UPDATE 9:30am get me rewrite! Readers ask for more clarity on what my point is, so a little added rewriting.
There has been a lot of passionate moral debate about US income inequality (Greg Mankiw recently got a torrent of abuse for the horrific sin of admitting that he was a rich person). But you have to UNDERSTAND income inequality before you CONDEMN it. By the end of this post, I’ll suggest a different angle.
So what if we step back from the moral judgments and just try to describe the upper echelons of US riches. Figure 1 below shows the likelihood of each level of income in the US income distribution, using the same logarithmic graph which was greeted with total incomprehension wild enthusiasm in a previous post.
Figure 1
In this graph, the vertical axis shows your chances out of 10,000 in reaching the income level shown on the horizontal axis, assuming very stupidly that you are typical of the entire American population. 1 out of every 10,000 Americans clears on average more than $10 million a year (the data are from the great and famous paper by Piketty and Saez). Every movement on either axis multiplies by 10. So 10 out of 10,000 (or 1 out of a 1000) have to settle for being only millionaires instead of deca-millionaires. 1000 out 10,000 (or one out of 10) clear a measly $100,000 a year. (Since the line in Figure 1 is almost straight, we could say the upper limits of the income distribution fit a Power Law, which as mentioned in the previous post is a special type of fat-tailed distribution that many people (at least three) find fascinating.)
Figure 2 shows an alternative way of becoming rich at great odds. This is an exact power law with a slope of -1, meaning that if your chances get 10 times worse, you get 10 times the payoff if you succeed.
Figure 2
We call this alternative income-generating-process “Las Vegas.” The line shows the payoff if you bet $10,000 at the odds shown. Ignoring the tiny detail that the house takes its cut, betting a fixed amount at longer and longer odds follows an exact Power Law.
So is getting rich in America just a matter of making a big bet at very long odds? It’s not the worse metaphor ever – an awful lot of things all have to go right for somebody to become very rich, so the odds are indeed long. A lot of economic outcomes follow Power Laws – the sizes of firms, the sizes of cities, the export value of different exported goods, the cumulative growth of nations, etc. – for similar reasons.
So what if one of the contributing factors to income inequality is just that finding your own personal VERY BIG HIT is rare? This is equivalent to the usual description of income inequality as a very small proportion of the population having a VERY LARGE INCOME. Moreover, by comparing Figure 1 and Figure 2, you can see the payoff from the “bet” in figure 1 is not large enough to be a ”fair bet” in the sense of fully compensating for the very long odds. (Mischievous Question to provoke discussion: does this mean the income distribution is unfair to the rich?) And furthermore the rest of us want somebody to take on the very long odds of finding a VERY BIG HIT, like the movies Titanic and Avatar, or the iPhone and iPad, because the very big payoff reflects how valuable the Big Hit is to consumers.
So (as @dillardsarah on Twitter suggested as a summary of this post) could inequality just be big, valuable, unlikely bets paying off?
Of course, not everyone faces the same betting odds in the American income distribution, which is when the passionate moral debate kicks back in.
21 Comments
What’s your point? What you’ve shown is that the odds of getting very rich in the US are slim, but the odds of being less rich are higher. Then you compare this to a betting scenario, which fits a similar pattern.
Then you say that this isn’t actually true, since as we all know, ability, initial volume of resources, who you know, background etc. all have a significant impact on how rich you can become.
Greg Mankiw did not cop a torrent of abuse for being rich.
Greg Mankiw copped a torrent of abuse for being clueless, whiny, and rich.
In a time of ~10% unemployment, he is someone with lifelong tenure and a household income in the top 1-2% of the nation.
As a Harvard professor no less, he should be smart enough to know when to shut the f**k up.
The odds of being rich in America are decidedly better if your parents are rich. Not everyone starts out in life facing the same set of odds which is why there is passionate moral debate about wealth distribution.
The lower limit on the abscissa is $100,000? You know you have a lot of aid workers in your readership, right?
