Tag Archives: Inequality

Housing Envy

By Robin Hanson · February 10, 2012 10:35 am · Comments (9)

Envy is real, but people claim to care more than they do about the size of their neighbor’s houses:

Unlike much of the stated preference literature, the results of this paper indicate that a increase in absolute house size is valued more than an increase in relative house size, suggesting that individuals value their absolute well-being more than their relative status if all parties are handed an equal increase. More specically, for the case of Columbus, the willingness to pay for an increase in own house size by 100 square feet from the mean is found to be $1,103 while the willingness to pay for a decrease in neighbor house size by 100 square feet from the mean is $400. (more)

Since envy looks ugly, why do people do out of their way to appear more envious than they are? Most likely because opposing wealth inequality is an ancient forager norm.

Note that this level of envy could justify taxing house size relative to some other category of consumption where envy is weaker, if such categories could be identified.

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Inequality Market Failure?

By Robin Hanson · February 5, 2012 5:20 pm · Comments (91)

In ordinary talk, you often hear arguments like:

  • There aren’t enough Jazz stations – government should subsidize them.
  • Too many kids today let their pants hanging low – that should be illegal.
  • Not enough kids want to be scientists – schools should push that earlier.

But to an economist, it is not enough to note that you do or don’t like something, to justify a policy to encourage or discourage it. We instead hold ourselves to a higher analysis standard – is there a net market failure sufficient to justify an intervention?

Except, alas, on (national at-a-time between-family) income and wealth inequality. There, most economists think it sufficient to just note that a policy influences inequality – they rarely feel a need to identity an associated market failure. For example, Christina Romer:

A successful argument for a government manufacturing policy has to go beyond the feeling that it’s better to produce “real things” than services. … The economic rationales for a policy aimed specifically at shoring up manufacturing largely fall into three categories. None are completely convincing:

MARKET FAILURES Government intervention can be justified on efficiency grounds if the free market won’t work well. … The market can malfunction if there are positive externalities across companies. … But large clustering effects have been hard to find. … A study of the semiconductor industry found that although learning by doing was substantial, most of the rewards went to companies doing the early investing. … We need a strong manufacturing base in case of war. … But it still doesn’t follow that all manufacturing deserves special treatment. …

JOBS A key argument for encouraging manufacturing is to create jobs and reduce unemployment. Unfortunately, those effects are probably small. … Today, we face a profound shortfall of demand. That truly is a terrible market failure, and it warrants government intervention. …

INCOME DISTRIBUTION A final argument for supporting manufacturing is distributional. Manufacturing jobs are seen as one of the few sources of well-paying jobs for less-educated workers. … But that is much less true today. … If increasing income equality is the goal, it might be wiser to put money into infrastructure than to subsidize manufacturing. …

Public policy needs to go beyond sentiment and history. It should be based on hard evidence of market failures, and reliable data on the proposals’ impact on jobs and income inequality. (more; HT Tyler)

Note that she even uses market failure to justify pushing jobs. But not for income equality – that is just obviously bad. I see the same thing over and over – only economists wary of equality-promoting policies talk market failures, and then they mainly ask what they are. For example Charles Lane:

Americans may never agree on an optimal distribution of income, either morally or practically. But they probably could agree that, to the extent possible, government should limit its interventions to bona fide cases of market failure. (more)

Well, no, Americans probably don’t agree on that. But you might hope economists would. Tyler Cowen has an article where he says there are market failures in the finance sector that increase inequality, and recommends fixing them. Which of course makes sense, but we’d want to fix those problems even if they reduced inequality.

The closest I could find to a market failure argument for reducing inequality was Ian Ayres and Aaron Edlin:

The progressive reformer and eminent jurist Louis D. Brandeis once said, “We may have democracy, or we may have wealth concentrated in the hands of a few, but we cannot have both.” (more)

But that is quite a stretch – there is no evidence that wealth concentration is threatening to stop our nation from being a democracy. And it is far from obvious that not being a democracy is a market failure.

As Obama has decided to make reducing inequality a central issue in his reelection campaign, we are going to hear a lot about it between now and November, including from economists. Could economists who support policies to reduce inequality please identify their market failure arguments?!  Why lower our usual standards for this topic?

(I argued here that a poverty insurance market failure seems implausible.)

Added 2p: In case it is not clear, this post is directed to economists, in their role as economists. I’m not saying market failure is the only consideration anyone uses to decide policy, but I am suggesting that it is the main consideration that economists use in their role as holders of economic expertise. Economists don’t have much expert to say about whether we have too much or too little inequality, outside of their expert ability to discern and fix market failures.

