One of the most talked about economics books of the last few years is Thomas Piketty’s Capital in the Twenty-First Century. It is not hard to see why. Piketty, an economics professor at the Paris School of Economics, argues that wealth inequality, which is already high, will increase in the coming decades and he advocates much higher taxes on the wealthy. That taps into people’s strong emotions about the “top 1 percent”—a popular topic of discussion in recent years.

Unlike many free-market critics of Piketty’s book, I find his big-picture statistical analysis somewhat compelling, although like the other critics I see some serious problems with it. But even if his analysis is correct, I find it much less important than he does, and I find his policy proposals appalling. Beyond his big-picture analysis and policy proposals, he discusses many issues: Social Security, the history of tax policy in the United States and France, global warming policy, immigration, and many others. On some of these, his analysis is good. On others, it is weak or outright wrong. Sometimes he gets his history wrong, and in important ways. Finally, Piketty has a bad habit of questioning the motives of those with whom he disagrees.

Front and center / Start with the big picture. “It is long past the time,” he writes in the Introduction, “when we should have put the question of inequality back at the center of economic analysis and begun asking questions first raised in the nineteenth century.” The center? Really? But if we put inequality at the center, we can easily miss the tremendous growth in well-being for a huge percentage of people in the world and for almost everyone in the United States and Western Europe.

Much later in the book, he shows that he is aware of those improved conditions, writing:

Nevertheless, according to official indices, the average per capita purchasing power in Britain and France in 1800 was about one-tenth what it was in 2010. In other words, with 20 to 30 times the average income in 1800, a person would probably have lived no better than with 2 or 3 times the average income today. With 5–10 times the average income in 1800, one would have been in a situation somewhere between the minimum and average wage today.

In his own way, he is pointing out, albeit less dramatically, what University of California, Berkeley economist Brad DeLong noted in a study aptly titled “Cornucopia.” That well-argued and documented paper examines the 20th century and shows that the price of almost every item we buy—if stated in hours of labor required to earn enough to pay for it—has fallen to a fraction of its cost in 1900. Moreover, that reduction in cost understates the improvement in well-being because many crucial items that we buy today did not exist in 1900. Antibiotics, for example, are a 20th century invention. Their price in 1900 was effectively infinite.

In my view, a steady increase in well-being for the vast majority of the world’s inhabitants, as well as the policies necessary to achieve that, are what should be central to economic analysis. But Piketty chooses to put inequality front and center, and so be it. He states his conclusion up front:

When the rate of return on capital significantly exceeds the growth rate of the economy (as it did through much of history until the nineteenth century and as is likely to be the case again in the twenty-first century), then it logically follows that inherited wealth grows faster than output and income.

The reasoning is fairly straightforward: Assume that someone who owns capital earns an average annual real return of 5 percent and that the rate of growth of the economy is 3 percent. If the owner of capital can live on 1 percentage point of the annual return, his wealth will grow at 4 percent per year, which is higher than the economy’s growth rate. We need only one more assumption: that the capital owner has only one son or daughter who, in turn, will live on that 1 percentage point per year. QED.

In short, Piketty’s conclusion follows logically, but only if we include assumptions about the number of heirs and their spending discipline. But if, for example, each wealthy person has three heirs who dissipate the wealth, those heirs will leave little to their heirs. So, based on just Piketty’s skimpy assumptions, his claim does not follow logically. He, unfortunately, starts out by overstating his case. He could be right empirically, though, and he presents evidence for the growing share of income earned by owners of capital, much of which they inherited.

We are still left with the question: “So what?” Imagine—as Piketty has convinced me seems at least plausible—that the share of income going to owners of capital could rise over time, which means that the share of income going to labor would fall. Would that mean that laborers are worse off? Not at all. In fact, they are likely to be better off. Unfortunately, many people who read the book, especially those who are not economists, could easily miss this point for two reasons: (1) Piketty’s emphasis on income shares rather than on real income; and (2) his misleading language. We would expect an emphasis on shares rather than real income from someone who believes that inequality of wealth and income, rather than improvements in standards of living, is “at the center of economic analysis.”

