[This is the fifth of five posts on Capital in the 21st Century. The first is here.]

The following are mini-summaries of some of the main criticisms of Piketty’s Capital in the 21st Century that relate to his descriptions of the historical changes in inequality and their current trends. I do not consider criticisms of Piketty’s policy prescriptions (a global wealth tax). I put some that I would describe as more substantive first, and the less important ones later. A good summary of criticisms is provided by Wolfers.

• Global growth (eg. Rogoff): The global income distribution has become more equal over the last decades. It is possible, perhaps even likely, that this is related to the lack of growth in median income in the rich countries. This has happened alongside the large increases in the shares of Income and Wealth of the top percentile, which is Piketty’s main focus. It is something worth remembering, but has no direct bearing on Piketty’s arguments about inequality in developed countries, expect perhaps putting them in the broader context. In short, while globalization may account for the increasing equality of the global income distribution, the stagnation of lower and middle incomes in developed countries, and the rising returns to higher education, it does not appear to explain the rising income share of the top percentile. (Global income growth. For global wealth distributions similar data simply does not exist (yet))
• Inequality within the 99% (eg. Autor):
• US after-tax vs pre-tax incomes (BL&S and Burtless), and changing US households (BL&S and GGKS): Piketty’s income inequality numbers are based on pre-tax incomes. One criticism of his numbers is thus that what really matters is after-tax incomes. Using after-tax incomes the top percentile still hugely increases it’s share of (after-tax) income. The main thing that looks different using after-tax incomes is that median US household incomes no longer look stagnant over the last few decades, they have increased (albeit not nearly as fast as those of top percentile). Another criticism of Piketty’s income inequality numbers for the US is that the ‘average’ US household has changed over time, it used to be the nuclear family (Mum, Dad, Two Children), but there are now many more households with only one parent. It also used to be case that only the Husband would work, this is no longer true and nowadays high income husbands tend to have high income wives. Accounting for changing households makes the increases in income inequality “less severe” (quotation marks as the increase is still the ‘same’, just changes how one sees the causes), although the trends are in the same direction. It does however change the story of stagnant median US incomes, which do grow, albeit still by less than the US economy.
• Wealth versus Capital (eg., Blume & Durlauf): Piketty does not really measure Capital, but rather Wealth. The distinction is that Wealth is the market value of all assets (ie. houses are valued by the price of houses), while Capital is only assets that are used in production and are valued by their marginal product. Among the criticisms this leads to are that Piketty measures aggregate Wealth by asset value as his numbers are susceptible to house price movements (hence BBCW and Rognlie criticisms below). Also since the inequality ‘share of income’ measures are based on marginal product there is an inconsistency between how Piketty measures aggregates and shares. They also observe that many of Piketty’s ideas about drivers of inequality — negotiating power of managers, ability of large funds to get better rates of return on assets — imply that the marginal product measures of inequality used will be invalid (validity of the marginal product measures assumes perfect competition).

Some less important criticisms are,

• Acemoglu & Robinson – The Rise and Fall of General Laws of Capitalism: Their first point is that there are no such thing as inescapable laws of capitalism (except accounting identities!). They provide some preliminary cross-country evidence on the relationship between income inequality and \( r-g \) which, while too weak to convince anyone not already convinced, does provide a useful starting point (also has weakness that it is income inequality, while argument is really about wealth inequality). Using examples of Sweden and South Africa they point out importance of looking at many different measures of inequality, not just focusing on the one percent.
• Krussell & Smith (VoxEU): Criticize the “theory” in Piketty’s book. The objection is essentially the following. Piketty uses the formula \( K/L = s/g \) (capital/output ratio=savings rate/growth rate) when he should use the formula \( K/Y = s/(g+n+\delta) \) (capital/output ratio=savings rate/(growth rate+population growth rate + capital depreciation rate)). The later formula being that of the Solow growth model (and the one I just used directly in my summary). Their objection is that if \( g \) goes to zero then Piketty’s formula would predict that the capital/income ratio goes to infinity — clearly unrealistic. It seems clear from the surrounding text that Piketty is aware of the Solow growth model and capital depreciation but leaves it out for simplicity, and because Piketty’s main use for the formula is to argue that as population growth rates slow, possibly accompanied by a slowing per-capita growth rate, we would expect the capital/income ratios to rise; and thus Frances historically lower population growth rate and higher capital/income ratios provide a better guide to what we should expect capital/income ratios to be in the future, than the historical experience of the US with its higher population growth rate. At least by my reading the book does not claim that \(K/Y\) is about to go off to infinity. I call this a lesser criticism not because the point is unimportant, but because it feels like they are taking down a Strawman.
• BBCW (the four French) Economists: Object to Piketty’s use of house prices as way to measure wealth. Suggest using rental prices of housing instead. Doing this for French data makes the increase in the French Capital/Income ratio since World War II smaller, but still in same direction, as Piketty’s findings. Their objection seems somewhat misguided as Piketty is using the price of assets as a measure of their value which is very much following the standard approach and it is not clear why using rental prices might be better (other than being less affected by booms and busts). In any case, they find much the same trends as Piketty; a rising ratio in France since WWII, only less pronounced. They also suggest that this is important for Piketty’s ideas on wealth inequality being self-reinforcing, but since the wealth of the rich is in stocks & bonds, not houses, it does not seem so important.
• Rognlie: Loosely, makes same point as the Four French Economists only for the US economy, and focusing on capital share of income rather than wealth-to-income ratio. Namely that it is substantially about housing prices.
  
• Financial Times: Points out some (¿)minor(?) spreadsheet errors relating to Chapter 11 (Wealth Inequality). Important, but do not appear to change any of the main conclusions. In his response Piketty mentions that the World Top Incomes Database, the definitive data source, will shortly be expanded to include Wealth data.