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Rising City Inequality

By Robin Hanson · January 31, 2012 3:15 pm · Comments (9)

Barkley Rosser pointed to me to an ’05 meta-analysis of tail-power estimates for city distributions:

The estimated [power α] is on average not 1.0. If the regression is properly specified in the Pareto form, the pooled estimate of α is considerably larger than one, close to 1.1. … Point estimates of α are significantly smaller if the estimate is based on population data for metropolitan areas (instead of inner cities), the estimate is based on data for recent years, the estimate is for the US city size distribution, the sample comprises only a small number of observations, and the study reports only a single estimate.

So while this confirms that for US cities recently the tail-power is close to one (as I had cited before), it is higher in the rest of the world, and in the past. See this graph of power vs. year AD:

Inequality in cities has indeed been increasing over the last few centuries. And it may well increase more in the future.

So who bemoans increasing city inequality? Who wants to redistribute success from the 1% of cities, e.g., Tokyo and New York, to the many smaller cities? Few it seems, because while many dislike inequality in wealth or firm size, most seem to like city inequality.

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The Future Of Inequality

By Robin Hanson · January 29, 2012 10:35 pm · Comments (11)

A few (3.6) years ago I wrote about the inequality over time induced by the big transitions, such as from primates to foragers to farmers to industry:

Advantages do accrue to early adopters of new growth modes, but these gains seem to have gotten smaller with each new [transition]. … 1. The number of generations per growth doubling time has decreased. … 2. … As we get better at sharing info in other ways, the first insight-holders displace others less. 3. Independent competitors can more easily displace each another than interdependent ones.

Earlier today I wrote about the inequality at each point in time, in the eras between transitions:

The number of species per genera and individuals per families has long declined with size as a tail power of two. After the farming revolution, cities and nations could have correlated internal successes and larger feasible sizes, giving a thicker tail of big items. In the industry era, firms could also get very large. Today, nations, cities, and firms are all distributed with a tail power of one, above threshold scales of (three) million, thousand, and one, thresholds that have been rising with time.

So, the unequal success that comes from some moving sooner in a big transition between growth eras has declined in more recent transitions. Yet the within-era inequality at a moment in time between groups like nations, cities, and firms has increased over time. As larger groups have become feasible, with more internal correlation in their success, the high tails of very large groups has gotten thicker, until they are now Zipf distributed evenly across many size scales. And in such Zipf distributions, typical group size increases with the both minimum efficient scale and total population, both of which have been increasing.

“But that is not all, no that is not all!” (Said the Cat in the Hat.) Continue reading "The Future Of Inequality" »

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The History of Inequality

By Robin Hanson · January 29, 2012 3:45 pm · Comments (5)

I recently posted on how cities and firms are like distributed as a Zipf power law, with a power of one, where above some threshold each scale holds roughly the same number of people, until the size where the world holds less than one. Turns out, this also holds for nations:

Log Nation Size v Log Rank

The threshold below which there are few nations is roughly three million people. For towns/cities this threshold scale is about three thousand, and for firms it is about three. What were such things distributed like in the past?

I recall that the US today produces few new towns, though centuries ago they formed often. So the threshold scale for towns has risen, probably due to minimum scales needed for efficient town services like electricity, sewers, etc. I’m also pretty sure that early in the farming era lots of folks lived in nations of a million or less. So the threshold scale for nations has also risen.

Before the industrial revolution, there were very few firms of any substantial scale. So during the farming era firms existed but could not have been distributed by Zipf’s law. So if firms had a power law distribution then, it must have had a much steeper power.

If we look all the way back to the forager era, then cities and nations could also not plausibly have had a Zipf distribution — there just were none of any substantial scale. So surely their size distribution also fell off faster than Zipf, as individual income does today.

Looking further back, at biology, the number of individuals per species is distributed nearly log-normally. The number of species per genera:

and the number of individuals with a given family name or ancestor:

have long been distributed via a steeper tail, with number falling as nearly the square of size:

This lower inequality comes because fluctuations in the size of genera and family names are mainly due to uncorrelated fluctuations of their members, rather than to correlated shocks that help or hurt an entire firm, city, or nation together. While this distribution holds less inequality in the short run, still over very long runs it accumulates into vast inequality. For example, most species today descend from a tiny fraction of the species alive hundreds of millions of years ago.

Putting this all together, the number of species per genera and individuals per families has long declined with size as a tail power of two. After the farming revolution, cities and nations could have correlated internal successes and larger feasible sizes, giving a thicker tail of big items. In the industry era, firms could also get very large. Today, nations, cities, and firms are all distributed with a tail power of one, above threshold scales of (three) million, thousand, and one, thresholds that have been rising with time.

My next post will discuss what these historical trends suggest about the future.

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Who Wants Kid $ Insure?

By Robin Hanson · January 25, 2012 11:00 am · Comments (29)

Financial inequality seems to be shaping up as a central issue in the US presidential campaign. (Other sorts of inequality, not so much.) Many note that such inequality has increased in recent decades. But let me repeat my anti-trend-tracking matra: if what matters is the efficiency of our institutions, trends are irrelevant unless they reveal such inefficiencies. So are the institutions that influence our financial inequality inefficient?

