qualify for many non-wage benefits. A simplification, sure, and not true in all cases but true in many.

      And even if non-wage compensation does vary by wage level, the above analysis still holds as long as the variation in non-wage compensation is smaller relative to the variation in wages. And I think it is true that non-wage compensation cannot be as easily adjusted based on marginal productivity as wages because all workers in firms are bound by the same non-wage compensation plan. At chase for example, I got the same health insurance options, same vacation policy, same access to onsite nurses, etc. as SVPs making 4 times my wage.

  2. Understood, I didn't see that one sentence...however I thought the point of this post is claiming inequality might not be as strong when you add fixed costs of labor. If low skilled labor don't have these fixed costs when higher skilled workers then inequality is even worse than if you only look at wages.

    1. Yes, it could be. It depends on which groups you are looking at and which time period.

      Low skilled jobs have never had certain non-wage compensation so the inequality between those workers and high skilled workers is likely larger than when only looking at wages and may or may not be increasing over time; it depends on whether the non-wage compensation as a proportion of income is going up. Of course with low skilled workers we would have to account for the govt benefits they receive, such as food stamps, subsidized health care, child care, heating, etc. If these are increasing over time faster than non-wage compensation inequality might be decreasing.

      For middle skilled vs. high skilled workers it could be decreasing over time rather than increasing if non-wage compensation is at the same rate for both high skilled and middle skilled.

      Regardless of whether inequality is increasing or decreasing, only looking at wages and ignoring both non-wage compensation and govt redistribution is misleading.