The Piketty Transition

We study the effects on inequality of a "Piketty transition" to zero growth. In a model with a worker-capitalist dichotomy, we show that the relationship between inequality (measured as a ratio of incomes for the two types) and growth is complicated; zero growth can raise or lower inequality, depending on parameters. In particular, the elasticity of substitution between capital and labor in production needs to be considerably greater than 1 in order for income inequality be higher with zero growth; furthermore, the inequality effects operate through labor supply when the elasticity is high, rather than through r - g. Extending our model to include idiosyncratic wage risk we show that growth has quantitatively negligible effects on inequality, and furthermore the effect is negative rather than positive. Modifications designed to mitigate the decline in returns (such as financial development or capital-biased technical change) along the transition either strengthen or do not affect our conclusions.