Income mobility can be viewed as a first-order Markov process, with a matrix of transition probabilities which measure how individuals move from an income status in time t to a new status in time t+1. Direct estimation of transition matrices is difficult, since time series panel data are unavailable and limited data on the distribution of income do not suffice to determine the coefficients mathematically, let alone provide enough degrees of freedom for estimation. In this paper, we show that maximum entropy econometrics offers a feasible way to estimate transition matrices using distributional data from Colombia. Using a cross-entropy estimation method, we make efficient use of prior information about the structure of the transition matrices and how they vary with age. The approach is very flexible, allowing the use of “information” in a variety of forms such as inequality constraints, errors in measurement, and prior estimates. Under weak assumptions about the error generation process, we can derive test statistics based on the likelihood ratio measuring the significance of the estimation. The model fits the data well in that the predicted and actual distributions for period t+1 are close. The results show that there is a large degree of upward mobility in Colombia, especially at the bottom of the income distribution and for the younger age cohorts.