A lot of the power law crazies are physicists, like physicists Jean-Philippe Bouchaud and Marc Mezard who constructed a mathematical experiment to show that when all parties make random bets, you still come out with a power law probability distribution. Tinkering with the initial parameters, Bouchaud and Mezard did leave room for hope: “Favoring exchanges (and, less surprisingly, increasing taxes) seems to be an efficient way to reduce inequalities.” Put in more practical terms, reducing transactions costs and opening up new avenues for economic activity is an effective way to reduce inequality. http://ideas.repec.org/p/sfi/sfiwpa/500026.html
I am still unclear what exactly you are trying to convince me of here. The comparison with betting is confusing when using statistical probabilities like this as there is no clear definition of what to wager?? Additionally, the outcomes don’t line up with what whatever the wager is. If I have 10 000 to 1 odds in Vegas I know that I can bet a dollar and win $10k.
Wouldn’t the Las Vegas equivalent be getting the Bellagio to open a betting lounge in the maternity ward at the local hospital and taking wagers on outcomes for newborns? I place a one dollar bet with the house that the super pink guy in crib 4 will earn over 10 million in his life and if he does then I get 10k. Of course, the baby I wagered on still makes 10 million and finds my bet completely irrelevant… Just like this discussion here on aidwatch.
In my opinion the odds are astonishingly long… I understand the attempt to understand rather than simply condemn inequality but what am I to make of an America where in a best case scenario of simple chance a person has 10% chance of making $100k. Only because I don’t believe that such simple chance exists and that there are many factors that drive that number way down for most people.
The title of Mankiw’s column is:
“I Can Afford Higher Taxes. But They’ll Make Me Work Less.”
Which means there would be fewer opeds by Harvard economics profs.
The republic might survive that shortage better than he thinks.
Bill, you’re usually more careful than this. If you want to make a point about inequality, fine. But trotting out the Mankiw thing is completely irrelevant to the subject of this post. Mankiw got “a torrent of abuse” because he wrote a misleading and disingenuous piece making a specious argument. If you want to have the Mankiw fight, why not take on the substance of Mankiw’s critics rather than pretend they’re just DFHs who hate rich people?
If we are going to have a moral debate about income inequality, then we need to stop using income inequality data since it’s totally worthless data set for a moral debate. I think most of the data sets are flawed. They ignore life cycle effects (I as a 16 year old am much poorer than my father); they usually ignore benefits (e.g. pensions, health insurance); and it’s usually calculated at the household level which is improper from a moral angle (someone making $250,000 when a wife and two kids is struggling a lot more than a single bachelor making $100,000).
But my biggest objection to income inequality data is that it’s not even measuring what we care about. What we care is is human welfare not some number on our IRS tax returns. And the best purely economic measure of human welfare is consumption. And consumption inequality is significant lower than income inequality. The best paper about inequality I’ve seen in recent years on the subject is Heathcote, Perri, and Violante’s “Unequal We Stand” ( http://www.econ.umn.edu/~fperri/papers/redusa_jan29.pdf ). They found that consumption inequality increased by less than half as much as disposable income inequality between 1967-2006. So, income inequality measures dramatically overstate welfare inequality.
Now there may be other reasons to tax the rich more. A fat right-tailed ability distribution would imply optimal rising marginal income tax rates and it simply may be the most “fair” way to finance an ever-growing government on the backs of those most able to afford it. But the purely moral argument is pretty weak (well, technically it would be cut in half given the consumption data I cited!).
Rod, thanks for your comment. I am trying to say that a possible descriptive model of high inequality is that some individual career paths could be incredibly risky and very unlikely to pay off, yet the there is a very high demand for the output of such a career path. So the equilibrium is for the market to offer an extremely large prize to compensate for the long odds of success, to induce many more people to try than will actually succeed. This is a highly simplified toy model of inequality that is only one of many possible ways to look at it, as is true of all models. And of course, the odds are not the same for everyone, as the post says, so those with better odds are the ones actually likely to try the riskiest paths, which is why you would get less than Las Vegas payoffs based on a simplistic probability number like fraction of the total population. Does that help?
Dear edawg: the Mankiw reference was an ironical aside and not a serious attempt to engage in the specific debate started by the Mankiw column. Besides the logical objections to his arguments, there was also an element of ad hominem attacks on Mankiw along the lines of “the spoiled rich person should just shut up.”
This just made me think “if we assume”…typical of models.
The assumption is that the person who is rich can’t redistribute wealth, not through philanthropy, but through actual structural changes; the most obvious one of which is a gap cap.
