The paper proposes an approach to evaluate hypotheses about transition dynamics when only the distributions at two points in time are observed. Using the principle of statistical mechanics, we show how to adjust in the most probable way a hypothesis so that it becomes compatible with the observed distributions. This adjustment procedure also allows to test hypotheses in a statistical sense. The test is based on the relative entropy and is equivalent to a likelihood ratio test. We apply our approach to compare the dynamics of the income distribution between men and women in the U.S. using PSID data.
transition matrices large deviation relative entropy income dynamics