Monday, July 14, 2008

Why Top Earners Earn More

I've always been fascinated with reports on how the top 1% or 10% of people earn as much as the bottom 10% or 50%. I don't see how this is news.

If you take 100 people, and each earns $1, $2, $3, ... $100, i.e. a perfectly flat distribution, then the top earner earns as much as the bottom 13. The top 10 earn as much the bottom 44.

This is because the top earner earns 100 times what the bottom one does. If the top earner earns only 5 times what the bottom one does, i.e. the salaries go from $100 to $500 in steps of $4 (and change), then the top earner earns as much as the bottom 4, and the top 10 as much as the bottom 29.

This assumes a flat distribution. With a natural bell curve, we end up somewhere back to something that looks more like the first case: the top earner is going to earn more than a boat load of people at the bottom. This makes sense.

This doesn't sit well with a lot of people. Either it's because the top earner is presumed to have acquired his wealth/income through unfairly distributed luck, childbirth, or access to resources, or because the top earner should be paying more to help society based on his income.

If everyone paid 10% of his income to taxes, then the top earner is paying 100, or 5, times more than the lowest earner. More is demanded, because even after this payment the richest should be able to afford more. Presumably, this more isn't so much so that, after paying, the richest earner takes home the same amount as the poorest.

So a "fair" amount is enough so that less well-to-do, less lucky, or less hard working people feel that the rich person has contributed more in both absolute and percentage terms, but not so much so that the rich person throws up his hands and says "why bother?" This "fair" amount is going to leave the rich person still richer than anyone else, by several multiples.

So if the highest earning person earns XXX% more than the lowest, or earns as much as X number of lowest earning people, does that mean that something is wrong? Is our goal to make the income of the highest and lowest earners as close as possible? Or to make the life of the lowest earners as good as possible?



David Klein said...

The point is obviously a question of degree. The claim is that in Israel the ratio of earnings between the top and bottom is "too large" a very subjective statement, but an important question non the less.

As a cute aside: If there was a boom in Israel's high tech industry, which doubled everyone's salary, what would be the effect on the number of poor people in the country?

Think about it for a few seconds...

Answer: The number of poor people would increase. The reason is that the poverty line is defined not by how much people can afford to buy, but as an arbitrary fraction of the average wage in the country. Increasing one sectors wealth is considered to harm others. I am not talking here of the possibly real effect of costs going up due to increased demand from the wealthy. When raising my kids I try hard to root out this type of feeling of jealousy. Just because one kid received something extra doesn't mean that the other kid is worse off. (I am not referring to playing favorites among kids, which should obviously be avoided)

Clay B. said...

It seems when conservatives give this type of statistic they are of the form "The top X% of individuals pay Y% of tax." to emphasize how much the top tiers are taxed, and when liberals do it they say "The top X% of individuals make Y% of the money." to emphasize the income inequality. It would be more informative if these items were presented together (X% of the people make Y% of the money and pay Z% of the taxes.).

Yehuda said...

David, my point, exactly. I don't think it matters who has more than you. All that matters is that you can live healthy and safe, and thrive if you try.


Mark (aka pastor guy) said...

Have you read Mark Buchanan's "The Social Atom"? One of the issues he tackles in the book (which is about applying principles from physics to the social sciences) is wealth distribution.

I'm not sure I agree with him (particularly on his views on religion) but I found the work fascinating to read.

.o. said...

Heh, this is funny. I stumbled across this blog among some D&D links, and now I'm pondering deep econ questions...

This is an interesting topic, and fairly complex. I know just enough about the topic to know that I don't know squat. Some things to consider:

Greater income inequality is associated with a decrease in income mobility. In other words, as the gap between income quartiles grows, people and their offspring are more likely to stay within the income quartile they were born into.

This is probably most apparent with education. Students who have early childhood education have very high correlations with positive post-secondary education outcomes. The lowest income quartiles have trouble paying for this, while the highest do not. Income inequality gets reinforced. Children who have greater choice in educational opportunities (parents willing to relocate for schooling opportunities, income to attend public or private schools or get supplemental tutoring) strongly have greater outcomes. This again ossifies classes. Same for high school prep, same for schools in neighborhoods with high HHI having superior per pupil revenue and resources due to private fundraising, same with the ability to afford and sustain post-secondary education, etc...

So a highly regressive taxation structure is meant to ameliorate this kind of calcified class stratification. Whew, that was a mouthful.

