Bayesian Investor Blog

Book review: Capital in the Twenty-First Century, by Thomas Piketty.

Capital in the Twenty-First Century is decent at history, mediocre at economics, unimpressive at forecasting, and gives policy advice that is thoughtfully adapted to his somewhat controversial goals. His goals involve a rather different set of priorities than I endorse, but the book mostly doesn’t try to persuade us to adopt his goals, so I won’t say much here about why I have different priorities.

That qualifies as a good deal less dumbed-down-for-popularity than I expected from a bestseller.

Even when he makes mistakes, he is often sufficiently thoughtful and clear to be somewhat entertaining.

Piketty provides a comprehensive view of changes in financial inequality since the start of the industrial revolution.

Piketty’s main story is that we’ve experienced moderately steady increases in inequality, as long as conditions remained somewhat normal. There was a big break in that trend associated with WW1, WW2, and to lesser extents the Great Depression and baby boom. Those equalizing forces (mainly decreases in wealth) seem unlikely to repeat. We’re back on a trend of increasing inequality, with no end in sight.

First Fundamental Law of Capitalism

Piketty’s First Law is a definition, not a law. In spite of being a tautology, it illustrates an important point of the book: given that returns to wealth are large compared to national income growth (r > g), financial inequalities tend to increase, because the rich grow richer faster than most other people can become richer.

One key component of that growth of inequality is that the wealthy have high savings rates. r is typically around 4-5%, and g tends to be more like 1%, so the First Law is doesn’t produce interesting results unless the wealthy save more than 20% of their income. Those savings rates seem more remarkable to me than r > g, yet Piketty treats those as if it were obvious that the wealthy can’t spend most of their income.

He seems to have some bias against caring about the savings rate, maybe because it undercuts his story about wealth not being due to merit. I consider a high savings rate to be a sign of merit. Not necessarily an especially important one, but enough for my attitude to differ noticeably from Piketty’s.

Piketty seems to imply (without providing any clear reason) that the rich save because they can’t find things to spend more money on. That seems mainly a case of Piketty limiting his imagination to small variations on conditions he’s familiar with.

Many people who become rich find ways to spend money that they didn’t imagine before they were rich: bigger yachts, bigger mansions that require many servants, getting their university to name a building after them, etc.

A more imaginative rich person can find ways to spend even more money: eradicating malaria, curing aging, colonizing Mars, visiting the far edge party, etc.

My impression is that many cultures have pressures which prevent the kind of savings rates that enable the capital accumulation upon which Piketty focuses. And even within western culture, there are plenty of people who earn high incomes for a while, yet quickly fall off Piketty’s radar because they’re too short-sighted to save.

Note that population growth has nontrivial effects on inequality: higher population growth means higher national income growth, making it harder for accumulated wealth to outgrow it.

Second Fundamental Law of Capitalism

Piketty’s second “law” says beta = s/g (the capital / national income ratio equals the net savings / income growth ratio).

It seems likely to be roughly true under typical conditions, but calling it a law just seems silly. Piketty says little about why we should consider this law to be true. He just asserts the law, then mostly focuses on countering weak objections, rather than explaining what led him to think this law was anything more than a rough guess.

I tried evaluating it by plugging in a variety of numbers. My first few attempts produced reasonable-looking results.

Then I tried a growth rate of zero (not far from what Piketty is concerned about), and noticed that beta goes to infinity. That’s a bit disturbing, but Piketty could plausibly defend that by claiming that there’s no equilibrium in that case, and capital keeps growing to larger and larger multiples of income.

But then a tiny decrease in the growth rate (as would happen if population declined slightly, in an otherwise stagnant world) results in the equation saying that the equilibrium capital levels become extremely negative, or else income becomes negative. Something seems quite wrong here, since I’m pretty confident that it’s still possible to accumulate capital with slightly negative growth, and I can’t see how we’d get negative income without declining capital.

Or as James Hamilton puts it:

Thinking these numbers through leads you to understand that the assumption of a constant net saving rate, regardless of the levels of income and the capital stock, could not possibly be a sensible characterization of the decisions that would be made by real people in the real world.

A more careful, but less readable, criticism: Is Piketty’s “Second Law of Capitalism” Fundamental?

we look at aggregate data to try to compare Piketty’s assumption to standard, alternative theories, and we find that the data speak rather clearly against Piketty’s theory. Equipped with theories that we find more plausible, we then show that if the rate of economic growth were, say, to fall by half, the capital-to-output ratio would increase only modestly rather than dramatically as the second law would predict.

The problems with the Second Law mean that Piketty has overstated the likely increase in inequality.

Executive Pay

Piketty estimates that something like 60 to 70% of income inequality in the west today is due to high incomes for high-level managers, as a result of the recent explosion in their pay.

It’s implausible that technology or manager productivity can explain the change, as changes in pay show some important patterns that seem unconnected to technology or productivity. The patterns often suggest it’s more “pay for luck”.

Piketty at one point suggests that perceived competition from Japan played an important role in changing executive pay, and that explains some of the timing fairly well (especially a big spurt around 1988).

