Why Average Incomes Tell Us Nothing About Real World Inequality

When the experts tell us that average incomes have risen, what does that actually tell us? Not much that’s useful in understanding real world politics and the inequities of economic life. I know that most of us understand averages, now don’t we? What’s there to explain? Well, let’s have a look at average incomes.

Incomes can be looked at using three measures of central tendency: the mean (the average), the median and the mode. For a technical explanation of these terms see: https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php.

Each of these measures has its advantages and disadvantages.¬† If we take a population and want to figure out their average height, it’s simple: measure each individual in the population, add the heights of all of them together and divide by the number of individuals measured. It’s unlikely that all people in a population would be of the same stature, and it doesn’t tell us anything about the range of heights. It’s always good to know what the range is otherwise there’s no way of judging just how variable the heights are in a population. Same goes for incomes. Scenario A below is of a fictitious population of income earners that each earns $100 thousand dollars each per year. That makes the total incomes earned by the group $1 million dollars and the average is $100 thousand. If you know where such a world exists, please let me know.

Scenario A  
Income Earner Income $ % of total income
Income earner 1 100,000 10
Income earner 2 100,000 10
Income earner 3 100,000 10
Income earner 4 100,000 10
Income earner 5 100,000 10
Income earner 6 100,000 10
Income earner 7 100,000 10
Income earner 8 100,000 10
Income earner 9 100,000 10
Income earner 10 100,000 10
Total Income 1,000,000 100
Average Income 100,000  

Now, let’s consider Scenario B below. The total income of all ten earners is still $1 million and the average is still $100 thousand. What’s changed? The distribution. In this scenario, the highest income earner brought in $200 thousand while the lowest earner brought in $45 thousand. That’s a significant difference and means that there is substantial income inequality but if a government wanted to obfuscate rather than clarify the issue, it might want to argue that average incomes haven’t changed. What are you worried about?

Scenario B  
Income Earner Income $ % of total income
Income earner 1 200,000 20.00
Income earner 2 150,000 15.00
Income earner 3 130,000 13.00
Income earner 4 100,000 10.00
Income earner 5 95,000 9.50
Income earner 6 85,000 8.50
Income earner 7 75,000 7.50
Income earner 8 65,000 6.50
Income earner 9 55,000 5.50
Income earner 10 45,000 4.50
Total Income 1,000,000 100.00
Average Income 100,000  

Now, consider this third scenario. The total incomes are still $1 million, the average is still $100 thousand. However, in this scenario, the highest income earner is taking in 72.7 of the total income. This scenario pushes income inequality to a much greater degree.

Scenario C  
Income Earner Income $ % of total income
Income earner 1 726,990 72.70
Income earner 2 85,000 8.50
Income earner 3 45,000 4.50
Income earner 4 20,430 2.04
Income earner 5 20,430 2.04
Income earner 6 20,430 2.04
Income earner 7 20,430 2.04
Income earner 8 20,430 2.04
Income earner 9 20,430 2.04
Income earner 10 20,430 2.04
Total Income 1,000,000 100.00
Average Income 100,000  

Now, think of a situation where aggregate incomes rise, but the lowest earners retain their share of earnings at 2.04 percent. Now the government can say: What are you worried about? Your income hasn’t changed at all and the country is getting richer. Silly you. Maybe you should just work a little harder.

Calculating median income isn’t much more helpful. The median income is the point where half the incomes are above and half below. That will tell us if a population distribution is changing in broad terms, but the median income in scenario C is $20,430.00. What does that tell you about the distribution of incomes in this population.

Calculating the modal income is interesting. The modal income is the one that appears most often in a distribution. In scenario C, the modal income is clearly $20,430.00. That’s the income most people make. It still doesn’t shed much light on the inequality in a distribution.

So, we always need more than a measure of central tendency to tell us what’s really going on in the world in terms of income inequality. If the government, or the head of the Bank of Canada for example, tells you that average incomes are rising, know that you’re not being told the whole story.

If you’re not concerned about these things, never mind.

Note: this post was inspired by a section of Robert Sapolsky’s book: Why Zebras don’t get ulcers.

 

Growing grapes on the Beaufort Range.

I live on one of the main roads that lead out of Cumberland, BC. Cumberland is on the eastern slopes of the Beaufort Range at about a 500 foot altitude. Over the past few weeks we have witnessed at least a dozen logging trucks headed out of town every week day down the Trent River Main headed who knows where. That’s been going on for years but it seems logging activity is picking up around here. Certainly, the clearcuts are getting bigger and bigger just up the slopes from our little community and they’re getting more numerous.

I don’t know much about what sustains a forest. I’m a sociologist, not a biologist nor an ecologist. What the ecologists tell me, however, is frightening. Logging and development are wreaking havoc with ecosystems and changing the landscape in very visible ways. I’m of two minds about that. Should we care?

But let me step back for a moment and ask a few questions some of you may have answers to.

  1. Given climate change and the report yesterday that increasing temperatures are accelerating, has anyone given thought to how a changing global climate will impact our forest and marshland ecosystems on Vancouver Island?
  2. Is there a tipping point where the amount of logging in any specific area will permanently change the local climate so that certain species of trees cannot grow here any longer?
  3. In the foreseeable future are we looking at the conditions ideal for growing grapes on the hillsides above Cumberland? Are we looking at a potential wine growing situation here?

I know that logging in the Comox Valley and in most areas on the eastern slopes of Vancouver Island mountain ranges is proceeding apace. I’m not at all against logging per se. After all, I’m a woodworker and sculptor in wood. We also still burn wood on occasion in our wood stove. I do, however, question the logic of the kind of clearcut logging we’re witnessing here. There are many ways that forests can serve the economic interests of communities and I’m not at all sure that what’s happening here at the moment is in our best interests. There are alternatives, but I doubt that they are given serious consideration.

Given that the mountain sides above us are all privately owned by logging companies who are themselves largely owned by pension funds, the current model is unlikely to change. Making pots of money is the name of the game and quarterly profits must increase or shareholders may look to invest their money elsewhere. I’m not sure pension managers know anything about logging or forestry, but they do know how to push for increased revenues. So, forestry managers must deliver the goods or risk losing their stake in the venture.

In some ways I grieve the loss of the wonderful forests that surround us, but I also realize that the land hereabouts was pretty much clearcut a hundred years ago to resemble a barren landscape. We live in second and third growth tree plantations, not forests. I’m quite shocked at the size of much of the timber I see leaving on the trucks by my home. I can’t image many of the logs on those trucks would be of much use except to make pulp or chips for strandboard, nor can I image you’d get as much as a 2X4 out of some of them.

That said, maybe I need to chill out and accept what’s happening. After all, I enjoy a nice Chardonnay. Maybe, soon enough, we’ll be a world class wine growing area with a balmy climate while California becomes a desert once again. Maybe we’ll have vineyards as far as the eye can see. Cheers! Maybe we can grow hops too!