This paper presents comparative qualitative and quantitative evidence from rural Kenya and Madagascar in an attempt to untangle the causality behind persistent poverty. We find striking differences in welfare dynamics depending on whether one uses total income, including stochastic terms and inevitable measurement error, or the predictable, structural component of income based on a household's asset holdings. Our results suggest the existence of multiple dynamic asset and structural income equilibria, consistent with the poverty traps hypothesis. Furthermore, we find supporting evidence of locally increasing returns to assets and of risk management behaviour consistent with poor households' defence of a critical asset threshold through asset smoothing.