But his main explanation is that lower marginal tax rates on high incomes gave executives more incentive to demand higher pay. But if that were true, wouldn’t it imply even less equal executive pay before WW1, when the top tax rates were less than 10%? I don’t see good evidence on pre-WW1 executive pay, but my impression is that it was more equal than today.

I suspect that a fair amount of what changed in the 1980s and 1990s was that stock ownership shifted from being owned via pension funds to being owned more directly by individuals. That worsened the principal-agent problem: pension funds had a modest ability to coordinate restraints on executive pay, but individual investors don’t have any comparable ability that would be a cost-effective use of their time.

Note that none of this says much about how high manager pay ought to be.

Piketty wants to return to high marginal tax rates, in order to discourage that high pay, even if it doesn’t collect more taxes.

I suggest an alternative: create etfs/mutual funds that invest in companies with low-to-average executive compensation. If such funds get significant investment, that will create incentives to equalize executive pay[1]. The effects will be weaker than Piketty’s approach, but they’ll be much more carefully targeted. E.g. it won’t affect professions where high pay implies high productivity (see below). Alas, people who care about inequality seem unlikely to develop the expertise needed to start an etf.

Increasing Returns to Wealth?

Piketty wants us to believe that the wealthiest people and institutions can earn higher returns on wealth than the rest of us.

He has some examples which illustrate correlations between wealth and returns, particularly prestigious universities, Bill Gates, and Liliane Bettencourt. I expect that some patterns like this will persist (often due to persistence of the reasons why someone got rich to start with), and will contribute to inequality. But he’s wrong to claim that wealth is what’s causing those high returns.

He imagines that the main reason for those higher returns is that wealthy people and institutions can hire better consultants.

One problem with that is that markets are efficient enough that very few people have the skill to beat the market, and there are a much larger set of people with the skill of marketing themselves as being able to beat the market. Being rich isn’t a good explanation for why someone can distinguish those two categories[2].

Having $100 million gives someone better access to hedge funds with impressive track records (including Madoff), and Nobel winning teams, which aren’t available to someone with a mere $500,000 to invest. Even if that explained differences between those levels of wealth, it wouldn’t tell us much about the differences around the billion dollar level that Piketty cares somewhat more about.

What does Piketty think determines the compensation going to an expert who has demonstrated an ability to manage $100+ million in ways that beat the market?

It looks to me like many such people run hedge funds that charge 2% of assets and 20% of profits. It looks to me like more than half of the outperformance of prestigious universities is due to their ability to hire unusually competent investors for something like a regular salary, when they could often make a few additional million dollars a year by running a hedge fund.

Harvard pays 0.3% of assets in management fees, when I’d expect the money managers could get more than 2.5% if they did as well at a hedge fund as they did at Harvard. (Wikipedia suggests that Harvard is having some trouble keeping its money managers.)

So I’d say the biggest single reason why the top universities have higher returns than smaller university funds is that they’re able to hire good money managers at below-market prices. And the most obvious guesses about how they can do that involve prestige that the universities offer, and the wisdom about hiring that generates that prestige.

I.e. the top universities help maintain a little bit of the old-time wage equality which Piketty desires, at the cost of greater inequality of wealth.

I can’t rule out a role for insider information – the returns on endowments appear to correlate moderately well with political and financial connections.

What about Piketty’s other examples? Bill Gates, who increased his fortune by 12.5 times between 1990 and 2010. It looks to me like Microsoft stock price increased about 24 fold in that time period. I suppose Bill might have hired some top-notch consultants who talked him out of selling more of his Microsoft stock, but that doesn’t seem like the most obvious hypothesis.

Piketty mentions that Norway’s sovereign wealth fund produces rather ordinary returns, and suggests that other such funds are too opaque to evaluate. He overlooked CalPers (bigger than Harvard’s endowment), which seems to have underperformed the S&P500 from 1992 to 2016 (but it likely looks a bit better under a risk-adjusted comparison). And China’s sovereign wealth fund invests a lot in US bonds, which tends to suggest it’s not outperforming.

I suppose I should be a bit concerned that Piketty looks worst in the area I know best. But that looks more likely due to finance being further from his area of expertise, than to Piketty being wrong many places that I didn’t detect. Or maybe it’s mostly that my standards are lower for historians?

Piketty does have some good points buried in this section: wealth can bring increased risk tolerance, and increased patience, which help produce good returns. Patience is pretty important for producing good investment returns. Piketty probably overestimates the value of risk tolerance, because he assumes standard portfolio theory, whereas in practice, investors concern for their relative (not absolute) wealth prevents high-risk investments from generating higher returns.

Why these measures of inequality?

Piketty focuses mainly on inequality of income and wealth at the level of nations, and cares more about the harm associated with a few people being unusually rich than he cares about eradicating poverty.

Some of that is presumably due to the availability of good data. But it seems weird that he mostly takes for granted that he’s focused on something important. Whereas when I think of harm from inequality, I focus more on local effects. If I’m harmed from others being richer than me, it’s mostly a function of inequality among the people with whom I interact, not distant strangers such as Bill Gates.