Misstatement / What compounds the misleading impression is Piketty’s misleading language. For example, in discussing his country, France, he writes, “Probate records also enable us to observe that the decrease in the upper decile’s share of national wealth in the twentieth century benefited the middle 40 percent of the population exclusively.” But as he well knows, French wealth per capita grew enormously in the 20th century, and so the decline in share of the wealthiest does not imply an absolute decline in wealth. Moreover, even if the wealthiest French people had lost wealth in absolute terms, the higher share of the people below them is not sufficient evidence that the wealthiest group’s decline benefited the middle 40 percent. The middle 40 percent could have done better simply because of their own savings and investments.

Piketty’s misleading explanation of the French case above is not an isolated weakness. Throughout the book, he writes as if he thinks that wealth is zero-sum and, thus, that increases in various groups’ wealth must come at the expense of others. Writing about early 19th-century France, for example, he refers to a “transfer of 10 percent of national income to capital.” But a look at his Figure 6.1, on which he bases this claim, shows no such transfer. All it shows is that the share of income going to capital rose. Similarly, in discussing the United States in the late 20th century, he calls an increase in the income share of the top 10 percent an “internal transfer between social groups.” Never mind that on the very same page he admits that income for the bottom 90 percent slowly grew over the same period.

Or consider Piketty’s statement about the United States and France: “And the poorer half of the population are as poor today as they were in the past, with barely 5 percent of total wealth, just as in 1910.” That is nonsense. If the poor have the same percentage of wealth as they had in 1910, they are much richer because wealth is much greater, as Piketty well knows. Here, he has gone beyond misleading language into actual error.

One important factor that Piketty gives very little attention is the mobility of people between wealth levels. There is a constant churn as people gain and lose wealth. Much of this churn is due to what Joseph Schumpeter called “creative destruction.” Entrepreneurs and investors come along with new ideas that, if they succeed, will make them a lot of money (the creative part) and cause existing firms to lose money (the destructive part). Piketty’s neglect of that churn shows up in his discussion of the Forbes 400 list of the wealthiest people in the world. He writes that the average wealth of the Forbes 400 rose from about $1.5 billion in 1987 to nearly $15 billion in 2013, “for an average growth rate of 6.4 percent above inflation.” Fine, so far. But from this he concludes, “[T]he largest fortunes grew much more rapidly than average wealth.” But we can’t reach that conclusion based on the Forbes 400 data. The reason: in those 16 years, there was huge turnover in who was in the Forbes 400. Undoubtedly, the wealth of many of the 1987 Forbes 400 who dropped out in later years fell. Whether that was enough to cause the average wealth of members of the 1987 Forbes 400 to grow more slowly than the average wealth of the general population, I don’t know. What I do know is that Piketty would have had to check that to reach his conclusion—and he did not do so. Or, more correctly, neither his book nor his online technical appendix contains the data that would allow one to reach his conclusion.

Central wealth planner / For those who are worried about growing wealth inequality because their own wealth is not growing, there is a simple solution: save more and invest in stock market index funds. And, to the extent possible, do so with tax-favored 401(k) and 403(b) plans and Individual Retirement Accounts (Roth or non-Roth). When a friend who studies saving patterns of various ethnic groups in America visited me some years ago, I told him that my wife and I normally save between 15 and 20 percent of our before-tax income. His eyes grew wide. “You’re Korean,” he said, jokingly. Of course, hitting that saving rate meant that we didn’t go to Europe or Asia, didn’t buy $40,000 cars or $200 shoes, didn’t buy expensive clothes, and didn’t drink alcohol when we went to restaurants. What a tough life!

Piketty does not give any space in his tome to making that point. He writes as if he is the central planner making decisions from the top down and essentially disregards the fact that people are individuals who want to deal with their individual situations.

