Thomas Piketty and the rate of time preference

Using a standard model in which the individual consumption path is computed solving an optimal control problem, we investigate central claims of Piketty (2014). Rather than r > g (confirmed in the data) r−ρ>g - with ρ being the rate of time preference - matters. If this condition holds and the elasticity of substitution in the production function is larger than one, the capital share converges to one in the long run. Nevertheless, this does not have major impact on the distribution of wealth. The latter, however, converges to maximum inequality for heterogeneous time preferences or rates of interest (either persistent or stochastic). For the latter, the presence of finite life times leads to a distribution with finite wealth inequality featuring fat tails.