Probably the simplest and strongest argument is insurance market failure: being risk-averse, we want to insure against variations in our distant future income, but since this insurance is not available privately, governments must provide it. Why exactly this is not available privately if customers want it isn’t usually clarified. And it could be that the incentive costs of the insurance outweigh its risk-reduction benefits. But this is at least in the ballpark of a plausible institutional argument.

However, it seems to me that as a parent I wouldn’t have wanted to insure against any but the very low tail of possibilities of for my kids future income. I like the idea that one of my kids might someday be very successful or famous. And asking this of my undergrads consistently gets the same answer – very few want such insurance for their own or their kids’ future. Furthermore, parents do not much use the one clear insurance option they have – to teach their kids to share their future income with each other. Most societies used to do this, and our culture evolved away from that. So while teaching kids to share income is both personally and culturally possible, we just don’t do it.

Now you might argue that this is a signaling failure – that we would each in fact like such insurance, but dislike what our willingness to take it would say about us. But you could also tell your kids to keep this income-sharing policy a family secret, only to tell potential spouses. And once such sharing became a long family tradition then continuing it would say much less about personal features. But it seems to me that even if given the option to legally commit all their descendants to such a policy, to prevent all future signaling about it, most folks would still reject such insurance.

Thus it seems to me that most folks think the incentives costs outweigh the risk-reduction gains for such insurance, and do not want it. Thus the insurance market failure rationale for taxing the rich extra just fails.

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Future Wealth Inequity

By Robin Hanson · January 13, 2012 11:00 pm · Comments (22)

My last two posts described inequality in firm and city sizes, and in individual wealth. Today, firms and cities are quite unequal, following a Zipf distribution, with a tail power near one (giving a very thick tail.) Individual wealth is a bit more equal, with a bigger power of ~1.4 (and hence a thinner tail).

This distribution of firms and cities seems to result from their being tolerably effective across a wide range of sizes, having long unequal lifetimes, having little net local growth, and holding a roughly fixed total number of people. In contrast, individuals have more equal lifespans, are psychologically inclined to spend more as they get richer, and have spending habits that correlate only weakly across generations. (“Rags to rags in three generations.”)

How might these change in the future? In the em era, I expect firm distributions to stay similar, but expect city and individual wealth distributions to change. I’ve talked before about how I suspect strong gains to em concentration, as they suffer less from travel congestion, leading perhaps to most being in a few dense cities. In this post, let me talk about em wealth.

Since em lifespans should be limited mainly by em wealth, em lifetimes can vary a lot more than human lifetimes, and ems can have more long-term spending consistency. While some ems will spend their wealth on more copies, others will hoard their wealth. Some may even manage to consistently reinvest most of their wealth via something like a Kelly criteria. This seems likely to make future em wealth evolution more akin to today’s firm and city evolution. I thus expect a near Zipf distribution for the high tail of em wealth.

This change in tail power should make em wealth distributions more unequal. Under a tail power of ~1.4, today’s richest person has about $75B, which is about 0.04% of the world’s $200T wealth. Under a power of ~1, the richest person might be about a hundred times richer, holding ~4% of the world’s wealth, or $7.5T.

Since a Zipf distribution has an unbounded expected value, its inequality also depends on the total population size (which follows it). The following table shows this dependence:

The “% of Richest” column says what fraction of the total wealth is held by the one richest person. The “MidW %” column shows the (smallest) fraction of the population that holds half of the total wealth. And the “MidW/ave” column shows how much richer is the mid-wealth person (for whom half of all wealth is held by richer folks) than the average person.

For a Zipf wealth distribution, as the population gets larger wealth gets more concentrated. Even so, the very richest person holds a smaller fraction of the total wealth. The same should apply to firms and cities if they retain a Zipf distribution — the firm and cities that hold most people will get larger, even though the largest firm or city would be a smaller fraction of the total.

In sum, as the population gets larger, I expect firms and cities to get larger.  And for “immortal” ems, I also expect a more unequal distribution of wealth. Even so, as population increases the very largest firms, cities, and rich folks should hold smaller fractions of their respective totals.

Added 11p 14Jan: This post has now been up for a whole day, with zero comments and one vote. Which has to be some sort of record for reader disinterest. This is especially noteworthy, given that I’m especially proud of this post, culminating several days work trying to understand something important about the future. Alas that I  sometimes bore readers, but I’m writing this blog mainly for me, so I’ll continue to write about what most interests me, even if past responses suggest readers won’t be as interested.