Another consideration is that wealth of correlates with political influence, in a variety of ways. Extremely wealthy people are able to disproportionately leverage political influence. I used to work for a national non-profit that was ostensibly grassroots but in reality was entirely beholden to Don Fisher, founder of the GAP. This organization has significant influence in some local and national policy decisions - while I happen to passionately support the cause, I'd be hard-pressed to call it a democratic process. People who happen to be against this cause are less than thrilled about our being bankrolled by billionaires, and simply can't compete with our funding. They tend to lose most political skirmishes with us not necessarily because our ideas have more merit (as much as I like to think that they do), but because we can out-spend them and have a well-coordinated central organization. Quite simply, if you live in America, Don Fisher's opinions on social policies probably matters a lot more than yours.

High levels of income inequality also result in exacerbating scarcity issues. Housing prices are most apparent where I live - income inequality has forced tremendous numbers to move out of the SF Bay Area and has priced home-ownership out of the reach for a large portion of the remainder.

There are other studies that demonstrate the multi-generational impact of home ownership. Homes are incredible capital generation machines - both in how they accumulate value over time and the ability to secure access to capital.

I think asking whether income inequality (or to what degree) is right or wrong, or what's the goal at a philosophical level, somewhat misses the point. Income inequality has very practical implications that directly affect whether a given person can "live healthy and safe, and thrive if you try".

Of course, I'm biased - I happened to have been born into the bottom quartile of HHI in 1977, and have managed to claw my way into a comfortable middle-class existence (albeit still unable to afford a house in SF...). But I credit regressive taxation for this achievement (food stamps, subsidized housing, education grants).

Anywho, apologies for the long post - I hadn't mulled this topic over in a while and it was fun to think about it!

Yehuda said...

Mark, .o.: Thanks.

What board games would most reflect these lessons?


David Klein said...

Yehuda said: "What board games would most reflect these lessons?"

Assuming Yehuda was referring to the excellent post of .o, I think that only poor board games would reflect those lessons. It is well known that board games that encourage "runaway leaders" are problematic.

(You can go too far in the other direction also though, I am starting to feel that only the very last turn of Power Grid has any effect on the outcome, barring truly lousy play in the initial 7 rounds or so)

.o. said...


Way to bring it back to gaming! That's a really good question. David's right - any game with runaway leader phenomena is generally considered a poor game. Even worse would be a game that allowed you to carry over advantage from one game to the next!

In game terms, I guess the core lessons I noted could be summarized as:

1. Once a player starts falling behind, often through no fault of one's own, it's easier to lose. The converse is also true. (This is common in any luck-driven game with resource management and cumulative advantage. e.g. Settlers of Catan, Monopoly)

2. Large amounts of advantage can allow a player to direct the game in a non-democratic fashion. (Republic of Rome, vote-buying is awesome!)

3. Exacerbating scarcity. I can't think of a game where this applies within the game mechanics. However, the interaction of real-world wealth and collectible games might illustrate this point. The Vintage and Legacy formats of Magic the Gathering are simply inaccessible to most players because of the astounding costs for older cards.

4. Perception of inequality. This wasn't part of my original meandering post, but it is important to note that a sensitivity to inequality seem to be hard-wired into human beings. There are many fascinating studies exploring inequality and fairness in game theory. The "tear down the leader even at my own expense" phenomena in games certainly must be part of any discussion on real-world income inequality.

5. Regressive taxation. In game design, we call these balancing or handicapping mechanisms. I can't think of any game that directly transfers wealth from one player to another, but many games have some sort of handicapping mechanism. (Warhammer's campaign system provides diminishing returns for more successful armies, Republic of Rome has a random mortality system that tends to harm the largest faction more, Shogun/Samurai Swords guarantees a substantial minimum income to keep a player in the game, Magic the Gathering allows the loser to decide who goes 1st in the next round, etc.)

All of these are poor analogies because games generally have a winner and a bunch of losers and are vectored toward creating that condition. But I guess they can somewhat reflect these points. I'd be stoked to hear other ideas.


David Klein said...

.o said:

"5. Regressive taxation. In game design, we call these balancing or handicapping mechanisms. I can't think of any game that directly transfers wealth from one player to another..."

Cities and Knights comes to mind. It has at least two differnt cards that allow you to take cards from a player who has more victory points than you.