Non-stationary transition matrices: An overlooked issue in intra-distribution dynamics

Previous papers dealing with the dynamics of income distributions have generally assumed stationary transition probabilities, effectively ruling out the possibility that intra-distribution dynamics change over time. This paper shows that the Chapman-Kolmogorov equation can be used to capture this added complexity. The paper also emphasizes that a test for stationarity should be carried out routinely because the stationarity assumption could lead to misleading conclusions.