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Old Money Goes Broke

By Robin Hanson · January 12, 2012 7:30 pm · Comments (8)

My last post talked about inequality among sand grains, diamonds, firms, and cities. Specifically, that their sizes are distributed like lognormals, but with thicker power law tails. I noted that firms and cities are distributed quite unequally, with a (Zipf’s law) upper tail power near one.

In this post I’ll focus on wealth. In the 1890s Pareto found that the (upper tail of) wealth and income are distributed as power laws. Recent studies of US and world rich folks

estimate powers of 1.3 to 1.5, similar to Pareto’s original findings. This distributes individual wealth more equally than firm and city sizes.

Consider a simple differential equation model:

w‘ = s*w + c*(1-w)

Here the time rate of change w’ of an individual’s wealth w is given by a zero-mean randomly-fluctuating proportional growth s, and a redistribution c. This equation gives a steady state distribution proportional to:

exp((1-a)/w)*w^(-1-a)

This approaches a power law for large wealth, with power a = 1 + c/s. This model illustrates two key points:

1) While a (Zipf’s law) power of one implies no local net change, as with cities and firms, a power above one implies net local change. In particular, the wealth of individual rich (w>1) folk tends to fall on average, while the wealth of individual poor (w<1) folk tends to rise on average. The numbers of the slowly-getting-poorer rich are only held steady by a large influx of recently poorer folks. On average, old money goes broke, while the poorest bounce back.

2) Risk-averse folks (i.e., most everyone) dislike fluctuations s, and would prefer to eliminate them. But when people are forced to suffer larger fluctuations s, the distribution of wealth will spread out, creating more very rich people. Thus policy changes that result in there being more very rich people do not necessarily favor rich people. Policies that induce larger fluctuations s create more very rich but hurt each one of them. In fact, very rich folks are often especially risk averse, investing primarily in bonds. While the US has more very rich folks than other nations, and more than in prior decades, this might be because of policies forcing the rich to suffer more challenges to their positions, and to hold larger stakes in their enterprises.

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Inequality Math

By Robin Hanson · January 12, 2012 4:20 pm · Comments (12)

Here is a distribution of aeolian sand grain sizes:

Here is a distribution of diamond sizes:

On a log-log scale like these, a power law is a straight line, while a lognormal distribution is a downward facing parabola. These distributions look like a lognormal in the middle with power law tails on either side.

Important social variables are distributed similarly, including the (people) size of firms:

and of cities:

In these two cases the upper tail follows Zipf’s law, with a slope very close to one, implying that each factor of two in size contains the same number of people. That is, there are just as many people in all the cities with 100,000 to 200,000 people as there are in all the cities with one million to two million people. (Since there are an infinite number of such ranges, this adds up to an infinite expected number of people in huge cities, but actual samples are finite.)

The double Pareto lognormal distribution models this via an exponential distribution over lognormal lifetimes. In a simple diffusion process, positions that start out concentrated at a point spread out into a normal distribution whose variance increases steadily with time. With a normal distribution over the point where this process started, and a constant chance in time of ending it, the distribution over ending positions is normal in the middle, but has fat exponential tails. And via a log transform, this becomes a lognormal with power-law tails.

This makes sense as a model of sizes for particles, firms, and cities when such things have widely (e.g., exponentially) varying lifetimes. Random collisions between grains chip off pieces, giving both a fluctuating drift in particle size and an exponential distribution of grain ages (since starting as a chip). Firms and cities also tend to start and die at somewhat constant rates, and to drift randomly in size.

In the math, a Zipf upper tail, with a power of near one, implies little local net growth of each item, so that size drift nearly counters birth and death rates. For example, if a typical thousand-person firm grows by 1% per year (with half growing slower and half growing faster than 1%), but has a 1% chance each year of dying (assuming no firms start at that size), it will keep the same expected number of employees. Such a firm has no local net growth.

Interestingly, individual wealth is distributed similarly. More on that in my next post.

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We Need The Very Rich

By Robin Hanson · January 8, 2012 12:50 pm · Comments (40)

Two years ago I posted:

The number of new businesses we get seems limited by the number of folks personally wealthy enough to start new businesses. So having more really rich folks benefits everyone via innovation.

Now I learn that very rich folks are crucial not only for business starts, but also for most business investment that takes more than a year or so to payoff! Consider:

As is common in factories, [public firm] Standard [Motor Products] invests only in machinery that will earn back its cost within two years. (The Atlantic, Jan 2012, p.66)

Why look at years-to-payback instead of return on investment? A new NBER paper on private vs. public firms makes the answer clear. Unless project gains can be very clearly proven to analysts, or perhaps so small and numerous to allow averaging over them, public firms are basically incapable of taking a loss on earnings this quarter in order to make gains several years later, no matter how big those gains. CEOs are strongly tempted to instead please analysts by grabbing higher short-term quarterly earnings. So we need the very rich to make long-term investments. The details: Continue reading "We Need The Very Rich" »

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