I see some evidence that high manager pay has good effects, and inequality is more likely to cause harm when it’s between peers. I’m unsure what to make of that.

Why does Piketty worry so much about inequality? Is it because inequality conflicts with the ideals of democracy? Is it due to Piketty’s concern that more inequality would probably cause a revolution? I’m unclear on how inequality contributes to revolutions, but I’m pretty sure there other factors that are reducing the risk, such as the fraction of the population who are young males (declining). I also expect the harm from inequality to be lower when the poor can meet their basic needs, and can escape to virtual worlds where their situation is different.

Whatever his reasons are, I have trouble translating them into large impacts on people.

I expect a fair amount of the harm from inequality derives from people perceiving themselves as having low social status. Wealth and income only reflect a modest fraction of the fluctuations in those perceptions. Here are some other factors I’d look at if I were attempting a thorough perspective on inequality:

• If I disagree with a higher-status person, how likely is that person to listen carefully, yell at me, shun me, etc.?
• How much credit does the leader a team/company/country get relative to the average person in that organization?
• Differing risks of jail, controlling for whether a person commits a crime
• Can anyone start a business, or does it require special connections?
• How hard is it to marry someone of different status?
• Differing availability of sex (does access to good sexbots count?)
• Unequal reproduction rates (less of a problem now than in Genghis Khan’s era)

Miscellaneous Smaller Points

Piketty expects slower income growth over the next century or so, as if we’re running out of innovations. He alternates between saying it’s hard to predict, and sounding confident that growth won’t exceed 1.5%/year.

That’s a weird contrast to the concerns I’ve been hearing about AI causing disaster or utopia.

He sees some of the long-term patterns of accelerating change, then just dismisses them, mainly based on the observation that we haven’t been able to sustain growth rates above 1.5% in the past.

He also predicts that population growth will drop to zero or less in much of the world, based on fairly standard extrapolations. I prefer to predict population by looking a multiple scenarios, such as by extrapolating the trend of the Amish population, which appears on track to reach a billion in around two centuries, and then adding in a smaller chance of stranger scenarios.

Piketty claims, without explanation, that central banks can’t set inflation, and then a page later he advocates a policy (a limit on the size of central bank balance sheets) that would limit central banks’ ability to fight deflation. His reason for those limits seems to be unrelated to inflation, and could be accomplished without limiting central banks’ ability to buy government bonds. His other comments related to macroeconomics aren’t much better – he should avoid that topic.

Policy Advice

Piketty’s main recommendation is a progressive global tax on capital (i.e. wealth).

He makes some good points about the importance and feasibility of the increased transparency needed to implement that.

He glosses over some of the pitfalls. The wealthy use trust funds, partly to reduce transparency about who owns what (i.e. they give up enough control to satisfy a legal threshold concerning whether it qualifies as owned by the creator of the trust, yet the trust still tends to serve their interests). There’s strong political power that maintains that situation, coming from those who build careers out of creating and managing those trusts, and there are few people who are sufficiently harmed by those trusts to prioritize changing the rules.

He wants the tax to be based on the market value of assets and debts. That works better than the alternatives in many cases (probably the majority of cases). But using market values will create some new injustices compared to the current rules based on purchase price. For example, a small technology startup with no revenues yet, which hasn’t gotten any new investment recently. VCs do a mediocre job of estimating their market value, in spite of being selected for being good at that. An employee of a tax agency is going to do worse.

But these harms aren’t obviously large in comparison to existing taxation. Piketty seems to have a fairly consistent worldview in which they’re not important enough to distract him from his goals. And I suspect I’d agree with his his policy advice if I agreed with his priorities.

Conclusion

There’s plenty of uncertainty about the future of inequality, but Piketty has some good reasons for expecting that the default path is for the rich to get richer.

He wants us to believe those increases in inequality are mostly due to factors unrelated to merit, whereas I believe that merit will be responsible for a bit more than half of those increases.

I devoted much of this review to what he got wrong, which creates a somewhat misleading impression. Roughly 2/3 of the book’s ideas are well thought out. I’m somewhat biased against them, but I wasn’t able to generate any important complaints about that good 2/3.

Footnotes

[1] – see Performance for pay? The relationship between CEO incentive compensation and future stock price performance for evidence that such a fund would perform well.

[2] – Contrast Piketty with Warren Buffett:

In many aspects of life, indeed, wealth does command top-grade products or services. For that reason, the financial “elites” – wealthy individuals, pension funds, college endowments and the like – have great trouble meekly signing up for a financial product or service that is available as well to people investing only a few thousand dollars. This reluctance of the rich normally prevails even though the product at issue is –on an expectancy basis – clearly the best choice. My calculation, admittedly very rough, is that the search by the elite for superior investment advice has caused it, in aggregate, to waste more than $100 billion over the past decade. Figure it out: Even a 1% fee on a few trillion dollars adds up. Of course, not every investor who put money in hedge funds ten years ago lagged S&P returns. But I believe my calculation of the aggregate shortfall is conservative.