But also, we assume that people are remunerated for their services on a valid system of principles of valuation. For example: someone who helps someone play the stock market/’invest’ well, high value. Someone who drives you from point a to point b – or who builds the roads that drive you from point a to point b, low value. Someone who sells you your coffee: low value. Someone who trades the coffee on futures markets: high value. Someone who ‘adds’ value – say a roaster or a retailer – deserves more than the person who grows the coffee. Forget the fact that, if not for the person who grows the coffee we would have NO COFFEE, no value chain, no roaster, no trader, no retailer, etc. etc. Schwartz would be a poor man, blah blah blah…the grower is not valuable, because s(he) offers no value-added. The entire system is far more complicated and interconnected than just riches being born of chance.
Economy is just a social construct. I’m not saying that makes it meaningless or that we just dismiss it. But I do believe that we can rethink it in innovative ways that also lend to greater social justice, which includes fewer inequalities. The real problem is politics.
“I Can Afford Higher Taxes. But They’ll Make Me Work Less.”
Which means there would be fewer opeds by Harvard economics profs.
The republic might survive that shortage better than he thinks.
The lower limit on the abscissa is $100,000? You know you have a lot of aid workers in your readership, right?
So life is just a big bet, right? It turns out that life is a bunch of bets, some bigger than others. Did you study in school or just have fun? Did you go to college? Did you pick a major in college that would help land you a high paying job? These are all bets that you make in life.
Poor people tend to make lousy bets in life. They bet that not studying in school won’t matter. They bet that they can get pregnant out of wedlock and it won’t matter. They bet that they can be a poor worker and it won’t matter.
Good behavior leads to a better outcome. Bad behavior leads to a worse outcome. This is the thinking of conservatives.
If you achieve a better outcome, then you must have cheated. If you achieve a worse outcome, then you must have been victimized. This is the thinking of modern liberals.
Is there any empirical evidence to make us think that individuals are less likely to pursue this highly valued activity when the financial reward is less? I know there is experimental evidence that shows that financial incentives actually diminish performance on creative tasks (while they improve performance on simple, narrow, pre-determined tasks). I just wonder if we may be believing in this relationship because it sounds as if it must be true….when it may not be.
Generally speaking, I am very interested in understanding the range of mechanisms through which inequality diminishes performance (economy wide, individual) and satisfaction. I don’t find the macro relationships very helpful. How does living in a more unequal society make an individual happier?? Not clear to me. On the other hand, how does living in a less taxed (more unequal) society lead to higher productivity/ innovation (a bigger pie, if you will)? This relationship is also becoming less clear to me.
I use Mankiw’s text and happened to be discussing Mankiw’s chapter which makes some of the same points. Taxes redistribute income and require interpersonal comparisons of utility. Mankiw bases his conclusions of lost efficiency on willingness to pay which assumes a given distribution of income. Mankiw’s valid main point is that the “costs” of a higher marginal tax are the opportunity costs of foregone output (Mankiw implies by the most productive labor). He fails to mention that the tax revenues collected are spent on public goods or tranfers which society values greater than opportunity costs .
I used to work in development for an alphabet donor who paid me a bundle to work in one of the poorest countries on earth. I did pretty good work and much of what I did was not undone after I finished and left the project. If translated into local currency I earned way way out on the right edge. Income distribution locally was very unequal but with 30 years experience in my field I did not earn above my peer’s intl mean. There was no one else in the entire country who could do my job so my “odds” were more than 1,000,000 to 1.
Rich is relative. I know guy (former investment banker) who made so much money he bought a yacht and now hates his life. There is always someone with more and his “big” yacht looks petite in Cap d’Antibes. Yacht envy is not a pretty sight.
Risk? Fair bets? Power Laws? Are you joking? Of course you are. I am sure you know your Frank Knight by heart. And we all revere Donald Rumsfeld for his inspired description of “unknown unknowns”. Life can be many things, but usually it is not a lottery. If we want to understand inequality, we better look at social institutions outside Nevada.
Which means there would be fewer opeds by Harvard economics profs.
The republic might survive that shortage better than he thinks.
Now there may be other reasons to tax the rich more. A fat right-tailed ability distribution would imply optimal rising marginal income tax rates and it simply may be the most “fair” way to finance an ever-growing government on the backs of those most able to afford it. But the purely moral argument is pretty weak (well, technically it would be cut in half given the consumption data I cited!).
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