Boats and Tides and Trickle Down Theories: What Stochastic Process Theory Has To Say About Modeling Poverty, Inequality, Mobility and Polarization

Aphorisms that "Rising tides raise all boats" or that material advances of the rich eventually "Trickle Down" to the poor are really maxims regarding the nature of stochastic processes that underlay the income paths of groups of individuals. This paper looks at the implications of conventional assumptions made by economists concerning such processes for the empirical analysis of wellbeing in terms of poverty, inequality, mobility and polarization. The implications of attributing different processes to different groups in society following the club convergence literature are also discussed. Various forms of poverty, inequality and income mobility structures are considered and much of the conventional wisdom afforded us by such aphorisms is questioned. To exemplify these ideas the results are applied to the distribution of GDP per capita in the continent of Africa.