Thomas Piketty's early thesis in Capital in the 21st Century is that capital has been accumulating faster than income in advanced countries over the last decades, and this trend would be due to high returns on capital relative to growth rates. We challenge this view in this article.
First, capital is heterogeneous; second, capital (return value) should be distinguished from wealth (market value). Second, the trend arises from only one of the components of capital, namely housing capital, and, as we show, the non-productive component of housing capital, that is land. Third, if the value of housing capital was measured with rental prices, the capital/income ratio would actually remain fairly stable over the last four decades in most countries.
We then examine the consequences of these findings for optimal capital taxation. Instead of a uniform world tax on wealth, we claim that taxation should account for the fact that capital is heterogenous, extending Judd (1985) to housing and land. A positive tax rate of land restores the first best, and if a property tax is not available, a positive tax rate on housing rents leads to a second-best. More generally, taxation should differ depending on the types of capital: land should be taxed rather than productive capital: land taxation avoids the under-accumulation of physical capital.