But even as central planner, Piketty fails. The driver of his model is his strongly held assumption that the rate of return on stocks will substantially exceed the growth rate of the economy and the growth rate of real wages. Under Social Security, your benefits will grow at no more than the growth rate of real wages because your benefits are paid by Social Security taxes on current workers. So, wouldn’t it make sense to let people invest their Social Security taxes in stocks rather than get only the low rate of return that they get now? Piketty says no. He makes one good argument for this, one I myself have made: the transition problem out of the Social Security Ponzi scheme is wicked. But his other argument is that investing in stocks is “a roll of the dice.” What happened to his confidence about the rate of return on stocks?

Given his emphasis on—and distaste for—inequality and his conclusion that owners of capital will get an increasing share of an economy’s output, it’s not surprising that Piketty favors much higher taxes on wealthy people. He argues briefly that the optimal top income tax rate in richer countries is “probably above 80 percent.” He claims that such a rate on incomes above $500,000 or $1 million “will not bring the government much in the way of revenue”—I agree—but will drastically reduce the compensation of high-paid people. He also suggests an annual “global tax on capital,” with rates that would rise with wealth. “One might imagine,” he writes, “a rate of 0 percent for net assets below 1 million euros, 1 percent between 1 million and 5 million, and 2 percent above 5 million.” One might imagine many things; I take it, as virtually every reviewer pro or con has, that Piketty is not just “imagining” those taxes, but actually advocating them. He adds that “one might prefer” a stiff annual tax of “5 or 10 percent on assets above 1 billion euros.”

But if there is anything we know in economics, it is that incentives matter. An annual tax on capital will reduce the incentive to create capital. With less capital than otherwise, the marginal product of workers will be lower than otherwise. Bottom line: Piketty’s proposed tax on capital would hurt labor.

How does Piketty handle this serious problem? He doesn’t. The only behavioral response to a tax on capital that he discusses at length is that owners of capital would move to lower-tax countries. To avoid that happening, he puts a lot of thought into how to form, essentially, a tax “cartel” in Europe. He would have countries in the European Union agree to tax capital, making it harder for people to move to lower-tax countries.

Even an economist who likes Piketty’s book and favors his tax on capital has pointed out its bad effects on economic well-being. In his New Republic review, MIT economist Robert Solow, who won the Nobel Prize in economics for his pioneering work on economic growth, wrote:

The labor share of national income is arithmetically the same thing as the real wage divided by the productivity of labor. Would you rather live in a society in which the real wage was rising rapidly but the labor share was falling (because productivity was increasing even faster), or one in which the real wage was stagnating, along with productivity, so the labor share was unchanging? The first is surely better on narrowly economic grounds: you eat your wage, not your share of national income. But there could be political and social advantages to the second option. If a small class of owners of wealth—and it is small—comes to collect a growing share of the national income, it is likely to dominate the society in other ways as well.

Translation: if capital is taxed heavily, workers’ well-being will not improve, but because a tax on capital will likely stem the increase in the share of income going to owners of capital, wealthy people will dominate the society less than otherwise.

What’s the problem? / For Piketty and, presumably, Solow to calmly countenance the possibility of stagnating real wages just to keep capital’s share from increasing, they would have to see some large problems with increasing inequality. Solow does not point out any such problems, which makes sense because his review is short. But Piketty, in over 600 pages, does not make a clear statement about why increasing inequality is a problem in a society where almost everyone’s lot in life is getting better and better.

So let’s fill in the gaps. How big a problem is wealth inequality? In my opinion, if people came by their money without cheating others and without getting special government favors, then there is no problem with those people becoming very wealthy. What really matters is inequality in consumption and, here, the differences between poorer Americans and wealthier Americans are probably as low as they have ever been. Most lower-income people have color televisions, cell phones, refrigerators, comfortable clothing, and three square meals a day. That was not true 60 years ago. Or take a longer view: In the mid-19th century, the poorest people in American were probably slaves. The largely rich people who “owned” them could treat them very badly if they wanted to. And even if they did not want to, let me repeat that these poor people were slaves.

