It is well known in theory that certain forms of non-linear dynamics in household
incomes can yield poverty traps and distribution-dependent growth. The potential
implications for policy are dramatic: effective social protection from transient poverty
will be an investment with lasting benefits, and pro-poor redistribution will promote
aggregate economic growth. We test for non-linearity in the dynamics of household
expenditures and incomes using panel data for rural south-west China. While we find
evidence of non-linearity, there is no sign of a dynamic poverty trap. Existing private
and social arrangements in this setting appear to protect vulnerable households from the
risk of destitution. However, the concavity we find in the recursion diagram does imply
that the speed of recovery from an income shock is lower for the poor, and that current
inequality reduces growth in mean incomes.