Or consider finer differences between the middle class and the wealthiest. You would have to look carefully—at least, I would—to see the difference in the quality of clothing between billionaires and those with a net worth of “only” $100,000. Both can travel by jet, but the wealthier person can get there more quickly and easily on his private jet. The rest of us have to share space. The private jet is certainly nicer, but is that really a major social problem?

Irrelevancies and error / Piketty, not to his credit, sometimes uses ad hominems in place of actual argument. I note two. Although Piketty does not name the targets outright, one ad hominem is targeted at my Hoover Institution colleague Kenneth Judd and economist Christophe Chamley. Judd and Chamley, in separate articles, found that under certain strong assumptions, the optimal tax rate on capital is zero. Under those assumptions, they concluded, taxing capital would, by reducing capital, make workers worse off than otherwise. How does Piketty deal with their finding? By challenging their motives. He writes, “Some economists have an unfortunate tendency to defend their private interest while implausibly claiming to champion the general interest.” It might surprise Piketty that Judd is a dyed-in-the-wool registered Democrat with whom I argue about redistribution. (I’m the one who’s against it.)

Piketty’s second ad hominem is, surprisingly, against Yale University economist William Nordhaus. In discussing global warming, Piketty contrasts the views of Nordhaus and British economist Nicholas Stern. Stern wants governments to act quickly and massively to reduce global warming, while Nordhaus wants a more gradual approach. Piketty claims that Nord-haus’s position is “opportunely consistent with the U.S. strategy of unrestricted carbon emissions.” Besides being an ad hominem, Piketty’s accusation of opportunism makes no sense. Why? Because Nordhaus is one of the leading U.S. economists who does want the U.S. government to use carbon taxes to restrict carbon emissions.

On this issue, Piketty is also badly misinformed in another way. He argues correctly that one main difference between Stern and Nordhaus is the interest rate they use to compute future benefits of reducing carbon. But he incorrectly claims that Stern uses a discount rate of about 1 percent per year. In fact, Stern uses a discount rate of 0.1 percent per year, a big difference when considering benefits out over 100 years.

Interestingly, Piketty does not completely understand the economic case for carbon taxes as a way to deal with global warming. He writes, “There is good reason to believe, however, that the price signal [that carbon taxes would lead to] has less of an impact on emissions than public investments and changes to building codes (requiring thermal insulation, for example).” Certainly some level of carbon taxes could have a greater effect on emissions. But that is not the point. The case for carbon taxes over government picking of winners and government regulation is that the taxes lead to a given reduction of emissions at a lower cost.

Early in the book, Piketty writes about his frustration with mainstream economics: “My thesis consisted of several relatively abstract mathematical theorems.” I share that frustration. But there is a lot of very good economics, both within and outside the math. You do not need much math to show the superiority of carbon taxes over government spending and regulation.

I should not leave this review without mentioning a glaring historical error on tax rates. According to Piketty, the top income tax rate under President Herbert Hoover, Franklin D. Roosevelt’s predecessor, was 25 percent. In fact, it was Hoover, a president from the progressive wing of the Republican Party, who raised the top rate to a whopping 63 percent.

Conclusion / I end with a positive: In his chapter on global capital taxes, Piketty writes:

A seemingly more peaceful form of redistribution and regulation of global wealth inequality is immigration. Rather than move capital, which poses all sorts of difficulties, it is sometimes simpler to allow labor to move to places where wages are higher.

He calls immigration “the mortar that holds the United States together.” Unfortunately, he also sees immigration as something that “postpones the problem” of global wealth concentration. Let’s see: Deregulation of labor markets will allow hundreds of millions of poor immigrants to be substantially better off but will only postpone a problem that Piketty worries about and I don’t. I’ll take it.